<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/num-rational-0.4.1/src/lib.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>lib.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../source-files.js"></script><script defer src="../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="alternate icon" type="image/png" href="../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../num_rational/index.html"><img class="rust-logo" src="../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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<a href="#922" id="922">922</a>
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<a href="#933" id="933">933</a>
<a href="#934" id="934">934</a>
<a href="#935" id="935">935</a>
<a href="#936" id="936">936</a>
<a href="#937" id="937">937</a>
<a href="#938" id="938">938</a>
<a href="#939" id="939">939</a>
<a href="#940" id="940">940</a>
<a href="#941" id="941">941</a>
<a href="#942" id="942">942</a>
<a href="#943" id="943">943</a>
<a href="#944" id="944">944</a>
<a href="#945" id="945">945</a>
<a href="#946" id="946">946</a>
<a href="#947" id="947">947</a>
<a href="#948" id="948">948</a>
<a href="#949" id="949">949</a>
<a href="#950" id="950">950</a>
<a href="#951" id="951">951</a>
<a href="#952" id="952">952</a>
<a href="#953" id="953">953</a>
<a href="#954" id="954">954</a>
<a href="#955" id="955">955</a>
<a href="#956" id="956">956</a>
<a href="#957" id="957">957</a>
<a href="#958" id="958">958</a>
<a href="#959" id="959">959</a>
<a href="#960" id="960">960</a>
<a href="#961" id="961">961</a>
<a href="#962" id="962">962</a>
<a href="#963" id="963">963</a>
<a href="#964" id="964">964</a>
<a href="#965" id="965">965</a>
<a href="#966" id="966">966</a>
<a href="#967" id="967">967</a>
<a href="#968" id="968">968</a>
<a href="#969" id="969">969</a>
<a href="#970" id="970">970</a>
<a href="#971" id="971">971</a>
<a href="#972" id="972">972</a>
<a href="#973" id="973">973</a>
<a href="#974" id="974">974</a>
<a href="#975" id="975">975</a>
<a href="#976" id="976">976</a>
<a href="#977" id="977">977</a>
<a href="#978" id="978">978</a>
<a href="#979" id="979">979</a>
<a href="#980" id="980">980</a>
<a href="#981" id="981">981</a>
<a href="#982" id="982">982</a>
<a href="#983" id="983">983</a>
<a href="#984" id="984">984</a>
<a href="#985" id="985">985</a>
<a href="#986" id="986">986</a>
<a href="#987" id="987">987</a>
<a href="#988" id="988">988</a>
<a href="#989" id="989">989</a>
<a href="#990" id="990">990</a>
<a href="#991" id="991">991</a>
<a href="#992" id="992">992</a>
<a href="#993" id="993">993</a>
<a href="#994" id="994">994</a>
<a href="#995" id="995">995</a>
<a href="#996" id="996">996</a>
<a href="#997" id="997">997</a>
<a href="#998" id="998">998</a>
<a href="#999" id="999">999</a>
<a href="#1000" id="1000">1000</a>
<a href="#1001" id="1001">1001</a>
<a href="#1002" id="1002">1002</a>
<a href="#1003" id="1003">1003</a>
<a href="#1004" id="1004">1004</a>
<a href="#1005" id="1005">1005</a>
<a href="#1006" id="1006">1006</a>
<a href="#1007" id="1007">1007</a>
<a href="#1008" id="1008">1008</a>
<a href="#1009" id="1009">1009</a>
<a href="#1010" id="1010">1010</a>
<a href="#1011" id="1011">1011</a>
<a href="#1012" id="1012">1012</a>
<a href="#1013" id="1013">1013</a>
<a href="#1014" id="1014">1014</a>
<a href="#1015" id="1015">1015</a>
<a href="#1016" id="1016">1016</a>
<a href="#1017" id="1017">1017</a>
<a href="#1018" id="1018">1018</a>
<a href="#1019" id="1019">1019</a>
<a href="#1020" id="1020">1020</a>
<a href="#1021" id="1021">1021</a>
<a href="#1022" id="1022">1022</a>
<a href="#1023" id="1023">1023</a>
<a href="#1024" id="1024">1024</a>
<a href="#1025" id="1025">1025</a>
<a href="#1026" id="1026">1026</a>
<a href="#1027" id="1027">1027</a>
<a href="#1028" id="1028">1028</a>
<a href="#1029" id="1029">1029</a>
<a href="#1030" id="1030">1030</a>
<a href="#1031" id="1031">1031</a>
<a href="#1032" id="1032">1032</a>
<a href="#1033" id="1033">1033</a>
<a href="#1034" id="1034">1034</a>
<a href="#1035" id="1035">1035</a>
<a href="#1036" id="1036">1036</a>
<a href="#1037" id="1037">1037</a>
<a href="#1038" id="1038">1038</a>
<a href="#1039" id="1039">1039</a>
<a href="#1040" id="1040">1040</a>
<a href="#1041" id="1041">1041</a>
<a href="#1042" id="1042">1042</a>
<a href="#1043" id="1043">1043</a>
<a href="#1044" id="1044">1044</a>
<a href="#1045" id="1045">1045</a>
<a href="#1046" id="1046">1046</a>
<a href="#1047" id="1047">1047</a>
<a href="#1048" id="1048">1048</a>
<a href="#1049" id="1049">1049</a>
<a href="#1050" id="1050">1050</a>
<a href="#1051" id="1051">1051</a>
<a href="#1052" id="1052">1052</a>
<a href="#1053" id="1053">1053</a>
<a href="#1054" id="1054">1054</a>
<a href="#1055" id="1055">1055</a>
<a href="#1056" id="1056">1056</a>
<a href="#1057" id="1057">1057</a>
<a href="#1058" id="1058">1058</a>
<a href="#1059" id="1059">1059</a>
<a href="#1060" id="1060">1060</a>
<a href="#1061" id="1061">1061</a>
<a href="#1062" id="1062">1062</a>
<a href="#1063" id="1063">1063</a>
<a href="#1064" id="1064">1064</a>
<a href="#1065" id="1065">1065</a>
<a href="#1066" id="1066">1066</a>
<a href="#1067" id="1067">1067</a>
<a href="#1068" id="1068">1068</a>
<a href="#1069" id="1069">1069</a>
<a href="#1070" id="1070">1070</a>
<a href="#1071" id="1071">1071</a>
<a href="#1072" id="1072">1072</a>
<a href="#1073" id="1073">1073</a>
<a href="#1074" id="1074">1074</a>
<a href="#1075" id="1075">1075</a>
<a href="#1076" id="1076">1076</a>
<a href="#1077" id="1077">1077</a>
<a href="#1078" id="1078">1078</a>
<a href="#1079" id="1079">1079</a>
<a href="#1080" id="1080">1080</a>
<a href="#1081" id="1081">1081</a>
<a href="#1082" id="1082">1082</a>
<a href="#1083" id="1083">1083</a>
<a href="#1084" id="1084">1084</a>
<a href="#1085" id="1085">1085</a>
<a href="#1086" id="1086">1086</a>
<a href="#1087" id="1087">1087</a>
<a href="#1088" id="1088">1088</a>
<a href="#1089" id="1089">1089</a>
<a href="#1090" id="1090">1090</a>
<a href="#1091" id="1091">1091</a>
<a href="#1092" id="1092">1092</a>
<a href="#1093" id="1093">1093</a>
<a href="#1094" id="1094">1094</a>
<a href="#1095" id="1095">1095</a>
<a href="#1096" id="1096">1096</a>
<a href="#1097" id="1097">1097</a>
<a href="#1098" id="1098">1098</a>
<a href="#1099" id="1099">1099</a>
<a href="#1100" id="1100">1100</a>
<a href="#1101" id="1101">1101</a>
<a href="#1102" id="1102">1102</a>
<a href="#1103" id="1103">1103</a>
<a href="#1104" id="1104">1104</a>
<a href="#1105" id="1105">1105</a>
<a href="#1106" id="1106">1106</a>
<a href="#1107" id="1107">1107</a>
<a href="#1108" id="1108">1108</a>
<a href="#1109" id="1109">1109</a>
<a href="#1110" id="1110">1110</a>
<a href="#1111" id="1111">1111</a>
<a href="#1112" id="1112">1112</a>
<a href="#1113" id="1113">1113</a>
<a href="#1114" id="1114">1114</a>
<a href="#1115" id="1115">1115</a>
<a href="#1116" id="1116">1116</a>
<a href="#1117" id="1117">1117</a>
<a href="#1118" id="1118">1118</a>
<a href="#1119" id="1119">1119</a>
<a href="#1120" id="1120">1120</a>
<a href="#1121" id="1121">1121</a>
<a href="#1122" id="1122">1122</a>
<a href="#1123" id="1123">1123</a>
<a href="#1124" id="1124">1124</a>
<a href="#1125" id="1125">1125</a>
<a href="#1126" id="1126">1126</a>
<a href="#1127" id="1127">1127</a>
<a href="#1128" id="1128">1128</a>
<a href="#1129" id="1129">1129</a>
<a href="#1130" id="1130">1130</a>
<a href="#1131" id="1131">1131</a>
<a href="#1132" id="1132">1132</a>
<a href="#1133" id="1133">1133</a>
<a href="#1134" id="1134">1134</a>
<a href="#1135" id="1135">1135</a>
<a href="#1136" id="1136">1136</a>
<a href="#1137" id="1137">1137</a>
<a href="#1138" id="1138">1138</a>
<a href="#1139" id="1139">1139</a>
<a href="#1140" id="1140">1140</a>
<a href="#1141" id="1141">1141</a>
<a href="#1142" id="1142">1142</a>
<a href="#1143" id="1143">1143</a>
<a href="#1144" id="1144">1144</a>
<a href="#1145" id="1145">1145</a>
<a href="#1146" id="1146">1146</a>
<a href="#1147" id="1147">1147</a>
<a href="#1148" id="1148">1148</a>
<a href="#1149" id="1149">1149</a>
<a href="#1150" id="1150">1150</a>
<a href="#1151" id="1151">1151</a>
<a href="#1152" id="1152">1152</a>
<a href="#1153" id="1153">1153</a>
<a href="#1154" id="1154">1154</a>
<a href="#1155" id="1155">1155</a>
<a href="#1156" id="1156">1156</a>
<a href="#1157" id="1157">1157</a>
<a href="#1158" id="1158">1158</a>
<a href="#1159" id="1159">1159</a>
<a href="#1160" id="1160">1160</a>
<a href="#1161" id="1161">1161</a>
<a href="#1162" id="1162">1162</a>
<a href="#1163" id="1163">1163</a>
<a href="#1164" id="1164">1164</a>
<a href="#1165" id="1165">1165</a>
<a href="#1166" id="1166">1166</a>
<a href="#1167" id="1167">1167</a>
<a href="#1168" id="1168">1168</a>
<a href="#1169" id="1169">1169</a>
<a href="#1170" id="1170">1170</a>
<a href="#1171" id="1171">1171</a>
<a href="#1172" id="1172">1172</a>
<a href="#1173" id="1173">1173</a>
<a href="#1174" id="1174">1174</a>
<a href="#1175" id="1175">1175</a>
<a href="#1176" id="1176">1176</a>
<a href="#1177" id="1177">1177</a>
<a href="#1178" id="1178">1178</a>
<a href="#1179" id="1179">1179</a>
<a href="#1180" id="1180">1180</a>
<a href="#1181" id="1181">1181</a>
<a href="#1182" id="1182">1182</a>
<a href="#1183" id="1183">1183</a>
<a href="#1184" id="1184">1184</a>
<a href="#1185" id="1185">1185</a>
<a href="#1186" id="1186">1186</a>
<a href="#1187" id="1187">1187</a>
<a href="#1188" id="1188">1188</a>
<a href="#1189" id="1189">1189</a>
<a href="#1190" id="1190">1190</a>
<a href="#1191" id="1191">1191</a>
<a href="#1192" id="1192">1192</a>
<a href="#1193" id="1193">1193</a>
<a href="#1194" id="1194">1194</a>
<a href="#1195" id="1195">1195</a>
<a href="#1196" id="1196">1196</a>
<a href="#1197" id="1197">1197</a>
<a href="#1198" id="1198">1198</a>
<a href="#1199" id="1199">1199</a>
<a href="#1200" id="1200">1200</a>
<a href="#1201" id="1201">1201</a>
<a href="#1202" id="1202">1202</a>
<a href="#1203" id="1203">1203</a>
<a href="#1204" id="1204">1204</a>
<a href="#1205" id="1205">1205</a>
<a href="#1206" id="1206">1206</a>
<a href="#1207" id="1207">1207</a>
<a href="#1208" id="1208">1208</a>
<a href="#1209" id="1209">1209</a>
<a href="#1210" id="1210">1210</a>
<a href="#1211" id="1211">1211</a>
<a href="#1212" id="1212">1212</a>
<a href="#1213" id="1213">1213</a>
<a href="#1214" id="1214">1214</a>
<a href="#1215" id="1215">1215</a>
<a href="#1216" id="1216">1216</a>
<a href="#1217" id="1217">1217</a>
<a href="#1218" id="1218">1218</a>
<a href="#1219" id="1219">1219</a>
<a href="#1220" id="1220">1220</a>
<a href="#1221" id="1221">1221</a>
<a href="#1222" id="1222">1222</a>
<a href="#1223" id="1223">1223</a>
<a href="#1224" id="1224">1224</a>
<a href="#1225" id="1225">1225</a>
<a href="#1226" id="1226">1226</a>
<a href="#1227" id="1227">1227</a>
<a href="#1228" id="1228">1228</a>
<a href="#1229" id="1229">1229</a>
<a href="#1230" id="1230">1230</a>
<a href="#1231" id="1231">1231</a>
<a href="#1232" id="1232">1232</a>
<a href="#1233" id="1233">1233</a>
<a href="#1234" id="1234">1234</a>
<a href="#1235" id="1235">1235</a>
<a href="#1236" id="1236">1236</a>
<a href="#1237" id="1237">1237</a>
<a href="#1238" id="1238">1238</a>
<a href="#1239" id="1239">1239</a>
<a href="#1240" id="1240">1240</a>
<a href="#1241" id="1241">1241</a>
<a href="#1242" id="1242">1242</a>
<a href="#1243" id="1243">1243</a>
<a href="#1244" id="1244">1244</a>
<a href="#1245" id="1245">1245</a>
<a href="#1246" id="1246">1246</a>
<a href="#1247" id="1247">1247</a>
<a href="#1248" id="1248">1248</a>
<a href="#1249" id="1249">1249</a>
<a href="#1250" id="1250">1250</a>
<a href="#1251" id="1251">1251</a>
<a href="#1252" id="1252">1252</a>
<a href="#1253" id="1253">1253</a>
<a href="#1254" id="1254">1254</a>
<a href="#1255" id="1255">1255</a>
<a href="#1256" id="1256">1256</a>
<a href="#1257" id="1257">1257</a>
<a href="#1258" id="1258">1258</a>
<a href="#1259" id="1259">1259</a>
<a href="#1260" id="1260">1260</a>
<a href="#1261" id="1261">1261</a>
<a href="#1262" id="1262">1262</a>
<a href="#1263" id="1263">1263</a>
<a href="#1264" id="1264">1264</a>
<a href="#1265" id="1265">1265</a>
<a href="#1266" id="1266">1266</a>
<a href="#1267" id="1267">1267</a>
<a href="#1268" id="1268">1268</a>
<a href="#1269" id="1269">1269</a>
<a href="#1270" id="1270">1270</a>
<a href="#1271" id="1271">1271</a>
<a href="#1272" id="1272">1272</a>
<a href="#1273" id="1273">1273</a>
<a href="#1274" id="1274">1274</a>
<a href="#1275" id="1275">1275</a>
<a href="#1276" id="1276">1276</a>
<a href="#1277" id="1277">1277</a>
<a href="#1278" id="1278">1278</a>
<a href="#1279" id="1279">1279</a>
<a href="#1280" id="1280">1280</a>
<a href="#1281" id="1281">1281</a>
<a href="#1282" id="1282">1282</a>
<a href="#1283" id="1283">1283</a>
<a href="#1284" id="1284">1284</a>
<a href="#1285" id="1285">1285</a>
<a href="#1286" id="1286">1286</a>
<a href="#1287" id="1287">1287</a>
<a href="#1288" id="1288">1288</a>
<a href="#1289" id="1289">1289</a>
<a href="#1290" id="1290">1290</a>
<a href="#1291" id="1291">1291</a>
<a href="#1292" id="1292">1292</a>
<a href="#1293" id="1293">1293</a>
<a href="#1294" id="1294">1294</a>
<a href="#1295" id="1295">1295</a>
<a href="#1296" id="1296">1296</a>
<a href="#1297" id="1297">1297</a>
<a href="#1298" id="1298">1298</a>
<a href="#1299" id="1299">1299</a>
<a href="#1300" id="1300">1300</a>
<a href="#1301" id="1301">1301</a>
<a href="#1302" id="1302">1302</a>
<a href="#1303" id="1303">1303</a>
<a href="#1304" id="1304">1304</a>
<a href="#1305" id="1305">1305</a>
<a href="#1306" id="1306">1306</a>
<a href="#1307" id="1307">1307</a>
<a href="#1308" id="1308">1308</a>
<a href="#1309" id="1309">1309</a>
<a href="#1310" id="1310">1310</a>
<a href="#1311" id="1311">1311</a>
<a href="#1312" id="1312">1312</a>
<a href="#1313" id="1313">1313</a>
<a href="#1314" id="1314">1314</a>
<a href="#1315" id="1315">1315</a>
<a href="#1316" id="1316">1316</a>
<a href="#1317" id="1317">1317</a>
<a href="#1318" id="1318">1318</a>
<a href="#1319" id="1319">1319</a>
<a href="#1320" id="1320">1320</a>
<a href="#1321" id="1321">1321</a>
<a href="#1322" id="1322">1322</a>
<a href="#1323" id="1323">1323</a>
<a href="#1324" id="1324">1324</a>
<a href="#1325" id="1325">1325</a>
<a href="#1326" id="1326">1326</a>
<a href="#1327" id="1327">1327</a>
<a href="#1328" id="1328">1328</a>
<a href="#1329" id="1329">1329</a>
<a href="#1330" id="1330">1330</a>
<a href="#1331" id="1331">1331</a>
<a href="#1332" id="1332">1332</a>
<a href="#1333" id="1333">1333</a>
<a href="#1334" id="1334">1334</a>
<a href="#1335" id="1335">1335</a>
<a href="#1336" id="1336">1336</a>
<a href="#1337" id="1337">1337</a>
<a href="#1338" id="1338">1338</a>
<a href="#1339" id="1339">1339</a>
<a href="#1340" id="1340">1340</a>
<a href="#1341" id="1341">1341</a>
<a href="#1342" id="1342">1342</a>
<a href="#1343" id="1343">1343</a>
<a href="#1344" id="1344">1344</a>
<a href="#1345" id="1345">1345</a>
<a href="#1346" id="1346">1346</a>
<a href="#1347" id="1347">1347</a>
<a href="#1348" id="1348">1348</a>
<a href="#1349" id="1349">1349</a>
<a href="#1350" id="1350">1350</a>
<a href="#1351" id="1351">1351</a>
<a href="#1352" id="1352">1352</a>
<a href="#1353" id="1353">1353</a>
<a href="#1354" id="1354">1354</a>
<a href="#1355" id="1355">1355</a>
<a href="#1356" id="1356">1356</a>
<a href="#1357" id="1357">1357</a>
<a href="#1358" id="1358">1358</a>
<a href="#1359" id="1359">1359</a>
<a href="#1360" id="1360">1360</a>
<a href="#1361" id="1361">1361</a>
<a href="#1362" id="1362">1362</a>
<a href="#1363" id="1363">1363</a>
<a href="#1364" id="1364">1364</a>
<a href="#1365" id="1365">1365</a>
<a href="#1366" id="1366">1366</a>
<a href="#1367" id="1367">1367</a>
<a href="#1368" id="1368">1368</a>
<a href="#1369" id="1369">1369</a>
<a href="#1370" id="1370">1370</a>
<a href="#1371" id="1371">1371</a>
<a href="#1372" id="1372">1372</a>
<a href="#1373" id="1373">1373</a>
<a href="#1374" id="1374">1374</a>
<a href="#1375" id="1375">1375</a>
<a href="#1376" id="1376">1376</a>
<a href="#1377" id="1377">1377</a>
<a href="#1378" id="1378">1378</a>
<a href="#1379" id="1379">1379</a>
<a href="#1380" id="1380">1380</a>
<a href="#1381" id="1381">1381</a>
<a href="#1382" id="1382">1382</a>
<a href="#1383" id="1383">1383</a>
<a href="#1384" id="1384">1384</a>
<a href="#1385" id="1385">1385</a>
<a href="#1386" id="1386">1386</a>
<a href="#1387" id="1387">1387</a>
<a href="#1388" id="1388">1388</a>
<a href="#1389" id="1389">1389</a>
<a href="#1390" id="1390">1390</a>
<a href="#1391" id="1391">1391</a>
<a href="#1392" id="1392">1392</a>
<a href="#1393" id="1393">1393</a>
<a href="#1394" id="1394">1394</a>
<a href="#1395" id="1395">1395</a>
<a href="#1396" id="1396">1396</a>
<a href="#1397" id="1397">1397</a>
<a href="#1398" id="1398">1398</a>
<a href="#1399" id="1399">1399</a>
<a href="#1400" id="1400">1400</a>
<a href="#1401" id="1401">1401</a>
<a href="#1402" id="1402">1402</a>
<a href="#1403" id="1403">1403</a>
<a href="#1404" id="1404">1404</a>
<a href="#1405" id="1405">1405</a>
<a href="#1406" id="1406">1406</a>
<a href="#1407" id="1407">1407</a>
<a href="#1408" id="1408">1408</a>
<a href="#1409" id="1409">1409</a>
<a href="#1410" id="1410">1410</a>
<a href="#1411" id="1411">1411</a>
<a href="#1412" id="1412">1412</a>
<a href="#1413" id="1413">1413</a>
<a href="#1414" id="1414">1414</a>
<a href="#1415" id="1415">1415</a>
<a href="#1416" id="1416">1416</a>
<a href="#1417" id="1417">1417</a>
<a href="#1418" id="1418">1418</a>
<a href="#1419" id="1419">1419</a>
<a href="#1420" id="1420">1420</a>
<a href="#1421" id="1421">1421</a>
<a href="#1422" id="1422">1422</a>
<a href="#1423" id="1423">1423</a>
<a href="#1424" id="1424">1424</a>
<a href="#1425" id="1425">1425</a>
<a href="#1426" id="1426">1426</a>
<a href="#1427" id="1427">1427</a>
<a href="#1428" id="1428">1428</a>
<a href="#1429" id="1429">1429</a>
<a href="#1430" id="1430">1430</a>
<a href="#1431" id="1431">1431</a>
<a href="#1432" id="1432">1432</a>
<a href="#1433" id="1433">1433</a>
<a href="#1434" id="1434">1434</a>
<a href="#1435" id="1435">1435</a>
<a href="#1436" id="1436">1436</a>
<a href="#1437" id="1437">1437</a>
<a href="#1438" id="1438">1438</a>
<a href="#1439" id="1439">1439</a>
<a href="#1440" id="1440">1440</a>
<a href="#1441" id="1441">1441</a>
<a href="#1442" id="1442">1442</a>
<a href="#1443" id="1443">1443</a>
<a href="#1444" id="1444">1444</a>
<a href="#1445" id="1445">1445</a>
<a href="#1446" id="1446">1446</a>
<a href="#1447" id="1447">1447</a>
<a href="#1448" id="1448">1448</a>
<a href="#1449" id="1449">1449</a>
<a href="#1450" id="1450">1450</a>
<a href="#1451" id="1451">1451</a>
<a href="#1452" id="1452">1452</a>
<a href="#1453" id="1453">1453</a>
<a href="#1454" id="1454">1454</a>
<a href="#1455" id="1455">1455</a>
<a href="#1456" id="1456">1456</a>
<a href="#1457" id="1457">1457</a>
<a href="#1458" id="1458">1458</a>
<a href="#1459" id="1459">1459</a>
<a href="#1460" id="1460">1460</a>
<a href="#1461" id="1461">1461</a>
<a href="#1462" id="1462">1462</a>
<a href="#1463" id="1463">1463</a>
<a href="#1464" id="1464">1464</a>
<a href="#1465" id="1465">1465</a>
<a href="#1466" id="1466">1466</a>
<a href="#1467" id="1467">1467</a>
<a href="#1468" id="1468">1468</a>
<a href="#1469" id="1469">1469</a>
<a href="#1470" id="1470">1470</a>
<a href="#1471" id="1471">1471</a>
<a href="#1472" id="1472">1472</a>
<a href="#1473" id="1473">1473</a>
<a href="#1474" id="1474">1474</a>
<a href="#1475" id="1475">1475</a>
<a href="#1476" id="1476">1476</a>
<a href="#1477" id="1477">1477</a>
<a href="#1478" id="1478">1478</a>
<a href="#1479" id="1479">1479</a>
<a href="#1480" id="1480">1480</a>
<a href="#1481" id="1481">1481</a>
<a href="#1482" id="1482">1482</a>
<a href="#1483" id="1483">1483</a>
<a href="#1484" id="1484">1484</a>
<a href="#1485" id="1485">1485</a>
<a href="#1486" id="1486">1486</a>
<a href="#1487" id="1487">1487</a>
<a href="#1488" id="1488">1488</a>
<a href="#1489" id="1489">1489</a>
<a href="#1490" id="1490">1490</a>
<a href="#1491" id="1491">1491</a>
<a href="#1492" id="1492">1492</a>
<a href="#1493" id="1493">1493</a>
<a href="#1494" id="1494">1494</a>
<a href="#1495" id="1495">1495</a>
<a href="#1496" id="1496">1496</a>
<a href="#1497" id="1497">1497</a>
<a href="#1498" id="1498">1498</a>
<a href="#1499" id="1499">1499</a>
<a href="#1500" id="1500">1500</a>
<a href="#1501" id="1501">1501</a>
<a href="#1502" id="1502">1502</a>
<a href="#1503" id="1503">1503</a>
<a href="#1504" id="1504">1504</a>
<a href="#1505" id="1505">1505</a>
<a href="#1506" id="1506">1506</a>
<a href="#1507" id="1507">1507</a>
<a href="#1508" id="1508">1508</a>
<a href="#1509" id="1509">1509</a>
<a href="#1510" id="1510">1510</a>
<a href="#1511" id="1511">1511</a>
<a href="#1512" id="1512">1512</a>
<a href="#1513" id="1513">1513</a>
<a href="#1514" id="1514">1514</a>
<a href="#1515" id="1515">1515</a>
<a href="#1516" id="1516">1516</a>
<a href="#1517" id="1517">1517</a>
<a href="#1518" id="1518">1518</a>
<a href="#1519" id="1519">1519</a>
<a href="#1520" id="1520">1520</a>
<a href="#1521" id="1521">1521</a>
<a href="#1522" id="1522">1522</a>
<a href="#1523" id="1523">1523</a>
<a href="#1524" id="1524">1524</a>
<a href="#1525" id="1525">1525</a>
<a href="#1526" id="1526">1526</a>
<a href="#1527" id="1527">1527</a>
<a href="#1528" id="1528">1528</a>
<a href="#1529" id="1529">1529</a>
<a href="#1530" id="1530">1530</a>
<a href="#1531" id="1531">1531</a>
<a href="#1532" id="1532">1532</a>
<a href="#1533" id="1533">1533</a>
<a href="#1534" id="1534">1534</a>
<a href="#1535" id="1535">1535</a>
<a href="#1536" id="1536">1536</a>
<a href="#1537" id="1537">1537</a>
<a href="#1538" id="1538">1538</a>
<a href="#1539" id="1539">1539</a>
<a href="#1540" id="1540">1540</a>
<a href="#1541" id="1541">1541</a>
<a href="#1542" id="1542">1542</a>
<a href="#1543" id="1543">1543</a>
<a href="#1544" id="1544">1544</a>
<a href="#1545" id="1545">1545</a>
<a href="#1546" id="1546">1546</a>
<a href="#1547" id="1547">1547</a>
<a href="#1548" id="1548">1548</a>
<a href="#1549" id="1549">1549</a>
<a href="#1550" id="1550">1550</a>
<a href="#1551" id="1551">1551</a>
<a href="#1552" id="1552">1552</a>
<a href="#1553" id="1553">1553</a>
<a href="#1554" id="1554">1554</a>
<a href="#1555" id="1555">1555</a>
<a href="#1556" id="1556">1556</a>
<a href="#1557" id="1557">1557</a>
<a href="#1558" id="1558">1558</a>
<a href="#1559" id="1559">1559</a>
<a href="#1560" id="1560">1560</a>
<a href="#1561" id="1561">1561</a>
<a href="#1562" id="1562">1562</a>
<a href="#1563" id="1563">1563</a>
<a href="#1564" id="1564">1564</a>
<a href="#1565" id="1565">1565</a>
<a href="#1566" id="1566">1566</a>
<a href="#1567" id="1567">1567</a>
<a href="#1568" id="1568">1568</a>
<a href="#1569" id="1569">1569</a>
<a href="#1570" id="1570">1570</a>
<a href="#1571" id="1571">1571</a>
<a href="#1572" id="1572">1572</a>
<a href="#1573" id="1573">1573</a>
<a href="#1574" id="1574">1574</a>
<a href="#1575" id="1575">1575</a>
<a href="#1576" id="1576">1576</a>
<a href="#1577" id="1577">1577</a>
<a href="#1578" id="1578">1578</a>
<a href="#1579" id="1579">1579</a>
<a href="#1580" id="1580">1580</a>
<a href="#1581" id="1581">1581</a>
<a href="#1582" id="1582">1582</a>
<a href="#1583" id="1583">1583</a>
<a href="#1584" id="1584">1584</a>
<a href="#1585" id="1585">1585</a>
<a href="#1586" id="1586">1586</a>
<a href="#1587" id="1587">1587</a>
<a href="#1588" id="1588">1588</a>
<a href="#1589" id="1589">1589</a>
<a href="#1590" id="1590">1590</a>
<a href="#1591" id="1591">1591</a>
<a href="#1592" id="1592">1592</a>
<a href="#1593" id="1593">1593</a>
<a href="#1594" id="1594">1594</a>
<a href="#1595" id="1595">1595</a>
<a href="#1596" id="1596">1596</a>
<a href="#1597" id="1597">1597</a>
<a href="#1598" id="1598">1598</a>
<a href="#1599" id="1599">1599</a>
<a href="#1600" id="1600">1600</a>
<a href="#1601" id="1601">1601</a>
<a href="#1602" id="1602">1602</a>
<a href="#1603" id="1603">1603</a>
<a href="#1604" id="1604">1604</a>
<a href="#1605" id="1605">1605</a>
<a href="#1606" id="1606">1606</a>
<a href="#1607" id="1607">1607</a>
<a href="#1608" id="1608">1608</a>
<a href="#1609" id="1609">1609</a>
<a href="#1610" id="1610">1610</a>
<a href="#1611" id="1611">1611</a>
<a href="#1612" id="1612">1612</a>
<a href="#1613" id="1613">1613</a>
<a href="#1614" id="1614">1614</a>
<a href="#1615" id="1615">1615</a>
<a href="#1616" id="1616">1616</a>
<a href="#1617" id="1617">1617</a>
<a href="#1618" id="1618">1618</a>
<a href="#1619" id="1619">1619</a>
<a href="#1620" id="1620">1620</a>
<a href="#1621" id="1621">1621</a>
<a href="#1622" id="1622">1622</a>
<a href="#1623" id="1623">1623</a>
<a href="#1624" id="1624">1624</a>
<a href="#1625" id="1625">1625</a>
<a href="#1626" id="1626">1626</a>
<a href="#1627" id="1627">1627</a>
<a href="#1628" id="1628">1628</a>
<a href="#1629" id="1629">1629</a>
<a href="#1630" id="1630">1630</a>
<a href="#1631" id="1631">1631</a>
<a href="#1632" id="1632">1632</a>
<a href="#1633" id="1633">1633</a>
<a href="#1634" id="1634">1634</a>
<a href="#1635" id="1635">1635</a>
<a href="#1636" id="1636">1636</a>
<a href="#1637" id="1637">1637</a>
<a href="#1638" id="1638">1638</a>
<a href="#1639" id="1639">1639</a>
<a href="#1640" id="1640">1640</a>
<a href="#1641" id="1641">1641</a>
<a href="#1642" id="1642">1642</a>
<a href="#1643" id="1643">1643</a>
<a href="#1644" id="1644">1644</a>
<a href="#1645" id="1645">1645</a>
<a href="#1646" id="1646">1646</a>
<a href="#1647" id="1647">1647</a>
<a href="#1648" id="1648">1648</a>
<a href="#1649" id="1649">1649</a>
