<!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-integer-0.1.45/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_integer/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>
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</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">//! Integer trait and functions.
//!
//! ## Compatibility
//!
//! The `num-integer` crate is tested for rustc 1.8 and greater.
</span><span class="attr">#![doc(html_root_url = <span class="string">"https://docs.rs/num-integer/0.1"</span>)]
#![no_std]
#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="kw">extern crate </span>std;
<span class="kw">extern crate </span>num_traits <span class="kw">as </span>traits;
<span class="kw">use </span>core::mem;
<span class="kw">use </span>core::ops::Add;
<span class="kw">use </span>traits::{Num, Signed, Zero};
<span class="kw">mod </span>roots;
<span class="kw">pub use </span>roots::Roots;
<span class="kw">pub use </span>roots::{cbrt, nth_root, sqrt};
<span class="kw">mod </span>average;
<span class="kw">pub use </span>average::Average;
<span class="kw">pub use </span>average::{average_ceil, average_floor};
<span class="kw">pub trait </span>Integer: Sized + Num + PartialOrd + Ord + Eq {
<span class="doccomment">/// Floored integer division.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert!(( 8).div_floor(& 3) == 2);
/// assert!(( 8).div_floor(&-3) == -3);
/// assert!((-8).div_floor(& 3) == -3);
/// assert!((-8).div_floor(&-3) == 2);
///
/// assert!(( 1).div_floor(& 2) == 0);
/// assert!(( 1).div_floor(&-2) == -1);
/// assert!((-1).div_floor(& 2) == -1);
/// assert!((-1).div_floor(&-2) == 0);
/// ~~~
</span><span class="kw">fn </span>div_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Floored integer modulo, satisfying:
///
/// ~~~
/// # use num_integer::Integer;
/// # let n = 1; let d = 1;
/// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)
/// ~~~
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert!(( 8).mod_floor(& 3) == 2);
/// assert!(( 8).mod_floor(&-3) == -1);
/// assert!((-8).mod_floor(& 3) == 1);
/// assert!((-8).mod_floor(&-3) == -2);
///
/// assert!(( 1).mod_floor(& 2) == 1);
/// assert!(( 1).mod_floor(&-2) == -1);
/// assert!((-1).mod_floor(& 2) == 1);
/// assert!((-1).mod_floor(&-2) == -1);
/// ~~~
</span><span class="kw">fn </span>mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Ceiled integer division.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(( 8).div_ceil( &3), 3);
/// assert_eq!(( 8).div_ceil(&-3), -2);
/// assert_eq!((-8).div_ceil( &3), -2);
/// assert_eq!((-8).div_ceil(&-3), 3);
///
/// assert_eq!(( 1).div_ceil( &2), 1);
/// assert_eq!(( 1).div_ceil(&-2), 0);
/// assert_eq!((-1).div_ceil( &2), 0);
/// assert_eq!((-1).div_ceil(&-2), 1);
/// ~~~
</span><span class="kw">fn </span>div_ceil(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>(q, r) = <span class="self">self</span>.div_mod_floor(other);
<span class="kw">if </span>r.is_zero() {
q
} <span class="kw">else </span>{
q + <span class="self">Self</span>::one()
}
}
<span class="doccomment">/// Greatest Common Divisor (GCD).
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(6.gcd(&8), 2);
/// assert_eq!(7.gcd(&3), 1);
/// ~~~
</span><span class="kw">fn </span>gcd(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Lowest Common Multiple (LCM).
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(7.lcm(&3), 21);
/// assert_eq!(2.lcm(&4), 4);
/// assert_eq!(0.lcm(&0), 0);
/// ~~~
</span><span class="kw">fn </span>lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Greatest Common Divisor (GCD) and
/// Lowest Common Multiple (LCM) together.
///
/// Potentially more efficient than calling `gcd` and `lcm`
/// individually for identical inputs.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(10.gcd_lcm(&4), (2, 20));
/// assert_eq!(8.gcd_lcm(&9), (1, 72));
/// ~~~
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="self">self</span>.gcd(other), <span class="self">self</span>.lcm(other))
}
<span class="doccomment">/// Greatest common divisor and Bézout coefficients.
///
/// # Examples
///
/// ~~~
/// # extern crate num_integer;
/// # extern crate num_traits;
/// # fn main() {
/// # use num_integer::{ExtendedGcd, Integer};
/// # use num_traits::NumAssign;
/// fn check<A: Copy + Integer + NumAssign>(a: A, b: A) -> bool {
/// let ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(&b);
/// gcd == x * a + y * b
/// }
/// assert!(check(10isize, 4isize));
/// assert!(check(8isize, 9isize));
/// # }
/// ~~~
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>extended_gcd(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> ExtendedGcd<<span class="self">Self</span>>
<span class="kw">where
</span><span class="self">Self</span>: Clone,
{
<span class="kw">let </span><span class="kw-2">mut </span>s = (<span class="self">Self</span>::zero(), <span class="self">Self</span>::one());
<span class="kw">let </span><span class="kw-2">mut </span>t = (<span class="self">Self</span>::one(), <span class="self">Self</span>::zero());
<span class="kw">let </span><span class="kw-2">mut </span>r = (other.clone(), <span class="self">self</span>.clone());
<span class="kw">while </span>!r.<span class="number">0</span>.is_zero() {
<span class="kw">let </span>q = r.<span class="number">1</span>.clone() / r.<span class="number">0</span>.clone();
<span class="kw">let </span>f = |<span class="kw-2">mut </span>r: (<span class="self">Self</span>, <span class="self">Self</span>)| {
mem::swap(<span class="kw-2">&mut </span>r.<span class="number">0</span>, <span class="kw-2">&mut </span>r.<span class="number">1</span>);
r.<span class="number">0 </span>= r.<span class="number">0 </span>- q.clone() * r.<span class="number">1</span>.clone();
r
};
r = f(r);
s = f(s);
t = f(t);
}
<span class="kw">if </span>r.<span class="number">1 </span>>= <span class="self">Self</span>::zero() {
ExtendedGcd {
gcd: r.<span class="number">1</span>,
x: s.<span class="number">1</span>,
y: t.<span class="number">1</span>,
}
} <span class="kw">else </span>{
ExtendedGcd {
gcd: <span class="self">Self</span>::zero() - r.<span class="number">1</span>,
x: <span class="self">Self</span>::zero() - s.<span class="number">1</span>,
y: <span class="self">Self</span>::zero() - t.<span class="number">1</span>,
}
}
}
<span class="doccomment">/// Greatest common divisor, least common multiple, and Bézout coefficients.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>extended_gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (ExtendedGcd<<span class="self">Self</span>>, <span class="self">Self</span>)
<span class="kw">where
</span><span class="self">Self</span>: Clone + Signed,
{
(<span class="self">self</span>.extended_gcd(other), <span class="self">self</span>.lcm(other))
}
<span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
</span><span class="kw">fn </span>divides(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> bool;
<span class="doccomment">/// Returns `true` if `self` is a multiple of `other`.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(9.is_multiple_of(&3), true);
/// assert_eq!(3.is_multiple_of(&9), false);
/// ~~~
</span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> bool;
<span class="doccomment">/// Returns `true` if the number is even.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(3.is_even(), false);
/// assert_eq!(4.is_even(), true);
/// ~~~
</span><span class="kw">fn </span>is_even(<span class="kw-2">&</span><span class="self">self</span>) -> bool;
<span class="doccomment">/// Returns `true` if the number is odd.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(3.is_odd(), true);
/// assert_eq!(4.is_odd(), false);
/// ~~~
</span><span class="kw">fn </span>is_odd(<span class="kw-2">&</span><span class="self">self</span>) -> bool;
<span class="doccomment">/// Simultaneous truncated integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(( 8).div_rem( &3), ( 2, 2));
/// assert_eq!(( 8).div_rem(&-3), (-2, 2));
/// assert_eq!((-8).div_rem( &3), (-2, -2));
/// assert_eq!((-8).div_rem(&-3), ( 2, -2));
///
/// assert_eq!(( 1).div_rem( &2), ( 0, 1));
/// assert_eq!(( 1).div_rem(&-2), ( 0, 1));
/// assert_eq!((-1).div_rem( &2), ( 0, -1));
/// assert_eq!((-1).div_rem(&-2), ( 0, -1));
/// ~~~
</span><span class="kw">fn </span>div_rem(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>);
<span class="doccomment">/// Simultaneous floored integer division and modulus.