<a href="#1650" id="1650">1650</a>
<a href="#1651" id="1651">1651</a>
<a href="#1652" id="1652">1652</a>
<a href="#1653" id="1653">1653</a>
<a href="#1654" id="1654">1654</a>
<a href="#1655" id="1655">1655</a>
<a href="#1656" id="1656">1656</a>
<a href="#1657" id="1657">1657</a>
<a href="#1658" id="1658">1658</a>
<a href="#1659" id="1659">1659</a>
<a href="#1660" id="1660">1660</a>
<a href="#1661" id="1661">1661</a>
<a href="#1662" id="1662">1662</a>
<a href="#1663" id="1663">1663</a>
<a href="#1664" id="1664">1664</a>
<a href="#1665" id="1665">1665</a>
<a href="#1666" id="1666">1666</a>
<a href="#1667" id="1667">1667</a>
<a href="#1668" id="1668">1668</a>
<a href="#1669" id="1669">1669</a>
<a href="#1670" id="1670">1670</a>
<a href="#1671" id="1671">1671</a>
<a href="#1672" id="1672">1672</a>
<a href="#1673" id="1673">1673</a>
<a href="#1674" id="1674">1674</a>
<a href="#1675" id="1675">1675</a>
<a href="#1676" id="1676">1676</a>
<a href="#1677" id="1677">1677</a>
<a href="#1678" id="1678">1678</a>
<a href="#1679" id="1679">1679</a>
<a href="#1680" id="1680">1680</a>
<a href="#1681" id="1681">1681</a>
<a href="#1682" id="1682">1682</a>
<a href="#1683" id="1683">1683</a>
<a href="#1684" id="1684">1684</a>
<a href="#1685" id="1685">1685</a>
<a href="#1686" id="1686">1686</a>
<a href="#1687" id="1687">1687</a>
<a href="#1688" id="1688">1688</a>
<a href="#1689" id="1689">1689</a>
<a href="#1690" id="1690">1690</a>
<a href="#1691" id="1691">1691</a>
<a href="#1692" id="1692">1692</a>
<a href="#1693" id="1693">1693</a>
<a href="#1694" id="1694">1694</a>
<a href="#1695" id="1695">1695</a>
<a href="#1696" id="1696">1696</a>
<a href="#1697" id="1697">1697</a>
<a href="#1698" id="1698">1698</a>
<a href="#1699" id="1699">1699</a>
<a href="#1700" id="1700">1700</a>
<a href="#1701" id="1701">1701</a>
<a href="#1702" id="1702">1702</a>
<a href="#1703" id="1703">1703</a>
<a href="#1704" id="1704">1704</a>
<a href="#1705" id="1705">1705</a>
<a href="#1706" id="1706">1706</a>
<a href="#1707" id="1707">1707</a>
<a href="#1708" id="1708">1708</a>
<a href="#1709" id="1709">1709</a>
<a href="#1710" id="1710">1710</a>
<a href="#1711" id="1711">1711</a>
<a href="#1712" id="1712">1712</a>
<a href="#1713" id="1713">1713</a>
<a href="#1714" id="1714">1714</a>
<a href="#1715" id="1715">1715</a>
<a href="#1716" id="1716">1716</a>
<a href="#1717" id="1717">1717</a>
<a href="#1718" id="1718">1718</a>
<a href="#1719" id="1719">1719</a>
<a href="#1720" id="1720">1720</a>
<a href="#1721" id="1721">1721</a>
<a href="#1722" id="1722">1722</a>
<a href="#1723" id="1723">1723</a>
<a href="#1724" id="1724">1724</a>
<a href="#1725" id="1725">1725</a>
<a href="#1726" id="1726">1726</a>
<a href="#1727" id="1727">1727</a>
<a href="#1728" id="1728">1728</a>
<a href="#1729" id="1729">1729</a>
<a href="#1730" id="1730">1730</a>
<a href="#1731" id="1731">1731</a>
<a href="#1732" id="1732">1732</a>
<a href="#1733" id="1733">1733</a>
<a href="#1734" id="1734">1734</a>
<a href="#1735" id="1735">1735</a>
<a href="#1736" id="1736">1736</a>
<a href="#1737" id="1737">1737</a>
<a href="#1738" id="1738">1738</a>
<a href="#1739" id="1739">1739</a>
<a href="#1740" id="1740">1740</a>
<a href="#1741" id="1741">1741</a>
<a href="#1742" id="1742">1742</a>
<a href="#1743" id="1743">1743</a>
<a href="#1744" id="1744">1744</a>
<a href="#1745" id="1745">1745</a>
<a href="#1746" id="1746">1746</a>
<a href="#1747" id="1747">1747</a>
<a href="#1748" id="1748">1748</a>
<a href="#1749" id="1749">1749</a>
<a href="#1750" id="1750">1750</a>
<a href="#1751" id="1751">1751</a>
<a href="#1752" id="1752">1752</a>
<a href="#1753" id="1753">1753</a>
<a href="#1754" id="1754">1754</a>
<a href="#1755" id="1755">1755</a>
<a href="#1756" id="1756">1756</a>
<a href="#1757" id="1757">1757</a>
<a href="#1758" id="1758">1758</a>
<a href="#1759" id="1759">1759</a>
<a href="#1760" id="1760">1760</a>
<a href="#1761" id="1761">1761</a>
<a href="#1762" id="1762">1762</a>
<a href="#1763" id="1763">1763</a>
<a href="#1764" id="1764">1764</a>
<a href="#1765" id="1765">1765</a>
<a href="#1766" id="1766">1766</a>
<a href="#1767" id="1767">1767</a>
<a href="#1768" id="1768">1768</a>
<a href="#1769" id="1769">1769</a>
<a href="#1770" id="1770">1770</a>
<a href="#1771" id="1771">1771</a>
<a href="#1772" id="1772">1772</a>
<a href="#1773" id="1773">1773</a>
<a href="#1774" id="1774">1774</a>
<a href="#1775" id="1775">1775</a>
<a href="#1776" id="1776">1776</a>
<a href="#1777" id="1777">1777</a>
<a href="#1778" id="1778">1778</a>
<a href="#1779" id="1779">1779</a>
<a href="#1780" id="1780">1780</a>
<a href="#1781" id="1781">1781</a>
<a href="#1782" id="1782">1782</a>
<a href="#1783" id="1783">1783</a>
<a href="#1784" id="1784">1784</a>
<a href="#1785" id="1785">1785</a>
<a href="#1786" id="1786">1786</a>
<a href="#1787" id="1787">1787</a>
<a href="#1788" id="1788">1788</a>
<a href="#1789" id="1789">1789</a>
<a href="#1790" id="1790">1790</a>
<a href="#1791" id="1791">1791</a>
<a href="#1792" id="1792">1792</a>
<a href="#1793" id="1793">1793</a>
<a href="#1794" id="1794">1794</a>
<a href="#1795" id="1795">1795</a>
<a href="#1796" id="1796">1796</a>
<a href="#1797" id="1797">1797</a>
<a href="#1798" id="1798">1798</a>
<a href="#1799" id="1799">1799</a>
<a href="#1800" id="1800">1800</a>
<a href="#1801" id="1801">1801</a>
<a href="#1802" id="1802">1802</a>
<a href="#1803" id="1803">1803</a>
<a href="#1804" id="1804">1804</a>
<a href="#1805" id="1805">1805</a>
<a href="#1806" id="1806">1806</a>
<a href="#1807" id="1807">1807</a>
<a href="#1808" id="1808">1808</a>
<a href="#1809" id="1809">1809</a>
<a href="#1810" id="1810">1810</a>
<a href="#1811" id="1811">1811</a>
<a href="#1812" id="1812">1812</a>
<a href="#1813" id="1813">1813</a>
<a href="#1814" id="1814">1814</a>
<a href="#1815" id="1815">1815</a>
<a href="#1816" id="1816">1816</a>
<a href="#1817" id="1817">1817</a>
<a href="#1818" id="1818">1818</a>
<a href="#1819" id="1819">1819</a>
<a href="#1820" id="1820">1820</a>
<a href="#1821" id="1821">1821</a>
<a href="#1822" id="1822">1822</a>
<a href="#1823" id="1823">1823</a>
<a href="#1824" id="1824">1824</a>
<a href="#1825" id="1825">1825</a>
<a href="#1826" id="1826">1826</a>
<a href="#1827" id="1827">1827</a>
<a href="#1828" id="1828">1828</a>
<a href="#1829" id="1829">1829</a>
<a href="#1830" id="1830">1830</a>
<a href="#1831" id="1831">1831</a>
<a href="#1832" id="1832">1832</a>
<a href="#1833" id="1833">1833</a>
<a href="#1834" id="1834">1834</a>
<a href="#1835" id="1835">1835</a>
<a href="#1836" id="1836">1836</a>
<a href="#1837" id="1837">1837</a>
<a href="#1838" id="1838">1838</a>
<a href="#1839" id="1839">1839</a>
<a href="#1840" id="1840">1840</a>
<a href="#1841" id="1841">1841</a>
<a href="#1842" id="1842">1842</a>
<a href="#1843" id="1843">1843</a>
<a href="#1844" id="1844">1844</a>
<a href="#1845" id="1845">1845</a>
<a href="#1846" id="1846">1846</a>
<a href="#1847" id="1847">1847</a>
<a href="#1848" id="1848">1848</a>
<a href="#1849" id="1849">1849</a>
<a href="#1850" id="1850">1850</a>
<a href="#1851" id="1851">1851</a>
<a href="#1852" id="1852">1852</a>
<a href="#1853" id="1853">1853</a>
<a href="#1854" id="1854">1854</a>
<a href="#1855" id="1855">1855</a>
<a href="#1856" id="1856">1856</a>
<a href="#1857" id="1857">1857</a>
<a href="#1858" id="1858">1858</a>
<a href="#1859" id="1859">1859</a>
<a href="#1860" id="1860">1860</a>
<a href="#1861" id="1861">1861</a>
<a href="#1862" id="1862">1862</a>
<a href="#1863" id="1863">1863</a>
<a href="#1864" id="1864">1864</a>
<a href="#1865" id="1865">1865</a>
<a href="#1866" id="1866">1866</a>
<a href="#1867" id="1867">1867</a>
<a href="#1868" id="1868">1868</a>
<a href="#1869" id="1869">1869</a>
<a href="#1870" id="1870">1870</a>
<a href="#1871" id="1871">1871</a>
<a href="#1872" id="1872">1872</a>
<a href="#1873" id="1873">1873</a>
<a href="#1874" id="1874">1874</a>
<a href="#1875" id="1875">1875</a>
<a href="#1876" id="1876">1876</a>
<a href="#1877" id="1877">1877</a>
<a href="#1878" id="1878">1878</a>
<a href="#1879" id="1879">1879</a>
<a href="#1880" id="1880">1880</a>
<a href="#1881" id="1881">1881</a>
<a href="#1882" id="1882">1882</a>
<a href="#1883" id="1883">1883</a>
<a href="#1884" id="1884">1884</a>
<a href="#1885" id="1885">1885</a>
<a href="#1886" id="1886">1886</a>
<a href="#1887" id="1887">1887</a>
<a href="#1888" id="1888">1888</a>
<a href="#1889" id="1889">1889</a>
<a href="#1890" id="1890">1890</a>
<a href="#1891" id="1891">1891</a>
<a href="#1892" id="1892">1892</a>
<a href="#1893" id="1893">1893</a>
<a href="#1894" id="1894">1894</a>
<a href="#1895" id="1895">1895</a>
<a href="#1896" id="1896">1896</a>
<a href="#1897" id="1897">1897</a>
<a href="#1898" id="1898">1898</a>
<a href="#1899" id="1899">1899</a>
<a href="#1900" id="1900">1900</a>
<a href="#1901" id="1901">1901</a>
<a href="#1902" id="1902">1902</a>
<a href="#1903" id="1903">1903</a>
<a href="#1904" id="1904">1904</a>
<a href="#1905" id="1905">1905</a>
<a href="#1906" id="1906">1906</a>
<a href="#1907" id="1907">1907</a>
<a href="#1908" id="1908">1908</a>
<a href="#1909" id="1909">1909</a>
<a href="#1910" id="1910">1910</a>
<a href="#1911" id="1911">1911</a>
<a href="#1912" id="1912">1912</a>
<a href="#1913" id="1913">1913</a>
<a href="#1914" id="1914">1914</a>
<a href="#1915" id="1915">1915</a>
<a href="#1916" id="1916">1916</a>
<a href="#1917" id="1917">1917</a>
<a href="#1918" id="1918">1918</a>
<a href="#1919" id="1919">1919</a>
<a href="#1920" id="1920">1920</a>
<a href="#1921" id="1921">1921</a>
<a href="#1922" id="1922">1922</a>
<a href="#1923" id="1923">1923</a>
<a href="#1924" id="1924">1924</a>
<a href="#1925" id="1925">1925</a>
<a href="#1926" id="1926">1926</a>
<a href="#1927" id="1927">1927</a>
<a href="#1928" id="1928">1928</a>
<a href="#1929" id="1929">1929</a>
<a href="#1930" id="1930">1930</a>
<a href="#1931" id="1931">1931</a>
<a href="#1932" id="1932">1932</a>
<a href="#1933" id="1933">1933</a>
<a href="#1934" id="1934">1934</a>
<a href="#1935" id="1935">1935</a>
<a href="#1936" id="1936">1936</a>
<a href="#1937" id="1937">1937</a>
<a href="#1938" id="1938">1938</a>
<a href="#1939" id="1939">1939</a>
<a href="#1940" id="1940">1940</a>
<a href="#1941" id="1941">1941</a>
<a href="#1942" id="1942">1942</a>
<a href="#1943" id="1943">1943</a>
<a href="#1944" id="1944">1944</a>
<a href="#1945" id="1945">1945</a>
<a href="#1946" id="1946">1946</a>
<a href="#1947" id="1947">1947</a>
<a href="#1948" id="1948">1948</a>
<a href="#1949" id="1949">1949</a>
<a href="#1950" id="1950">1950</a>
<a href="#1951" id="1951">1951</a>
<a href="#1952" id="1952">1952</a>
<a href="#1953" id="1953">1953</a>
<a href="#1954" id="1954">1954</a>
<a href="#1955" id="1955">1955</a>
<a href="#1956" id="1956">1956</a>
<a href="#1957" id="1957">1957</a>
<a href="#1958" id="1958">1958</a>
<a href="#1959" id="1959">1959</a>
<a href="#1960" id="1960">1960</a>
<a href="#1961" id="1961">1961</a>
<a href="#1962" id="1962">1962</a>
<a href="#1963" id="1963">1963</a>
<a href="#1964" id="1964">1964</a>
<a href="#1965" id="1965">1965</a>
<a href="#1966" id="1966">1966</a>
<a href="#1967" id="1967">1967</a>
<a href="#1968" id="1968">1968</a>
<a href="#1969" id="1969">1969</a>
<a href="#1970" id="1970">1970</a>
<a href="#1971" id="1971">1971</a>
<a href="#1972" id="1972">1972</a>
<a href="#1973" id="1973">1973</a>
<a href="#1974" id="1974">1974</a>
<a href="#1975" id="1975">1975</a>
<a href="#1976" id="1976">1976</a>
<a href="#1977" id="1977">1977</a>
<a href="#1978" id="1978">1978</a>
<a href="#1979" id="1979">1979</a>
<a href="#1980" id="1980">1980</a>
<a href="#1981" id="1981">1981</a>
<a href="#1982" id="1982">1982</a>
<a href="#1983" id="1983">1983</a>
<a href="#1984" id="1984">1984</a>
<a href="#1985" id="1985">1985</a>
<a href="#1986" id="1986">1986</a>
<a href="#1987" id="1987">1987</a>
<a href="#1988" id="1988">1988</a>
<a href="#1989" id="1989">1989</a>
<a href="#1990" id="1990">1990</a>
<a href="#1991" id="1991">1991</a>
<a href="#1992" id="1992">1992</a>
<a href="#1993" id="1993">1993</a>
<a href="#1994" id="1994">1994</a>
<a href="#1995" id="1995">1995</a>
<a href="#1996" id="1996">1996</a>
<a href="#1997" id="1997">1997</a>
<a href="#1998" id="1998">1998</a>
<a href="#1999" id="1999">1999</a>
<a href="#2000" id="2000">2000</a>
<a href="#2001" id="2001">2001</a>
<a href="#2002" id="2002">2002</a>
<a href="#2003" id="2003">2003</a>
<a href="#2004" id="2004">2004</a>
<a href="#2005" id="2005">2005</a>
<a href="#2006" id="2006">2006</a>
<a href="#2007" id="2007">2007</a>
<a href="#2008" id="2008">2008</a>
<a href="#2009" id="2009">2009</a>
<a href="#2010" id="2010">2010</a>
<a href="#2011" id="2011">2011</a>
<a href="#2012" id="2012">2012</a>
<a href="#2013" id="2013">2013</a>
<a href="#2014" id="2014">2014</a>
<a href="#2015" id="2015">2015</a>
<a href="#2016" id="2016">2016</a>
<a href="#2017" id="2017">2017</a>
<a href="#2018" id="2018">2018</a>
<a href="#2019" id="2019">2019</a>
<a href="#2020" id="2020">2020</a>
<a href="#2021" id="2021">2021</a>
<a href="#2022" id="2022">2022</a>
<a href="#2023" id="2023">2023</a>
<a href="#2024" id="2024">2024</a>
<a href="#2025" id="2025">2025</a>
<a href="#2026" id="2026">2026</a>
<a href="#2027" id="2027">2027</a>
<a href="#2028" id="2028">2028</a>
<a href="#2029" id="2029">2029</a>
<a href="#2030" id="2030">2030</a>
<a href="#2031" id="2031">2031</a>
<a href="#2032" id="2032">2032</a>
<a href="#2033" id="2033">2033</a>
<a href="#2034" id="2034">2034</a>
<a href="#2035" id="2035">2035</a>
<a href="#2036" id="2036">2036</a>
<a href="#2037" id="2037">2037</a>
<a href="#2038" id="2038">2038</a>
<a href="#2039" id="2039">2039</a>
<a href="#2040" id="2040">2040</a>
<a href="#2041" id="2041">2041</a>
<a href="#2042" id="2042">2042</a>
<a href="#2043" id="2043">2043</a>
<a href="#2044" id="2044">2044</a>
<a href="#2045" id="2045">2045</a>
<a href="#2046" id="2046">2046</a>
<a href="#2047" id="2047">2047</a>
<a href="#2048" id="2048">2048</a>
<a href="#2049" id="2049">2049</a>
<a href="#2050" id="2050">2050</a>
<a href="#2051" id="2051">2051</a>
<a href="#2052" id="2052">2052</a>
<a href="#2053" id="2053">2053</a>
<a href="#2054" id="2054">2054</a>
<a href="#2055" id="2055">2055</a>
<a href="#2056" id="2056">2056</a>
<a href="#2057" id="2057">2057</a>
<a href="#2058" id="2058">2058</a>
<a href="#2059" id="2059">2059</a>
<a href="#2060" id="2060">2060</a>
<a href="#2061" id="2061">2061</a>
<a href="#2062" id="2062">2062</a>
<a href="#2063" id="2063">2063</a>
<a href="#2064" id="2064">2064</a>
<a href="#2065" id="2065">2065</a>
<a href="#2066" id="2066">2066</a>
<a href="#2067" id="2067">2067</a>
<a href="#2068" id="2068">2068</a>
<a href="#2069" id="2069">2069</a>
<a href="#2070" id="2070">2070</a>
<a href="#2071" id="2071">2071</a>
<a href="#2072" id="2072">2072</a>
<a href="#2073" id="2073">2073</a>
<a href="#2074" id="2074">2074</a>
<a href="#2075" id="2075">2075</a>
<a href="#2076" id="2076">2076</a>
<a href="#2077" id="2077">2077</a>
<a href="#2078" id="2078">2078</a>
<a href="#2079" id="2079">2079</a>
<a href="#2080" id="2080">2080</a>
<a href="#2081" id="2081">2081</a>
<a href="#2082" id="2082">2082</a>
<a href="#2083" id="2083">2083</a>
<a href="#2084" id="2084">2084</a>
<a href="#2085" id="2085">2085</a>
<a href="#2086" id="2086">2086</a>
<a href="#2087" id="2087">2087</a>
<a href="#2088" id="2088">2088</a>
<a href="#2089" id="2089">2089</a>
<a href="#2090" id="2090">2090</a>
<a href="#2091" id="2091">2091</a>
<a href="#2092" id="2092">2092</a>
<a href="#2093" id="2093">2093</a>
<a href="#2094" id="2094">2094</a>
<a href="#2095" id="2095">2095</a>
<a href="#2096" id="2096">2096</a>
<a href="#2097" id="2097">2097</a>
<a href="#2098" id="2098">2098</a>
<a href="#2099" id="2099">2099</a>
<a href="#2100" id="2100">2100</a>
<a href="#2101" id="2101">2101</a>
<a href="#2102" id="2102">2102</a>
<a href="#2103" id="2103">2103</a>
<a href="#2104" id="2104">2104</a>
<a href="#2105" id="2105">2105</a>
<a href="#2106" id="2106">2106</a>
<a href="#2107" id="2107">2107</a>
<a href="#2108" id="2108">2108</a>
<a href="#2109" id="2109">2109</a>
<a href="#2110" id="2110">2110</a>
<a href="#2111" id="2111">2111</a>
<a href="#2112" id="2112">2112</a>
<a href="#2113" id="2113">2113</a>
<a href="#2114" id="2114">2114</a>
<a href="#2115" id="2115">2115</a>
<a href="#2116" id="2116">2116</a>
<a href="#2117" id="2117">2117</a>
<a href="#2118" id="2118">2118</a>
<a href="#2119" id="2119">2119</a>
<a href="#2120" id="2120">2120</a>
<a href="#2121" id="2121">2121</a>
<a href="#2122" id="2122">2122</a>
<a href="#2123" id="2123">2123</a>
<a href="#2124" id="2124">2124</a>
<a href="#2125" id="2125">2125</a>
<a href="#2126" id="2126">2126</a>
<a href="#2127" id="2127">2127</a>
<a href="#2128" id="2128">2128</a>
<a href="#2129" id="2129">2129</a>
<a href="#2130" id="2130">2130</a>
<a href="#2131" id="2131">2131</a>
<a href="#2132" id="2132">2132</a>
<a href="#2133" id="2133">2133</a>
<a href="#2134" id="2134">2134</a>
<a href="#2135" id="2135">2135</a>
<a href="#2136" id="2136">2136</a>
<a href="#2137" id="2137">2137</a>
<a href="#2138" id="2138">2138</a>
<a href="#2139" id="2139">2139</a>
<a href="#2140" id="2140">2140</a>
<a href="#2141" id="2141">2141</a>
<a href="#2142" id="2142">2142</a>
<a href="#2143" id="2143">2143</a>
<a href="#2144" id="2144">2144</a>
<a href="#2145" id="2145">2145</a>
<a href="#2146" id="2146">2146</a>
<a href="#2147" id="2147">2147</a>
<a href="#2148" id="2148">2148</a>
<a href="#2149" id="2149">2149</a>
<a href="#2150" id="2150">2150</a>
<a href="#2151" id="2151">2151</a>
<a href="#2152" id="2152">2152</a>
<a href="#2153" id="2153">2153</a>
<a href="#2154" id="2154">2154</a>
<a href="#2155" id="2155">2155</a>
<a href="#2156" id="2156">2156</a>
<a href="#2157" id="2157">2157</a>
<a href="#2158" id="2158">2158</a>
<a href="#2159" id="2159">2159</a>
<a href="#2160" id="2160">2160</a>
<a href="#2161" id="2161">2161</a>
<a href="#2162" id="2162">2162</a>
<a href="#2163" id="2163">2163</a>
<a href="#2164" id="2164">2164</a>
<a href="#2165" id="2165">2165</a>
<a href="#2166" id="2166">2166</a>
<a href="#2167" id="2167">2167</a>
<a href="#2168" id="2168">2168</a>
<a href="#2169" id="2169">2169</a>
<a href="#2170" id="2170">2170</a>
<a href="#2171" id="2171">2171</a>
<a href="#2172" id="2172">2172</a>
<a href="#2173" id="2173">2173</a>
<a href="#2174" id="2174">2174</a>
<a href="#2175" id="2175">2175</a>
<a href="#2176" id="2176">2176</a>
<a href="#2177" id="2177">2177</a>
<a href="#2178" id="2178">2178</a>
<a href="#2179" id="2179">2179</a>
<a href="#2180" id="2180">2180</a>
<a href="#2181" id="2181">2181</a>
<a href="#2182" id="2182">2182</a>
<a href="#2183" id="2183">2183</a>
<a href="#2184" id="2184">2184</a>
<a href="#2185" id="2185">2185</a>
<a href="#2186" id="2186">2186</a>
<a href="#2187" id="2187">2187</a>
<a href="#2188" id="2188">2188</a>
<a href="#2189" id="2189">2189</a>
<a href="#2190" id="2190">2190</a>
<a href="#2191" id="2191">2191</a>
<a href="#2192" id="2192">2192</a>
<a href="#2193" id="2193">2193</a>
<a href="#2194" id="2194">2194</a>
<a href="#2195" id="2195">2195</a>
<a href="#2196" id="2196">2196</a>
<a href="#2197" id="2197">2197</a>
<a href="#2198" id="2198">2198</a>
<a href="#2199" id="2199">2199</a>
<a href="#2200" id="2200">2200</a>
<a href="#2201" id="2201">2201</a>
<a href="#2202" id="2202">2202</a>
<a href="#2203" id="2203">2203</a>
<a href="#2204" id="2204">2204</a>
<a href="#2205" id="2205">2205</a>
<a href="#2206" id="2206">2206</a>
<a href="#2207" id="2207">2207</a>
<a href="#2208" id="2208">2208</a>
<a href="#2209" id="2209">2209</a>
<a href="#2210" id="2210">2210</a>
<a href="#2211" id="2211">2211</a>
<a href="#2212" id="2212">2212</a>
<a href="#2213" id="2213">2213</a>
<a href="#2214" id="2214">2214</a>
<a href="#2215" id="2215">2215</a>
<a href="#2216" id="2216">2216</a>
<a href="#2217" id="2217">2217</a>
<a href="#2218" id="2218">2218</a>
<a href="#2219" id="2219">2219</a>
<a href="#2220" id="2220">2220</a>
<a href="#2221" id="2221">2221</a>
<a href="#2222" id="2222">2222</a>
<a href="#2223" id="2223">2223</a>
<a href="#2224" id="2224">2224</a>
<a href="#2225" id="2225">2225</a>
<a href="#2226" id="2226">2226</a>
<a href="#2227" id="2227">2227</a>
<a href="#2228" id="2228">2228</a>
<a href="#2229" id="2229">2229</a>
<a href="#2230" id="2230">2230</a>
<a href="#2231" id="2231">2231</a>
<a href="#2232" id="2232">2232</a>
<a href="#2233" id="2233">2233</a>
<a href="#2234" id="2234">2234</a>
<a href="#2235" id="2235">2235</a>
<a href="#2236" id="2236">2236</a>
<a href="#2237" id="2237">2237</a>
<a href="#2238" id="2238">2238</a>
<a href="#2239" id="2239">2239</a>
<a href="#2240" id="2240">2240</a>
<a href="#2241" id="2241">2241</a>
<a href="#2242" id="2242">2242</a>
<a href="#2243" id="2243">2243</a>
<a href="#2244" id="2244">2244</a>
<a href="#2245" id="2245">2245</a>
<a href="#2246" id="2246">2246</a>
<a href="#2247" id="2247">2247</a>
<a href="#2248" id="2248">2248</a>
<a href="#2249" id="2249">2249</a>
<a href="#2250" id="2250">2250</a>
<a href="#2251" id="2251">2251</a>
<a href="#2252" id="2252">2252</a>
<a href="#2253" id="2253">2253</a>
<a href="#2254" id="2254">2254</a>
<a href="#2255" id="2255">2255</a>
<a href="#2256" id="2256">2256</a>
<a href="#2257" id="2257">2257</a>
<a href="#2258" id="2258">2258</a>
<a href="#2259" id="2259">2259</a>
<a href="#2260" id="2260">2260</a>
<a href="#2261" id="2261">2261</a>
<a href="#2262" id="2262">2262</a>
<a href="#2263" id="2263">2263</a>
<a href="#2264" id="2264">2264</a>
<a href="#2265" id="2265">2265</a>
<a href="#2266" id="2266">2266</a>
<a href="#2267" id="2267">2267</a>
<a href="#2268" id="2268">2268</a>
<a href="#2269" id="2269">2269</a>
<a href="#2270" id="2270">2270</a>
<a href="#2271" id="2271">2271</a>
<a href="#2272" id="2272">2272</a>
<a href="#2273" id="2273">2273</a>
<a href="#2274" id="2274">2274</a>
<a href="#2275" id="2275">2275</a>
<a href="#2276" id="2276">2276</a>
<a href="#2277" id="2277">2277</a>
<a href="#2278" id="2278">2278</a>
<a href="#2279" id="2279">2279</a>
<a href="#2280" id="2280">2280</a>
<a href="#2281" id="2281">2281</a>
<a href="#2282" id="2282">2282</a>
<a href="#2283" id="2283">2283</a>
<a href="#2284" id="2284">2284</a>
<a href="#2285" id="2285">2285</a>
<a href="#2286" id="2286">2286</a>
<a href="#2287" id="2287">2287</a>
<a href="#2288" id="2288">2288</a>
<a href="#2289" id="2289">2289</a>
<a href="#2290" id="2290">2290</a>
<a href="#2291" id="2291">2291</a>
<a href="#2292" id="2292">2292</a>
<a href="#2293" id="2293">2293</a>
<a href="#2294" id="2294">2294</a>
<a href="#2295" id="2295">2295</a>
<a href="#2296" id="2296">2296</a>
<a href="#2297" id="2297">2297</a>
<a href="#2298" id="2298">2298</a>
<a href="#2299" id="2299">2299</a>
<a href="#2300" id="2300">2300</a>
<a href="#2301" id="2301">2301</a>
<a href="#2302" id="2302">2302</a>
<a href="#2303" id="2303">2303</a>
<a href="#2304" id="2304">2304</a>
<a href="#2305" id="2305">2305</a>
<a href="#2306" id="2306">2306</a>
<a href="#2307" id="2307">2307</a>
<a href="#2308" id="2308">2308</a>
<a href="#2309" id="2309">2309</a>
<a href="#2310" id="2310">2310</a>
<a href="#2311" id="2311">2311</a>
<a href="#2312" id="2312">2312</a>
<a href="#2313" id="2313">2313</a>
<a href="#2314" id="2314">2314</a>
<a href="#2315" id="2315">2315</a>
<a href="#2316" id="2316">2316</a>
<a href="#2317" id="2317">2317</a>
<a href="#2318" id="2318">2318</a>
<a href="#2319" id="2319">2319</a>
<a href="#2320" id="2320">2320</a>
<a href="#2321" id="2321">2321</a>
<a href="#2322" id="2322">2322</a>
<a href="#2323" id="2323">2323</a>
<a href="#2324" id="2324">2324</a>
<a href="#2325" id="2325">2325</a>
<a href="#2326" id="2326">2326</a>
<a href="#2327" id="2327">2327</a>
<a href="#2328" id="2328">2328</a>
<a href="#2329" id="2329">2329</a>
<a href="#2330" id="2330">2330</a>
<a href="#2331" id="2331">2331</a>
<a href="#2332" id="2332">2332</a>
<a href="#2333" id="2333">2333</a>
<a href="#2334" id="2334">2334</a>
<a href="#2335" id="2335">2335</a>
<a href="#2336" id="2336">2336</a>
<a href="#2337" id="2337">2337</a>
<a href="#2338" id="2338">2338</a>
<a href="#2339" id="2339">2339</a>
<a href="#2340" id="2340">2340</a>
<a href="#2341" id="2341">2341</a>
<a href="#2342" id="2342">2342</a>
<a href="#2343" id="2343">2343</a>
<a href="#2344" id="2344">2344</a>
<a href="#2345" id="2345">2345</a>
<a href="#2346" id="2346">2346</a>
<a href="#2347" id="2347">2347</a>
<a href="#2348" id="2348">2348</a>
<a href="#2349" id="2349">2349</a>
<a href="#2350" id="2350">2350</a>
<a href="#2351" id="2351">2351</a>
<a href="#2352" id="2352">2352</a>
<a href="#2353" id="2353">2353</a>
<a href="#2354" id="2354">2354</a>
<a href="#2355" id="2355">2355</a>
<a href="#2356" id="2356">2356</a>
<a href="#2357" id="2357">2357</a>
<a href="#2358" id="2358">2358</a>
<a href="#2359" id="2359">2359</a>
<a href="#2360" id="2360">2360</a>
<a href="#2361" id="2361">2361</a>
<a href="#2362" id="2362">2362</a>
<a href="#2363" id="2363">2363</a>
<a href="#2364" id="2364">2364</a>
<a href="#2365" id="2365">2365</a>
<a href="#2366" id="2366">2366</a>
<a href="#2367" id="2367">2367</a>
<a href="#2368" id="2368">2368</a>
<a href="#2369" id="2369">2369</a>
<a href="#2370" id="2370">2370</a>
<a href="#2371" id="2371">2371</a>
<a href="#2372" id="2372">2372</a>
<a href="#2373" id="2373">2373</a>
<a href="#2374" id="2374">2374</a>
<a href="#2375" id="2375">2375</a>
<a href="#2376" id="2376">2376</a>
<a href="#2377" id="2377">2377</a>
<a href="#2378" id="2378">2378</a>
<a href="#2379" id="2379">2379</a>
<a href="#2380" id="2380">2380</a>
<a href="#2381" id="2381">2381</a>
<a href="#2382" id="2382">2382</a>
<a href="#2383" id="2383">2383</a>
<a href="#2384" id="2384">2384</a>
<a href="#2385" id="2385">2385</a>
<a href="#2386" id="2386">2386</a>
<a href="#2387" id="2387">2387</a>
<a href="#2388" id="2388">2388</a>
<a href="#2389" id="2389">2389</a>
<a href="#2390" id="2390">2390</a>
<a href="#2391" id="2391">2391</a>
<a href="#2392" id="2392">2392</a>
<a href="#2393" id="2393">2393</a>
<a href="#2394" id="2394">2394</a>
<a href="#2395" id="2395">2395</a>
<a href="#2396" id="2396">2396</a>
<a href="#2397" id="2397">2397</a>
<a href="#2398" id="2398">2398</a>
<a href="#2399" id="2399">2399</a>
<a href="#2400" id="2400">2400</a>
<a href="#2401" id="2401">2401</a>
<a href="#2402" id="2402">2402</a>
<a href="#2403" id="2403">2403</a>
<a href="#2404" id="2404">2404</a>
<a href="#2405" id="2405">2405</a>
<a href="#2406" id="2406">2406</a>
<a href="#2407" id="2407">2407</a>
<a href="#2408" id="2408">2408</a>
<a href="#2409" id="2409">2409</a>
<a href="#2410" id="2410">2410</a>
<a href="#2411" id="2411">2411</a>
<a href="#2412" id="2412">2412</a>
<a href="#2413" id="2413">2413</a>
<a href="#2414" id="2414">2414</a>
<a href="#2415" id="2415">2415</a>
<a href="#2416" id="2416">2416</a>
<a href="#2417" id="2417">2417</a>
<a href="#2418" id="2418">2418</a>
<a href="#2419" id="2419">2419</a>
<a href="#2420" id="2420">2420</a>
<a href="#2421" id="2421">2421</a>
<a href="#2422" id="2422">2422</a>
<a href="#2423" id="2423">2423</a>
<a href="#2424" id="2424">2424</a>
<a href="#2425" id="2425">2425</a>
<a href="#2426" id="2426">2426</a>
<a href="#2427" id="2427">2427</a>
<a href="#2428" id="2428">2428</a>
<a href="#2429" id="2429">2429</a>
<a href="#2430" id="2430">2430</a>
<a href="#2431" id="2431">2431</a>
<a href="#2432" id="2432">2432</a>
<a href="#2433" id="2433">2433</a>
<a href="#2434" id="2434">2434</a>
<a href="#2435" id="2435">2435</a>
<a href="#2436" id="2436">2436</a>
<a href="#2437" id="2437">2437</a>
<a href="#2438" id="2438">2438</a>
<a href="#2439" id="2439">2439</a>
<a href="#2440" id="2440">2440</a>
<a href="#2441" id="2441">2441</a>
<a href="#2442" id="2442">2442</a>
<a href="#2443" id="2443">2443</a>
<a href="#2444" id="2444">2444</a>
<a href="#2445" id="2445">2445</a>
<a href="#2446" id="2446">2446</a>
<a href="#2447" id="2447">2447</a>
<a href="#2448" id="2448">2448</a>
<a href="#2449" id="2449">2449</a>
<a href="#2450" id="2450">2450</a>
<a href="#2451" id="2451">2451</a>
<a href="#2452" id="2452">2452</a>
<a href="#2453" id="2453">2453</a>
<a href="#2454" id="2454">2454</a>
<a href="#2455" id="2455">2455</a>
<a href="#2456" id="2456">2456</a>
<a href="#2457" id="2457">2457</a>
<a href="#2458" id="2458">2458</a>
<a href="#2459" id="2459">2459</a>
<a href="#2460" id="2460">2460</a>
<a href="#2461" id="2461">2461</a>
<a href="#2462" id="2462">2462</a>
<a href="#2463" id="2463">2463</a>
<a href="#2464" id="2464">2464</a>
<a href="#2465" id="2465">2465</a>
<a href="#2466" id="2466">2466</a>
<a href="#2467" id="2467">2467</a>
<a href="#2468" id="2468">2468</a>
<a href="#2469" id="2469">2469</a>
<a href="#2470" id="2470">2470</a>
<a href="#2471" id="2471">2471</a>
<a href="#2472" id="2472">2472</a>
<a href="#2473" id="2473">2473</a>
<a href="#2474" id="2474">2474</a>
<a href="#2475" id="2475">2475</a>
<a href="#2476" id="2476">2476</a>
<a href="#2477" id="2477">2477</a>
<a href="#2478" id="2478">2478</a>
<a href="#2479" id="2479">2479</a>
<a href="#2480" id="2480">2480</a>
<a href="#2481" id="2481">2481</a>
<a href="#2482" id="2482">2482</a>
<a href="#2483" id="2483">2483</a>
<a href="#2484" id="2484">2484</a>
<a href="#2485" id="2485">2485</a>
<a href="#2486" id="2486">2486</a>
<a href="#2487" id="2487">2487</a>
<a href="#2488" id="2488">2488</a>
<a href="#2489" id="2489">2489</a>
<a href="#2490" id="2490">2490</a>
<a href="#2491" id="2491">2491</a>
<a href="#2492" id="2492">2492</a>
<a href="#2493" id="2493">2493</a>
<a href="#2494" id="2494">2494</a>
<a href="#2495" id="2495">2495</a>
<a href="#2496" id="2496">2496</a>
<a href="#2497" id="2497">2497</a>
<a href="#2498" id="2498">2498</a>
<a href="#2499" id="2499">2499</a>
<a href="#2500" id="2500">2500</a>
<a href="#2501" id="2501">2501</a>
<a href="#2502" id="2502">2502</a>
<a href="#2503" id="2503">2503</a>
<a href="#2504" id="2504">2504</a>
<a href="#2505" id="2505">2505</a>
<a href="#2506" id="2506">2506</a>
<a href="#2507" id="2507">2507</a>
<a href="#2508" id="2508">2508</a>
<a href="#2509" id="2509">2509</a>
<a href="#2510" id="2510">2510</a>
<a href="#2511" id="2511">2511</a>
<a href="#2512" id="2512">2512</a>
<a href="#2513" id="2513">2513</a>
<a href="#2514" id="2514">2514</a>
<a href="#2515" id="2515">2515</a>
<a href="#2516" id="2516">2516</a>
<a href="#2517" id="2517">2517</a>
<a href="#2518" id="2518">2518</a>
<a href="#2519" id="2519">2519</a>
<a href="#2520" id="2520">2520</a>
<a href="#2521" id="2521">2521</a>
<a href="#2522" id="2522">2522</a>
<a href="#2523" id="2523">2523</a>
<a href="#2524" id="2524">2524</a>
<a href="#2525" id="2525">2525</a>
<a href="#2526" id="2526">2526</a>
<a href="#2527" id="2527">2527</a>
<a href="#2528" id="2528">2528</a>
<a href="#2529" id="2529">2529</a>
<a href="#2530" id="2530">2530</a>
<a href="#2531" id="2531">2531</a>
<a href="#2532" id="2532">2532</a>
<a href="#2533" id="2533">2533</a>
<a href="#2534" id="2534">2534</a>
<a href="#2535" id="2535">2535</a>
<a href="#2536" id="2536">2536</a>
<a href="#2537" id="2537">2537</a>
<a href="#2538" id="2538">2538</a>
<a href="#2539" id="2539">2539</a>
<a href="#2540" id="2540">2540</a>
<a href="#2541" id="2541">2541</a>
<a href="#2542" id="2542">2542</a>
<a href="#2543" id="2543">2543</a>
<a href="#2544" id="2544">2544</a>
<a href="#2545" id="2545">2545</a>
<a href="#2546" id="2546">2546</a>
<a href="#2547" id="2547">2547</a>
<a href="#2548" id="2548">2548</a>
<a href="#2549" id="2549">2549</a>
<a href="#2550" id="2550">2550</a>
<a href="#2551" id="2551">2551</a>
<a href="#2552" id="2552">2552</a>
<a href="#2553" id="2553">2553</a>
<a href="#2554" id="2554">2554</a>
<a href="#2555" id="2555">2555</a>
<a href="#2556" id="2556">2556</a>
<a href="#2557" id="2557">2557</a>
<a href="#2558" id="2558">2558</a>
<a href="#2559" id="2559">2559</a>
<a href="#2560" id="2560">2560</a>
<a href="#2561" id="2561">2561</a>
<a href="#2562" id="2562">2562</a>
<a href="#2563" id="2563">2563</a>
<a href="#2564" id="2564">2564</a>
<a href="#2565" id="2565">2565</a>
<a href="#2566" id="2566">2566</a>
<a href="#2567" id="2567">2567</a>
<a href="#2568" id="2568">2568</a>
<a href="#2569" id="2569">2569</a>
<a href="#2570" id="2570">2570</a>
<a href="#2571" id="2571">2571</a>
<a href="#2572" id="2572">2572</a>
<a href="#2573" id="2573">2573</a>
<a href="#2574" id="2574">2574</a>
<a href="#2575" id="2575">2575</a>
<a href="#2576" id="2576">2576</a>
<a href="#2577" id="2577">2577</a>
<a href="#2578" id="2578">2578</a>
<a href="#2579" id="2579">2579</a>
<a href="#2580" id="2580">2580</a>
<a href="#2581" id="2581">2581</a>
<a href="#2582" id="2582">2582</a>
<a href="#2583" id="2583">2583</a>
<a href="#2584" id="2584">2584</a>
<a href="#2585" id="2585">2585</a>
<a href="#2586" id="2586">2586</a>
<a href="#2587" id="2587">2587</a>
<a href="#2588" id="2588">2588</a>
<a href="#2589" id="2589">2589</a>
<a href="#2590" id="2590">2590</a>
<a href="#2591" id="2591">2591</a>
<a href="#2592" id="2592">2592</a>
<a href="#2593" id="2593">2593</a>
<a href="#2594" id="2594">2594</a>
<a href="#2595" id="2595">2595</a>
<a href="#2596" id="2596">2596</a>
<a href="#2597" id="2597">2597</a>
<a href="#2598" id="2598">2598</a>
<a href="#2599" id="2599">2599</a>
<a href="#2600" id="2600">2600</a>
<a href="#2601" id="2601">2601</a>
<a href="#2602" id="2602">2602</a>
<a href="#2603" id="2603">2603</a>
<a href="#2604" id="2604">2604</a>
<a href="#2605" id="2605">2605</a>
<a href="#2606" id="2606">2606</a>
<a href="#2607" id="2607">2607</a>
<a href="#2608" id="2608">2608</a>
<a href="#2609" id="2609">2609</a>
<a href="#2610" id="2610">2610</a>
<a href="#2611" id="2611">2611</a>
<a href="#2612" id="2612">2612</a>
<a href="#2613" id="2613">2613</a>
<a href="#2614" id="2614">2614</a>
<a href="#2615" id="2615">2615</a>
<a href="#2616" id="2616">2616</a>
<a href="#2617" id="2617">2617</a>
<a href="#2618" id="2618">2618</a>
<a href="#2619" id="2619">2619</a>
<a href="#2620" id="2620">2620</a>
<a href="#2621" id="2621">2621</a>
<a href="#2622" id="2622">2622</a>
<a href="#2623" id="2623">2623</a>
<a href="#2624" id="2624">2624</a>
<a href="#2625" id="2625">2625</a>
<a href="#2626" id="2626">2626</a>
<a href="#2627" id="2627">2627</a>
<a href="#2628" id="2628">2628</a>
<a href="#2629" id="2629">2629</a>
<a href="#2630" id="2630">2630</a>
<a href="#2631" id="2631">2631</a>
<a href="#2632" id="2632">2632</a>
<a href="#2633" id="2633">2633</a>
<a href="#2634" id="2634">2634</a>
<a href="#2635" id="2635">2635</a>
<a href="#2636" id="2636">2636</a>
<a href="#2637" id="2637">2637</a>
<a href="#2638" id="2638">2638</a>
<a href="#2639" id="2639">2639</a>
<a href="#2640" id="2640">2640</a>
<a href="#2641" id="2641">2641</a>
<a href="#2642" id="2642">2642</a>
<a href="#2643" id="2643">2643</a>
<a href="#2644" id="2644">2644</a>
<a href="#2645" id="2645">2645</a>
<a href="#2646" id="2646">2646</a>
<a href="#2647" id="2647">2647</a>
<a href="#2648" id="2648">2648</a>
<a href="#2649" id="2649">2649</a>
<a href="#2650" id="2650">2650</a>
<a href="#2651" id="2651">2651</a>
<a href="#2652" id="2652">2652</a>
<a href="#2653" id="2653">2653</a>
<a href="#2654" id="2654">2654</a>
<a href="#2655" id="2655">2655</a>
<a href="#2656" id="2656">2656</a>
<a href="#2657" id="2657">2657</a>
<a href="#2658" id="2658">2658</a>
<a href="#2659" id="2659">2659</a>
<a href="#2660" id="2660">2660</a>
<a href="#2661" id="2661">2661</a>
<a href="#2662" id="2662">2662</a>
<a href="#2663" id="2663">2663</a>
<a href="#2664" id="2664">2664</a>
<a href="#2665" id="2665">2665</a>
<a href="#2666" id="2666">2666</a>
<a href="#2667" id="2667">2667</a>
<a href="#2668" id="2668">2668</a>
<a href="#2669" id="2669">2669</a>
<a href="#2670" id="2670">2670</a>
<a href="#2671" id="2671">2671</a>
<a href="#2672" id="2672">2672</a>
<a href="#2673" id="2673">2673</a>
<a href="#2674" id="2674">2674</a>
<a href="#2675" id="2675">2675</a>
<a href="#2676" id="2676">2676</a>
<a href="#2677" id="2677">2677</a>
<a href="#2678" id="2678">2678</a>
<a href="#2679" id="2679">2679</a>
<a href="#2680" id="2680">2680</a>
<a href="#2681" id="2681">2681</a>
<a href="#2682" id="2682">2682</a>
<a href="#2683" id="2683">2683</a>
<a href="#2684" id="2684">2684</a>
<a href="#2685" id="2685">2685</a>
<a href="#2686" id="2686">2686</a>
<a href="#2687" id="2687">2687</a>
<a href="#2688" id="2688">2688</a>
<a href="#2689" id="2689">2689</a>
<a href="#2690" id="2690">2690</a>
<a href="#2691" id="2691">2691</a>
<a href="#2692" id="2692">2692</a>
<a href="#2693" id="2693">2693</a>
<a href="#2694" id="2694">2694</a>
<a href="#2695" id="2695">2695</a>
<a href="#2696" id="2696">2696</a>
<a href="#2697" id="2697">2697</a>
<a href="#2698" id="2698">2698</a>
<a href="#2699" id="2699">2699</a>
<a href="#2700" id="2700">2700</a>
<a href="#2701" id="2701">2701</a>
<a href="#2702" id="2702">2702</a>
<a href="#2703" id="2703">2703</a>
<a href="#2704" id="2704">2704</a>
<a href="#2705" id="2705">2705</a>
<a href="#2706" id="2706">2706</a>
<a href="#2707" id="2707">2707</a>
<a href="#2708" id="2708">2708</a>
<a href="#2709" id="2709">2709</a>
<a href="#2710" id="2710">2710</a>
<a href="#2711" id="2711">2711</a>
<a href="#2712" id="2712">2712</a>
<a href="#2713" id="2713">2713</a>
<a href="#2714" id="2714">2714</a>
<a href="#2715" id="2715">2715</a>
<a href="#2716" id="2716">2716</a>
<a href="#2717" id="2717">2717</a>
<a href="#2718" id="2718">2718</a>
<a href="#2719" id="2719">2719</a>
<a href="#2720" id="2720">2720</a>
<a href="#2721" id="2721">2721</a>
<a href="#2722" id="2722">2722</a>
<a href="#2723" id="2723">2723</a>
<a href="#2724" id="2724">2724</a>
<a href="#2725" id="2725">2725</a>
<a href="#2726" id="2726">2726</a>
<a href="#2727" id="2727">2727</a>
<a href="#2728" id="2728">2728</a>
<a href="#2729" id="2729">2729</a>
<a href="#2730" id="2730">2730</a>
<a href="#2731" id="2731">2731</a>
<a href="#2732" id="2732">2732</a>
<a href="#2733" id="2733">2733</a>
<a href="#2734" id="2734">2734</a>
<a href="#2735" id="2735">2735</a>
<a href="#2736" id="2736">2736</a>
<a href="#2737" id="2737">2737</a>
<a href="#2738" id="2738">2738</a>
<a href="#2739" id="2739">2739</a>
<a href="#2740" id="2740">2740</a>
<a href="#2741" id="2741">2741</a>
<a href="#2742" id="2742">2742</a>
<a href="#2743" id="2743">2743</a>
<a href="#2744" id="2744">2744</a>
<a href="#2745" id="2745">2745</a>
<a href="#2746" id="2746">2746</a>
<a href="#2747" id="2747">2747</a>
<a href="#2748" id="2748">2748</a>
<a href="#2749" id="2749">2749</a>
<a href="#2750" id="2750">2750</a>
<a href="#2751" id="2751">2751</a>
<a href="#2752" id="2752">2752</a>
<a href="#2753" id="2753">2753</a>
<a href="#2754" id="2754">2754</a>
<a href="#2755" id="2755">2755</a>
<a href="#2756" id="2756">2756</a>
<a href="#2757" id="2757">2757</a>
<a href="#2758" id="2758">2758</a>
<a href="#2759" id="2759">2759</a>
<a href="#2760" id="2760">2760</a>
<a href="#2761" id="2761">2761</a>
<a href="#2762" id="2762">2762</a>
<a href="#2763" id="2763">2763</a>
<a href="#2764" id="2764">2764</a>
<a href="#2765" id="2765">2765</a>
<a href="#2766" id="2766">2766</a>
<a href="#2767" id="2767">2767</a>
<a href="#2768" id="2768">2768</a>
<a href="#2769" id="2769">2769</a>
<a href="#2770" id="2770">2770</a>
<a href="#2771" id="2771">2771</a>
<a href="#2772" id="2772">2772</a>
<a href="#2773" id="2773">2773</a>
<a href="#2774" id="2774">2774</a>
<a href="#2775" id="2775">2775</a>
<a href="#2776" id="2776">2776</a>
<a href="#2777" id="2777">2777</a>
<a href="#2778" id="2778">2778</a>
<a href="#2779" id="2779">2779</a>
<a href="#2780" id="2780">2780</a>
<a href="#2781" id="2781">2781</a>
<a href="#2782" id="2782">2782</a>
<a href="#2783" id="2783">2783</a>
<a href="#2784" id="2784">2784</a>
<a href="#2785" id="2785">2785</a>
<a href="#2786" id="2786">2786</a>
<a href="#2787" id="2787">2787</a>
<a href="#2788" id="2788">2788</a>
<a href="#2789" id="2789">2789</a>
<a href="#2790" id="2790">2790</a>
<a href="#2791" id="2791">2791</a>
<a href="#2792" id="2792">2792</a>
<a href="#2793" id="2793">2793</a>
<a href="#2794" id="2794">2794</a>
<a href="#2795" id="2795">2795</a>
<a href="#2796" id="2796">2796</a>
<a href="#2797" id="2797">2797</a>
<a href="#2798" id="2798">2798</a>
<a href="#2799" id="2799">2799</a>
<a href="#2800" id="2800">2800</a>
<a href="#2801" id="2801">2801</a>
<a href="#2802" id="2802">2802</a>
<a href="#2803" id="2803">2803</a>
<a href="#2804" id="2804">2804</a>
<a href="#2805" id="2805">2805</a>
<a href="#2806" id="2806">2806</a>
<a href="#2807" id="2807">2807</a>
<a href="#2808" id="2808">2808</a>
<a href="#2809" id="2809">2809</a>
<a href="#2810" id="2810">2810</a>
<a href="#2811" id="2811">2811</a>
<a href="#2812" id="2812">2812</a>
<a href="#2813" id="2813">2813</a>
<a href="#2814" id="2814">2814</a>
<a href="#2815" id="2815">2815</a>
<a href="#2816" id="2816">2816</a>
<a href="#2817" id="2817">2817</a>
<a href="#2818" id="2818">2818</a>
<a href="#2819" id="2819">2819</a>
<a href="#2820" id="2820">2820</a>
<a href="#2821" id="2821">2821</a>
<a href="#2822" id="2822">2822</a>
<a href="#2823" id="2823">2823</a>
<a href="#2824" id="2824">2824</a>
<a href="#2825" id="2825">2825</a>
<a href="#2826" id="2826">2826</a>
<a href="#2827" id="2827">2827</a>
<a href="#2828" id="2828">2828</a>
<a href="#2829" id="2829">2829</a>
<a href="#2830" id="2830">2830</a>
<a href="#2831" id="2831">2831</a>
<a href="#2832" id="2832">2832</a>
<a href="#2833" id="2833">2833</a>
<a href="#2834" id="2834">2834</a>
<a href="#2835" id="2835">2835</a>
<a href="#2836" id="2836">2836</a>
<a href="#2837" id="2837">2837</a>
<a href="#2838" id="2838">2838</a>
<a href="#2839" id="2839">2839</a>
<a href="#2840" id="2840">2840</a>
<a href="#2841" id="2841">2841</a>
<a href="#2842" id="2842">2842</a>
<a href="#2843" id="2843">2843</a>
<a href="#2844" id="2844">2844</a>
<a href="#2845" id="2845">2845</a>
<a href="#2846" id="2846">2846</a>
<a href="#2847" id="2847">2847</a>
<a href="#2848" id="2848">2848</a>
<a href="#2849" id="2849">2849</a>
<a href="#2850" id="2850">2850</a>
<a href="#2851" id="2851">2851</a>
<a href="#2852" id="2852">2852</a>
<a href="#2853" id="2853">2853</a>
<a href="#2854" id="2854">2854</a>
<a href="#2855" id="2855">2855</a>
<a href="#2856" id="2856">2856</a>
<a href="#2857" id="2857">2857</a>
<a href="#2858" id="2858">2858</a>
<a href="#2859" id="2859">2859</a>
<a href="#2860" id="2860">2860</a>
<a href="#2861" id="2861">2861</a>
<a href="#2862" id="2862">2862</a>
<a href="#2863" id="2863">2863</a>
<a href="#2864" id="2864">2864</a>
<a href="#2865" id="2865">2865</a>
<a href="#2866" id="2866">2866</a>
<a href="#2867" id="2867">2867</a>
<a href="#2868" id="2868">2868</a>
<a href="#2869" id="2869">2869</a>
<a href="#2870" id="2870">2870</a>
<a href="#2871" id="2871">2871</a>
<a href="#2872" id="2872">2872</a>
<a href="#2873" id="2873">2873</a>
<a href="#2874" id="2874">2874</a>
<a href="#2875" id="2875">2875</a>
<a href="#2876" id="2876">2876</a>
<a href="#2877" id="2877">2877</a>
<a href="#2878" id="2878">2878</a>
<a href="#2879" id="2879">2879</a>
<a href="#2880" id="2880">2880</a>
<a href="#2881" id="2881">2881</a>
<a href="#2882" id="2882">2882</a>
<a href="#2883" id="2883">2883</a>
<a href="#2884" id="2884">2884</a>
<a href="#2885" id="2885">2885</a>
<a href="#2886" id="2886">2886</a>
<a href="#2887" id="2887">2887</a>
<a href="#2888" id="2888">2888</a>
<a href="#2889" id="2889">2889</a>
<a href="#2890" id="2890">2890</a>
<a href="#2891" id="2891">2891</a>
<a href="#2892" id="2892">2892</a>
<a href="#2893" id="2893">2893</a>
<a href="#2894" id="2894">2894</a>
<a href="#2895" id="2895">2895</a>
<a href="#2896" id="2896">2896</a>
<a href="#2897" id="2897">2897</a>
<a href="#2898" id="2898">2898</a>
<a href="#2899" id="2899">2899</a>
<a href="#2900" id="2900">2900</a>
<a href="#2901" id="2901">2901</a>
<a href="#2902" id="2902">2902</a>
<a href="#2903" id="2903">2903</a>
<a href="#2904" id="2904">2904</a>
<a href="#2905" id="2905">2905</a>
<a href="#2906" id="2906">2906</a>
<a href="#2907" id="2907">2907</a>
<a href="#2908" id="2908">2908</a>
<a href="#2909" id="2909">2909</a>
<a href="#2910" id="2910">2910</a>
<a href="#2911" id="2911">2911</a>
<a href="#2912" id="2912">2912</a>
<a href="#2913" id="2913">2913</a>
<a href="#2914" id="2914">2914</a>
<a href="#2915" id="2915">2915</a>
<a href="#2916" id="2916">2916</a>
<a href="#2917" id="2917">2917</a>
<a href="#2918" id="2918">2918</a>
<a href="#2919" id="2919">2919</a>
<a href="#2920" id="2920">2920</a>
<a href="#2921" id="2921">2921</a>
<a href="#2922" id="2922">2922</a>
<a href="#2923" id="2923">2923</a>
<a href="#2924" id="2924">2924</a>
<a href="#2925" id="2925">2925</a>
<a href="#2926" id="2926">2926</a>
<a href="#2927" id="2927">2927</a>
<a href="#2928" id="2928">2928</a>
<a href="#2929" id="2929">2929</a>
<a href="#2930" id="2930">2930</a>
<a href="#2931" id="2931">2931</a>
<a href="#2932" id="2932">2932</a>
<a href="#2933" id="2933">2933</a>
<a href="#2934" id="2934">2934</a>
<a href="#2935" id="2935">2935</a>
<a href="#2936" id="2936">2936</a>
<a href="#2937" id="2937">2937</a>
<a href="#2938" id="2938">2938</a>
<a href="#2939" id="2939">2939</a>
<a href="#2940" id="2940">2940</a>
<a href="#2941" id="2941">2941</a>
<a href="#2942" id="2942">2942</a>
<a href="#2943" id="2943">2943</a>
<a href="#2944" id="2944">2944</a>
<a href="#2945" id="2945">2945</a>
<a href="#2946" id="2946">2946</a>
<a href="#2947" id="2947">2947</a>
<a href="#2948" id="2948">2948</a>
<a href="#2949" id="2949">2949</a>
<a href="#2950" id="2950">2950</a>
<a href="#2951" id="2951">2951</a>
<a href="#2952" id="2952">2952</a>
<a href="#2953" id="2953">2953</a>
<a href="#2954" id="2954">2954</a>
<a href="#2955" id="2955">2955</a>
<a href="#2956" id="2956">2956</a>
<a href="#2957" id="2957">2957</a>
<a href="#2958" id="2958">2958</a>
<a href="#2959" id="2959">2959</a>
<a href="#2960" id="2960">2960</a>
<a href="#2961" id="2961">2961</a>
<a href="#2962" id="2962">2962</a>
<a href="#2963" id="2963">2963</a>
<a href="#2964" id="2964">2964</a>
<a href="#2965" id="2965">2965</a>
<a href="#2966" id="2966">2966</a>
<a href="#2967" id="2967">2967</a>
<a href="#2968" id="2968">2968</a>
<a href="#2969" id="2969">2969</a>
<a href="#2970" id="2970">2970</a>
<a href="#2971" id="2971">2971</a>
<a href="#2972" id="2972">2972</a>
<a href="#2973" id="2973">2973</a>
<a href="#2974" id="2974">2974</a>
<a href="#2975" id="2975">2975</a>
<a href="#2976" id="2976">2976</a>
<a href="#2977" id="2977">2977</a>
<a href="#2978" id="2978">2978</a>
<a href="#2979" id="2979">2979</a>
<a href="#2980" id="2980">2980</a>
<a href="#2981" id="2981">2981</a>
<a href="#2982" id="2982">2982</a>
<a href="#2983" id="2983">2983</a>
<a href="#2984" id="2984">2984</a>
<a href="#2985" id="2985">2985</a>
<a href="#2986" id="2986">2986</a>
<a href="#2987" id="2987">2987</a>
<a href="#2988" id="2988">2988</a>
<a href="#2989" id="2989">2989</a>
<a href="#2990" id="2990">2990</a>
<a href="#2991" id="2991">2991</a>
<a href="#2992" id="2992">2992</a>
<a href="#2993" id="2993">2993</a>
<a href="#2994" id="2994">2994</a>
<a href="#2995" id="2995">2995</a>
<a href="#2996" id="2996">2996</a>
<a href="#2997" id="2997">2997</a>
<a href="#2998" id="2998">2998</a>
<a href="#2999" id="2999">2999</a>
<a href="#3000" id="3000">3000</a>
<a href="#3001" id="3001">3001</a>
<a href="#3002" id="3002">3002</a>
<a href="#3003" id="3003">3003</a>
<a href="#3004" id="3004">3004</a>
<a href="#3005" id="3005">3005</a>
<a href="#3006" id="3006">3006</a>
<a href="#3007" id="3007">3007</a>
<a href="#3008" id="3008">3008</a>
<a href="#3009" id="3009">3009</a>
<a href="#3010" id="3010">3010</a>
<a href="#3011" id="3011">3011</a>
<a href="#3012" id="3012">3012</a>
<a href="#3013" id="3013">3013</a>
<a href="#3014" id="3014">3014</a>
<a href="#3015" id="3015">3015</a>
<a href="#3016" id="3016">3016</a>
<a href="#3017" id="3017">3017</a>
<a href="#3018" id="3018">3018</a>
<a href="#3019" id="3019">3019</a>
<a href="#3020" id="3020">3020</a>
<a href="#3021" id="3021">3021</a>
<a href="#3022" id="3022">3022</a>
<a href="#3023" id="3023">3023</a>
<a href="#3024" id="3024">3024</a>
<a href="#3025" id="3025">3025</a>
<a href="#3026" id="3026">3026</a>
<a href="#3027" id="3027">3027</a>
<a href="#3028" id="3028">3028</a>
<a href="#3029" id="3029">3029</a>
<a href="#3030" id="3030">3030</a>
<a href="#3031" id="3031">3031</a>
<a href="#3032" id="3032">3032</a>
<a href="#3033" id="3033">3033</a>
<a href="#3034" id="3034">3034</a>
<a href="#3035" id="3035">3035</a>
<a href="#3036" id="3036">3036</a>
<a href="#3037" id="3037">3037</a>
<a href="#3038" id="3038">3038</a>
<a href="#3039" id="3039">3039</a>
<a href="#3040" id="3040">3040</a>
<a href="#3041" id="3041">3041</a>
<a href="#3042" id="3042">3042</a>
<a href="#3043" id="3043">3043</a>
<a href="#3044" id="3044">3044</a>
<a href="#3045" id="3045">3045</a>
<a href="#3046" id="3046">3046</a>
<a href="#3047" id="3047">3047</a>
<a href="#3048" id="3048">3048</a>
<a href="#3049" id="3049">3049</a>
<a href="#3050" id="3050">3050</a>
<a href="#3051" id="3051">3051</a>
<a href="#3052" id="3052">3052</a>
<a href="#3053" id="3053">3053</a>
<a href="#3054" id="3054">3054</a>
<a href="#3055" id="3055">3055</a>
<a href="#3056" id="3056">3056</a>
<a href="#3057" id="3057">3057</a>
<a href="#3058" id="3058">3058</a>
<a href="#3059" id="3059">3059</a>
<a href="#3060" id="3060">3060</a>
<a href="#3061" id="3061">3061</a>
<a href="#3062" id="3062">3062</a>
<a href="#3063" id="3063">3063</a>
<a href="#3064" id="3064">3064</a>
<a href="#3065" id="3065">3065</a>
<a href="#3066" id="3066">3066</a>
<a href="#3067" id="3067">3067</a>
<a href="#3068" id="3068">3068</a>
<a href="#3069" id="3069">3069</a>
<a href="#3070" id="3070">3070</a>
<a href="#3071" id="3071">3071</a>
<a href="#3072" id="3072">3072</a>
<a href="#3073" id="3073">3073</a>
<a href="#3074" id="3074">3074</a>
<a href="#3075" id="3075">3075</a>
<a href="#3076" id="3076">3076</a>
<a href="#3077" id="3077">3077</a>
<a href="#3078" id="3078">3078</a>
<a href="#3079" id="3079">3079</a>
<a href="#3080" id="3080">3080</a>
<a href="#3081" id="3081">3081</a>
<a href="#3082" id="3082">3082</a>
<a href="#3083" id="3083">3083</a>
<a href="#3084" id="3084">3084</a>
<a href="#3085" id="3085">3085</a>
<a href="#3086" id="3086">3086</a>
<a href="#3087" id="3087">3087</a>
<a href="#3088" id="3088">3088</a>
<a href="#3089" id="3089">3089</a>
<a href="#3090" id="3090">3090</a>
<a href="#3091" id="3091">3091</a>
<a href="#3092" id="3092">3092</a>
<a href="#3093" id="3093">3093</a>
<a href="#3094" id="3094">3094</a>
<a href="#3095" id="3095">3095</a>
<a href="#3096" id="3096">3096</a>
<a href="#3097" id="3097">3097</a>
<a href="#3098" id="3098">3098</a>
<a href="#3099" id="3099">3099</a>
<a href="#3100" id="3100">3100</a>
<a href="#3101" id="3101">3101</a>
<a href="#3102" id="3102">3102</a>
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<a href="#3106" id="3106">3106</a>
</pre><pre class="rust"><code><span class="comment">// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
</span><span class="doccomment">//! Rational numbers
//!