/// Returns `(quotient, remainder)`.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(( 8).div_mod_floor( &3), ( 2, 2));
/// assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));
/// assert_eq!((-8).div_mod_floor( &3), (-3, 1));
/// assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));
///
/// assert_eq!(( 1).div_mod_floor( &2), ( 0, 1));
/// assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));
/// assert_eq!((-1).div_mod_floor( &2), (-1, 1));
/// assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));
/// ~~~
</span><span class="kw">fn </span>div_mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="self">self</span>.div_floor(other), <span class="self">self</span>.mod_floor(other))
}
<span class="doccomment">/// Rounds up to nearest multiple of argument.
///
/// # Notes
///
/// For signed types, `a.next_multiple_of(b) = a.prev_multiple_of(b.neg())`.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(( 16).next_multiple_of(& 8), 16);
/// assert_eq!(( 23).next_multiple_of(& 8), 24);
/// assert_eq!(( 16).next_multiple_of(&-8), 16);
/// assert_eq!(( 23).next_multiple_of(&-8), 16);
/// assert_eq!((-16).next_multiple_of(& 8), -16);
/// assert_eq!((-23).next_multiple_of(& 8), -16);
/// assert_eq!((-16).next_multiple_of(&-8), -16);
/// assert_eq!((-23).next_multiple_of(&-8), -24);
/// ~~~
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>next_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self
</span><span class="kw">where
</span><span class="self">Self</span>: Clone,
{
<span class="kw">let </span>m = <span class="self">self</span>.mod_floor(other);
<span class="self">self</span>.clone()
+ <span class="kw">if </span>m.is_zero() {
<span class="self">Self</span>::zero()
} <span class="kw">else </span>{
other.clone() - m
}
}
<span class="doccomment">/// Rounds down to nearest multiple of argument.
///
/// # Notes
///
/// For signed types, `a.prev_multiple_of(b) = a.next_multiple_of(b.neg())`.
///
/// # Examples
///
/// ~~~
/// # use num_integer::Integer;
/// assert_eq!(( 16).prev_multiple_of(& 8), 16);
/// assert_eq!(( 23).prev_multiple_of(& 8), 16);
/// assert_eq!(( 16).prev_multiple_of(&-8), 16);
/// assert_eq!(( 23).prev_multiple_of(&-8), 24);
/// assert_eq!((-16).prev_multiple_of(& 8), -16);
/// assert_eq!((-23).prev_multiple_of(& 8), -24);
/// assert_eq!((-16).prev_multiple_of(&-8), -16);
/// assert_eq!((-23).prev_multiple_of(&-8), -16);
/// ~~~
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>prev_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self
</span><span class="kw">where
</span><span class="self">Self</span>: Clone,
{
<span class="self">self</span>.clone() - <span class="self">self</span>.mod_floor(other)
}
}
<span class="doccomment">/// Greatest common divisor and Bézout coefficients
///
/// ```no_build
/// let e = isize::extended_gcd(a, b);
/// assert_eq!(e.gcd, e.x*a + e.y*b);
/// ```
</span><span class="attr">#[derive(Debug, Clone, Copy, PartialEq, Eq)]
</span><span class="kw">pub struct </span>ExtendedGcd<A> {
<span class="kw">pub </span>gcd: A,
<span class="kw">pub </span>x: A,
<span class="kw">pub </span>y: A,
}
<span class="doccomment">/// Simultaneous integer division and modulus
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>div_rem<T: Integer>(x: T, y: T) -> (T, T) {
x.div_rem(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Floored integer division
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>div_floor<T: Integer>(x: T, y: T) -> T {
x.div_floor(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Floored integer modulus
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>mod_floor<T: Integer>(x: T, y: T) -> T {
x.mod_floor(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Simultaneous floored integer division and modulus
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) {
x.div_mod_floor(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Ceiled integer division
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>div_ceil<T: Integer>(x: T, y: T) -> T {
x.div_ceil(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The
/// result is always non-negative.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub fn </span>gcd<T: Integer>(x: T, y: T) -> T {
x.gcd(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub fn </span>lcm<T: Integer>(x: T, y: T) -> T {
x.lcm(<span class="kw-2">&</span>y)
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
/// Lowest Common Multiple (LCM) of the number and `other`.
</span><span class="attr">#[inline(always)]
</span><span class="kw">pub fn </span>gcd_lcm<T: Integer>(x: T, y: T) -> (T, T) {
x.gcd_lcm(<span class="kw-2">&</span>y)
}
<span class="macro">macro_rules! </span>impl_integer_for_isize {
(<span class="macro-nonterminal">$T</span>:ty, <span class="macro-nonterminal">$test_mod</span>:ident) => {
<span class="kw">impl </span>Integer <span class="kw">for </span><span class="macro-nonterminal">$T </span>{
<span class="doccomment">/// Floored integer division
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>div_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
</span><span class="kw">let </span>(d, r) = <span class="self">self</span>.div_rem(other);
<span class="kw">if </span>(r > <span class="number">0 </span>&& <span class="kw-2">*</span>other < <span class="number">0</span>) || (r < <span class="number">0 </span>&& <span class="kw-2">*</span>other > <span class="number">0</span>) {
d - <span class="number">1
</span>} <span class="kw">else </span>{
d
}
}
<span class="doccomment">/// Floored integer modulo
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
</span><span class="kw">let </span>r = <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other;
<span class="kw">if </span>(r > <span class="number">0 </span>&& <span class="kw-2">*</span>other < <span class="number">0</span>) || (r < <span class="number">0 </span>&& <span class="kw-2">*</span>other > <span class="number">0</span>) {
r + <span class="kw-2">*</span>other
} <span class="kw">else </span>{
r
}
}
<span class="doccomment">/// Calculates `div_floor` and `mod_floor` simultaneously
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>div_mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
<span class="comment">// Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_,
// December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf)
</span><span class="kw">let </span>(d, r) = <span class="self">self</span>.div_rem(other);
<span class="kw">if </span>(r > <span class="number">0 </span>&& <span class="kw-2">*</span>other < <span class="number">0</span>) || (r < <span class="number">0 </span>&& <span class="kw-2">*</span>other > <span class="number">0</span>) {
(d - <span class="number">1</span>, r + <span class="kw-2">*</span>other)
} <span class="kw">else </span>{
(d, r)
}
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>div_ceil(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>(d, r) = <span class="self">self</span>.div_rem(other);
<span class="kw">if </span>(r > <span class="number">0 </span>&& <span class="kw-2">*</span>other > <span class="number">0</span>) || (r < <span class="number">0 </span>&& <span class="kw-2">*</span>other < <span class="number">0</span>) {
d + <span class="number">1
</span>} <span class="kw">else </span>{
d
}
}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and
/// `other`. The result is always non-negative.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>gcd(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="comment">// Use Stein's algorithm
</span><span class="kw">let </span><span class="kw-2">mut </span>m = <span class="kw-2">*</span><span class="self">self</span>;
<span class="kw">let </span><span class="kw-2">mut </span>n = <span class="kw-2">*</span>other;
<span class="kw">if </span>m == <span class="number">0 </span>|| n == <span class="number">0 </span>{
<span class="kw">return </span>(m | n).abs();
}
<span class="comment">// find common factors of 2
</span><span class="kw">let </span>shift = (m | n).trailing_zeros();
<span class="comment">// The algorithm needs positive numbers, but the minimum value
// can't be represented as a positive one.
// It's also a power of two, so the gcd can be
// calculated by bitshifting in that case
// Assuming two's complement, the number created by the shift
// is positive for all numbers except gcd = abs(min value)
// The call to .abs() causes a panic in debug mode
</span><span class="kw">if </span>m == <span class="self">Self</span>::min_value() || n == <span class="self">Self</span>::min_value() {
<span class="kw">return </span>(<span class="number">1 </span><< shift).abs();
}
<span class="comment">// guaranteed to be positive now, rest like unsigned algorithm
</span>m = m.abs();
n = n.abs();
<span class="comment">// divide n and m by 2 until odd
</span>m >>= m.trailing_zeros();
n >>= n.trailing_zeros();
<span class="kw">while </span>m != n {
<span class="kw">if </span>m > n {
m -= n;
m >>= m.trailing_zeros();
} <span class="kw">else </span>{
n -= m;
n >>= n.trailing_zeros();
}
}
m << shift
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>extended_gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (ExtendedGcd<<span class="self">Self</span>>, <span class="self">Self</span>) {
<span class="kw">let </span>egcd = <span class="self">self</span>.extended_gcd(other);
<span class="comment">// should not have to recalculate abs
</span><span class="kw">let </span>lcm = <span class="kw">if </span>egcd.gcd.is_zero() {
<span class="self">Self</span>::zero()
} <span class="kw">else </span>{
(<span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / egcd.gcd)).abs()
};
(egcd, lcm)
}
<span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and
/// `other`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="self">self</span>.gcd_lcm(other).<span class="number">1
</span>}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
/// Lowest Common Multiple (LCM) of the number and `other`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
<span class="kw">if </span><span class="self">self</span>.is_zero() && other.is_zero() {
<span class="kw">return </span>(<span class="self">Self</span>::zero(), <span class="self">Self</span>::zero());
}
<span class="kw">let </span>gcd = <span class="self">self</span>.gcd(other);
<span class="comment">// should not have to recalculate abs
</span><span class="kw">let </span>lcm = (<span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / gcd)).abs();
(gcd, lcm)
}
<span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>divides(<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>.is_multiple_of(other)
}
<span class="doccomment">/// Returns `true` if the number is a multiple of `other`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="kw">if </span>other.is_zero() {
<span class="kw">return </span><span class="self">self</span>.is_zero();
}
<span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other == <span class="number">0
</span>}
<span class="doccomment">/// Returns `true` if the number is divisible by `2`
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_even(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
(<span class="kw-2">*</span><span class="self">self</span>) & <span class="number">1 </span>== <span class="number">0
</span>}
<span class="doccomment">/// Returns `true` if the number is not divisible by `2`
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_odd(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
!<span class="self">self</span>.is_even()
}
<span class="doccomment">/// Simultaneous truncated integer division and modulus.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>div_rem(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other, <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other)
}
<span class="doccomment">/// Rounds up to nearest multiple of argument.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>next_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="comment">// Avoid the overflow of `MIN % -1`
</span><span class="kw">if </span><span class="kw-2">*</span>other == -<span class="number">1 </span>{
<span class="kw">return </span><span class="kw-2">*</span><span class="self">self</span>;
}
<span class="kw">let </span>m = Integer::mod_floor(<span class="self">self</span>, other);
<span class="kw-2">*</span><span class="self">self </span>+ <span class="kw">if </span>m == <span class="number">0 </span>{ <span class="number">0 </span>} <span class="kw">else </span>{ other - m }
}
<span class="doccomment">/// Rounds down to nearest multiple of argument.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>prev_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="comment">// Avoid the overflow of `MIN % -1`