//! ## Compatibility
//!
//! The `num-rational` crate is tested for rustc 1.31 and greater.
</span><span class="attr">#![doc(html_root_url = <span class="string">"https://docs.rs/num-rational/0.4"</span>)]
#![no_std]
</span><span class="comment">// Ratio ops often use other "suspicious" ops
</span><span class="attr">#![allow(clippy::suspicious_arithmetic_impl)]
#![allow(clippy::suspicious_op_assign_impl)]
#[cfg(feature = <span class="string">"std"</span>)]
#[macro_use]
</span><span class="kw">extern crate </span>std;
<span class="kw">use </span>core::cmp;
<span class="kw">use </span>core::fmt;
<span class="kw">use </span>core::fmt::{Binary, Display, Formatter, LowerExp, LowerHex, Octal, UpperExp, UpperHex};
<span class="kw">use </span>core::hash::{Hash, Hasher};
<span class="kw">use </span>core::ops::{Add, Div, Mul, Neg, Rem, ShlAssign, Sub};
<span class="kw">use </span>core::str::FromStr;
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">use </span>std::error::Error;
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">use </span>num_bigint::{BigInt, BigUint, Sign, ToBigInt};
<span class="kw">use </span>num_integer::Integer;
<span class="kw">use </span>num_traits::float::FloatCore;
<span class="kw">use </span>num_traits::ToPrimitive;
<span class="kw">use </span>num_traits::{
Bounded, CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, FromPrimitive, Inv, Num, NumCast, One,
Pow, Signed, Zero,
};
<span class="kw">mod </span>pow;
<span class="doccomment">/// Represents the ratio between two numbers.
</span><span class="attr">#[derive(Copy, Clone, Debug)]
#[allow(missing_docs)]
</span><span class="kw">pub struct </span>Ratio<T> {
<span class="doccomment">/// Numerator.
</span>numer: T,
<span class="doccomment">/// Denominator.
</span>denom: T,
}
<span class="doccomment">/// Alias for a `Ratio` of machine-sized integers.
</span><span class="attr">#[deprecated(
since = <span class="string">"0.4.0"</span>,
note = <span class="string">"it's better to use a specific size, like `Rational32` or `Rational64`"
</span>)]
</span><span class="kw">pub type </span>Rational = Ratio<isize>;
<span class="doccomment">/// Alias for a `Ratio` of 32-bit-sized integers.
</span><span class="kw">pub type </span>Rational32 = Ratio<i32>;
<span class="doccomment">/// Alias for a `Ratio` of 64-bit-sized integers.
</span><span class="kw">pub type </span>Rational64 = Ratio<i64>;
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="doccomment">/// Alias for arbitrary precision rationals.
</span><span class="kw">pub type </span>BigRational = Ratio<BigInt>;
<span class="doccomment">/// These method are `const` for Rust 1.31 and later.
</span><span class="kw">impl</span><T> Ratio<T> {
<span class="doccomment">/// Creates a `Ratio` without checking for `denom == 0` or reducing.
///
/// **There are several methods that will panic if used on a `Ratio` with
/// `denom == 0`.**
</span><span class="attr">#[inline]
</span><span class="kw">pub const fn </span>new_raw(numer: T, denom: T) -> Ratio<T> {
Ratio { numer, denom }
}
<span class="doccomment">/// Gets an immutable reference to the numerator.
</span><span class="attr">#[inline]
</span><span class="kw">pub const fn </span>numer(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>T {
<span class="kw-2">&</span><span class="self">self</span>.numer
}
<span class="doccomment">/// Gets an immutable reference to the denominator.
</span><span class="attr">#[inline]
</span><span class="kw">pub const fn </span>denom(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>T {
<span class="kw-2">&</span><span class="self">self</span>.denom
}
}
<span class="kw">impl</span><T: Clone + Integer> Ratio<T> {
<span class="doccomment">/// Creates a new `Ratio`.
///
/// **Panics if `denom` is zero.**
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>new(numer: T, denom: T) -> Ratio<T> {
<span class="kw">let </span><span class="kw-2">mut </span>ret = Ratio::new_raw(numer, denom);
ret.reduce();
ret
}
<span class="doccomment">/// Creates a `Ratio` representing the integer `t`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_integer(t: T) -> Ratio<T> {
Ratio::new_raw(t, One::one())
}
<span class="doccomment">/// Converts to an integer, rounding towards zero.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>to_integer(<span class="kw-2">&</span><span class="self">self</span>) -> T {
<span class="self">self</span>.trunc().numer
}
<span class="doccomment">/// Returns true if the rational number is an integer (denominator is 1).
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>is_integer(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="self">self</span>.denom.is_one()
}
<span class="doccomment">/// Puts self into lowest terms, with `denom` > 0.
///
/// **Panics if `denom` is zero.**
</span><span class="kw">fn </span>reduce(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="kw">if </span><span class="self">self</span>.denom.is_zero() {
<span class="macro">panic!</span>(<span class="string">"denominator == 0"</span>);
}
<span class="kw">if </span><span class="self">self</span>.numer.is_zero() {
<span class="self">self</span>.denom.set_one();
<span class="kw">return</span>;
}
<span class="kw">if </span><span class="self">self</span>.numer == <span class="self">self</span>.denom {
<span class="self">self</span>.set_one();
<span class="kw">return</span>;
}
<span class="kw">let </span>g: T = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span><span class="self">self</span>.denom);
<span class="comment">// FIXME(#5992): assignment operator overloads
// T: Clone + Integer != T: Clone + NumAssign
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>replace_with<T: Zero>(x: <span class="kw-2">&mut </span>T, f: <span class="kw">impl </span>FnOnce(T) -> T) {
<span class="kw">let </span>y = core::mem::replace(x, T::zero());
<span class="kw-2">*</span>x = f(y);
}
<span class="comment">// self.numer /= g;
</span>replace_with(<span class="kw-2">&mut </span><span class="self">self</span>.numer, |x| x / g.clone());
<span class="comment">// self.denom /= g;
</span>replace_with(<span class="kw-2">&mut </span><span class="self">self</span>.denom, |x| x / g);
<span class="comment">// keep denom positive!
</span><span class="kw">if </span><span class="self">self</span>.denom < T::zero() {
replace_with(<span class="kw-2">&mut </span><span class="self">self</span>.numer, |x| T::zero() - x);
replace_with(<span class="kw-2">&mut </span><span class="self">self</span>.denom, |x| T::zero() - x);
}
}
<span class="doccomment">/// Returns a reduced copy of self.
///
/// In general, it is not necessary to use this method, as the only
/// method of procuring a non-reduced fraction is through `new_raw`.
///
/// **Panics if `denom` is zero.**
</span><span class="kw">pub fn </span>reduced(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="kw">let </span><span class="kw-2">mut </span>ret = <span class="self">self</span>.clone();
ret.reduce();
ret
}
<span class="doccomment">/// Returns the reciprocal.
///
/// **Panics if the `Ratio` is zero.**
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>recip(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="self">self</span>.clone().into_recip()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>into_recip(<span class="self">self</span>) -> Ratio<T> {
<span class="kw">match </span><span class="self">self</span>.numer.cmp(<span class="kw-2">&</span>T::zero()) {
cmp::Ordering::Equal => <span class="macro">panic!</span>(<span class="string">"division by zero"</span>),
cmp::Ordering::Greater => Ratio::new_raw(<span class="self">self</span>.denom, <span class="self">self</span>.numer),
cmp::Ordering::Less => Ratio::new_raw(T::zero() - <span class="self">self</span>.denom, T::zero() - <span class="self">self</span>.numer),
}
}
<span class="doccomment">/// Rounds towards minus infinity.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>floor(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="kw">if </span><span class="kw-2">*</span><span class="self">self </span>< Zero::zero() {
<span class="kw">let </span>one: T = One::one();
Ratio::from_integer(
(<span class="self">self</span>.numer.clone() - <span class="self">self</span>.denom.clone() + one) / <span class="self">self</span>.denom.clone(),
)
} <span class="kw">else </span>{
Ratio::from_integer(<span class="self">self</span>.numer.clone() / <span class="self">self</span>.denom.clone())
}
}
<span class="doccomment">/// Rounds towards plus infinity.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>ceil(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="kw">if </span><span class="kw-2">*</span><span class="self">self </span>< Zero::zero() {
Ratio::from_integer(<span class="self">self</span>.numer.clone() / <span class="self">self</span>.denom.clone())
} <span class="kw">else </span>{
<span class="kw">let </span>one: T = One::one();
Ratio::from_integer(
(<span class="self">self</span>.numer.clone() + <span class="self">self</span>.denom.clone() - one) / <span class="self">self</span>.denom.clone(),
)
}
}
<span class="doccomment">/// Rounds to the nearest integer. Rounds half-way cases away from zero.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>round(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="kw">let </span>zero: Ratio<T> = Zero::zero();
<span class="kw">let </span>one: T = One::one();
<span class="kw">let </span>two: T = one.clone() + one.clone();
<span class="comment">// Find unsigned fractional part of rational number
</span><span class="kw">let </span><span class="kw-2">mut </span>fractional = <span class="self">self</span>.fract();
<span class="kw">if </span>fractional < zero {
fractional = zero - fractional
};
<span class="comment">// The algorithm compares the unsigned fractional part with 1/2, that
// is, a/b >= 1/2, or a >= b/2. For odd denominators, we use
// a >= (b/2)+1. This avoids overflow issues.
</span><span class="kw">let </span>half_or_larger = <span class="kw">if </span>fractional.denom.is_even() {
fractional.numer >= fractional.denom / two
} <span class="kw">else </span>{
fractional.numer >= (fractional.denom / two) + one
};
<span class="kw">if </span>half_or_larger {
<span class="kw">let </span>one: Ratio<T> = One::one();
<span class="kw">if </span><span class="kw-2">*</span><span class="self">self </span>>= Zero::zero() {
<span class="self">self</span>.trunc() + one
} <span class="kw">else </span>{
<span class="self">self</span>.trunc() - one
}
} <span class="kw">else </span>{
<span class="self">self</span>.trunc()
}
}
<span class="doccomment">/// Rounds towards zero.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>trunc(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
Ratio::from_integer(<span class="self">self</span>.numer.clone() / <span class="self">self</span>.denom.clone())
}
<span class="doccomment">/// Returns the fractional part of a number, with division rounded towards zero.
///
/// Satisfies `self == self.trunc() + self.fract()`.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>fract(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
Ratio::new_raw(<span class="self">self</span>.numer.clone() % <span class="self">self</span>.denom.clone(), <span class="self">self</span>.denom.clone())
}
<span class="doccomment">/// Raises the `Ratio` to the power of an exponent.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>pow(<span class="kw-2">&</span><span class="self">self</span>, expon: i32) -> Ratio<T>
<span class="kw">where
for</span><<span class="lifetime">'a</span>> <span class="kw-2">&</span><span class="lifetime">'a </span>T: Pow<u32, Output = T>,
{
Pow::pow(<span class="self">self</span>, expon)
}
}
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">impl </span>Ratio<BigInt> {
<span class="doccomment">/// Converts a float into a rational number.
</span><span class="kw">pub fn </span>from_float<T: FloatCore>(f: T) -> <span class="prelude-ty">Option</span><BigRational> {
<span class="kw">if </span>!f.is_finite() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw">let </span>(mantissa, exponent, sign) = f.integer_decode();
<span class="kw">let </span>bigint_sign = <span class="kw">if </span>sign == <span class="number">1 </span>{ Sign::Plus } <span class="kw">else </span>{ Sign::Minus };
<span class="kw">if </span>exponent < <span class="number">0 </span>{
<span class="kw">let </span>one: BigInt = One::one();
<span class="kw">let </span>denom: BigInt = one << ((-exponent) <span class="kw">as </span>usize);
<span class="kw">let </span>numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
<span class="prelude-val">Some</span>(Ratio::new(BigInt::from_biguint(bigint_sign, numer), denom))
} <span class="kw">else </span>{
<span class="kw">let </span><span class="kw-2">mut </span>numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap();
numer <<= exponent <span class="kw">as </span>usize;
<span class="prelude-val">Some</span>(Ratio::from_integer(BigInt::from_biguint(
bigint_sign,
numer,
)))
}
}
}
<span class="kw">impl</span><T: Clone + Integer> Default <span class="kw">for </span>Ratio<T> {
<span class="doccomment">/// Returns zero
</span><span class="kw">fn </span>default() -> <span class="self">Self </span>{
Ratio::zero()
}
}
<span class="comment">// From integer
</span><span class="kw">impl</span><T> From<T> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">fn </span>from(x: T) -> Ratio<T> {
Ratio::from_integer(x)
}
}
<span class="comment">// From pair (through the `new` constructor)
</span><span class="kw">impl</span><T> From<(T, T)> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">fn </span>from(pair: (T, T)) -> Ratio<T> {
Ratio::new(pair.<span class="number">0</span>, pair.<span class="number">1</span>)
}
}
<span class="comment">// Comparisons
// Mathematically, comparing a/b and c/d is the same as comparing a*d and b*c, but it's very easy
// for those multiplications to overflow fixed-size integers, so we need to take care.
</span><span class="kw">impl</span><T: Clone + Integer> Ord <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>cmp(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> cmp::Ordering {
<span class="comment">// With equal denominators, the numerators can be directly compared
</span><span class="kw">if </span><span class="self">self</span>.denom == other.denom {
<span class="kw">let </span>ord = <span class="self">self</span>.numer.cmp(<span class="kw-2">&</span>other.numer);
<span class="kw">return if </span><span class="self">self</span>.denom < T::zero() {
ord.reverse()
} <span class="kw">else </span>{
ord
};
}
<span class="comment">// With equal numerators, the denominators can be inversely compared
</span><span class="kw">if </span><span class="self">self</span>.numer == other.numer {
<span class="kw">if </span><span class="self">self</span>.numer.is_zero() {
<span class="kw">return </span>cmp::Ordering::Equal;
}
<span class="kw">let </span>ord = <span class="self">self</span>.denom.cmp(<span class="kw-2">&</span>other.denom);
<span class="kw">return if </span><span class="self">self</span>.numer < T::zero() {
ord
} <span class="kw">else </span>{
ord.reverse()
};
}
<span class="comment">// Unfortunately, we don't have CheckedMul to try. That could sometimes avoid all the
// division below, or even always avoid it for BigInt and BigUint.
// FIXME- future breaking change to add Checked* to Integer?
// Compare as floored integers and remainders
</span><span class="kw">let </span>(self_int, self_rem) = <span class="self">self</span>.numer.div_mod_floor(<span class="kw-2">&</span><span class="self">self</span>.denom);
<span class="kw">let </span>(other_int, other_rem) = other.numer.div_mod_floor(<span class="kw-2">&</span>other.denom);
<span class="kw">match </span>self_int.cmp(<span class="kw-2">&</span>other_int) {
cmp::Ordering::Greater => cmp::Ordering::Greater,
cmp::Ordering::Less => cmp::Ordering::Less,
cmp::Ordering::Equal => {
<span class="kw">match </span>(self_rem.is_zero(), other_rem.is_zero()) {
(<span class="bool-val">true</span>, <span class="bool-val">true</span>) => cmp::Ordering::Equal,
(<span class="bool-val">true</span>, <span class="bool-val">false</span>) => cmp::Ordering::Less,
(<span class="bool-val">false</span>, <span class="bool-val">true</span>) => cmp::Ordering::Greater,
(<span class="bool-val">false</span>, <span class="bool-val">false</span>) => {
<span class="comment">// Compare the reciprocals of the remaining fractions in reverse
</span><span class="kw">let </span>self_recip = Ratio::new_raw(<span class="self">self</span>.denom.clone(), self_rem);
<span class="kw">let </span>other_recip = Ratio::new_raw(other.denom.clone(), other_rem);
self_recip.cmp(<span class="kw-2">&</span>other_recip).reverse()
}
}
}
}
}
}
<span class="kw">impl</span><T: Clone + Integer> PartialOrd <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>partial_cmp(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="prelude-ty">Option</span><cmp::Ordering> {
<span class="prelude-val">Some</span>(<span class="self">self</span>.cmp(other))
}
}
<span class="kw">impl</span><T: Clone + Integer> PartialEq <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="self">self</span>.cmp(other) == cmp::Ordering::Equal
}
}
<span class="kw">impl</span><T: Clone + Integer> Eq <span class="kw">for </span>Ratio<T> {}
<span class="comment">// NB: We can't just `#[derive(Hash)]`, because it needs to agree
// with `Eq` even for non-reduced ratios.
</span><span class="kw">impl</span><T: Clone + Integer + Hash> Hash <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>hash<H: Hasher>(<span class="kw-2">&</span><span class="self">self</span>, state: <span class="kw-2">&mut </span>H) {
recurse(<span class="kw-2">&</span><span class="self">self</span>.numer, <span class="kw-2">&</span><span class="self">self</span>.denom, state);
<span class="kw">fn </span>recurse<T: Integer + Hash, H: Hasher>(numer: <span class="kw-2">&</span>T, denom: <span class="kw-2">&</span>T, state: <span class="kw-2">&mut </span>H) {
<span class="kw">if </span>!denom.is_zero() {
<span class="kw">let </span>(int, rem) = numer.div_mod_floor(denom);
int.hash(state);
recurse(denom, <span class="kw-2">&</span>rem, state);
} <span class="kw">else </span>{
denom.hash(state);
}
}
}
}
<span class="kw">mod </span>iter_sum_product {
<span class="kw">use </span><span class="kw">crate</span>::Ratio;
<span class="kw">use </span>core::iter::{Product, Sum};
<span class="kw">use </span>num_integer::Integer;
<span class="kw">use </span>num_traits::{One, Zero};
<span class="kw">impl</span><T: Integer + Clone> Sum <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>sum<I>(iter: I) -> <span class="self">Self
</span><span class="kw">where
</span>I: Iterator<Item = Ratio<T>>,
{
iter.fold(<span class="self">Self</span>::zero(), |sum, num| sum + num)
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T: Integer + Clone> Sum<<span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>sum<I>(iter: I) -> <span class="self">Self
</span><span class="kw">where
</span>I: Iterator<Item = <span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>>,
{
iter.fold(<span class="self">Self</span>::zero(), |sum, num| sum + num)
}
}
<span class="kw">impl</span><T: Integer + Clone> Product <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>product<I>(iter: I) -> <span class="self">Self
</span><span class="kw">where
</span>I: Iterator<Item = Ratio<T>>,
{
iter.fold(<span class="self">Self</span>::one(), |prod, num| prod * num)
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T: Integer + Clone> Product<<span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>product<I>(iter: I) -> <span class="self">Self
</span><span class="kw">where
</span>I: Iterator<Item = <span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>>,
{
iter.fold(<span class="self">Self</span>::one(), |prod, num| prod * num)
}
}
}
<span class="kw">mod </span>opassign {
<span class="kw">use </span>core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
<span class="kw">use </span><span class="kw">crate</span>::Ratio;
<span class="kw">use </span>num_integer::Integer;
<span class="kw">use </span>num_traits::NumAssign;
<span class="kw">impl</span><T: Clone + Integer + NumAssign> AddAssign <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: Ratio<T>) {
<span class="kw">if </span><span class="self">self</span>.denom == other.denom {
<span class="self">self</span>.numer += other.numer
} <span class="kw">else </span>{
<span class="kw">let </span>lcm = <span class="self">self</span>.denom.lcm(<span class="kw-2">&</span>other.denom);
<span class="kw">let </span>lhs_numer = <span class="self">self</span>.numer.clone() * (lcm.clone() / <span class="self">self</span>.denom.clone());
<span class="kw">let </span>rhs_numer = other.numer * (lcm.clone() / other.denom);
<span class="self">self</span>.numer = lhs_numer + rhs_numer;
<span class="self">self</span>.denom = lcm;
}
<span class="self">self</span>.reduce();
}
}
<span class="comment">// (a/b) / (c/d) = (a/gcd_ac)*(d/gcd_bd) / ((c/gcd_ac)*(b/gcd_bd))
</span><span class="kw">impl</span><T: Clone + Integer + NumAssign> DivAssign <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>div_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: Ratio<T>) {
<span class="kw">let </span>gcd_ac = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>other.numer);
<span class="kw">let </span>gcd_bd = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>other.denom);
<span class="self">self</span>.numer /= gcd_ac.clone();
<span class="self">self</span>.numer <span class="kw-2">*</span>= other.denom / gcd_bd.clone();
<span class="self">self</span>.denom /= gcd_bd;
<span class="self">self</span>.denom <span class="kw-2">*</span>= other.numer / gcd_ac;
<span class="self">self</span>.reduce(); <span class="comment">// TODO: remove this line. see #8.
</span>}
}
<span class="comment">// a/b * c/d = (a/gcd_ad)*(c/gcd_bc) / ((d/gcd_ad)*(b/gcd_bc))
</span><span class="kw">impl</span><T: Clone + Integer + NumAssign> MulAssign <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>mul_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: Ratio<T>) {
<span class="kw">let </span>gcd_ad = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>other.denom);
<span class="kw">let </span>gcd_bc = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>other.numer);
<span class="self">self</span>.numer /= gcd_ad.clone();
<span class="self">self</span>.numer <span class="kw-2">*</span>= other.numer / gcd_bc.clone();
<span class="self">self</span>.denom /= gcd_bc;
<span class="self">self</span>.denom <span class="kw-2">*</span>= other.denom / gcd_ad;
<span class="self">self</span>.reduce(); <span class="comment">// TODO: remove this line. see #8.
</span>}
}
<span class="kw">impl</span><T: Clone + Integer + NumAssign> RemAssign <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>rem_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: Ratio<T>) {
<span class="kw">if </span><span class="self">self</span>.denom == other.denom {
<span class="self">self</span>.numer %= other.numer
} <span class="kw">else </span>{
<span class="kw">let </span>lcm = <span class="self">self</span>.denom.lcm(<span class="kw-2">&</span>other.denom);
<span class="kw">let </span>lhs_numer = <span class="self">self</span>.numer.clone() * (lcm.clone() / <span class="self">self</span>.denom.clone());
<span class="kw">let </span>rhs_numer = other.numer * (lcm.clone() / other.denom);
<span class="self">self</span>.numer = lhs_numer % rhs_numer;
<span class="self">self</span>.denom = lcm;
}
<span class="self">self</span>.reduce();
}
}
<span class="kw">impl</span><T: Clone + Integer + NumAssign> SubAssign <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>sub_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: Ratio<T>) {
<span class="kw">if </span><span class="self">self</span>.denom == other.denom {
<span class="self">self</span>.numer -= other.numer
} <span class="kw">else </span>{
<span class="kw">let </span>lcm = <span class="self">self</span>.denom.lcm(<span class="kw-2">&</span>other.denom);
<span class="kw">let </span>lhs_numer = <span class="self">self</span>.numer.clone() * (lcm.clone() / <span class="self">self</span>.denom.clone());
<span class="kw">let </span>rhs_numer = other.numer * (lcm.clone() / other.denom);
<span class="self">self</span>.numer = lhs_numer - rhs_numer;
<span class="self">self</span>.denom = lcm;
}
<span class="self">self</span>.reduce();
}
}
<span class="comment">// a/b + c/1 = (a*1 + b*c) / (b*1) = (a + b*c) / b
</span><span class="kw">impl</span><T: Clone + Integer + NumAssign> AddAssign<T> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>add_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) {
<span class="self">self</span>.numer += <span class="self">self</span>.denom.clone() * other;
<span class="self">self</span>.reduce();
}
}
<span class="kw">impl</span><T: Clone + Integer + NumAssign> DivAssign<T> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>div_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) {
<span class="kw">let </span>gcd = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>other);
<span class="self">self</span>.numer /= gcd.clone();
<span class="self">self</span>.denom <span class="kw-2">*</span>= other / gcd;
<span class="self">self</span>.reduce(); <span class="comment">// TODO: remove this line. see #8.
</span>}
}
<span class="kw">impl</span><T: Clone + Integer + NumAssign> MulAssign<T> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>mul_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) {
<span class="kw">let </span>gcd = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>other);
<span class="self">self</span>.denom /= gcd.clone();
<span class="self">self</span>.numer <span class="kw-2">*</span>= other / gcd;
<span class="self">self</span>.reduce(); <span class="comment">// TODO: remove this line. see #8.