</span><span class="kw">if </span><span class="kw-2">*</span>other == -<span class="number">1 </span>{
<span class="kw">return </span><span class="kw-2">*</span><span class="self">self</span>;
}
<span class="kw-2">*</span><span class="self">self </span>- Integer::mod_floor(<span class="self">self</span>, other)
}
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span><span class="macro-nonterminal">$test_mod </span>{
<span class="kw">use </span>core::mem;
<span class="kw">use </span>Integer;
<span class="doccomment">/// Checks that the division rule holds for:
///
/// - `n`: numerator (dividend)
/// - `d`: denominator (divisor)
/// - `qr`: quotient and remainder
</span><span class="attr">#[cfg(test)]
</span><span class="kw">fn </span>test_division_rule((n, d): (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>), (q, r): (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>)) {
<span class="macro">assert_eq!</span>(d * q + r, n);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_div_rem() {
<span class="kw">fn </span>test_nd_dr(nd: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>), qr: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>)) {
<span class="kw">let </span>(n, d) = nd;
<span class="kw">let </span>separate_div_rem = (n / d, n % d);
<span class="kw">let </span>combined_div_rem = n.div_rem(<span class="kw-2">&</span>d);
<span class="macro">assert_eq!</span>(separate_div_rem, qr);
<span class="macro">assert_eq!</span>(combined_div_rem, qr);
test_division_rule(nd, separate_div_rem);
test_division_rule(nd, combined_div_rem);
}
test_nd_dr((<span class="number">8</span>, <span class="number">3</span>), (<span class="number">2</span>, <span class="number">2</span>));
test_nd_dr((<span class="number">8</span>, -<span class="number">3</span>), (-<span class="number">2</span>, <span class="number">2</span>));
test_nd_dr((-<span class="number">8</span>, <span class="number">3</span>), (-<span class="number">2</span>, -<span class="number">2</span>));
test_nd_dr((-<span class="number">8</span>, -<span class="number">3</span>), (<span class="number">2</span>, -<span class="number">2</span>));
test_nd_dr((<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
test_nd_dr((<span class="number">1</span>, -<span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
test_nd_dr((-<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, -<span class="number">1</span>));
test_nd_dr((-<span class="number">1</span>, -<span class="number">2</span>), (<span class="number">0</span>, -<span class="number">1</span>));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_div_mod_floor() {
<span class="kw">fn </span>test_nd_dm(nd: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>), dm: (<span class="macro-nonterminal">$T</span>, <span class="macro-nonterminal">$T</span>)) {
<span class="kw">let </span>(n, d) = nd;
<span class="kw">let </span>separate_div_mod_floor =
(Integer::div_floor(<span class="kw-2">&</span>n, <span class="kw-2">&</span>d), Integer::mod_floor(<span class="kw-2">&</span>n, <span class="kw-2">&</span>d));
<span class="kw">let </span>combined_div_mod_floor = Integer::div_mod_floor(<span class="kw-2">&</span>n, <span class="kw-2">&</span>d);
<span class="macro">assert_eq!</span>(separate_div_mod_floor, dm);
<span class="macro">assert_eq!</span>(combined_div_mod_floor, dm);
test_division_rule(nd, separate_div_mod_floor);
test_division_rule(nd, combined_div_mod_floor);
}
test_nd_dm((<span class="number">8</span>, <span class="number">3</span>), (<span class="number">2</span>, <span class="number">2</span>));
test_nd_dm((<span class="number">8</span>, -<span class="number">3</span>), (-<span class="number">3</span>, -<span class="number">1</span>));
test_nd_dm((-<span class="number">8</span>, <span class="number">3</span>), (-<span class="number">3</span>, <span class="number">1</span>));
test_nd_dm((-<span class="number">8</span>, -<span class="number">3</span>), (<span class="number">2</span>, -<span class="number">2</span>));
test_nd_dm((<span class="number">1</span>, <span class="number">2</span>), (<span class="number">0</span>, <span class="number">1</span>));
test_nd_dm((<span class="number">1</span>, -<span class="number">2</span>), (-<span class="number">1</span>, -<span class="number">1</span>));
test_nd_dm((-<span class="number">1</span>, <span class="number">2</span>), (-<span class="number">1</span>, <span class="number">1</span>));
test_nd_dm((-<span class="number">1</span>, -<span class="number">2</span>), (<span class="number">0</span>, -<span class="number">1</span>));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd() {
<span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">2</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">56 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">42</span>), <span class="number">14 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span>-<span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((-<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((-<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span>-<span class="number">2</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd_cmp_with_euclidean() {
<span class="kw">fn </span>euclidean_gcd(<span class="kw-2">mut </span>m: <span class="macro-nonterminal">$T</span>, <span class="kw-2">mut </span>n: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{
<span class="kw">while </span>m != <span class="number">0 </span>{
mem::swap(<span class="kw-2">&mut </span>m, <span class="kw-2">&mut </span>n);
m %= n;
}
n.abs()
}
<span class="comment">// gcd(-128, b) = 128 is not representable as positive value
// for i8
</span><span class="kw">for </span>i <span class="kw">in </span>-<span class="number">127</span>..<span class="number">127 </span>{
<span class="kw">for </span>j <span class="kw">in </span>-<span class="number">127</span>..<span class="number">127 </span>{
<span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&</span>j));
}
}
<span class="comment">// last value
// FIXME: Use inclusive ranges for above loop when implemented
</span><span class="kw">let </span>i = <span class="number">127</span>;
<span class="kw">for </span>j <span class="kw">in </span>-<span class="number">127</span>..<span class="number">127 </span>{
<span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&</span>j));
}
<span class="macro">assert_eq!</span>(<span class="number">127</span>.gcd(<span class="kw-2">&</span><span class="number">127</span>), <span class="number">127</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd_min_val() {
<span class="kw">let </span>min = <<span class="macro-nonterminal">$T</span>>::min_value();
<span class="kw">let </span>max = <<span class="macro-nonterminal">$T</span>>::max_value();
<span class="kw">let </span>max_pow2 = max / <span class="number">2 </span>+ <span class="number">1</span>;
<span class="macro">assert_eq!</span>(min.gcd(<span class="kw-2">&</span>max), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(max.gcd(<span class="kw-2">&</span>min), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(min.gcd(<span class="kw-2">&</span>max_pow2), max_pow2);
<span class="macro">assert_eq!</span>(max_pow2.gcd(<span class="kw-2">&</span>min), max_pow2);
<span class="macro">assert_eq!</span>(min.gcd(<span class="kw-2">&</span><span class="number">42</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">42 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span>min), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
}
<span class="attr">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_gcd_min_val_min_val() {
<span class="kw">let </span>min = <<span class="macro-nonterminal">$T</span>>::min_value();
<span class="macro">assert!</span>(min.gcd(<span class="kw-2">&</span>min) >= <span class="number">0</span>);
}
<span class="attr">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_gcd_min_val_0() {
<span class="kw">let </span>min = <<span class="macro-nonterminal">$T</span>>::min_value();
<span class="macro">assert!</span>(min.gcd(<span class="kw-2">&</span><span class="number">0</span>) >= <span class="number">0</span>);
}
<span class="attr">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_gcd_0_min_val() {
<span class="kw">let </span>min = <<span class="macro-nonterminal">$T</span>>::min_value();
<span class="macro">assert!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span>min) >= <span class="number">0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_lcm() {
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">0</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span>-<span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span>-<span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">8 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">9</span>), <span class="number">72 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">11 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">5</span>), <span class="number">55 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd_lcm() {
<span class="kw">use </span>core::iter::once;
<span class="kw">for </span>i <span class="kw">in </span>once(<span class="number">0</span>)
.chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
.chain(once(-<span class="number">128</span>))
{
<span class="kw">for </span>j <span class="kw">in </span>once(<span class="number">0</span>)
.chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
.chain(once(-<span class="number">128</span>))
{
<span class="macro">assert_eq!</span>(i.gcd_lcm(<span class="kw-2">&</span>j), (i.gcd(<span class="kw-2">&</span>j), i.lcm(<span class="kw-2">&</span>j)));
}
}
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_extended_gcd_lcm() {
<span class="kw">use </span>core::fmt::Debug;
<span class="kw">use </span>traits::NumAssign;
<span class="kw">use </span>ExtendedGcd;
<span class="kw">fn </span>check<A: Copy + Debug + Integer + NumAssign>(a: A, b: A) {
<span class="kw">let </span>ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(<span class="kw-2">&</span>b);
<span class="macro">assert_eq!</span>(gcd, x * a + y * b);
}
<span class="kw">use </span>core::iter::once;
<span class="kw">for </span>i <span class="kw">in </span>once(<span class="number">0</span>)
.chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
.chain(once(-<span class="number">128</span>))
{
<span class="kw">for </span>j <span class="kw">in </span>once(<span class="number">0</span>)
.chain((<span class="number">1</span>..).take(<span class="number">127</span>).flat_map(|a| once(a).chain(once(-a))))
.chain(once(-<span class="number">128</span>))
{
check(i, j);
<span class="kw">let </span>(ExtendedGcd { gcd, .. }, lcm) = i.extended_gcd_lcm(<span class="kw-2">&</span>j);
<span class="macro">assert_eq!</span>((gcd, lcm), (i.gcd(<span class="kw-2">&</span>j), i.lcm(<span class="kw-2">&</span>j)));
}
}
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_even() {
<span class="macro">assert_eq!</span>((-<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((-<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((-<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_odd() {
<span class="macro">assert_eq!</span>((-<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((-<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((-<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((-<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_multiple_of_one_limits() {
<span class="kw">for </span>x <span class="kw">in </span><span class="kw-2">&</span>[<<span class="macro-nonterminal">$T</span>>::min_value(), <<span class="macro-nonterminal">$T</span>>::max_value()] {
<span class="kw">for </span>one <span class="kw">in </span><span class="kw-2">&</span>[<span class="number">1</span>, -<span class="number">1</span>] {
<span class="macro">assert_eq!</span>(Integer::next_multiple_of(x, one), <span class="kw-2">*</span>x);
<span class="macro">assert_eq!</span>(Integer::prev_multiple_of(x, one), <span class="kw-2">*</span>x);
}
}
}
}
};
}
<span class="macro">impl_integer_for_isize!</span>(i8, test_integer_i8);
<span class="macro">impl_integer_for_isize!</span>(i16, test_integer_i16);
<span class="macro">impl_integer_for_isize!</span>(i32, test_integer_i32);
<span class="macro">impl_integer_for_isize!</span>(i64, test_integer_i64);
<span class="macro">impl_integer_for_isize!</span>(isize, test_integer_isize);
<span class="attr">#[cfg(has_i128)]
</span><span class="macro">impl_integer_for_isize!</span>(i128, test_integer_i128);
<span class="macro">macro_rules! </span>impl_integer_for_usize {
(<span class="macro-nonterminal">$T</span>:ty, <span class="macro-nonterminal">$test_mod</span>:ident) => {
<span class="kw">impl </span>Integer <span class="kw">for </span><span class="macro-nonterminal">$T </span>{
<span class="doccomment">/// Unsigned integer division. Returns the same result as `div` (`/`).
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>div_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other
}
<span class="doccomment">/// Unsigned integer modulo operation. Returns the same result as `rem` (`%`).
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>mod_floor(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>div_ceil(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other + (<span class="number">0 </span>!= <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other) <span class="kw">as </span><span class="self">Self
</span>}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) of the number and `other`
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>gcd(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="comment">// Use Stein's algorithm
</span><span class="kw">let </span><span class="kw-2">mut </span>m = <span class="kw-2">*</span><span class="self">self</span>;
<span class="kw">let </span><span class="kw-2">mut </span>n = <span class="kw-2">*</span>other;
<span class="kw">if </span>m == <span class="number">0 </span>|| n == <span class="number">0 </span>{
<span class="kw">return </span>m | n;
}
<span class="comment">// find common factors of 2
</span><span class="kw">let </span>shift = (m | n).trailing_zeros();
<span class="comment">// divide n and m by 2 until odd
</span>m >>= m.trailing_zeros();
n >>= n.trailing_zeros();
<span class="kw">while </span>m != n {
<span class="kw">if </span>m > n {
m -= n;
m >>= m.trailing_zeros();
} <span class="kw">else </span>{
n -= m;
n >>= n.trailing_zeros();
}
}
m << shift
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>extended_gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (ExtendedGcd<<span class="self">Self</span>>, <span class="self">Self</span>) {
<span class="kw">let </span>egcd = <span class="self">self</span>.extended_gcd(other);
<span class="comment">// should not have to recalculate abs
</span><span class="kw">let </span>lcm = <span class="kw">if </span>egcd.gcd.is_zero() {
<span class="self">Self</span>::zero()
} <span class="kw">else </span>{
<span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / egcd.gcd)
};
(egcd, lcm)
}
<span class="doccomment">/// Calculates the Lowest Common Multiple (LCM) of the number and `other`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="self">self</span>.gcd_lcm(other).<span class="number">1
</span>}
<span class="doccomment">/// Calculates the Greatest Common Divisor (GCD) and
/// Lowest Common Multiple (LCM) of the number and `other`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>gcd_lcm(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
<span class="kw">if </span><span class="self">self</span>.is_zero() && other.is_zero() {
<span class="kw">return </span>(<span class="self">Self</span>::zero(), <span class="self">Self</span>::zero());
}
<span class="kw">let </span>gcd = <span class="self">self</span>.gcd(other);
<span class="kw">let </span>lcm = <span class="kw-2">*</span><span class="self">self </span>* (<span class="kw-2">*</span>other / gcd);
(gcd, lcm)
}
<span class="doccomment">/// Deprecated, use `is_multiple_of` instead.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>divides(<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>.is_multiple_of(other)
}
<span class="doccomment">/// Returns `true` if the number is a multiple of `other`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_multiple_of(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="kw">if </span>other.is_zero() {
<span class="kw">return </span><span class="self">self</span>.is_zero();
}
<span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other == <span class="number">0
</span>}