</span>}
}
<span class="comment">// a/b % c/1 = (a*1 % b*c) / (b*1) = (a % b*c) / b
</span><span class="kw">impl</span><T: Clone + Integer + NumAssign> RemAssign<T> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>rem_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) {
<span class="self">self</span>.numer %= <span class="self">self</span>.denom.clone() * other;
<span class="self">self</span>.reduce();
}
}
<span class="comment">// a/b - c/1 = (a*1 - b*c) / (b*1) = (a - b*c) / b
</span><span class="kw">impl</span><T: Clone + Integer + NumAssign> SubAssign<T> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>sub_assign(<span class="kw-2">&mut </span><span class="self">self</span>, other: T) {
<span class="self">self</span>.numer -= <span class="self">self</span>.denom.clone() * other;
<span class="self">self</span>.reduce();
}
}
<span class="macro">macro_rules! </span>forward_op_assign {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Integer + NumAssign> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>> <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span>Ratio<T>) {
<span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone())
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T: Clone + Integer + NumAssign> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>T> <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="kw-2">&mut </span><span class="self">self</span>, other: <span class="kw-2">&</span>T) {
<span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone())
}
}
};
}
<span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>AddAssign, add_assign);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>DivAssign, div_assign);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>MulAssign, mul_assign);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>RemAssign, rem_assign);
<span class="macro">forward_op_assign!</span>(<span class="kw">impl </span>SubAssign, sub_assign);
}
<span class="macro">macro_rules! </span>forward_ref_ref_binop {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>, T: Clone + Integer> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'b </span>Ratio<T>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T> {
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span><span class="lifetime">'b </span>Ratio<T>) -> Ratio<T> {
<span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other.clone())
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>, T: Clone + Integer> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'b </span>T> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T> {
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span><span class="lifetime">'b </span>T) -> Ratio<T> {
<span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other.clone())
}
}
};
}
<span class="macro">macro_rules! </span>forward_ref_val_binop {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="kw">impl</span><<span class="lifetime">'a</span>, T> <span class="macro-nonterminal">$imp</span><Ratio<T>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: Ratio<T>) -> Ratio<T> {
<span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other)
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T> <span class="macro-nonterminal">$imp</span><T> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: T) -> Ratio<T> {
<span class="self">self</span>.clone().<span class="macro-nonterminal">$method</span>(other)
}
}
};
}
<span class="macro">macro_rules! </span>forward_val_ref_binop {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="kw">impl</span><<span class="lifetime">'a</span>, T> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>Ratio<T>) -> Ratio<T> {
<span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone())
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T> <span class="macro-nonterminal">$imp</span><<span class="kw-2">&</span><span class="lifetime">'a </span>T> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, other: <span class="kw-2">&</span>T) -> Ratio<T> {
<span class="self">self</span>.<span class="macro-nonterminal">$method</span>(other.clone())
}
}
};
}
<span class="macro">macro_rules! </span>forward_all_binop {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="macro">forward_ref_ref_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>);
<span class="macro">forward_ref_val_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>);
<span class="macro">forward_val_ref_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>);
};
}
<span class="comment">// Arithmetic
</span><span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Mul, mul);
<span class="comment">// a/b * c/d = (a/gcd_ad)*(c/gcd_bc) / ((d/gcd_ad)*(b/gcd_bc))
</span><span class="kw">impl</span><T> Mul<Ratio<T>> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>mul(<span class="self">self</span>, rhs: Ratio<T>) -> Ratio<T> {
<span class="kw">let </span>gcd_ad = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>rhs.denom);
<span class="kw">let </span>gcd_bc = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>rhs.numer);
Ratio::new(
<span class="self">self</span>.numer / gcd_ad.clone() * (rhs.numer / gcd_bc.clone()),
<span class="self">self</span>.denom / gcd_bc * (rhs.denom / gcd_ad),
)
}
}
<span class="comment">// a/b * c/1 = (a*c) / (b*1) = (a*c) / b
</span><span class="kw">impl</span><T> Mul<T> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>mul(<span class="self">self</span>, rhs: T) -> Ratio<T> {
<span class="kw">let </span>gcd = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>rhs);
Ratio::new(<span class="self">self</span>.numer * (rhs / gcd.clone()), <span class="self">self</span>.denom / gcd)
}
}
<span class="macro">forward_all_binop!</span>(<span class="kw">impl </span>Div, div);
<span class="comment">// (a/b) / (c/d) = (a/gcd_ac)*(d/gcd_bd) / ((c/gcd_ac)*(b/gcd_bd))
</span><span class="kw">impl</span><T> Div<Ratio<T>> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, rhs: Ratio<T>) -> Ratio<T> {
<span class="kw">let </span>gcd_ac = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>rhs.numer);
<span class="kw">let </span>gcd_bd = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>rhs.denom);
Ratio::new(
<span class="self">self</span>.numer / gcd_ac.clone() * (rhs.denom / gcd_bd.clone()),
<span class="self">self</span>.denom / gcd_bd * (rhs.numer / gcd_ac),
)
}
}
<span class="comment">// (a/b) / (c/1) = (a*1) / (b*c) = a / (b*c)
</span><span class="kw">impl</span><T> Div<T> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>div(<span class="self">self</span>, rhs: T) -> Ratio<T> {
<span class="kw">let </span>gcd = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>rhs);
Ratio::new(<span class="self">self</span>.numer / gcd.clone(), <span class="self">self</span>.denom * (rhs / gcd))
}
}
<span class="macro">macro_rules! </span>arith_impl {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="macro">forward_all_binop!</span>(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>, <span class="macro-nonterminal">$method</span>);
<span class="comment">// Abstracts a/b `op` c/d = (a*lcm/b `op` c*lcm/d)/lcm where lcm = lcm(b,d)
</span><span class="kw">impl</span><T: Clone + Integer> <span class="macro-nonterminal">$imp</span><Ratio<T>> <span class="kw">for </span>Ratio<T> {
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, rhs: Ratio<T>) -> Ratio<T> {
<span class="kw">if </span><span class="self">self</span>.denom == rhs.denom {
<span class="kw">return </span>Ratio::new(<span class="self">self</span>.numer.<span class="macro-nonterminal">$method</span>(rhs.numer), rhs.denom);
}
<span class="kw">let </span>lcm = <span class="self">self</span>.denom.lcm(<span class="kw-2">&</span>rhs.denom);
<span class="kw">let </span>lhs_numer = <span class="self">self</span>.numer * (lcm.clone() / <span class="self">self</span>.denom);
<span class="kw">let </span>rhs_numer = rhs.numer * (lcm.clone() / rhs.denom);
Ratio::new(lhs_numer.<span class="macro-nonterminal">$method</span>(rhs_numer), lcm)
}
}
<span class="comment">// Abstracts the a/b `op` c/1 = (a*1 `op` b*c) / (b*1) = (a `op` b*c) / b pattern
</span><span class="kw">impl</span><T: Clone + Integer> <span class="macro-nonterminal">$imp</span><T> <span class="kw">for </span>Ratio<T> {
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="self">self</span>, rhs: T) -> Ratio<T> {
Ratio::new(<span class="self">self</span>.numer.<span class="macro-nonterminal">$method</span>(<span class="self">self</span>.denom.clone() * rhs), <span class="self">self</span>.denom)
}
}
};
}
<span class="macro">arith_impl!</span>(<span class="kw">impl </span>Add, add);
<span class="macro">arith_impl!</span>(<span class="kw">impl </span>Sub, sub);
<span class="macro">arith_impl!</span>(<span class="kw">impl </span>Rem, rem);
<span class="comment">// a/b * c/d = (a*c)/(b*d)
</span><span class="kw">impl</span><T> CheckedMul <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer + CheckedMul,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>checked_mul(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Ratio<T>) -> <span class="prelude-ty">Option</span><Ratio<T>> {
<span class="kw">let </span>gcd_ad = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>rhs.denom);
<span class="kw">let </span>gcd_bc = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>rhs.numer);
<span class="prelude-val">Some</span>(Ratio::new(
(<span class="self">self</span>.numer.clone() / gcd_ad.clone())
.checked_mul(<span class="kw-2">&</span>(rhs.numer.clone() / gcd_bc.clone()))<span class="question-mark">?</span>,
(<span class="self">self</span>.denom.clone() / gcd_bc).checked_mul(<span class="kw-2">&</span>(rhs.denom.clone() / gcd_ad))<span class="question-mark">?</span>,
))
}
}
<span class="comment">// (a/b) / (c/d) = (a*d)/(b*c)
</span><span class="kw">impl</span><T> CheckedDiv <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer + CheckedMul,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>checked_div(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Ratio<T>) -> <span class="prelude-ty">Option</span><Ratio<T>> {
<span class="kw">if </span>rhs.is_zero() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw">let </span>(numer, denom) = <span class="kw">if </span><span class="self">self</span>.denom == rhs.denom {
(<span class="self">self</span>.numer.clone(), rhs.numer.clone())
} <span class="kw">else if </span><span class="self">self</span>.numer == rhs.numer {
(rhs.denom.clone(), <span class="self">self</span>.denom.clone())
} <span class="kw">else </span>{
<span class="kw">let </span>gcd_ac = <span class="self">self</span>.numer.gcd(<span class="kw-2">&</span>rhs.numer);
<span class="kw">let </span>gcd_bd = <span class="self">self</span>.denom.gcd(<span class="kw-2">&</span>rhs.denom);
(
(<span class="self">self</span>.numer.clone() / gcd_ac.clone())
.checked_mul(<span class="kw-2">&</span>(rhs.denom.clone() / gcd_bd.clone()))<span class="question-mark">?</span>,
(<span class="self">self</span>.denom.clone() / gcd_bd).checked_mul(<span class="kw-2">&</span>(rhs.numer.clone() / gcd_ac))<span class="question-mark">?</span>,
)
};
<span class="comment">// Manual `reduce()`, avoiding sharp edges
</span><span class="kw">if </span>denom.is_zero() {
<span class="prelude-val">None
</span>} <span class="kw">else if </span>numer.is_zero() {
<span class="prelude-val">Some</span>(<span class="self">Self</span>::zero())
} <span class="kw">else if </span>numer == denom {
<span class="prelude-val">Some</span>(<span class="self">Self</span>::one())
} <span class="kw">else </span>{
<span class="kw">let </span>g = numer.gcd(<span class="kw-2">&</span>denom);
<span class="kw">let </span>numer = numer / g.clone();
<span class="kw">let </span>denom = denom / g;
<span class="kw">let </span>raw = <span class="kw">if </span>denom < T::zero() {
<span class="comment">// We need to keep denom positive, but 2's-complement MIN may
// overflow negation -- instead we can check multiplying -1.
</span><span class="kw">let </span>n1 = T::zero() - T::one();
Ratio::new_raw(numer.checked_mul(<span class="kw-2">&</span>n1)<span class="question-mark">?</span>, denom.checked_mul(<span class="kw-2">&</span>n1)<span class="question-mark">?</span>)
} <span class="kw">else </span>{
Ratio::new_raw(numer, denom)
};
<span class="prelude-val">Some</span>(raw)
}
}
}
<span class="comment">// As arith_impl! but for Checked{Add,Sub} traits
</span><span class="macro">macro_rules! </span>checked_arith_impl {
(<span class="kw">impl </span><span class="macro-nonterminal">$imp</span>:ident, <span class="macro-nonterminal">$method</span>:ident) => {
<span class="kw">impl</span><T: Clone + Integer + CheckedMul + <span class="macro-nonterminal">$imp</span>> <span class="macro-nonterminal">$imp </span><span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span><span class="macro-nonterminal">$method</span>(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Ratio<T>) -> <span class="prelude-ty">Option</span><Ratio<T>> {
<span class="kw">let </span>gcd = <span class="self">self</span>.denom.clone().gcd(<span class="kw-2">&</span>rhs.denom);
<span class="kw">let </span>lcm = (<span class="self">self</span>.denom.clone() / gcd.clone()).checked_mul(<span class="kw-2">&</span>rhs.denom)<span class="question-mark">?</span>;
<span class="kw">let </span>lhs_numer = (lcm.clone() / <span class="self">self</span>.denom.clone()).checked_mul(<span class="kw-2">&</span><span class="self">self</span>.numer)<span class="question-mark">?</span>;
<span class="kw">let </span>rhs_numer = (lcm.clone() / rhs.denom.clone()).checked_mul(<span class="kw-2">&</span>rhs.numer)<span class="question-mark">?</span>;
<span class="prelude-val">Some</span>(Ratio::new(lhs_numer.<span class="macro-nonterminal">$method</span>(<span class="kw-2">&</span>rhs_numer)<span class="question-mark">?</span>, lcm))
}
}
};
}
<span class="comment">// a/b + c/d = (lcm/b*a + lcm/d*c)/lcm, where lcm = lcm(b,d)
</span><span class="macro">checked_arith_impl!</span>(<span class="kw">impl </span>CheckedAdd, checked_add);
<span class="comment">// a/b - c/d = (lcm/b*a - lcm/d*c)/lcm, where lcm = lcm(b,d)
</span><span class="macro">checked_arith_impl!</span>(<span class="kw">impl </span>CheckedSub, checked_sub);
<span class="kw">impl</span><T> Neg <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer + Neg<Output = T>,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>neg(<span class="self">self</span>) -> Ratio<T> {
Ratio::new_raw(-<span class="self">self</span>.numer, <span class="self">self</span>.denom)
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T> Neg <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer + Neg<Output = T>,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>neg(<span class="self">self</span>) -> Ratio<T> {
-<span class="self">self</span>.clone()
}
}
<span class="kw">impl</span><T> Inv <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>inv(<span class="self">self</span>) -> Ratio<T> {
<span class="self">self</span>.recip()
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, T> Inv <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span>Ratio<T>
<span class="kw">where
</span>T: Clone + Integer,
{
<span class="kw">type </span>Output = Ratio<T>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>inv(<span class="self">self</span>) -> Ratio<T> {
<span class="self">self</span>.recip()
}
}
<span class="comment">// Constants
</span><span class="kw">impl</span><T: Clone + Integer> Zero <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>zero() -> Ratio<T> {
Ratio::new_raw(Zero::zero(), One::one())
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>is_zero(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="self">self</span>.numer.is_zero()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>set_zero(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="self">self</span>.numer.set_zero();
<span class="self">self</span>.denom.set_one();
}
}
<span class="kw">impl</span><T: Clone + Integer> One <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>one() -> Ratio<T> {
Ratio::new_raw(One::one(), One::one())
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>is_one(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="self">self</span>.numer == <span class="self">self</span>.denom
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>set_one(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="self">self</span>.numer.set_one();
<span class="self">self</span>.denom.set_one();
}
}
<span class="kw">impl</span><T: Clone + Integer> Num <span class="kw">for </span>Ratio<T> {
<span class="kw">type </span>FromStrRadixErr = ParseRatioError;
<span class="doccomment">/// Parses `numer/denom` where the numbers are in base `radix`.
</span><span class="kw">fn </span>from_str_radix(s: <span class="kw-2">&</span>str, radix: u32) -> <span class="prelude-ty">Result</span><Ratio<T>, ParseRatioError> {
<span class="kw">if </span>s.splitn(<span class="number">2</span>, <span class="string">'/'</span>).count() == <span class="number">2 </span>{
<span class="kw">let </span><span class="kw-2">mut </span>parts = s.splitn(<span class="number">2</span>, <span class="string">'/'</span>).map(|ss| {
T::from_str_radix(ss, radix).map_err(|<span class="kw">_</span>| ParseRatioError {
kind: RatioErrorKind::ParseError,
})
});
<span class="kw">let </span>numer: T = parts.next().unwrap()<span class="question-mark">?</span>;
<span class="kw">let </span>denom: T = parts.next().unwrap()<span class="question-mark">?</span>;
<span class="kw">if </span>denom.is_zero() {
<span class="prelude-val">Err</span>(ParseRatioError {
kind: RatioErrorKind::ZeroDenominator,
})
} <span class="kw">else </span>{
<span class="prelude-val">Ok</span>(Ratio::new(numer, denom))
}
} <span class="kw">else </span>{
<span class="prelude-val">Err</span>(ParseRatioError {
kind: RatioErrorKind::ParseError,
})
}
}
}
<span class="kw">impl</span><T: Clone + Integer + Signed> Signed <span class="kw">for </span>Ratio<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>abs(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="kw">if </span><span class="self">self</span>.is_negative() {
-<span class="self">self</span>.clone()
} <span class="kw">else </span>{
<span class="self">self</span>.clone()
}
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>abs_sub(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>Ratio<T>) -> Ratio<T> {
<span class="kw">if </span><span class="kw-2">*</span><span class="self">self </span><= <span class="kw-2">*</span>other {
Zero::zero()
} <span class="kw">else </span>{
<span class="self">self </span>- other
}
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>signum(<span class="kw-2">&</span><span class="self">self</span>) -> Ratio<T> {
<span class="kw">if </span><span class="self">self</span>.is_positive() {
<span class="self">Self</span>::one()
} <span class="kw">else if </span><span class="self">self</span>.is_zero() {
<span class="self">Self</span>::zero()
} <span class="kw">else </span>{
-<span class="self">Self</span>::one()
}
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>is_positive(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
(<span class="self">self</span>.numer.is_positive() && <span class="self">self</span>.denom.is_positive())
|| (<span class="self">self</span>.numer.is_negative() && <span class="self">self</span>.denom.is_negative())
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>is_negative(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
(<span class="self">self</span>.numer.is_negative() && <span class="self">self</span>.denom.is_positive())
|| (<span class="self">self</span>.numer.is_positive() && <span class="self">self</span>.denom.is_negative())
}
}
<span class="comment">// String conversions
</span><span class="macro">macro_rules! </span>impl_formatting {
(<span class="macro-nonterminal">$fmt_trait</span>:ident, <span class="macro-nonterminal">$prefix</span>:expr, <span class="macro-nonterminal">$fmt_str</span>:expr, <span class="macro-nonterminal">$fmt_alt</span>:expr) => {
<span class="kw">impl</span><T: <span class="macro-nonterminal">$fmt_trait </span>+ Clone + Integer> <span class="macro-nonterminal">$fmt_trait </span><span class="kw">for </span>Ratio<T> {
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
<span class="kw">let </span>pre_pad = <span class="kw">if </span><span class="self">self</span>.denom.is_one() {
<span class="macro">format!</span>(<span class="macro-nonterminal">$fmt_str</span>, <span class="self">self</span>.numer)
} <span class="kw">else </span>{
<span class="kw">if </span>f.alternate() {
<span class="macro">format!</span>(<span class="macro">concat!</span>(<span class="macro-nonterminal">$fmt_str</span>, <span class="string">"/"</span>, <span class="macro-nonterminal">$fmt_alt</span>), <span class="self">self</span>.numer, <span class="self">self</span>.denom)
} <span class="kw">else </span>{
<span class="macro">format!</span>(<span class="macro">concat!</span>(<span class="macro-nonterminal">$fmt_str</span>, <span class="string">"/"</span>, <span class="macro-nonterminal">$fmt_str</span>), <span class="self">self</span>.numer, <span class="self">self</span>.denom)
}
};
<span class="comment">// TODO: replace with strip_prefix, when stabalized
</span><span class="kw">let </span>(pre_pad, non_negative) = {
<span class="kw">if </span>pre_pad.starts_with(<span class="string">"-"</span>) {
(<span class="kw-2">&</span>pre_pad[<span class="number">1</span>..], <span class="bool-val">false</span>)
} <span class="kw">else </span>{
(<span class="kw-2">&</span>pre_pad[..], <span class="bool-val">true</span>)
}
};
f.pad_integral(non_negative, <span class="macro-nonterminal">$prefix</span>, pre_pad)
}
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span><span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
<span class="kw">let </span>plus = <span class="kw">if </span>f.sign_plus() && <span class="self">self</span>.numer >= T::zero() {
<span class="string">"+"
</span>} <span class="kw">else </span>{
<span class="string">""
</span>};
<span class="kw">if </span><span class="self">self</span>.denom.is_one() {
<span class="kw">if </span>f.alternate() {
<span class="macro">write!</span>(f, <span class="macro">concat!</span>(<span class="string">"{}"</span>, <span class="macro-nonterminal">$fmt_alt</span>), plus, <span class="self">self</span>.numer)
} <span class="kw">else </span>{
<span class="macro">write!</span>(f, <span class="macro">concat!</span>(<span class="string">"{}"</span>, <span class="macro-nonterminal">$fmt_str</span>), plus, <span class="self">self</span>.numer)
}
} <span class="kw">else </span>{
<span class="kw">if </span>f.alternate() {
<span class="macro">write!</span>(
f,
<span class="macro">concat!</span>(<span class="string">"{}"</span>, <span class="macro-nonterminal">$fmt_alt</span>, <span class="string">"/"</span>, <span class="macro-nonterminal">$fmt_alt</span>),
plus, <span class="self">self</span>.numer, <span class="self">self</span>.denom
)
} <span class="kw">else </span>{
<span class="macro">write!</span>(
f,
<span class="macro">concat!</span>(<span class="string">"{}"</span>, <span class="macro-nonterminal">$fmt_str</span>, <span class="string">"/"</span>, <span class="macro-nonterminal">$fmt_str</span>),
plus, <span class="self">self</span>.numer, <span class="self">self</span>.denom
)
}
}
}
}
};
}
<span class="macro">impl_formatting!</span>(Display, <span class="string">""</span>, <span class="string">"{}"</span>, <span class="string">"{:#}"</span>);
<span class="macro">impl_formatting!</span>(Octal, <span class="string">"0o"</span>, <span class="string">"{:o}"</span>, <span class="string">"{:#o}"</span>);
<span class="macro">impl_formatting!</span>(Binary, <span class="string">"0b"</span>, <span class="string">"{:b}"</span>, <span class="string">"{:#b}"</span>);
<span class="macro">impl_formatting!</span>(LowerHex, <span class="string">"0x"</span>, <span class="string">"{:x}"</span>, <span class="string">"{:#x}"</span>);
<span class="macro">impl_formatting!</span>(UpperHex, <span class="string">"0x"</span>, <span class="string">"{:X}"</span>, <span class="string">"{:#X}"</span>);
<span class="macro">impl_formatting!</span>(LowerExp, <span class="string">""</span>, <span class="string">"{:e}"</span>, <span class="string">"{:#e}"</span>);
<span class="macro">impl_formatting!</span>(UpperExp, <span class="string">""</span>, <span class="string">"{:E}"</span>, <span class="string">"{:#E}"</span>);
<span class="kw">impl</span><T: FromStr + Clone + Integer> FromStr <span class="kw">for </span>Ratio<T> {
<span class="kw">type </span><span class="prelude-val">Err </span>= ParseRatioError;
<span class="doccomment">/// Parses `numer/denom` or just `numer`.
</span><span class="kw">fn </span>from_str(s: <span class="kw-2">&</span>str) -> <span class="prelude-ty">Result</span><Ratio<T>, ParseRatioError> {
<span class="kw">let </span><span class="kw-2">mut </span>split = s.splitn(<span class="number">2</span>, <span class="string">'/'</span>);
<span class="kw">let </span>n = split.next().ok_or(ParseRatioError {
kind: RatioErrorKind::ParseError,
})<span class="question-mark">?</span>;
<span class="kw">let </span>num = FromStr::from_str(n).map_err(|<span class="kw">_</span>| ParseRatioError {
kind: RatioErrorKind::ParseError,
})<span class="question-mark">?</span>;
<span class="kw">let </span>d = split.next().unwrap_or(<span class="string">"1"</span>);
<span class="kw">let </span>den = FromStr::from_str(d).map_err(|<span class="kw">_</span>| ParseRatioError {
kind: RatioErrorKind::ParseError,
})<span class="question-mark">?</span>;
<span class="kw">if </span>Zero::is_zero(<span class="kw-2">&</span>den) {
<span class="prelude-val">Err</span>(ParseRatioError {
kind: RatioErrorKind::ZeroDenominator,
})
} <span class="kw">else </span>{
<span class="prelude-val">Ok</span>(Ratio::new(num, den))
}
}
}
<span class="kw">impl</span><T> Into<(T, T)> <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>into(<span class="self">self</span>) -> (T, T) {
(<span class="self">self</span>.numer, <span class="self">self</span>.denom)
}
}
<span class="attr">#[cfg(feature = <span class="string">"serde"</span>)]
</span><span class="kw">impl</span><T> serde::Serialize <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: serde::Serialize + Clone + Integer + PartialOrd,
{
<span class="kw">fn </span>serialize<S>(<span class="kw-2">&</span><span class="self">self</span>, serializer: S) -> <span class="prelude-ty">Result</span><S::Ok, S::Error>
<span class="kw">where
</span>S: serde::Serializer,
{
(<span class="self">self</span>.numer(), <span class="self">self</span>.denom()).serialize(serializer)
}
}
<span class="attr">#[cfg(feature = <span class="string">"serde"</span>)]
</span><span class="kw">impl</span><<span class="lifetime">'de</span>, T> serde::Deserialize<<span class="lifetime">'de</span>> <span class="kw">for </span>Ratio<T>
<span class="kw">where
</span>T: serde::Deserialize<<span class="lifetime">'de</span>> + Clone + Integer + PartialOrd,
{
<span class="kw">fn </span>deserialize<D>(deserializer: D) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, D::Error>
<span class="kw">where
</span>D: serde::Deserializer<<span class="lifetime">'de</span>>,
{
<span class="kw">use </span>serde::de::Error;
<span class="kw">use </span>serde::de::Unexpected;
<span class="kw">let </span>(numer, denom): (T, T) = serde::Deserialize::deserialize(deserializer)<span class="question-mark">?</span>;
<span class="kw">if </span>denom.is_zero() {
<span class="prelude-val">Err</span>(Error::invalid_value(
Unexpected::Signed(<span class="number">0</span>),
<span class="kw-2">&</span><span class="string">"a ratio with non-zero denominator"</span>,
))
} <span class="kw">else </span>{
<span class="prelude-val">Ok</span>(Ratio::new_raw(numer, denom))
}
}
}
<span class="comment">// FIXME: Bubble up specific errors
</span><span class="attr">#[derive(Copy, Clone, Debug, PartialEq)]
</span><span class="kw">pub struct </span>ParseRatioError {
kind: RatioErrorKind,
}
<span class="attr">#[derive(Copy, Clone, Debug, PartialEq)]
</span><span class="kw">enum </span>RatioErrorKind {
ParseError,
ZeroDenominator,
}
<span class="kw">impl </span>fmt::Display <span class="kw">for </span>ParseRatioError {
<span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result {
<span class="self">self</span>.kind.description().fmt(f)
}
}
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">impl </span>Error <span class="kw">for </span>ParseRatioError {
<span class="attr">#[allow(deprecated)]
</span><span class="kw">fn </span>description(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>str {
<span class="self">self</span>.kind.description()
}
}
<span class="kw">impl </span>RatioErrorKind {
<span class="kw">fn </span>description(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span><span class="lifetime">'static </span>str {
<span class="kw">match </span><span class="kw-2">*</span><span class="self">self </span>{
RatioErrorKind::ParseError => <span class="string">"failed to parse integer"</span>,
RatioErrorKind::ZeroDenominator => <span class="string">"zero value denominator"</span>,
}
}
}
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">impl </span>FromPrimitive <span class="kw">for </span>Ratio<BigInt> {
<span class="kw">fn </span>from_i64(n: i64) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="prelude-val">Some</span>(Ratio::from_integer(n.into()))
}
<span class="kw">fn </span>from_i128(n: i128) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="prelude-val">Some</span>(Ratio::from_integer(n.into()))
}
<span class="kw">fn </span>from_u64(n: u64) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="prelude-val">Some</span>(Ratio::from_integer(n.into()))
}
<span class="kw">fn </span>from_u128(n: u128) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="prelude-val">Some</span>(Ratio::from_integer(n.into()))
}
<span class="kw">fn </span>from_f32(n: f32) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
Ratio::from_float(n)
}
<span class="kw">fn </span>from_f64(n: f64) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
Ratio::from_float(n)
}
}
<span class="macro">macro_rules! </span>from_primitive_integer {
(<span class="macro-nonterminal">$typ</span>:ty, <span class="macro-nonterminal">$approx</span>:ident) => {
<span class="kw">impl </span>FromPrimitive <span class="kw">for </span>Ratio<<span class="macro-nonterminal">$typ</span>> {
<span class="kw">fn </span>from_i64(n: i64) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<<span class="macro-nonterminal">$typ </span><span class="kw">as </span>FromPrimitive>::from_i64(n).map(Ratio::from_integer)
}
<span class="kw">fn </span>from_i128(n: i128) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<<span class="macro-nonterminal">$typ </span><span class="kw">as </span>FromPrimitive>::from_i128(n).map(Ratio::from_integer)
}
<span class="kw">fn </span>from_u64(n: u64) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<<span class="macro-nonterminal">$typ </span><span class="kw">as </span>FromPrimitive>::from_u64(n).map(Ratio::from_integer)
}
<span class="kw">fn </span>from_u128(n: u128) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<<span class="macro-nonterminal">$typ </span><span class="kw">as </span>FromPrimitive>::from_u128(n).map(Ratio::from_integer)
}
<span class="kw">fn </span>from_f32(n: f32) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="macro-nonterminal">$approx</span>(n, <span class="number">10e-20</span>, <span class="number">30</span>)
}
<span class="kw">fn </span>from_f64(n: f64) -> <span class="prelude-ty">Option</span><<span class="self">Self</span>> {
<span class="macro-nonterminal">$approx</span>(n, <span class="number">10e-20</span>, <span class="number">30</span>)
}
}
};
}
<span class="macro">from_primitive_integer!</span>(i8, approximate_float);
<span class="macro">from_primitive_integer!</span>(i16, approximate_float);
<span class="macro">from_primitive_integer!</span>(i32, approximate_float);
<span class="macro">from_primitive_integer!</span>(i64, approximate_float);
<span class="macro">from_primitive_integer!</span>(i128, approximate_float);
<span class="macro">from_primitive_integer!</span>(isize, approximate_float);
<span class="macro">from_primitive_integer!</span>(u8, approximate_float_unsigned);
<span class="macro">from_primitive_integer!</span>(u16, approximate_float_unsigned);
<span class="macro">from_primitive_integer!</span>(u32, approximate_float_unsigned);
<span class="macro">from_primitive_integer!</span>(u64, approximate_float_unsigned);
<span class="macro">from_primitive_integer!</span>(u128, approximate_float_unsigned);
<span class="macro">from_primitive_integer!</span>(usize, approximate_float_unsigned);
<span class="kw">impl</span><T: Integer + Signed + Bounded + NumCast + Clone> Ratio<T> {
<span class="kw">pub fn </span>approximate_float<F: FloatCore + NumCast>(f: F) -> <span class="prelude-ty">Option</span><Ratio<T>> {
<span class="comment">// 1/10e-20 < 1/2**32 which seems like a good default, and 30 seems
// to work well. Might want to choose something based on the types in the future, e.g.
// T::max().recip() and T::bits() or something similar.