<span class="doccomment">/// Returns `true` if the number is divisible by `2`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_even(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
<span class="kw-2">*</span><span class="self">self </span>% <span class="number">2 </span>== <span class="number">0
</span>}
<span class="doccomment">/// Returns `true` if the number is not divisible by `2`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_odd(<span class="kw-2">&</span><span class="self">self</span>) -> bool {
!<span class="self">self</span>.is_even()
}
<span class="doccomment">/// Simultaneous truncated integer division and modulus.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>div_rem(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>) {
(<span class="kw-2">*</span><span class="self">self </span>/ <span class="kw-2">*</span>other, <span class="kw-2">*</span><span class="self">self </span>% <span class="kw-2">*</span>other)
}
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span><span class="macro-nonterminal">$test_mod </span>{
<span class="kw">use </span>core::mem;
<span class="kw">use </span>Integer;
<span class="attr">#[test]
</span><span class="kw">fn </span>test_div_mod_floor() {
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_floor(<span class="kw-2">&</span><span class="number">10</span>, <span class="kw-2">&</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::mod_floor(<span class="kw-2">&</span><span class="number">10</span>, <span class="kw-2">&</span><span class="number">3</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_mod_floor(<span class="kw-2">&</span><span class="number">10</span>, <span class="kw-2">&</span><span class="number">3</span>), (<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>, <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>));
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_floor(<span class="kw-2">&</span><span class="number">5</span>, <span class="kw-2">&</span><span class="number">5</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::mod_floor(<span class="kw-2">&</span><span class="number">5</span>, <span class="kw-2">&</span><span class="number">5</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_mod_floor(<span class="kw-2">&</span><span class="number">5</span>, <span class="kw-2">&</span><span class="number">5</span>), (<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>, <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>));
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_floor(<span class="kw-2">&</span><span class="number">3</span>, <span class="kw-2">&</span><span class="number">7</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_floor(<span class="kw-2">&</span><span class="number">3</span>, <span class="kw-2">&</span><span class="number">7</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::mod_floor(<span class="kw-2">&</span><span class="number">3</span>, <span class="kw-2">&</span><span class="number">7</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>(<<span class="macro-nonterminal">$T </span><span class="kw">as </span>Integer>::div_mod_floor(<span class="kw-2">&</span><span class="number">3</span>, <span class="kw-2">&</span><span class="number">7</span>), (<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>, <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd() {
<span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">2</span>), <span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">10 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">3</span>), <span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">56 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).gcd(<span class="kw-2">&</span><span class="number">42</span>), <span class="number">14 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd_cmp_with_euclidean() {
<span class="kw">fn </span>euclidean_gcd(<span class="kw-2">mut </span>m: <span class="macro-nonterminal">$T</span>, <span class="kw-2">mut </span>n: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{
<span class="kw">while </span>m != <span class="number">0 </span>{
mem::swap(<span class="kw-2">&mut </span>m, <span class="kw-2">&mut </span>n);
m %= n;
}
n
}
<span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">255 </span>{
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="number">255 </span>{
<span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&</span>j));
}
}
<span class="comment">// last value
// FIXME: Use inclusive ranges for above loop when implemented
</span><span class="kw">let </span>i = <span class="number">255</span>;
<span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="number">255 </span>{
<span class="macro">assert_eq!</span>(euclidean_gcd(i, j), i.gcd(<span class="kw-2">&</span>j));
}
<span class="macro">assert_eq!</span>(<span class="number">255</span>.gcd(<span class="kw-2">&</span><span class="number">255</span>), <span class="number">255</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_lcm() {
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">0</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">1</span>), <span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">8 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">9</span>), <span class="number">72 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">11 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">5</span>), <span class="number">55 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
<span class="macro">assert_eq!</span>((<span class="number">15 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).lcm(<span class="kw-2">&</span><span class="number">17</span>), <span class="number">255 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_gcd_lcm() {
<span class="kw">for </span>i <span class="kw">in </span>(<span class="number">0</span>..).take(<span class="number">256</span>) {
<span class="kw">for </span>j <span class="kw">in </span>(<span class="number">0</span>..).take(<span class="number">256</span>) {
<span class="macro">assert_eq!</span>(i.gcd_lcm(<span class="kw-2">&</span>j), (i.gcd(<span class="kw-2">&</span>j), i.lcm(<span class="kw-2">&</span>j)));
}
}
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_is_multiple_of() {
<span class="macro">assert!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
<span class="macro">assert!</span>((<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
<span class="macro">assert!</span>((<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
<span class="macro">assert!</span>((<span class="number">6 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
<span class="macro">assert!</span>(!(<span class="number">42 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">5 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
<span class="macro">assert!</span>(!(<span class="number">5 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
<span class="macro">assert!</span>(!(<span class="number">42 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_multiple_of(<span class="kw-2">&</span>(<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>)));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_even() {
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_even(), <span class="bool-val">true</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_odd() {
<span class="macro">assert_eq!</span>((<span class="number">0 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">1 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">2 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>((<span class="number">3 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>((<span class="number">4 </span><span class="kw">as </span><span class="macro-nonterminal">$T</span>).is_odd(), <span class="bool-val">false</span>);
}
}
};
}
<span class="macro">impl_integer_for_usize!</span>(u8, test_integer_u8);
<span class="macro">impl_integer_for_usize!</span>(u16, test_integer_u16);
<span class="macro">impl_integer_for_usize!</span>(u32, test_integer_u32);
<span class="macro">impl_integer_for_usize!</span>(u64, test_integer_u64);
<span class="macro">impl_integer_for_usize!</span>(usize, test_integer_usize);
<span class="attr">#[cfg(has_i128)]
</span><span class="macro">impl_integer_for_usize!</span>(u128, test_integer_u128);
<span class="doccomment">/// An iterator over binomial coefficients.
</span><span class="kw">pub struct </span>IterBinomial<T> {
a: T,
n: T,
k: T,
}
<span class="kw">impl</span><T> IterBinomial<T>
<span class="kw">where
</span>T: Integer,
{
<span class="doccomment">/// For a given n, iterate over all binomial coefficients binomial(n, k), for k=0...n.
///
/// Note that this might overflow, depending on `T`. For the primitive
/// integer types, the following n are the largest ones for which there will
/// be no overflow:
///
/// type | n
/// -----|---
/// u8 | 10
/// i8 | 9
/// u16 | 18
/// i16 | 17
/// u32 | 34
/// i32 | 33
/// u64 | 67
/// i64 | 66
///
/// For larger n, `T` should be a bigint type.
</span><span class="kw">pub fn </span>new(n: T) -> IterBinomial<T> {
IterBinomial {
k: T::zero(),
a: T::one(),
n: n,
}
}
}
<span class="kw">impl</span><T> Iterator <span class="kw">for </span>IterBinomial<T>
<span class="kw">where
</span>T: Integer + Clone,
{
<span class="kw">type </span>Item = T;
<span class="kw">fn </span>next(<span class="kw-2">&mut </span><span class="self">self</span>) -> <span class="prelude-ty">Option</span><T> {
<span class="kw">if </span><span class="self">self</span>.k > <span class="self">self</span>.n {
<span class="kw">return </span><span class="prelude-val">None</span>;
}
<span class="self">self</span>.a = <span class="kw">if </span>!<span class="self">self</span>.k.is_zero() {
multiply_and_divide(
<span class="self">self</span>.a.clone(),
<span class="self">self</span>.n.clone() - <span class="self">self</span>.k.clone() + T::one(),
<span class="self">self</span>.k.clone(),
)
} <span class="kw">else </span>{
T::one()
};
<span class="self">self</span>.k = <span class="self">self</span>.k.clone() + T::one();
<span class="prelude-val">Some</span>(<span class="self">self</span>.a.clone())
}
}
<span class="doccomment">/// Calculate r * a / b, avoiding overflows and fractions.
///
/// Assumes that b divides r * a evenly.
</span><span class="kw">fn </span>multiply_and_divide<T: Integer + Clone>(r: T, a: T, b: T) -> T {
<span class="comment">// See http://blog.plover.com/math/choose-2.html for the idea.
</span><span class="kw">let </span>g = gcd(r.clone(), b.clone());
r / g.clone() * (a / (b / g))
}
<span class="doccomment">/// Calculate the binomial coefficient.
///
/// Note that this might overflow, depending on `T`. For the primitive integer
/// types, the following n are the largest ones possible such that there will
/// be no overflow for any k:
///
/// type | n
/// -----|---
/// u8 | 10
/// i8 | 9
/// u16 | 18
/// i16 | 17
/// u32 | 34
/// i32 | 33
/// u64 | 67
/// i64 | 66
///
/// For larger n, consider using a bigint type for `T`.
</span><span class="kw">pub fn </span>binomial<T: Integer + Clone>(<span class="kw-2">mut </span>n: T, k: T) -> T {
<span class="comment">// See http://blog.plover.com/math/choose.html for the idea.
</span><span class="kw">if </span>k > n {
<span class="kw">return </span>T::zero();
}
<span class="kw">if </span>k > n.clone() - k.clone() {
<span class="kw">return </span>binomial(n.clone(), n - k);
}
<span class="kw">let </span><span class="kw-2">mut </span>r = T::one();
<span class="kw">let </span><span class="kw-2">mut </span>d = T::one();
<span class="kw">loop </span>{
<span class="kw">if </span>d > k {
<span class="kw">break</span>;
}
r = multiply_and_divide(r, n.clone(), d.clone());
n = n - T::one();
d = d + T::one();
}
r
}
<span class="doccomment">/// Calculate the multinomial coefficient.
</span><span class="kw">pub fn </span>multinomial<T: Integer + Clone>(k: <span class="kw-2">&</span>[T]) -> T
<span class="kw">where
for</span><<span class="lifetime">'a</span>> T: Add<<span class="kw-2">&</span><span class="lifetime">'a </span>T, Output = T>,
{
<span class="kw">let </span><span class="kw-2">mut </span>r = T::one();
<span class="kw">let </span><span class="kw-2">mut </span>p = T::zero();
<span class="kw">for </span>i <span class="kw">in </span>k {
p = p + i;
r = r * binomial(p.clone(), i.clone());
}
r
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_lcm_overflow() {
<span class="macro">macro_rules! </span>check {
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$x</span>:expr, <span class="macro-nonterminal">$y</span>:expr, <span class="macro-nonterminal">$r</span>:expr) => {{
<span class="kw">let </span>x: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$x</span>;
<span class="kw">let </span>y: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$y</span>;
<span class="kw">let </span>o = x.checked_mul(y);
<span class="macro">assert!</span>(
o.is_none(),
<span class="string">"sanity checking that {} input {} * {} overflows"</span>,
<span class="macro">stringify!</span>(<span class="macro-nonterminal">$t</span>),
x,
y
);
<span class="macro">assert_eq!</span>(x.lcm(<span class="kw-2">&</span>y), <span class="macro-nonterminal">$r</span>);
<span class="macro">assert_eq!</span>(y.lcm(<span class="kw-2">&</span>x), <span class="macro-nonterminal">$r</span>);
}};
}
<span class="comment">// Original bug (Issue #166)
</span><span class="macro">check!</span>(i64, <span class="number">46656000000000000</span>, <span class="number">600</span>, <span class="number">46656000000000000</span>);
<span class="macro">check!</span>(i8, <span class="number">0x40</span>, <span class="number">0x04</span>, <span class="number">0x40</span>);
<span class="macro">check!</span>(u8, <span class="number">0x80</span>, <span class="number">0x02</span>, <span class="number">0x80</span>);
<span class="macro">check!</span>(i16, <span class="number">0x40_00</span>, <span class="number">0x04</span>, <span class="number">0x40_00</span>);
<span class="macro">check!</span>(u16, <span class="number">0x80_00</span>, <span class="number">0x02</span>, <span class="number">0x80_00</span>);
<span class="macro">check!</span>(i32, <span class="number">0x4000_0000</span>, <span class="number">0x04</span>, <span class="number">0x4000_0000</span>);
<span class="macro">check!</span>(u32, <span class="number">0x8000_0000</span>, <span class="number">0x02</span>, <span class="number">0x8000_0000</span>);
<span class="macro">check!</span>(i64, <span class="number">0x4000_0000_0000_0000</span>, <span class="number">0x04</span>, <span class="number">0x4000_0000_0000_0000</span>);
<span class="macro">check!</span>(u64, <span class="number">0x8000_0000_0000_0000</span>, <span class="number">0x02</span>, <span class="number">0x8000_0000_0000_0000</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_iter_binomial() {
<span class="macro">macro_rules! </span>check_simple {
(<span class="macro-nonterminal">$t</span>:ty) => {{
<span class="kw">let </span>n: <span class="macro-nonterminal">$t </span>= <span class="number">3</span>;
<span class="kw">let </span>expected = [<span class="number">1</span>, <span class="number">3</span>, <span class="number">3</span>, <span class="number">1</span>];
<span class="kw">for </span>(b, <span class="kw-2">&</span>e) <span class="kw">in </span>IterBinomial::new(n).zip(<span class="kw-2">&</span>expected) {
<span class="macro">assert_eq!</span>(b, e);
}
}};
}
<span class="macro">check_simple!</span>(u8);
<span class="macro">check_simple!</span>(i8);
<span class="macro">check_simple!</span>(u16);
<span class="macro">check_simple!</span>(i16);
<span class="macro">check_simple!</span>(u32);
<span class="macro">check_simple!</span>(i32);
<span class="macro">check_simple!</span>(u64);
<span class="macro">check_simple!</span>(i64);
<span class="macro">macro_rules! </span>check_binomial {
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$n</span>:expr) => {{
<span class="kw">let </span>n: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$n</span>;
<span class="kw">let </span><span class="kw-2">mut </span>k: <span class="macro-nonterminal">$t </span>= <span class="number">0</span>;
<span class="kw">for </span>b <span class="kw">in </span>IterBinomial::new(n) {
<span class="macro">assert_eq!</span>(b, binomial(n, k));
k += <span class="number">1</span>;
}
}};
}
<span class="comment">// Check the largest n for which there is no overflow.