</span><span class="kw">let </span>epsilon = <F <span class="kw">as </span>NumCast>::from(<span class="number">10e-20</span>).expect(<span class="string">"Can't convert 10e-20"</span>);
approximate_float(f, epsilon, <span class="number">30</span>)
}
}
<span class="kw">fn </span>approximate_float<T, F>(val: F, max_error: F, max_iterations: usize) -> <span class="prelude-ty">Option</span><Ratio<T>>
<span class="kw">where
</span>T: Integer + Signed + Bounded + NumCast + Clone,
F: FloatCore + NumCast,
{
<span class="kw">let </span>negative = val.is_sign_negative();
<span class="kw">let </span>abs_val = val.abs();
<span class="kw">let </span>r = approximate_float_unsigned(abs_val, max_error, max_iterations)<span class="question-mark">?</span>;
<span class="comment">// Make negative again if needed
</span><span class="prelude-val">Some</span>(<span class="kw">if </span>negative { r.neg() } <span class="kw">else </span>{ r })
}
<span class="comment">// No Unsigned constraint because this also works on positive integers and is called
// like that, see above
</span><span class="kw">fn </span>approximate_float_unsigned<T, F>(val: F, max_error: F, max_iterations: usize) -> <span class="prelude-ty">Option</span><Ratio<T>>
<span class="kw">where
</span>T: Integer + Bounded + NumCast + Clone,
F: FloatCore + NumCast,
{
<span class="comment">// Continued fractions algorithm
// http://mathforum.org/dr.math/faq/faq.fractions.html#decfrac
</span><span class="kw">if </span>val < F::zero() || val.is_nan() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw">let </span><span class="kw-2">mut </span>q = val;
<span class="kw">let </span><span class="kw-2">mut </span>n0 = T::zero();
<span class="kw">let </span><span class="kw-2">mut </span>d0 = T::one();
<span class="kw">let </span><span class="kw-2">mut </span>n1 = T::one();
<span class="kw">let </span><span class="kw-2">mut </span>d1 = T::zero();
<span class="kw">let </span>t_max = T::max_value();
<span class="kw">let </span>t_max_f = <F <span class="kw">as </span>NumCast>::from(t_max.clone())<span class="question-mark">?</span>;
<span class="comment">// 1/epsilon > T::MAX
</span><span class="kw">let </span>epsilon = t_max_f.recip();
<span class="comment">// Overflow
</span><span class="kw">if </span>q > t_max_f {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="kw">for _ in </span><span class="number">0</span>..max_iterations {
<span class="kw">let </span>a = <span class="kw">match </span><T <span class="kw">as </span>NumCast>::from(q) {
<span class="prelude-val">None </span>=> <span class="kw">break</span>,
<span class="prelude-val">Some</span>(a) => a,
};
<span class="kw">let </span>a_f = <span class="kw">match </span><F <span class="kw">as </span>NumCast>::from(a.clone()) {
<span class="prelude-val">None </span>=> <span class="kw">break</span>,
<span class="prelude-val">Some</span>(a_f) => a_f,
};
<span class="kw">let </span>f = q - a_f;
<span class="comment">// Prevent overflow
</span><span class="kw">if </span>!a.is_zero()
&& (n1 > t_max.clone() / a.clone()
|| d1 > t_max.clone() / a.clone()
|| a.clone() * n1.clone() > t_max.clone() - n0.clone()
|| a.clone() * d1.clone() > t_max.clone() - d0.clone())
{
<span class="kw">break</span>;
}
<span class="kw">let </span>n = a.clone() * n1.clone() + n0.clone();
<span class="kw">let </span>d = a.clone() * d1.clone() + d0.clone();
n0 = n1;
d0 = d1;
n1 = n.clone();
d1 = d.clone();
<span class="comment">// Simplify fraction. Doing so here instead of at the end
// allows us to get closer to the target value without overflows
</span><span class="kw">let </span>g = Integer::gcd(<span class="kw-2">&</span>n1, <span class="kw-2">&</span>d1);
<span class="kw">if </span>!g.is_zero() {
n1 = n1 / g.clone();
d1 = d1 / g.clone();
}
<span class="comment">// Close enough?
</span><span class="kw">let </span>(n_f, d_f) = <span class="kw">match </span>(<F <span class="kw">as </span>NumCast>::from(n), <F <span class="kw">as </span>NumCast>::from(d)) {
(<span class="prelude-val">Some</span>(n_f), <span class="prelude-val">Some</span>(d_f)) => (n_f, d_f),
<span class="kw">_ </span>=> <span class="kw">break</span>,
};
<span class="kw">if </span>(n_f / d_f - val).abs() < max_error {
<span class="kw">break</span>;
}
<span class="comment">// Prevent division by ~0
</span><span class="kw">if </span>f < epsilon {
<span class="kw">break</span>;
}
q = f.recip();
}
<span class="comment">// Overflow
</span><span class="kw">if </span>d1.is_zero() {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="prelude-val">Some</span>(Ratio::new(n1, d1))
}
<span class="attr">#[cfg(not(feature = <span class="string">"num-bigint"</span>))]
</span><span class="macro">macro_rules! </span>to_primitive_small {
($(<span class="macro-nonterminal">$type_name</span>:ty)<span class="kw-2">*</span>) => ($(
<span class="kw">impl </span>ToPrimitive <span class="kw">for </span>Ratio<<span class="macro-nonterminal">$type_name</span>> {
<span class="kw">fn </span>to_i64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><i64> {
<span class="self">self</span>.to_integer().to_i64()
}
<span class="kw">fn </span>to_i128(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><i128> {
<span class="self">self</span>.to_integer().to_i128()
}
<span class="kw">fn </span>to_u64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u64> {
<span class="self">self</span>.to_integer().to_u64()
}
<span class="kw">fn </span>to_u128(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u128> {
<span class="self">self</span>.to_integer().to_u128()
}
<span class="kw">fn </span>to_f64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><f64> {
<span class="kw">let </span>float = <span class="self">self</span>.numer.to_f64().unwrap() / <span class="self">self</span>.denom.to_f64().unwrap();
<span class="kw">if </span>float.is_nan() {
<span class="prelude-val">None
</span>} <span class="kw">else </span>{
<span class="prelude-val">Some</span>(float)
}
}
}
)<span class="kw-2">*</span>)
}
<span class="attr">#[cfg(not(feature = <span class="string">"num-bigint"</span>))]
</span><span class="macro">to_primitive_small!</span>(u8 i8 u16 i16 u32 i32);
<span class="attr">#[cfg(all(target_pointer_width = <span class="string">"32"</span>, not(feature = <span class="string">"num-bigint"</span>)))]
</span><span class="macro">to_primitive_small!</span>(usize isize);
<span class="attr">#[cfg(not(feature = <span class="string">"num-bigint"</span>))]
</span><span class="macro">macro_rules! </span>to_primitive_64 {
($(<span class="macro-nonterminal">$type_name</span>:ty)<span class="kw-2">*</span>) => ($(
<span class="kw">impl </span>ToPrimitive <span class="kw">for </span>Ratio<<span class="macro-nonterminal">$type_name</span>> {
<span class="kw">fn </span>to_i64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><i64> {
<span class="self">self</span>.to_integer().to_i64()
}
<span class="kw">fn </span>to_i128(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><i128> {
<span class="self">self</span>.to_integer().to_i128()
}
<span class="kw">fn </span>to_u64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u64> {
<span class="self">self</span>.to_integer().to_u64()
}
<span class="kw">fn </span>to_u128(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u128> {
<span class="self">self</span>.to_integer().to_u128()
}
<span class="kw">fn </span>to_f64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><f64> {
<span class="kw">let </span>float = ratio_to_f64(
<span class="self">self</span>.numer <span class="kw">as </span>i128,
<span class="self">self</span>.denom <span class="kw">as </span>i128
);
<span class="kw">if </span>float.is_nan() {
<span class="prelude-val">None
</span>} <span class="kw">else </span>{
<span class="prelude-val">Some</span>(float)
}
}
}
)<span class="kw-2">*</span>)
}
<span class="attr">#[cfg(not(feature = <span class="string">"num-bigint"</span>))]
</span><span class="macro">to_primitive_64!</span>(u64 i64);
<span class="attr">#[cfg(all(target_pointer_width = <span class="string">"64"</span>, not(feature = <span class="string">"num-bigint"</span>)))]
</span><span class="macro">to_primitive_64!</span>(usize isize);
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">impl</span><T: Clone + Integer + ToPrimitive + ToBigInt> ToPrimitive <span class="kw">for </span>Ratio<T> {
<span class="kw">fn </span>to_i64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><i64> {
<span class="self">self</span>.to_integer().to_i64()
}
<span class="kw">fn </span>to_i128(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><i128> {
<span class="self">self</span>.to_integer().to_i128()
}
<span class="kw">fn </span>to_u64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u64> {
<span class="self">self</span>.to_integer().to_u64()
}
<span class="kw">fn </span>to_u128(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><u128> {
<span class="self">self</span>.to_integer().to_u128()
}
<span class="kw">fn </span>to_f64(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><f64> {
<span class="kw">let </span>float = <span class="kw">match </span>(<span class="self">self</span>.numer.to_i64(), <span class="self">self</span>.denom.to_i64()) {
(<span class="prelude-val">Some</span>(numer), <span class="prelude-val">Some</span>(denom)) => ratio_to_f64(
<i128 <span class="kw">as </span>From<<span class="kw">_</span>>>::from(numer),
<i128 <span class="kw">as </span>From<<span class="kw">_</span>>>::from(denom),
),
<span class="kw">_ </span>=> {
<span class="kw">let </span>numer: BigInt = <span class="self">self</span>.numer.to_bigint()<span class="question-mark">?</span>;
<span class="kw">let </span>denom: BigInt = <span class="self">self</span>.denom.to_bigint()<span class="question-mark">?</span>;
ratio_to_f64(numer, denom)
}
};
<span class="kw">if </span>float.is_nan() {
<span class="prelude-val">None
</span>} <span class="kw">else </span>{
<span class="prelude-val">Some</span>(float)
}
}
}
<span class="kw">trait </span>Bits {
<span class="kw">fn </span>bits(<span class="kw-2">&</span><span class="self">self</span>) -> u64;
}
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">impl </span>Bits <span class="kw">for </span>BigInt {
<span class="kw">fn </span>bits(<span class="kw-2">&</span><span class="self">self</span>) -> u64 {
<span class="self">self</span>.bits()
}
}
<span class="kw">impl </span>Bits <span class="kw">for </span>i128 {
<span class="kw">fn </span>bits(<span class="kw-2">&</span><span class="self">self</span>) -> u64 {
(<span class="number">128 </span>- <span class="self">self</span>.wrapping_abs().leading_zeros()).into()
}
}
<span class="doccomment">/// Converts a ratio of `T` to an f64.
///
/// In addition to stated trait bounds, `T` must be able to hold numbers 56 bits larger than
/// the largest of `numer` and `denom`. This is automatically true if `T` is `BigInt`.
</span><span class="kw">fn </span>ratio_to_f64<T: Bits + Clone + Integer + Signed + ShlAssign<usize> + ToPrimitive>(
numer: T,
denom: T,
) -> f64 {
<span class="kw">use </span>core::f64::{INFINITY, MANTISSA_DIGITS, MAX_EXP, MIN_EXP, RADIX};
<span class="macro">assert_eq!</span>(
RADIX, <span class="number">2</span>,
<span class="string">"only floating point implementations with radix 2 are supported"
</span>);
<span class="comment">// Inclusive upper and lower bounds to the range of exactly-representable ints in an f64.
</span><span class="kw">const </span>MAX_EXACT_INT: i64 = <span class="number">1i64 </span><< MANTISSA_DIGITS;
<span class="kw">const </span>MIN_EXACT_INT: i64 = -MAX_EXACT_INT;
<span class="kw">let </span>flo_sign = numer.signum().to_f64().unwrap() / denom.signum().to_f64().unwrap();
<span class="kw">if </span>!flo_sign.is_normal() {
<span class="kw">return </span>flo_sign;
}
<span class="comment">// Fast track: both sides can losslessly be converted to f64s. In this case, letting the
// FPU do the job is faster and easier. In any other case, converting to f64s may lead
// to an inexact result: https://stackoverflow.com/questions/56641441/.
</span><span class="kw">if let </span>(<span class="prelude-val">Some</span>(n), <span class="prelude-val">Some</span>(d)) = (numer.to_i64(), denom.to_i64()) {
<span class="kw">if </span>MIN_EXACT_INT <= n && n <= MAX_EXACT_INT && MIN_EXACT_INT <= d && d <= MAX_EXACT_INT {
<span class="kw">return </span>n.to_f64().unwrap() / d.to_f64().unwrap();
}
}
<span class="comment">// Otherwise, the goal is to obtain a quotient with at least 55 bits. 53 of these bits will
// be used as the mantissa of the resulting float, and the remaining two are for rounding.
// There's an error of up to 1 on the number of resulting bits, so we may get either 55 or
// 56 bits.
</span><span class="kw">let </span><span class="kw-2">mut </span>numer = numer.abs();
<span class="kw">let </span><span class="kw-2">mut </span>denom = denom.abs();
<span class="kw">let </span>(is_diff_positive, absolute_diff) = <span class="kw">match </span>numer.bits().checked_sub(denom.bits()) {
<span class="prelude-val">Some</span>(diff) => (<span class="bool-val">true</span>, diff),
<span class="prelude-val">None </span>=> (<span class="bool-val">false</span>, denom.bits() - numer.bits()),
};
<span class="comment">// Filter out overflows and underflows. After this step, the signed difference fits in an
// isize.
</span><span class="kw">if </span>is_diff_positive && absolute_diff > MAX_EXP <span class="kw">as </span>u64 {
<span class="kw">return </span>INFINITY * flo_sign;
}
<span class="kw">if </span>!is_diff_positive && absolute_diff > -MIN_EXP <span class="kw">as </span>u64 + MANTISSA_DIGITS <span class="kw">as </span>u64 + <span class="number">1 </span>{
<span class="kw">return </span><span class="number">0.0 </span>* flo_sign;
}
<span class="kw">let </span>diff = <span class="kw">if </span>is_diff_positive {
absolute_diff.to_isize().unwrap()
} <span class="kw">else </span>{
-absolute_diff.to_isize().unwrap()
};
<span class="comment">// Shift is chosen so that the quotient will have 55 or 56 bits. The exception is if the
// quotient is going to be subnormal, in which case it may have fewer bits.
</span><span class="kw">let </span>shift: isize = diff.max(MIN_EXP <span class="kw">as </span>isize) - MANTISSA_DIGITS <span class="kw">as </span>isize - <span class="number">2</span>;
<span class="kw">if </span>shift >= <span class="number">0 </span>{
denom <<= shift <span class="kw">as </span>usize
} <span class="kw">else </span>{
numer <<= -shift <span class="kw">as </span>usize
};
<span class="kw">let </span>(quotient, remainder) = numer.div_rem(<span class="kw-2">&</span>denom);
<span class="comment">// This is guaranteed to fit since we've set up quotient to be at most 56 bits.
</span><span class="kw">let </span><span class="kw-2">mut </span>quotient = quotient.to_u64().unwrap();
<span class="kw">let </span>n_rounding_bits = {
<span class="kw">let </span>quotient_bits = <span class="number">64 </span>- quotient.leading_zeros() <span class="kw">as </span>isize;
<span class="kw">let </span>subnormal_bits = MIN_EXP <span class="kw">as </span>isize - shift;
quotient_bits.max(subnormal_bits) - MANTISSA_DIGITS <span class="kw">as </span>isize
} <span class="kw">as </span>usize;
<span class="macro">debug_assert!</span>(n_rounding_bits == <span class="number">2 </span>|| n_rounding_bits == <span class="number">3</span>);
<span class="kw">let </span>rounding_bit_mask = (<span class="number">1u64 </span><< n_rounding_bits) - <span class="number">1</span>;
<span class="comment">// Round to 53 bits with round-to-even. For rounding, we need to take into account both
// our rounding bits and the division's remainder.
</span><span class="kw">let </span>ls_bit = quotient & (<span class="number">1u64 </span><< n_rounding_bits) != <span class="number">0</span>;
<span class="kw">let </span>ms_rounding_bit = quotient & (<span class="number">1u64 </span><< (n_rounding_bits - <span class="number">1</span>)) != <span class="number">0</span>;
<span class="kw">let </span>ls_rounding_bits = quotient & (rounding_bit_mask >> <span class="number">1</span>) != <span class="number">0</span>;
<span class="kw">if </span>ms_rounding_bit && (ls_bit || ls_rounding_bits || !remainder.is_zero()) {
quotient += <span class="number">1u64 </span><< n_rounding_bits;
}
quotient &= !rounding_bit_mask;
<span class="comment">// The quotient is guaranteed to be exactly representable as it's now 53 bits + 2 or 3
// trailing zeros, so there is no risk of a rounding error here.
</span><span class="kw">let </span>q_float = quotient <span class="kw">as </span>f64 * flo_sign;
ldexp(q_float, shift <span class="kw">as </span>i32)
}
<span class="doccomment">/// Multiply `x` by 2 to the power of `exp`. Returns an accurate result even if `2^exp` is not
/// representable.
</span><span class="kw">fn </span>ldexp(x: f64, exp: i32) -> f64 {
<span class="kw">use </span>core::f64::{INFINITY, MANTISSA_DIGITS, MAX_EXP, RADIX};
<span class="macro">assert_eq!</span>(
RADIX, <span class="number">2</span>,
<span class="string">"only floating point implementations with radix 2 are supported"
</span>);
<span class="kw">const </span>EXPONENT_MASK: u64 = <span class="number">0x7ff </span><< <span class="number">52</span>;
<span class="kw">const </span>MAX_UNSIGNED_EXPONENT: i32 = <span class="number">0x7fe</span>;
<span class="kw">const </span>MIN_SUBNORMAL_POWER: i32 = MANTISSA_DIGITS <span class="kw">as </span>i32;
<span class="kw">if </span>x.is_zero() || x.is_infinite() || x.is_nan() {
<span class="kw">return </span>x;
}
<span class="comment">// Filter out obvious over / underflows to make sure the resulting exponent fits in an isize.
</span><span class="kw">if </span>exp > <span class="number">3 </span>* MAX_EXP {
<span class="kw">return </span>INFINITY * x.signum();
} <span class="kw">else if </span>exp < -<span class="number">3 </span>* MAX_EXP {
<span class="kw">return </span><span class="number">0.0 </span>* x.signum();
}
<span class="comment">// curr_exp is the x's *biased* exponent, and is in the [-54, MAX_UNSIGNED_EXPONENT] range.
</span><span class="kw">let </span>(bits, curr_exp) = <span class="kw">if </span>!x.is_normal() {
<span class="comment">// If x is subnormal, we make it normal by multiplying by 2^53. This causes no loss of
// precision or rounding.
</span><span class="kw">let </span>normal_x = x * <span class="number">2f64</span>.powi(MIN_SUBNORMAL_POWER);
<span class="kw">let </span>bits = normal_x.to_bits();
<span class="comment">// This cast is safe because the exponent is at most 0x7fe, which fits in an i32.
</span>(
bits,
((bits & EXPONENT_MASK) >> <span class="number">52</span>) <span class="kw">as </span>i32 - MIN_SUBNORMAL_POWER,
)
} <span class="kw">else </span>{
<span class="kw">let </span>bits = x.to_bits();
<span class="kw">let </span>curr_exp = (bits & EXPONENT_MASK) >> <span class="number">52</span>;
<span class="comment">// This cast is safe because the exponent is at most 0x7fe, which fits in an i32.
</span>(bits, curr_exp <span class="kw">as </span>i32)
};
<span class="comment">// The addition can't overflow because exponent is between 0 and 0x7fe, and exp is between
// -2*MAX_EXP and 2*MAX_EXP.
</span><span class="kw">let </span>new_exp = curr_exp + exp;
<span class="kw">if </span>new_exp > MAX_UNSIGNED_EXPONENT {
INFINITY * x.signum()
} <span class="kw">else if </span>new_exp > <span class="number">0 </span>{
<span class="comment">// Normal case: exponent is not too large nor subnormal.
</span><span class="kw">let </span>new_bits = (bits & !EXPONENT_MASK) | ((new_exp <span class="kw">as </span>u64) << <span class="number">52</span>);
f64::from_bits(new_bits)
} <span class="kw">else if </span>new_exp >= -(MANTISSA_DIGITS <span class="kw">as </span>i32) {
<span class="comment">// Result is subnormal but may not be zero.
// In this case, we increase the exponent by 54 to make it normal, then multiply the end
// result by 2^-53. This results in a single multiplication with no prior rounding error,
// so there is no risk of double rounding.
</span><span class="kw">let </span>new_exp = new_exp + MIN_SUBNORMAL_POWER;
<span class="macro">debug_assert!</span>(new_exp >= <span class="number">0</span>);
<span class="kw">let </span>new_bits = (bits & !EXPONENT_MASK) | ((new_exp <span class="kw">as </span>u64) << <span class="number">52</span>);
f64::from_bits(new_bits) * <span class="number">2f64</span>.powi(-MIN_SUBNORMAL_POWER)
} <span class="kw">else </span>{
<span class="comment">// Result is zero.
</span><span class="kw">return </span><span class="number">0.0 </span>* x.signum();
}
}
<span class="attr">#[cfg(test)]
#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">fn </span>hash<T: Hash>(x: <span class="kw-2">&</span>T) -> u64 {
<span class="kw">use </span>std::collections::hash_map::RandomState;
<span class="kw">use </span>std::hash::BuildHasher;
<span class="kw">let </span><span class="kw-2">mut </span>hasher = <RandomState <span class="kw">as </span>BuildHasher>::Hasher::new();
x.hash(<span class="kw-2">&mut </span>hasher);
hasher.finish()
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>test {
<span class="kw">use </span><span class="kw">super</span>::ldexp;
<span class="attr">#[cfg(all(feature = <span class="string">"num-bigint"</span>))]
</span><span class="kw">use </span><span class="kw">super</span>::BigInt;
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">use </span><span class="kw">super</span>::BigRational;
<span class="kw">use super</span>::{Ratio, Rational64};
<span class="kw">use </span>core::f64;
<span class="kw">use </span>core::i32;
<span class="kw">use </span>core::i64;
<span class="kw">use </span>core::str::FromStr;
<span class="kw">use </span>num_integer::Integer;
<span class="kw">use </span>num_traits::ToPrimitive;
<span class="kw">use </span>num_traits::{FromPrimitive, One, Pow, Signed, Zero};
<span class="kw">pub const </span>_0: Rational64 = Ratio { numer: <span class="number">0</span>, denom: <span class="number">1 </span>};
<span class="kw">pub const </span>_1: Rational64 = Ratio { numer: <span class="number">1</span>, denom: <span class="number">1 </span>};
<span class="kw">pub const </span>_2: Rational64 = Ratio { numer: <span class="number">2</span>, denom: <span class="number">1 </span>};
<span class="kw">pub const </span>_NEG2: Rational64 = Ratio {
numer: -<span class="number">2</span>,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_8: Rational64 = Ratio { numer: <span class="number">8</span>, denom: <span class="number">1 </span>};
<span class="kw">pub const </span>_15: Rational64 = Ratio {
numer: <span class="number">15</span>,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_16: Rational64 = Ratio {
numer: <span class="number">16</span>,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_1_2: Rational64 = Ratio { numer: <span class="number">1</span>, denom: <span class="number">2 </span>};
<span class="kw">pub const </span>_1_8: Rational64 = Ratio { numer: <span class="number">1</span>, denom: <span class="number">8 </span>};
<span class="kw">pub const </span>_1_15: Rational64 = Ratio {
numer: <span class="number">1</span>,
denom: <span class="number">15</span>,
};
<span class="kw">pub const </span>_1_16: Rational64 = Ratio {
numer: <span class="number">1</span>,
denom: <span class="number">16</span>,
};
<span class="kw">pub const </span>_3_2: Rational64 = Ratio { numer: <span class="number">3</span>, denom: <span class="number">2 </span>};
<span class="kw">pub const </span>_5_2: Rational64 = Ratio { numer: <span class="number">5</span>, denom: <span class="number">2 </span>};
<span class="kw">pub const </span>_NEG1_2: Rational64 = Ratio {
numer: -<span class="number">1</span>,
denom: <span class="number">2</span>,
};
<span class="kw">pub const </span>_1_NEG2: Rational64 = Ratio {
numer: <span class="number">1</span>,
denom: -<span class="number">2</span>,
};
<span class="kw">pub const </span>_NEG1_NEG2: Rational64 = Ratio {
numer: -<span class="number">1</span>,
denom: -<span class="number">2</span>,
};
<span class="kw">pub const </span>_1_3: Rational64 = Ratio { numer: <span class="number">1</span>, denom: <span class="number">3 </span>};
<span class="kw">pub const </span>_NEG1_3: Rational64 = Ratio {
numer: -<span class="number">1</span>,
denom: <span class="number">3</span>,
};
<span class="kw">pub const </span>_2_3: Rational64 = Ratio { numer: <span class="number">2</span>, denom: <span class="number">3 </span>};
<span class="kw">pub const </span>_NEG2_3: Rational64 = Ratio {
numer: -<span class="number">2</span>,
denom: <span class="number">3</span>,
};
<span class="kw">pub const </span>_MIN: Rational64 = Ratio {
numer: i64::MIN,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_MIN_P1: Rational64 = Ratio {
numer: i64::MIN + <span class="number">1</span>,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_MAX: Rational64 = Ratio {
numer: i64::MAX,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_MAX_M1: Rational64 = Ratio {
numer: i64::MAX - <span class="number">1</span>,
denom: <span class="number">1</span>,
};
<span class="kw">pub const </span>_BILLION: Rational64 = Ratio {
numer: <span class="number">1_000_000_000</span>,
denom: <span class="number">1</span>,
};
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">pub fn </span>to_big(n: Rational64) -> BigRational {
Ratio::new(
FromPrimitive::from_i64(n.numer).unwrap(),
FromPrimitive::from_i64(n.denom).unwrap(),
)
}
<span class="attr">#[cfg(not(feature = <span class="string">"num-bigint"</span>))]
</span><span class="kw">pub fn </span>to_big(n: Rational64) -> Rational64 {
Ratio::new(
FromPrimitive::from_i64(n.numer).unwrap(),
FromPrimitive::from_i64(n.denom).unwrap(),
)
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_test_constants() {
<span class="comment">// check our constants are what Ratio::new etc. would make.
</span><span class="macro">assert_eq!</span>(_0, Zero::zero());
<span class="macro">assert_eq!</span>(_1, One::one());
<span class="macro">assert_eq!</span>(_2, Ratio::from_integer(<span class="number">2</span>));
<span class="macro">assert_eq!</span>(_1_2, Ratio::new(<span class="number">1</span>, <span class="number">2</span>));
<span class="macro">assert_eq!</span>(_3_2, Ratio::new(<span class="number">3</span>, <span class="number">2</span>));
<span class="macro">assert_eq!</span>(_NEG1_2, Ratio::new(-<span class="number">1</span>, <span class="number">2</span>));
<span class="macro">assert_eq!</span>(_2, From::from(<span class="number">2</span>));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_new_reduce() {
<span class="macro">assert_eq!</span>(Ratio::new(<span class="number">2</span>, <span class="number">2</span>), One::one());
<span class="macro">assert_eq!</span>(Ratio::new(<span class="number">0</span>, i32::MIN), Zero::zero());
<span class="macro">assert_eq!</span>(Ratio::new(i32::MIN, i32::MIN), One::one());
}
<span class="attr">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_new_zero() {
<span class="kw">let </span>_a = Ratio::new(<span class="number">1</span>, <span class="number">0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_approximate_float() {
<span class="macro">assert_eq!</span>(Ratio::from_f32(<span class="number">0.5f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">1i64</span>, <span class="number">2</span>)));
<span class="macro">assert_eq!</span>(Ratio::from_f64(<span class="number">0.5f64</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">1i32</span>, <span class="number">2</span>)));
<span class="macro">assert_eq!</span>(Ratio::from_f32(<span class="number">5f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">5i64</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(Ratio::from_f64(<span class="number">5f64</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">5i32</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(Ratio::from_f32(<span class="number">29.97f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">2997i64</span>, <span class="number">100</span>)));
<span class="macro">assert_eq!</span>(Ratio::from_f32(-<span class="number">29.97f32</span>), <span class="prelude-val">Some</span>(Ratio::new(-<span class="number">2997i64</span>, <span class="number">100</span>)));
<span class="macro">assert_eq!</span>(Ratio::<i8>::from_f32(<span class="number">63.5f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">127i8</span>, <span class="number">2</span>)));
<span class="macro">assert_eq!</span>(Ratio::<i8>::from_f32(<span class="number">126.5f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">126i8</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(Ratio::<i8>::from_f32(<span class="number">127.0f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">127i8</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(Ratio::<i8>::from_f32(<span class="number">127.5f32</span>), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<i8>::from_f32(-<span class="number">63.5f32</span>), <span class="prelude-val">Some</span>(Ratio::new(-<span class="number">127i8</span>, <span class="number">2</span>)));
<span class="macro">assert_eq!</span>(
Ratio::<i8>::from_f32(-<span class="number">126.5f32</span>),
<span class="prelude-val">Some</span>(Ratio::new(-<span class="number">126i8</span>, <span class="number">1</span>))
);
<span class="macro">assert_eq!</span>(
Ratio::<i8>::from_f32(-<span class="number">127.0f32</span>),
<span class="prelude-val">Some</span>(Ratio::new(-<span class="number">127i8</span>, <span class="number">1</span>))
);
<span class="macro">assert_eq!</span>(Ratio::<i8>::from_f32(-<span class="number">127.5f32</span>), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<u8>::from_f32(-<span class="number">127f32</span>), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<u8>::from_f32(<span class="number">127f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">127u8</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(Ratio::<u8>::from_f32(<span class="number">127.5f32</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">255u8</span>, <span class="number">2</span>)));
<span class="macro">assert_eq!</span>(Ratio::<u8>::from_f32(<span class="number">256f32</span>), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(-<span class="number">10e200</span>), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(<span class="number">10e200</span>), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(f64::INFINITY), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(f64::NEG_INFINITY), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(f64::NAN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(
Ratio::<i64>::from_f64(f64::EPSILON),
<span class="prelude-val">Some</span>(Ratio::new(<span class="number">1</span>, <span class="number">4503599627370496</span>))
);
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(<span class="number">0.0</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">0</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(Ratio::<i64>::from_f64(-<span class="number">0.0</span>), <span class="prelude-val">Some</span>(Ratio::new(<span class="number">0</span>, <span class="number">1</span>)));
}
<span class="attr">#[test]
#[allow(clippy::eq_op)]
</span><span class="kw">fn </span>test_cmp() {
<span class="macro">assert!</span>(_0 == _0 && _1 == _1);
<span class="macro">assert!</span>(_0 != _1 && _1 != _0);
<span class="macro">assert!</span>(_0 < _1 && !(_1 < _0));
<span class="macro">assert!</span>(_1 > _0 && !(_0 > _1));
<span class="macro">assert!</span>(_0 <= _0 && _1 <= _1);
<span class="macro">assert!</span>(_0 <= _1 && !(_1 <= _0));
<span class="macro">assert!</span>(_0 >= _0 && _1 >= _1);
<span class="macro">assert!</span>(_1 >= _0 && !(_0 >= _1));
<span class="kw">let </span>_0_2: Rational64 = Ratio::new_raw(<span class="number">0</span>, <span class="number">2</span>);
<span class="macro">assert_eq!</span>(_0, _0_2);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_cmp_overflow() {
<span class="kw">use </span>core::cmp::Ordering;
<span class="comment">// issue #7 example:
</span><span class="kw">let </span>big = Ratio::new(<span class="number">128u8</span>, <span class="number">1</span>);
<span class="kw">let </span>small = big.recip();
<span class="macro">assert!</span>(big > small);
<span class="comment">// try a few that are closer together
// (some matching numer, some matching denom, some neither)
</span><span class="kw">let </span>ratios = [
Ratio::new(<span class="number">125_i8</span>, <span class="number">127_i8</span>),
Ratio::new(<span class="number">63_i8</span>, <span class="number">64_i8</span>),
Ratio::new(<span class="number">124_i8</span>, <span class="number">125_i8</span>),
Ratio::new(<span class="number">125_i8</span>, <span class="number">126_i8</span>),
Ratio::new(<span class="number">126_i8</span>, <span class="number">127_i8</span>),
Ratio::new(<span class="number">127_i8</span>, <span class="number">126_i8</span>),
];
<span class="kw">fn </span>check_cmp(a: Ratio<i8>, b: Ratio<i8>, ord: Ordering) {
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">println!</span>(<span class="string">"comparing {} and {}"</span>, a, b);
<span class="macro">assert_eq!</span>(a.cmp(<span class="kw-2">&</span>b), ord);
<span class="macro">assert_eq!</span>(b.cmp(<span class="kw-2">&</span>a), ord.reverse());
}
<span class="kw">for </span>(i, <span class="kw-2">&</span>a) <span class="kw">in </span>ratios.iter().enumerate() {
check_cmp(a, a, Ordering::Equal);
check_cmp(-a, a, Ordering::Less);
<span class="kw">for </span><span class="kw-2">&</span>b <span class="kw">in </span><span class="kw-2">&</span>ratios[i + <span class="number">1</span>..] {
check_cmp(a, b, Ordering::Less);
check_cmp(-a, -b, Ordering::Greater);
check_cmp(a.recip(), b.recip(), Ordering::Greater);
check_cmp(-a.recip(), -b.recip(), Ordering::Less);
}
}
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_to_integer() {
<span class="macro">assert_eq!</span>(_0.to_integer(), <span class="number">0</span>);
<span class="macro">assert_eq!</span>(_1.to_integer(), <span class="number">1</span>);
<span class="macro">assert_eq!</span>(_2.to_integer(), <span class="number">2</span>);
<span class="macro">assert_eq!</span>(_1_2.to_integer(), <span class="number">0</span>);
<span class="macro">assert_eq!</span>(_3_2.to_integer(), <span class="number">1</span>);
<span class="macro">assert_eq!</span>(_NEG1_2.to_integer(), <span class="number">0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_numer() {
<span class="macro">assert_eq!</span>(_0.numer(), <span class="kw-2">&</span><span class="number">0</span>);
<span class="macro">assert_eq!</span>(_1.numer(), <span class="kw-2">&</span><span class="number">1</span>);
<span class="macro">assert_eq!</span>(_2.numer(), <span class="kw-2">&</span><span class="number">2</span>);
<span class="macro">assert_eq!</span>(_1_2.numer(), <span class="kw-2">&</span><span class="number">1</span>);
<span class="macro">assert_eq!</span>(_3_2.numer(), <span class="kw-2">&</span><span class="number">3</span>);
<span class="macro">assert_eq!</span>(_NEG1_2.numer(), <span class="kw-2">&</span>(-<span class="number">1</span>));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_denom() {
<span class="macro">assert_eq!</span>(_0.denom(), <span class="kw-2">&</span><span class="number">1</span>);
<span class="macro">assert_eq!</span>(_1.denom(), <span class="kw-2">&</span><span class="number">1</span>);
<span class="macro">assert_eq!</span>(_2.denom(), <span class="kw-2">&</span><span class="number">1</span>);
<span class="macro">assert_eq!</span>(_1_2.denom(), <span class="kw-2">&</span><span class="number">2</span>);
<span class="macro">assert_eq!</span>(_3_2.denom(), <span class="kw-2">&</span><span class="number">2</span>);
<span class="macro">assert_eq!</span>(_NEG1_2.denom(), <span class="kw-2">&</span><span class="number">2</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_is_integer() {
<span class="macro">assert!</span>(_0.is_integer());
<span class="macro">assert!</span>(_1.is_integer());
<span class="macro">assert!</span>(_2.is_integer());
<span class="macro">assert!</span>(!_1_2.is_integer());
<span class="macro">assert!</span>(!_3_2.is_integer());
<span class="macro">assert!</span>(!_NEG1_2.is_integer());
}
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span><span class="kw">use </span>core::fmt::{<span class="self">self</span>, Write};
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
#[derive(Debug)]
</span><span class="kw">struct </span>NoStdTester {
cursor: usize,
buf: [u8; NoStdTester::BUF_SIZE],
}
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span><span class="kw">impl </span>NoStdTester {
<span class="kw">fn </span>new() -> NoStdTester {
NoStdTester {
buf: [<span class="number">0</span>; <span class="self">Self</span>::BUF_SIZE],
cursor: <span class="number">0</span>,
}
}
<span class="kw">fn </span>clear(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="self">self</span>.buf = [<span class="number">0</span>; <span class="self">Self</span>::BUF_SIZE];
<span class="self">self</span>.cursor = <span class="number">0</span>;
}
<span class="kw">const </span>WRITE_ERR: <span class="kw-2">&</span><span class="lifetime">'static </span>str = <span class="string">"Formatted output too long"</span>;
<span class="kw">const </span>BUF_SIZE: usize = <span class="number">32</span>;
}
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span><span class="kw">impl </span>Write <span class="kw">for </span>NoStdTester {
<span class="kw">fn </span>write_str(<span class="kw-2">&mut </span><span class="self">self</span>, s: <span class="kw-2">&</span>str) -> fmt::Result {
<span class="kw">for </span>byte <span class="kw">in </span>s.bytes() {
<span class="self">self</span>.buf[<span class="self">self</span>.cursor] = byte;
<span class="self">self</span>.cursor += <span class="number">1</span>;
<span class="kw">if </span><span class="self">self</span>.cursor >= <span class="self">self</span>.buf.len() {
<span class="kw">return </span><span class="prelude-val">Err</span>(fmt::Error {});
}
}
<span class="prelude-val">Ok</span>(())
}
}
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span><span class="kw">impl </span>PartialEq<str> <span class="kw">for </span>NoStdTester {
<span class="kw">fn </span>eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span>str) -> bool {
<span class="kw">let </span>other = other.as_bytes();
<span class="kw">for </span>index <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.cursor {
<span class="kw">if </span><span class="self">self</span>.buf.get(index) != other.get(index) {
<span class="kw">return </span><span class="bool-val">false</span>;
}
}
<span class="bool-val">true
</span>}
}
<span class="macro">macro_rules! </span>assert_fmt_eq {
(<span class="macro-nonterminal">$fmt_args</span>:expr, <span class="macro-nonterminal">$string</span>:expr) => {
<span class="attr">#[cfg(not(feature = <span class="string">"std"</span>))]
</span>{
<span class="kw">let </span><span class="kw-2">mut </span>tester = NoStdTester::new();
<span class="macro">write!</span>(tester, <span class="string">"{}"</span>, <span class="macro-nonterminal">$fmt_args</span>).expect(NoStdTester::WRITE_ERR);
<span class="macro">assert_eq!</span>(tester, <span class="kw-2">*</span><span class="macro-nonterminal">$string</span>);
tester.clear();
}
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span>{
<span class="macro">assert_eq!</span>(std::fmt::format(<span class="macro-nonterminal">$fmt_args</span>), <span class="macro-nonterminal">$string</span>);
}
};
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_show() {
<span class="comment">// Test:
// :b :o :x, :X, :?
// alternate or not (#)
// positive and negative
// padding
// does not test precision (i.e. truncation)
</span><span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{}"</span>, _2), <span class="string">"2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+}"</span>, _2), <span class="string">"+2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:-}"</span>, _2), <span class="string">"2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{}"</span>, _1_2), <span class="string">"1/2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{}"</span>, -_1_2), <span class="string">"-1/2"</span>); <span class="comment">// test negatives
</span><span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{}"</span>, _0), <span class="string">"0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{}"</span>, -_2), <span class="string">"-2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+}"</span>, -_2), <span class="string">"-2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:b}"</span>, _2), <span class="string">"10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#b}"</span>, _2), <span class="string">"0b10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:b}"</span>, _1_2), <span class="string">"1/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+b}"</span>, _1_2), <span class="string">"+1/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:-b}"</span>, _1_2), <span class="string">"1/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:b}"</span>, _0), <span class="string">"0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#b}"</span>, _1_2), <span class="string">"0b1/0b10"</span>);
<span class="comment">// no std does not support padding
</span><span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:010b}"</span>, _1_2), <span class="string">"0000001/10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:#010b}"</span>, _1_2), <span class="string">"0b001/0b10"</span>);
<span class="kw">let </span>half_i8: Ratio<i8> = Ratio::new(<span class="number">1_i8</span>, <span class="number">2_i8</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:b}"</span>, -half_i8), <span class="string">"11111111/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#b}"</span>, -half_i8), <span class="string">"0b11111111/0b10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:05}"</span>, Ratio::new(-<span class="number">1_i8</span>, <span class="number">1_i8</span>)), <span class="string">"-0001"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:o}"</span>, _8), <span class="string">"10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:o}"</span>, _1_8), <span class="string">"1/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:o}"</span>, _0), <span class="string">"0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#o}"</span>, _1_8), <span class="string">"0o1/0o10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:010o}"</span>, _1_8), <span class="string">"0000001/10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:#010o}"</span>, _1_8), <span class="string">"0o001/0o10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:o}"</span>, -half_i8), <span class="string">"377/2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#o}"</span>, -half_i8), <span class="string">"0o377/0o2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:x}"</span>, _16), <span class="string">"10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:x}"</span>, _15), <span class="string">"f"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:x}"</span>, _1_16), <span class="string">"1/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:x}"</span>, _1_15), <span class="string">"1/f"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:x}"</span>, _0), <span class="string">"0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#x}"</span>, _1_16), <span class="string">"0x1/0x10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:010x}"</span>, _1_16), <span class="string">"0000001/10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="macro">format!</span>(<span class="string">"{:#010x}"</span>, _1_16), <span class="string">"0x001/0x10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:x}"</span>, -half_i8), <span class="string">"ff/2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#x}"</span>, -half_i8), <span class="string">"0xff/0x2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:X}"</span>, _16), <span class="string">"10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:X}"</span>, _15), <span class="string">"F"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:X}"</span>, _1_16), <span class="string">"1/10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:X}"</span>, _1_15), <span class="string">"1/F"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:X}"</span>, _0), <span class="string">"0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#X}"</span>, _1_16), <span class="string">"0x1/0x10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:010X}"</span>, _1_16), <span class="string">"0000001/10"</span>);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">assert_eq!</span>(<span class="macro">format!</span>(<span class="string">"{:#010X}"</span>, _1_16), <span class="string">"0x001/0x10"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:X}"</span>, -half_i8), <span class="string">"FF/2"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#X}"</span>, -half_i8), <span class="string">"0xFF/0x2"</span>);
<span class="attr">#[cfg(has_int_exp_fmt)]
</span>{
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:e}"</span>, -_2), <span class="string">"-2e0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#e}"</span>, -_2), <span class="string">"-2e0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+e}"</span>, -_2), <span class="string">"-2e0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:e}"</span>, _BILLION), <span class="string">"1e9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+e}"</span>, _BILLION), <span class="string">"+1e9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:e}"</span>, _BILLION.recip()), <span class="string">"1e0/1e9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+e}"</span>, _BILLION.recip()), <span class="string">"+1e0/1e9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:E}"</span>, -_2), <span class="string">"-2E0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:#E}"</span>, -_2), <span class="string">"-2E0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+E}"</span>, -_2), <span class="string">"-2E0"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:E}"</span>, _BILLION), <span class="string">"1E9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+E}"</span>, _BILLION), <span class="string">"+1E9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:E}"</span>, _BILLION.recip()), <span class="string">"1E0/1E9"</span>);
<span class="macro">assert_fmt_eq!</span>(<span class="macro">format_args!</span>(<span class="string">"{:+E}"</span>, _BILLION.recip()), <span class="string">"+1E0/1E9"</span>);
}
}
<span class="kw">mod </span>arith {
<span class="kw">use </span><span class="kw">super</span>::<span class="kw">super</span>::{Ratio, Rational64};
<span class="kw">use super</span>::{to_big, _0, _1, _1_2, _2, _3_2, _5_2, _MAX, _MAX_M1, _MIN, _MIN_P1, _NEG1_2};
<span class="kw">use </span>core::fmt::Debug;
<span class="kw">use </span>num_integer::Integer;
<span class="kw">use </span>num_traits::{Bounded, CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, NumAssign};
<span class="attr">#[test]
</span><span class="kw">fn </span>test_add() {
<span class="kw">fn </span>test(a: Rational64, b: Rational64, c: Rational64) {
<span class="macro">assert_eq!</span>(a + b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x += b;
x
},
c
);
<span class="macro">assert_eq!</span>(to_big(a) + to_big(b), to_big(c));
<span class="macro">assert_eq!</span>(a.checked_add(<span class="kw-2">&</span>b), <span class="prelude-val">Some</span>(c));
<span class="macro">assert_eq!</span>(to_big(a).checked_add(<span class="kw-2">&</span>to_big(b)), <span class="prelude-val">Some</span>(to_big(c)));
}
<span class="kw">fn </span>test_assign(a: Rational64, b: i64, c: Rational64) {
<span class="macro">assert_eq!</span>(a + b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x += b;
x
},
c
);
}
test(_1, _1_2, _3_2);
test(_1, _1, _2);
test(_1_2, _3_2, _2);
test(_1_2, _NEG1_2, _0);
test_assign(_1_2, <span class="number">1</span>, _3_2);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_add_overflow() {
<span class="comment">// compares Ratio(1, T::max_value()) + Ratio(1, T::max_value())
// to Ratio(1+1, T::max_value()) for each integer type.
// Previously, this calculation would overflow.
</span><span class="kw">fn </span>test_add_typed_overflow<T>()
<span class="kw">where
</span>T: Integer + Bounded + Clone + Debug + NumAssign,
{
<span class="kw">let </span>_1_max = Ratio::new(T::one(), T::max_value());
<span class="kw">let </span>_2_max = Ratio::new(T::one() + T::one(), T::max_value());
<span class="macro">assert_eq!</span>(_1_max.clone() + _1_max.clone(), _2_max);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>tmp = _1_max.clone();
tmp += _1_max;
tmp
},
_2_max
);
}
test_add_typed_overflow::<u8>();
test_add_typed_overflow::<u16>();
test_add_typed_overflow::<u32>();
test_add_typed_overflow::<u64>();
test_add_typed_overflow::<usize>();
test_add_typed_overflow::<u128>();
test_add_typed_overflow::<i8>();
test_add_typed_overflow::<i16>();
test_add_typed_overflow::<i32>();
test_add_typed_overflow::<i64>();
test_add_typed_overflow::<isize>();
test_add_typed_overflow::<i128>();
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_sub() {
<span class="kw">fn </span>test(a: Rational64, b: Rational64, c: Rational64) {
<span class="macro">assert_eq!</span>(a - b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x -= b;
x
},
c
);
<span class="macro">assert_eq!</span>(to_big(a) - to_big(b), to_big(c));
<span class="macro">assert_eq!</span>(a.checked_sub(<span class="kw-2">&</span>b), <span class="prelude-val">Some</span>(c));
<span class="macro">assert_eq!</span>(to_big(a).checked_sub(<span class="kw-2">&</span>to_big(b)), <span class="prelude-val">Some</span>(to_big(c)));
}
<span class="kw">fn </span>test_assign(a: Rational64, b: i64, c: Rational64) {
<span class="macro">assert_eq!</span>(a - b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x -= b;
x
},
c
);
}
test(_1, _1_2, _1_2);
test(_3_2, _1_2, _1);
test(_1, _NEG1_2, _3_2);
test_assign(_1_2, <span class="number">1</span>, _NEG1_2);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_sub_overflow() {
<span class="comment">// compares Ratio(1, T::max_value()) - Ratio(1, T::max_value()) to T::zero()
// for each integer type. Previously, this calculation would overflow.
</span><span class="kw">fn </span>test_sub_typed_overflow<T>()
<span class="kw">where
</span>T: Integer + Bounded + Clone + Debug + NumAssign,
{
<span class="kw">let </span>_1_max: Ratio<T> = Ratio::new(T::one(), T::max_value());
<span class="macro">assert!</span>(T::is_zero(<span class="kw-2">&</span>(_1_max.clone() - _1_max.clone()).numer));
{
<span class="kw">let </span><span class="kw-2">mut </span>tmp: Ratio<T> = _1_max.clone();
tmp -= _1_max;
<span class="macro">assert!</span>(T::is_zero(<span class="kw-2">&</span>tmp.numer));
}
}
test_sub_typed_overflow::<u8>();
test_sub_typed_overflow::<u16>();
test_sub_typed_overflow::<u32>();
test_sub_typed_overflow::<u64>();
test_sub_typed_overflow::<usize>();
test_sub_typed_overflow::<u128>();
test_sub_typed_overflow::<i8>();
test_sub_typed_overflow::<i16>();
test_sub_typed_overflow::<i32>();
test_sub_typed_overflow::<i64>();
test_sub_typed_overflow::<isize>();
test_sub_typed_overflow::<i128>();
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_mul() {
<span class="kw">fn </span>test(a: Rational64, b: Rational64, c: Rational64) {
<span class="macro">assert_eq!</span>(a * b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x <span class="kw-2">*</span>= b;
x
},
c
);
<span class="macro">assert_eq!</span>(to_big(a) * to_big(b), to_big(c));
<span class="macro">assert_eq!</span>(a.checked_mul(<span class="kw-2">&</span>b), <span class="prelude-val">Some</span>(c));
<span class="macro">assert_eq!</span>(to_big(a).checked_mul(<span class="kw-2">&</span>to_big(b)), <span class="prelude-val">Some</span>(to_big(c)));
}
<span class="kw">fn </span>test_assign(a: Rational64, b: i64, c: Rational64) {
<span class="macro">assert_eq!</span>(a * b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x <span class="kw-2">*</span>= b;
x
},
c
);
}
test(_1, _1_2, _1_2);
test(_1_2, _3_2, Ratio::new(<span class="number">3</span>, <span class="number">4</span>));
test(_1_2, _NEG1_2, Ratio::new(-<span class="number">1</span>, <span class="number">4</span>));
test_assign(_1_2, <span class="number">2</span>, _1);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_mul_overflow() {
<span class="kw">fn </span>test_mul_typed_overflow<T>()
<span class="kw">where
</span>T: Integer + Bounded + Clone + Debug + NumAssign + CheckedMul,
{
<span class="kw">let </span>two = T::one() + T::one();
<span class="kw">let </span>_3 = T::one() + T::one() + T::one();
<span class="comment">// 1/big * 2/3 = 1/(max/4*3), where big is max/2
// make big = max/2, but also divisible by 2
</span><span class="kw">let </span>big = T::max_value() / two.clone() / two.clone() * two.clone();
<span class="kw">let </span>_1_big: Ratio<T> = Ratio::new(T::one(), big.clone());
<span class="kw">let </span>_2_3: Ratio<T> = Ratio::new(two.clone(), _3.clone());
<span class="macro">assert_eq!</span>(<span class="prelude-val">None</span>, big.clone().checked_mul(<span class="kw-2">&</span>_3.clone()));
<span class="kw">let </span>expected = Ratio::new(T::one(), big / two.clone() * _3.clone());
<span class="macro">assert_eq!</span>(expected.clone(), _1_big.clone() * _2_3.clone());
<span class="macro">assert_eq!</span>(
<span class="prelude-val">Some</span>(expected.clone()),
_1_big.clone().checked_mul(<span class="kw-2">&</span>_2_3.clone())
);
<span class="macro">assert_eq!</span>(expected, {
<span class="kw">let </span><span class="kw-2">mut </span>tmp = _1_big;
tmp <span class="kw-2">*</span>= _2_3;
tmp
});
<span class="comment">// big/3 * 3 = big/1
// make big = max/2, but make it indivisible by 3
</span><span class="kw">let </span>big = T::max_value() / two / _3.clone() * _3.clone() + T::one();
<span class="macro">assert_eq!</span>(<span class="prelude-val">None</span>, big.clone().checked_mul(<span class="kw-2">&</span>_3.clone()));
<span class="kw">let </span>big_3 = Ratio::new(big.clone(), _3.clone());
<span class="kw">let </span>expected = Ratio::new(big, T::one());
<span class="macro">assert_eq!</span>(expected, big_3.clone() * _3.clone());
<span class="macro">assert_eq!</span>(expected, {
<span class="kw">let </span><span class="kw-2">mut </span>tmp = big_3;
tmp <span class="kw-2">*</span>= _3;
tmp
});
}
test_mul_typed_overflow::<u16>();
test_mul_typed_overflow::<u8>();
test_mul_typed_overflow::<u32>();
test_mul_typed_overflow::<u64>();
test_mul_typed_overflow::<usize>();
test_mul_typed_overflow::<u128>();
test_mul_typed_overflow::<i8>();
test_mul_typed_overflow::<i16>();
test_mul_typed_overflow::<i32>();
test_mul_typed_overflow::<i64>();
test_mul_typed_overflow::<isize>();
test_mul_typed_overflow::<i128>();
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_div() {
<span class="kw">fn </span>test(a: Rational64, b: Rational64, c: Rational64) {
<span class="macro">assert_eq!</span>(a / b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x /= b;
x
},
c
);
<span class="macro">assert_eq!</span>(to_big(a) / to_big(b), to_big(c));
<span class="macro">assert_eq!</span>(a.checked_div(<span class="kw-2">&</span>b), <span class="prelude-val">Some</span>(c));
<span class="macro">assert_eq!</span>(to_big(a).checked_div(<span class="kw-2">&</span>to_big(b)), <span class="prelude-val">Some</span>(to_big(c)));
}
<span class="kw">fn </span>test_assign(a: Rational64, b: i64, c: Rational64) {
<span class="macro">assert_eq!</span>(a / b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x /= b;
x
},
c
);
}
test(_1, _1_2, _2);
test(_3_2, _1_2, _1 + _2);
test(_1, _NEG1_2, _NEG1_2 + _NEG1_2 + _NEG1_2 + _NEG1_2);
test_assign(_1, <span class="number">2</span>, _1_2);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_div_overflow() {
<span class="kw">fn </span>test_div_typed_overflow<T>()
<span class="kw">where
</span>T: Integer + Bounded + Clone + Debug + NumAssign + CheckedMul,
{
<span class="kw">let </span>two = T::one() + T::one();
<span class="kw">let </span>_3 = T::one() + T::one() + T::one();
<span class="comment">// 1/big / 3/2 = 1/(max/4*3), where big is max/2
// big ~ max/2, and big is divisible by 2
</span><span class="kw">let </span>big = T::max_value() / two.clone() / two.clone() * two.clone();
<span class="macro">assert_eq!</span>(<span class="prelude-val">None</span>, big.clone().checked_mul(<span class="kw-2">&</span>_3.clone()));
<span class="kw">let </span>_1_big: Ratio<T> = Ratio::new(T::one(), big.clone());
<span class="kw">let </span>_3_two: Ratio<T> = Ratio::new(_3.clone(), two.clone());
<span class="kw">let </span>expected = Ratio::new(T::one(), big / two.clone() * _3.clone());
<span class="macro">assert_eq!</span>(expected.clone(), _1_big.clone() / _3_two.clone());
<span class="macro">assert_eq!</span>(
<span class="prelude-val">Some</span>(expected.clone()),
_1_big.clone().checked_div(<span class="kw-2">&</span>_3_two.clone())
);
<span class="macro">assert_eq!</span>(expected, {
<span class="kw">let </span><span class="kw-2">mut </span>tmp = _1_big;
tmp /= _3_two;
tmp
});
<span class="comment">// 3/big / 3 = 1/big where big is max/2
// big ~ max/2, and big is not divisible by 3
</span><span class="kw">let </span>big = T::max_value() / two / _3.clone() * _3.clone() + T::one();
<span class="macro">assert_eq!</span>(<span class="prelude-val">None</span>, big.clone().checked_mul(<span class="kw-2">&</span>_3.clone()));
<span class="kw">let </span>_3_big = Ratio::new(_3.clone(), big.clone());
<span class="kw">let </span>expected = Ratio::new(T::one(), big);
<span class="macro">assert_eq!</span>(expected, _3_big.clone() / _3.clone());
<span class="macro">assert_eq!</span>(expected, {
<span class="kw">let </span><span class="kw-2">mut </span>tmp = _3_big;
tmp /= _3;
tmp
});
}
test_div_typed_overflow::<u8>();
test_div_typed_overflow::<u16>();
test_div_typed_overflow::<u32>();
test_div_typed_overflow::<u64>();
test_div_typed_overflow::<usize>();
test_div_typed_overflow::<u128>();
test_div_typed_overflow::<i8>();
test_div_typed_overflow::<i16>();
test_div_typed_overflow::<i32>();
test_div_typed_overflow::<i64>();
test_div_typed_overflow::<isize>();
test_div_typed_overflow::<i128>();
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_rem() {
<span class="kw">fn </span>test(a: Rational64, b: Rational64, c: Rational64) {
<span class="macro">assert_eq!</span>(a % b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x %= b;
x
},
c
);
<span class="macro">assert_eq!</span>(to_big(a) % to_big(b), to_big(c))
}
<span class="kw">fn </span>test_assign(a: Rational64, b: i64, c: Rational64) {
<span class="macro">assert_eq!</span>(a % b, c);
<span class="macro">assert_eq!</span>(
{
<span class="kw">let </span><span class="kw-2">mut </span>x = a;
x %= b;
x
},
c
);
}
test(_3_2, _1, _1_2);
test(_3_2, _1_2, _0);
test(_5_2, _3_2, _1);
test(_2, _NEG1_2, _0);
test(_1_2, _2, _1_2);
test_assign(_3_2, <span class="number">1</span>, _1_2);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_rem_overflow() {
<span class="comment">// tests that Ratio(1,2) % Ratio(1, T::max_value()) equals 0
// for each integer type. Previously, this calculation would overflow.
</span><span class="kw">fn </span>test_rem_typed_overflow<T>()
<span class="kw">where
</span>T: Integer + Bounded + Clone + Debug + NumAssign,
{
<span class="kw">let </span>two = T::one() + T::one();
<span class="comment">// value near to maximum, but divisible by two
</span><span class="kw">let </span>max_div2 = T::max_value() / two.clone() * two.clone();
<span class="kw">let </span>_1_max: Ratio<T> = Ratio::new(T::one(), max_div2);
<span class="kw">let </span>_1_two: Ratio<T> = Ratio::new(T::one(), two);
<span class="macro">assert!</span>(T::is_zero(<span class="kw-2">&</span>(_1_two.clone() % _1_max.clone()).numer));
{
<span class="kw">let </span><span class="kw-2">mut </span>tmp: Ratio<T> = _1_two;
tmp %= _1_max;
<span class="macro">assert!</span>(T::is_zero(<span class="kw-2">&</span>tmp.numer));
}
}
test_rem_typed_overflow::<u8>();
test_rem_typed_overflow::<u16>();
test_rem_typed_overflow::<u32>();
test_rem_typed_overflow::<u64>();
test_rem_typed_overflow::<usize>();
test_rem_typed_overflow::<u128>();
test_rem_typed_overflow::<i8>();
test_rem_typed_overflow::<i16>();
test_rem_typed_overflow::<i32>();
test_rem_typed_overflow::<i64>();
test_rem_typed_overflow::<isize>();
test_rem_typed_overflow::<i128>();
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_neg() {
<span class="kw">fn </span>test(a: Rational64, b: Rational64) {
<span class="macro">assert_eq!</span>(-a, b);
<span class="macro">assert_eq!</span>(-to_big(a), to_big(b))
}
test(_0, _0);
test(_1_2, _NEG1_2);
test(-_1, _1);
}
<span class="attr">#[test]
#[allow(clippy::eq_op)]
</span><span class="kw">fn </span>test_zero() {
<span class="macro">assert_eq!</span>(_0 + _0, _0);
<span class="macro">assert_eq!</span>(_0 * _0, _0);
<span class="macro">assert_eq!</span>(_0 * _1, _0);
<span class="macro">assert_eq!</span>(_0 / _NEG1_2, _0);
<span class="macro">assert_eq!</span>(_0 - _0, _0);
}
<span class="attr">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_div_0() {
<span class="kw">let </span>_a = _1 / _0;
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_checked_failures() {
<span class="kw">let </span>big = Ratio::new(<span class="number">128u8</span>, <span class="number">1</span>);
<span class="kw">let </span>small = Ratio::new(<span class="number">1</span>, <span class="number">128u8</span>);
<span class="macro">assert_eq!</span>(big.checked_add(<span class="kw-2">&</span>big), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(small.checked_sub(<span class="kw-2">&</span>big), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(big.checked_mul(<span class="kw-2">&</span>big), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(small.checked_div(<span class="kw-2">&</span>big), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_1.checked_div(<span class="kw-2">&</span>_0), <span class="prelude-val">None</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_checked_zeros() {
<span class="macro">assert_eq!</span>(_0.checked_add(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_0.checked_sub(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_0.checked_mul(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_0.checked_div(<span class="kw-2">&</span>_0), <span class="prelude-val">None</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_checked_min() {
<span class="macro">assert_eq!</span>(_MIN.checked_add(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MIN.checked_sub(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_MIN.checked_mul(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MIN.checked_div(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_1));
<span class="macro">assert_eq!</span>(_0.checked_add(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_MIN));
<span class="macro">assert_eq!</span>(_0.checked_sub(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_0.checked_mul(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_0.checked_div(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_1.checked_add(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_MIN_P1));
<span class="macro">assert_eq!</span>(_1.checked_sub(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_1.checked_mul(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(_MIN));
<span class="macro">assert_eq!</span>(_1.checked_div(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MIN.checked_add(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_MIN));
<span class="macro">assert_eq!</span>(_MIN.checked_sub(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_MIN));
<span class="macro">assert_eq!</span>(_MIN.checked_mul(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_MIN.checked_div(<span class="kw-2">&</span>_0), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MIN.checked_add(<span class="kw-2">&</span>_1), <span class="prelude-val">Some</span>(_MIN_P1));
<span class="macro">assert_eq!</span>(_MIN.checked_sub(<span class="kw-2">&</span>_1), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MIN.checked_mul(<span class="kw-2">&</span>_1), <span class="prelude-val">Some</span>(_MIN));
<span class="macro">assert_eq!</span>(_MIN.checked_div(<span class="kw-2">&</span>_1), <span class="prelude-val">Some</span>(_MIN));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_checked_max() {
<span class="macro">assert_eq!</span>(_MAX.checked_add(<span class="kw-2">&</span>_MAX), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MAX.checked_sub(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_MAX.checked_mul(<span class="kw-2">&</span>_MAX), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MAX.checked_div(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_1));
<span class="macro">assert_eq!</span>(_0.checked_add(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_MAX));
<span class="macro">assert_eq!</span>(_0.checked_sub(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_MIN_P1));
<span class="macro">assert_eq!</span>(_0.checked_mul(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_0.checked_div(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_1.checked_add(<span class="kw-2">&</span>_MAX), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_1.checked_sub(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(-_MAX_M1));
<span class="macro">assert_eq!</span>(_1.checked_mul(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_MAX));
<span class="macro">assert_eq!</span>(_1.checked_div(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(_MAX.recip()));
<span class="macro">assert_eq!</span>(_MAX.checked_add(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_MAX));
<span class="macro">assert_eq!</span>(_MAX.checked_sub(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_MAX));
<span class="macro">assert_eq!</span>(_MAX.checked_mul(<span class="kw-2">&</span>_0), <span class="prelude-val">Some</span>(_0));
<span class="macro">assert_eq!</span>(_MAX.checked_div(<span class="kw-2">&</span>_0), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MAX.checked_add(<span class="kw-2">&</span>_1), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MAX.checked_sub(<span class="kw-2">&</span>_1), <span class="prelude-val">Some</span>(_MAX_M1));
<span class="macro">assert_eq!</span>(_MAX.checked_mul(<span class="kw-2">&</span>_1), <span class="prelude-val">Some</span>(_MAX));
<span class="macro">assert_eq!</span>(_MAX.checked_div(<span class="kw-2">&</span>_1), <span class="prelude-val">Some</span>(_MAX));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_checked_min_max() {
<span class="macro">assert_eq!</span>(_MIN.checked_add(<span class="kw-2">&</span>_MAX), <span class="prelude-val">Some</span>(-_1));
<span class="macro">assert_eq!</span>(_MIN.checked_sub(<span class="kw-2">&</span>_MAX), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MIN.checked_mul(<span class="kw-2">&</span>_MAX), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(
_MIN.checked_div(<span class="kw-2">&</span>_MAX),
<span class="prelude-val">Some</span>(Ratio::new(_MIN.numer, _MAX.numer))
);
<span class="macro">assert_eq!</span>(_MAX.checked_add(<span class="kw-2">&</span>_MIN), <span class="prelude-val">Some</span>(-_1));
<span class="macro">assert_eq!</span>(_MAX.checked_sub(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MAX.checked_mul(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(_MAX.checked_div(<span class="kw-2">&</span>_MIN), <span class="prelude-val">None</span>);
}
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_round() {
<span class="macro">assert_eq!</span>(_1_3.ceil(), _1);
<span class="macro">assert_eq!</span>(_1_3.floor(), _0);
<span class="macro">assert_eq!</span>(_1_3.round(), _0);
<span class="macro">assert_eq!</span>(_1_3.trunc(), _0);
<span class="macro">assert_eq!</span>(_NEG1_3.ceil(), _0);
<span class="macro">assert_eq!</span>(_NEG1_3.floor(), -_1);
<span class="macro">assert_eq!</span>(_NEG1_3.round(), _0);
<span class="macro">assert_eq!</span>(_NEG1_3.trunc(), _0);
<span class="macro">assert_eq!</span>(_2_3.ceil(), _1);
<span class="macro">assert_eq!</span>(_2_3.floor(), _0);
<span class="macro">assert_eq!</span>(_2_3.round(), _1);
<span class="macro">assert_eq!</span>(_2_3.trunc(), _0);
<span class="macro">assert_eq!</span>(_NEG2_3.ceil(), _0);
<span class="macro">assert_eq!</span>(_NEG2_3.floor(), -_1);
<span class="macro">assert_eq!</span>(_NEG2_3.round(), -_1);
<span class="macro">assert_eq!</span>(_NEG2_3.trunc(), _0);
<span class="macro">assert_eq!</span>(_1_2.ceil(), _1);
<span class="macro">assert_eq!</span>(_1_2.floor(), _0);
<span class="macro">assert_eq!</span>(_1_2.round(), _1);
<span class="macro">assert_eq!</span>(_1_2.trunc(), _0);
<span class="macro">assert_eq!</span>(_NEG1_2.ceil(), _0);
<span class="macro">assert_eq!</span>(_NEG1_2.floor(), -_1);
<span class="macro">assert_eq!</span>(_NEG1_2.round(), -_1);
<span class="macro">assert_eq!</span>(_NEG1_2.trunc(), _0);
<span class="macro">assert_eq!</span>(_1.ceil(), _1);
<span class="macro">assert_eq!</span>(_1.floor(), _1);
<span class="macro">assert_eq!</span>(_1.round(), _1);
<span class="macro">assert_eq!</span>(_1.trunc(), _1);
<span class="comment">// Overflow checks
</span><span class="kw">let </span>_neg1 = Ratio::from_integer(-<span class="number">1</span>);
<span class="kw">let </span>_large_rat1 = Ratio::new(i32::MAX, i32::MAX - <span class="number">1</span>);
<span class="kw">let </span>_large_rat2 = Ratio::new(i32::MAX - <span class="number">1</span>, i32::MAX);
<span class="kw">let </span>_large_rat3 = Ratio::new(i32::MIN + <span class="number">2</span>, i32::MIN + <span class="number">1</span>);
<span class="kw">let </span>_large_rat4 = Ratio::new(i32::MIN + <span class="number">1</span>, i32::MIN + <span class="number">2</span>);
<span class="kw">let </span>_large_rat5 = Ratio::new(i32::MIN + <span class="number">2</span>, i32::MAX);
<span class="kw">let </span>_large_rat6 = Ratio::new(i32::MAX, i32::MIN + <span class="number">2</span>);
<span class="kw">let </span>_large_rat7 = Ratio::new(<span class="number">1</span>, i32::MIN + <span class="number">1</span>);
<span class="kw">let </span>_large_rat8 = Ratio::new(<span class="number">1</span>, i32::MAX);
<span class="macro">assert_eq!</span>(_large_rat1.round(), One::one());
<span class="macro">assert_eq!</span>(_large_rat2.round(), One::one());
<span class="macro">assert_eq!</span>(_large_rat3.round(), One::one());
<span class="macro">assert_eq!</span>(_large_rat4.round(), One::one());
<span class="macro">assert_eq!</span>(_large_rat5.round(), _neg1);
<span class="macro">assert_eq!</span>(_large_rat6.round(), _neg1);
<span class="macro">assert_eq!</span>(_large_rat7.round(), Zero::zero());
<span class="macro">assert_eq!</span>(_large_rat8.round(), Zero::zero());
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_fract() {
<span class="macro">assert_eq!</span>(_1.fract(), _0);
<span class="macro">assert_eq!</span>(_NEG1_2.fract(), _NEG1_2);
<span class="macro">assert_eq!</span>(_1_2.fract(), _1_2);
<span class="macro">assert_eq!</span>(_3_2.fract(), _1_2);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_recip() {
<span class="macro">assert_eq!</span>(_1 * _1.recip(), _1);
<span class="macro">assert_eq!</span>(_2 * _2.recip(), _1);
<span class="macro">assert_eq!</span>(_1_2 * _1_2.recip(), _1);
<span class="macro">assert_eq!</span>(_3_2 * _3_2.recip(), _1);
<span class="macro">assert_eq!</span>(_NEG1_2 * _NEG1_2.recip(), _1);
<span class="macro">assert_eq!</span>(_3_2.recip(), _2_3);
<span class="macro">assert_eq!</span>(_NEG1_2.recip(), _NEG2);
<span class="macro">assert_eq!</span>(_NEG1_2.recip().denom(), <span class="kw-2">&</span><span class="number">1</span>);
}
<span class="attr">#[test]
#[should_panic(expected = <span class="string">"division by zero"</span>)]
</span><span class="kw">fn </span>test_recip_fail() {
<span class="kw">let </span>_a = Ratio::new(<span class="number">0</span>, <span class="number">1</span>).recip();
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_pow() {
<span class="kw">fn </span>test(r: Rational64, e: i32, expected: Rational64) {
<span class="macro">assert_eq!</span>(r.pow(e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(r, e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(r, <span class="kw-2">&</span>e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(<span class="kw-2">&</span>r, e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(<span class="kw-2">&</span>r, <span class="kw-2">&</span>e), expected);
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span>test_big(r, e, expected);
}
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">fn </span>test_big(r: Rational64, e: i32, expected: Rational64) {
<span class="kw">let </span>r = BigRational::new_raw(r.numer.into(), r.denom.into());
<span class="kw">let </span>expected = BigRational::new_raw(expected.numer.into(), expected.denom.into());
<span class="macro">assert_eq!</span>((<span class="kw-2">&</span>r).pow(e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(r.clone(), e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(r.clone(), <span class="kw-2">&</span>e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(<span class="kw-2">&</span>r, e), expected);
<span class="macro">assert_eq!</span>(Pow::pow(<span class="kw-2">&</span>r, <span class="kw-2">&</span>e), expected);
}
test(_1_2, <span class="number">2</span>, Ratio::new(<span class="number">1</span>, <span class="number">4</span>));
test(_1_2, -<span class="number">2</span>, Ratio::new(<span class="number">4</span>, <span class="number">1</span>));
test(_1, <span class="number">1</span>, _1);
test(_1, i32::MAX, _1);
test(_1, i32::MIN, _1);
test(_NEG1_2, <span class="number">2</span>, _1_2.pow(<span class="number">2i32</span>));
test(_NEG1_2, <span class="number">3</span>, -_1_2.pow(<span class="number">3i32</span>));
test(_3_2, <span class="number">0</span>, _1);
test(_3_2, -<span class="number">1</span>, _3_2.recip());
test(_3_2, <span class="number">3</span>, Ratio::new(<span class="number">27</span>, <span class="number">8</span>));
}
<span class="attr">#[test]
#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">fn </span>test_to_from_str() {
<span class="kw">use </span>std::string::{String, ToString};
<span class="kw">fn </span>test(r: Rational64, s: String) {
<span class="macro">assert_eq!</span>(FromStr::from_str(<span class="kw-2">&</span>s), <span class="prelude-val">Ok</span>(r));
<span class="macro">assert_eq!</span>(r.to_string(), s);
}
test(_1, <span class="string">"1"</span>.to_string());
test(_0, <span class="string">"0"</span>.to_string());
test(_1_2, <span class="string">"1/2"</span>.to_string());
test(_3_2, <span class="string">"3/2"</span>.to_string());
test(_2, <span class="string">"2"</span>.to_string());
test(_NEG1_2, <span class="string">"-1/2"</span>.to_string());
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_from_str_fail() {
<span class="kw">fn </span>test(s: <span class="kw-2">&</span>str) {
<span class="kw">let </span>rational: <span class="prelude-ty">Result</span><Rational64, <span class="kw">_</span>> = FromStr::from_str(s);
<span class="macro">assert!</span>(rational.is_err());
}
<span class="kw">let </span>xs = [<span class="string">"0 /1"</span>, <span class="string">"abc"</span>, <span class="string">""</span>, <span class="string">"1/"</span>, <span class="string">"--1/2"</span>, <span class="string">"3/2/1"</span>, <span class="string">"1/0"</span>];
<span class="kw">for </span><span class="kw-2">&</span>s <span class="kw">in </span>xs.iter() {
test(s);
}
}
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
#[test]
</span><span class="kw">fn </span>test_from_float() {
<span class="kw">use </span>num_traits::float::FloatCore;
<span class="kw">fn </span>test<T: FloatCore>(given: T, (numer, denom): (<span class="kw-2">&</span>str, <span class="kw-2">&</span>str)) {
<span class="kw">let </span>ratio: BigRational = Ratio::from_float(given).unwrap();
<span class="macro">assert_eq!</span>(
ratio,
Ratio::new(
FromStr::from_str(numer).unwrap(),
FromStr::from_str(denom).unwrap()
)
);
}
<span class="comment">// f32
</span>test(core::f32::consts::PI, (<span class="string">"13176795"</span>, <span class="string">"4194304"</span>));
test(<span class="number">2f32</span>.powf(<span class="number">100.</span>), (<span class="string">"1267650600228229401496703205376"</span>, <span class="string">"1"</span>));
test(
-(<span class="number">2f32</span>.powf(<span class="number">100.</span>)),
(<span class="string">"-1267650600228229401496703205376"</span>, <span class="string">"1"</span>),
);
test(
<span class="number">1.0 </span>/ <span class="number">2f32</span>.powf(<span class="number">100.</span>),
(<span class="string">"1"</span>, <span class="string">"1267650600228229401496703205376"</span>),
);
test(<span class="number">684729.48391f32</span>, (<span class="string">"1369459"</span>, <span class="string">"2"</span>));
test(-<span class="number">8573.5918555f32</span>, (<span class="string">"-4389679"</span>, <span class="string">"512"</span>));
<span class="comment">// f64
</span>test(
core::f64::consts::PI,
(<span class="string">"884279719003555"</span>, <span class="string">"281474976710656"</span>),
);
test(<span class="number">2f64</span>.powf(<span class="number">100.</span>), (<span class="string">"1267650600228229401496703205376"</span>, <span class="string">"1"</span>));
test(
-(<span class="number">2f64</span>.powf(<span class="number">100.</span>)),
(<span class="string">"-1267650600228229401496703205376"</span>, <span class="string">"1"</span>),
);
test(<span class="number">684729.48391f64</span>, (<span class="string">"367611342500051"</span>, <span class="string">"536870912"</span>));
test(-<span class="number">8573.5918555f64</span>, (<span class="string">"-4713381968463931"</span>, <span class="string">"549755813888"</span>));
test(
<span class="number">1.0 </span>/ <span class="number">2f64</span>.powf(<span class="number">100.</span>),
(<span class="string">"1"</span>, <span class="string">"1267650600228229401496703205376"</span>),
);
}
<span class="attr">#[cfg(feature = <span class="string">"num-bigint"</span>)]
#[test]
</span><span class="kw">fn </span>test_from_float_fail() {
<span class="kw">use </span>core::{f32, f64};
<span class="macro">assert_eq!</span>(Ratio::from_float(f32::NAN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::from_float(f32::INFINITY), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::from_float(f32::NEG_INFINITY), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::from_float(f64::NAN), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::from_float(f64::INFINITY), <span class="prelude-val">None</span>);
<span class="macro">assert_eq!</span>(Ratio::from_float(f64::NEG_INFINITY), <span class="prelude-val">None</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_signed() {
<span class="macro">assert_eq!</span>(_NEG1_2.abs(), _1_2);
<span class="macro">assert_eq!</span>(_3_2.abs_sub(<span class="kw-2">&</span>_1_2), _1);
<span class="macro">assert_eq!</span>(_1_2.abs_sub(<span class="kw-2">&</span>_3_2), Zero::zero());
<span class="macro">assert_eq!</span>(_1_2.signum(), One::one());
<span class="macro">assert_eq!</span>(_NEG1_2.signum(), -<Ratio<i64>>::one());
<span class="macro">assert_eq!</span>(_0.signum(), Zero::zero());
<span class="macro">assert!</span>(_NEG1_2.is_negative());
<span class="macro">assert!</span>(_1_NEG2.is_negative());
<span class="macro">assert!</span>(!_NEG1_2.is_positive());
<span class="macro">assert!</span>(!_1_NEG2.is_positive());
<span class="macro">assert!</span>(_1_2.is_positive());
<span class="macro">assert!</span>(_NEG1_NEG2.is_positive());
<span class="macro">assert!</span>(!_1_2.is_negative());
<span class="macro">assert!</span>(!_NEG1_NEG2.is_negative());
<span class="macro">assert!</span>(!_0.is_positive());
<span class="macro">assert!</span>(!_0.is_negative());
}
<span class="attr">#[test]
#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">fn </span>test_hash() {
<span class="macro">assert!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>_0) != <span class="kw">crate</span>::hash(<span class="kw-2">&</span>_1));
<span class="macro">assert!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>_0) != <span class="kw">crate</span>::hash(<span class="kw-2">&</span>_3_2));
<span class="comment">// a == b -> hash(a) == hash(b)
</span><span class="kw">let </span>a = Rational64::new_raw(<span class="number">4</span>, <span class="number">2</span>);
<span class="kw">let </span>b = Rational64::new_raw(<span class="number">6</span>, <span class="number">3</span>);
<span class="macro">assert_eq!</span>(a, b);
<span class="macro">assert_eq!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>a), <span class="kw">crate</span>::hash(<span class="kw-2">&</span>b));
<span class="kw">let </span>a = Rational64::new_raw(<span class="number">123456789</span>, <span class="number">1000</span>);
<span class="kw">let </span>b = Rational64::new_raw(<span class="number">123456789 </span>* <span class="number">5</span>, <span class="number">5000</span>);
<span class="macro">assert_eq!</span>(a, b);
<span class="macro">assert_eq!</span>(<span class="kw">crate</span>::hash(<span class="kw-2">&</span>a), <span class="kw">crate</span>::hash(<span class="kw-2">&</span>b));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_into_pair() {
<span class="macro">assert_eq!</span>((<span class="number">0</span>, <span class="number">1</span>), _0.into());
<span class="macro">assert_eq!</span>((-<span class="number">2</span>, <span class="number">1</span>), _NEG2.into());
<span class="macro">assert_eq!</span>((<span class="number">1</span>, -<span class="number">2</span>), _1_NEG2.into());
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_from_pair() {
<span class="macro">assert_eq!</span>(_0, Ratio::from((<span class="number">0</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(_1, Ratio::from((<span class="number">1</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(_NEG2, Ratio::from((-<span class="number">2</span>, <span class="number">1</span>)));
<span class="macro">assert_eq!</span>(_1_NEG2, Ratio::from((<span class="number">1</span>, -<span class="number">2</span>)));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>ratio_iter_sum() {
<span class="comment">// generic function to assure the iter method can be called
// for any Iterator with Item = Ratio<impl Integer> or Ratio<&impl Integer>
</span><span class="kw">fn </span>iter_sums<T: Integer + Clone>(slice: <span class="kw-2">&</span>[Ratio<T>]) -> [Ratio<T>; <span class="number">3</span>] {
<span class="kw">let </span><span class="kw-2">mut </span>manual_sum = Ratio::new(T::zero(), T::one());
<span class="kw">for </span>ratio <span class="kw">in </span>slice {
manual_sum = manual_sum + ratio;
}
[manual_sum, slice.iter().sum(), slice.iter().cloned().sum()]
}
<span class="comment">// collect into array so test works on no_std
</span><span class="kw">let </span><span class="kw-2">mut </span>nums = [Ratio::new(<span class="number">0</span>, <span class="number">1</span>); <span class="number">1000</span>];
<span class="kw">for </span>(i, r) <span class="kw">in </span>(<span class="number">0</span>..<span class="number">1000</span>).map(|n| Ratio::new(n, <span class="number">500</span>)).enumerate() {
nums[i] = r;
}
<span class="kw">let </span>sums = iter_sums(<span class="kw-2">&</span>nums[..]);
<span class="macro">assert_eq!</span>(sums[<span class="number">0</span>], sums[<span class="number">1</span>]);
<span class="macro">assert_eq!</span>(sums[<span class="number">0</span>], sums[<span class="number">2</span>]);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>ratio_iter_product() {
<span class="comment">// generic function to assure the iter method can be called
// for any Iterator with Item = Ratio<impl Integer> or Ratio<&impl Integer>
</span><span class="kw">fn </span>iter_products<T: Integer + Clone>(slice: <span class="kw-2">&</span>[Ratio<T>]) -> [Ratio<T>; <span class="number">3</span>] {
<span class="kw">let </span><span class="kw-2">mut </span>manual_prod = Ratio::new(T::one(), T::one());
<span class="kw">for </span>ratio <span class="kw">in </span>slice {
manual_prod = manual_prod * ratio;
}
[
manual_prod,
slice.iter().product(),
slice.iter().cloned().product(),
]
}
<span class="comment">// collect into array so test works on no_std
</span><span class="kw">let </span><span class="kw-2">mut </span>nums = [Ratio::new(<span class="number">0</span>, <span class="number">1</span>); <span class="number">1000</span>];
<span class="kw">for </span>(i, r) <span class="kw">in </span>(<span class="number">0</span>..<span class="number">1000</span>).map(|n| Ratio::new(n, <span class="number">500</span>)).enumerate() {
nums[i] = r;
}
<span class="kw">let </span>products = iter_products(<span class="kw-2">&</span>nums[..]);
<span class="macro">assert_eq!</span>(products[<span class="number">0</span>], products[<span class="number">1</span>]);
<span class="macro">assert_eq!</span>(products[<span class="number">0</span>], products[<span class="number">2</span>]);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_num_zero() {
<span class="kw">let </span>zero = Rational64::zero();
<span class="macro">assert!</span>(zero.is_zero());
<span class="kw">let </span><span class="kw-2">mut </span>r = Rational64::new(<span class="number">123</span>, <span class="number">456</span>);
<span class="macro">assert!</span>(!r.is_zero());
<span class="macro">assert_eq!</span>(r + zero, r);
r.set_zero();
<span class="macro">assert!</span>(r.is_zero());
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_num_one() {
<span class="kw">let </span>one = Rational64::one();
<span class="macro">assert!</span>(one.is_one());
<span class="kw">let </span><span class="kw-2">mut </span>r = Rational64::new(<span class="number">123</span>, <span class="number">456</span>);
<span class="macro">assert!</span>(!r.is_one());
<span class="macro">assert_eq!</span>(r * one, r);
r.set_one();
<span class="macro">assert!</span>(r.is_one());
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_const() {
<span class="kw">const </span>N: Ratio<i32> = Ratio::new_raw(<span class="number">123</span>, <span class="number">456</span>);
<span class="kw">const </span>N_NUMER: <span class="kw-2">&</span>i32 = N.numer();
<span class="kw">const </span>N_DENOM: <span class="kw-2">&</span>i32 = N.denom();
<span class="macro">assert_eq!</span>(N_NUMER, <span class="kw-2">&</span><span class="number">123</span>);
<span class="macro">assert_eq!</span>(N_DENOM, <span class="kw-2">&</span><span class="number">456</span>);
<span class="kw">let </span>r = N.reduced();
<span class="macro">assert_eq!</span>(r.numer(), <span class="kw-2">&</span>(<span class="number">123 </span>/ <span class="number">3</span>));
<span class="macro">assert_eq!</span>(r.denom(), <span class="kw-2">&</span>(<span class="number">456 </span>/ <span class="number">3</span>));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_ratio_to_i64() {
<span class="macro">assert_eq!</span>(<span class="number">5</span>, Rational64::new(<span class="number">70</span>, <span class="number">14</span>).to_u64().unwrap());
<span class="macro">assert_eq!</span>(-<span class="number">3</span>, Rational64::new(-<span class="number">31</span>, <span class="number">8</span>).to_i64().unwrap());
<span class="macro">assert_eq!</span>(<span class="prelude-val">None</span>, Rational64::new(-<span class="number">31</span>, <span class="number">8</span>).to_u64());
}
<span class="attr">#[test]
#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">fn </span>test_ratio_to_i128() {
<span class="macro">assert_eq!</span>(
<span class="number">1i128 </span><< <span class="number">70</span>,
Ratio::<i128>::new(<span class="number">1i128 </span><< <span class="number">77</span>, <span class="number">1i128 </span><< <span class="number">7</span>)
.to_i128()
.unwrap()
);
}
<span class="attr">#[test]
#[cfg(feature = <span class="string">"num-bigint"</span>)]
</span><span class="kw">fn </span>test_big_ratio_to_f64() {
<span class="macro">assert_eq!</span>(
BigRational::new(
<span class="string">"1234567890987654321234567890987654321234567890"
</span>.parse()
.unwrap(),
<span class="string">"3"</span>.parse().unwrap()
)
.to_f64(),
<span class="prelude-val">Some</span>(<span class="number">411522630329218100000000000000000000000000000f64</span>)
);
<span class="macro">assert_eq!</span>(Ratio::from_float(<span class="number">5e-324</span>).unwrap().to_f64(), <span class="prelude-val">Some</span>(<span class="number">5e-324</span>));
<span class="macro">assert_eq!</span>(
<span class="comment">// subnormal
</span>BigRational::new(BigInt::one(), BigInt::one() << <span class="number">1050</span>).to_f64(),
<span class="prelude-val">Some</span>(<span class="number">2.0f64</span>.powi(-<span class="number">50</span>).powi(<span class="number">21</span>))
);
<span class="macro">assert_eq!</span>(
<span class="comment">// definite underflow
</span>BigRational::new(BigInt::one(), BigInt::one() << <span class="number">1100</span>).to_f64(),
<span class="prelude-val">Some</span>(<span class="number">0.0</span>)
);
<span class="macro">assert_eq!</span>(
BigRational::from(BigInt::one() << <span class="number">1050</span>).to_f64(),
<span class="prelude-val">Some</span>(core::f64::INFINITY)
);
<span class="macro">assert_eq!</span>(
BigRational::from((-BigInt::one()) << <span class="number">1050</span>).to_f64(),
<span class="prelude-val">Some</span>(core::f64::NEG_INFINITY)
);
<span class="macro">assert_eq!</span>(
BigRational::new(
<span class="string">"1234567890987654321234567890"</span>.parse().unwrap(),
<span class="string">"987654321234567890987654321"</span>.parse().unwrap()
)
.to_f64(),
<span class="prelude-val">Some</span>(<span class="number">1.2499999893125f64</span>)
);
<span class="macro">assert_eq!</span>(
BigRational::new_raw(BigInt::one(), BigInt::zero()).to_f64(),
<span class="prelude-val">Some</span>(core::f64::INFINITY)
);
<span class="macro">assert_eq!</span>(
BigRational::new_raw(-BigInt::one(), BigInt::zero()).to_f64(),
<span class="prelude-val">Some</span>(core::f64::NEG_INFINITY)
);
<span class="macro">assert_eq!</span>(
BigRational::new_raw(BigInt::zero(), BigInt::zero()).to_f64(),
<span class="prelude-val">None
</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_ratio_to_f64() {
<span class="macro">assert_eq!</span>(Ratio::<u8>::new(<span class="number">1</span>, <span class="number">2</span>).to_f64(), <span class="prelude-val">Some</span>(<span class="number">0.5f64</span>));
<span class="macro">assert_eq!</span>(Rational64::new(<span class="number">1</span>, <span class="number">2</span>).to_f64(), <span class="prelude-val">Some</span>(<span class="number">0.5f64</span>));
<span class="macro">assert_eq!</span>(Rational64::new(<span class="number">1</span>, -<span class="number">2</span>).to_f64(), <span class="prelude-val">Some</span>(-<span class="number">0.5f64</span>));
<span class="macro">assert_eq!</span>(Rational64::new(<span class="number">0</span>, <span class="number">2</span>).to_f64(), <span class="prelude-val">Some</span>(<span class="number">0.0f64</span>));
<span class="macro">assert_eq!</span>(Rational64::new(<span class="number">0</span>, -<span class="number">2</span>).to_f64(), <span class="prelude-val">Some</span>(-<span class="number">0.0f64</span>));
<span class="macro">assert_eq!</span>(Rational64::new((<span class="number">1 </span><< <span class="number">57</span>) + <span class="number">1</span>, <span class="number">1 </span><< <span class="number">54</span>).to_f64(), <span class="prelude-val">Some</span>(<span class="number">8f64</span>));
<span class="macro">assert_eq!</span>(
Rational64::new((<span class="number">1 </span><< <span class="number">52</span>) + <span class="number">1</span>, <span class="number">1 </span><< <span class="number">52</span>).to_f64(),
<span class="prelude-val">Some</span>(<span class="number">1.0000000000000002f64</span>),
);
<span class="macro">assert_eq!</span>(
Rational64::new((<span class="number">1 </span><< <span class="number">60</span>) + (<span class="number">1 </span><< <span class="number">8</span>), <span class="number">1 </span><< <span class="number">60</span>).to_f64(),
<span class="prelude-val">Some</span>(<span class="number">1.0000000000000002f64</span>),
);
<span class="macro">assert_eq!</span>(
Ratio::<i32>::new_raw(<span class="number">1</span>, <span class="number">0</span>).to_f64(),
<span class="prelude-val">Some</span>(core::f64::INFINITY)
);
<span class="macro">assert_eq!</span>(
Ratio::<i32>::new_raw(-<span class="number">1</span>, <span class="number">0</span>).to_f64(),
<span class="prelude-val">Some</span>(core::f64::NEG_INFINITY)
);
<span class="macro">assert_eq!</span>(Ratio::<i32>::new_raw(<span class="number">0</span>, <span class="number">0</span>).to_f64(), <span class="prelude-val">None</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_ldexp() {
<span class="kw">use </span>core::f64::{INFINITY, MAX_EXP, MIN_EXP, NAN, NEG_INFINITY};
<span class="macro">assert_eq!</span>(ldexp(<span class="number">1.0</span>, <span class="number">0</span>), <span class="number">1.0</span>);
<span class="macro">assert_eq!</span>(ldexp(<span class="number">1.0</span>, <span class="number">1</span>), <span class="number">2.0</span>);
<span class="macro">assert_eq!</span>(ldexp(<span class="number">0.0</span>, <span class="number">1</span>), <span class="number">0.0</span>);
<span class="macro">assert_eq!</span>(ldexp(-<span class="number">0.0</span>, <span class="number">1</span>), -<span class="number">0.0</span>);
<span class="comment">// Cases where ldexp is equivalent to multiplying by 2^exp because there's no over- or
// underflow.
</span><span class="macro">assert_eq!</span>(ldexp(<span class="number">3.5</span>, <span class="number">5</span>), <span class="number">3.5 </span>* <span class="number">2f64</span>.powi(<span class="number">5</span>));
<span class="macro">assert_eq!</span>(ldexp(<span class="number">1.0</span>, MAX_EXP - <span class="number">1</span>), <span class="number">2f64</span>.powi(MAX_EXP - <span class="number">1</span>));
<span class="macro">assert_eq!</span>(ldexp(<span class="number">2.77</span>, MIN_EXP + <span class="number">3</span>), <span class="number">2.77 </span>* <span class="number">2f64</span>.powi(MIN_EXP + <span class="number">3</span>));
<span class="comment">// Case where initial value is subnormal
</span><span class="macro">assert_eq!</span>(ldexp(<span class="number">5e-324</span>, <span class="number">4</span>), <span class="number">5e-324 </span>* <span class="number">2f64</span>.powi(<span class="number">4</span>));
<span class="macro">assert_eq!</span>(ldexp(<span class="number">5e-324</span>, <span class="number">200</span>), <span class="number">5e-324 </span>* <span class="number">2f64</span>.powi(<span class="number">200</span>));
<span class="comment">// Near underflow (2^exp is too small to represent, but not x*2^exp)
</span><span class="macro">assert_eq!</span>(ldexp(<span class="number">4.0</span>, MIN_EXP - <span class="number">3</span>), <span class="number">2f64</span>.powi(MIN_EXP - <span class="number">1</span>));
<span class="comment">// Near overflow
</span><span class="macro">assert_eq!</span>(ldexp(<span class="number">0.125</span>, MAX_EXP + <span class="number">3</span>), <span class="number">2f64</span>.powi(MAX_EXP));
<span class="comment">// Overflow and underflow cases
</span><span class="macro">assert_eq!</span>(ldexp(<span class="number">1.0</span>, MIN_EXP - <span class="number">54</span>), <span class="number">0.0</span>);
<span class="macro">assert_eq!</span>(ldexp(-<span class="number">1.0</span>, MIN_EXP - <span class="number">54</span>), -<span class="number">0.0</span>);
<span class="macro">assert_eq!</span>(ldexp(<span class="number">1.0</span>, MAX_EXP), INFINITY);
<span class="macro">assert_eq!</span>(ldexp(-<span class="number">1.0</span>, MAX_EXP), NEG_INFINITY);
<span class="comment">// Special values
</span><span class="macro">assert_eq!</span>(ldexp(INFINITY, <span class="number">1</span>), INFINITY);
<span class="macro">assert_eq!</span>(ldexp(NEG_INFINITY, <span class="number">1</span>), NEG_INFINITY);
<span class="macro">assert!</span>(ldexp(NAN, <span class="number">1</span>).is_nan());
}
}
</code></pre></div>
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