</span><span class="macro">check_binomial!</span>(u8, <span class="number">10</span>);
<span class="macro">check_binomial!</span>(i8, <span class="number">9</span>);
<span class="macro">check_binomial!</span>(u16, <span class="number">18</span>);
<span class="macro">check_binomial!</span>(i16, <span class="number">17</span>);
<span class="macro">check_binomial!</span>(u32, <span class="number">34</span>);
<span class="macro">check_binomial!</span>(i32, <span class="number">33</span>);
<span class="macro">check_binomial!</span>(u64, <span class="number">67</span>);
<span class="macro">check_binomial!</span>(i64, <span class="number">66</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_binomial() {
<span class="macro">macro_rules! </span>check {
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$x</span>:expr, <span class="macro-nonterminal">$y</span>:expr, <span class="macro-nonterminal">$r</span>:expr) => {{
<span class="kw">let </span>x: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$x</span>;
<span class="kw">let </span>y: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$y</span>;
<span class="kw">let </span>expected: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$r</span>;
<span class="macro">assert_eq!</span>(binomial(x, y), expected);
<span class="kw">if </span>y <= x {
<span class="macro">assert_eq!</span>(binomial(x, x - y), expected);
}
}};
}
<span class="macro">check!</span>(u8, <span class="number">9</span>, <span class="number">4</span>, <span class="number">126</span>);
<span class="macro">check!</span>(u8, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(u8, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(i8, <span class="number">9</span>, <span class="number">4</span>, <span class="number">126</span>);
<span class="macro">check!</span>(i8, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(i8, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(u16, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(u16, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(u16, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(u16, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(i16, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(i16, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(i16, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(i16, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(u32, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(u32, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(u32, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(u32, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(u32, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(i32, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(i32, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(i32, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(i32, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(i32, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(u64, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(u64, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(u64, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(u64, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(u64, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
<span class="macro">check!</span>(i64, <span class="number">100</span>, <span class="number">2</span>, <span class="number">4950</span>);
<span class="macro">check!</span>(i64, <span class="number">35</span>, <span class="number">11</span>, <span class="number">417225900</span>);
<span class="macro">check!</span>(i64, <span class="number">14</span>, <span class="number">4</span>, <span class="number">1001</span>);
<span class="macro">check!</span>(i64, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>);
<span class="macro">check!</span>(i64, <span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>test_multinomial() {
<span class="macro">macro_rules! </span>check_binomial {
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$k</span>:expr) => {{
<span class="kw">let </span>n: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$k</span>.iter().fold(<span class="number">0</span>, |acc, <span class="kw-2">&</span>x| acc + x);
<span class="kw">let </span>k: <span class="kw-2">&</span>[<span class="macro-nonterminal">$t</span>] = <span class="macro-nonterminal">$k</span>;
<span class="macro">assert_eq!</span>(k.len(), <span class="number">2</span>);
<span class="macro">assert_eq!</span>(multinomial(k), binomial(n, k[<span class="number">0</span>]));
}};
}
<span class="macro">check_binomial!</span>(u8, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">5</span>]);
<span class="macro">check_binomial!</span>(i8, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">5</span>]);
<span class="macro">check_binomial!</span>(u16, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(u16, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(i16, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(i16, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(u32, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(u32, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(u32, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(i32, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(i32, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(i32, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">check_binomial!</span>(i64, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">98</span>]);
<span class="macro">check_binomial!</span>(i64, <span class="kw-2">&</span>[<span class="number">11</span>, <span class="number">24</span>]);
<span class="macro">check_binomial!</span>(i64, <span class="kw-2">&</span>[<span class="number">4</span>, <span class="number">10</span>]);
<span class="macro">macro_rules! </span>check_multinomial {
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$k</span>:expr, <span class="macro-nonterminal">$r</span>:expr) => {{
<span class="kw">let </span>k: <span class="kw-2">&</span>[<span class="macro-nonterminal">$t</span>] = <span class="macro-nonterminal">$k</span>;
<span class="kw">let </span>expected: <span class="macro-nonterminal">$t </span>= <span class="macro-nonterminal">$r</span>;
<span class="macro">assert_eq!</span>(multinomial(k), expected);
}};
}
<span class="macro">check_multinomial!</span>(u8, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(u8, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(i8, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(i8, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(u16, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(u16, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(i16, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(i16, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(u32, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(u32, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(i32, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(i32, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(i64, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">1</span>, <span class="number">2</span>], <span class="number">30</span>);
<span class="macro">check_multinomial!</span>(i64, <span class="kw-2">&</span>[<span class="number">2</span>, <span class="number">3</span>, <span class="number">0</span>], <span class="number">10</span>);
<span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&</span>[], <span class="number">1</span>);
<span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">0</span>], <span class="number">1</span>);
<span class="macro">check_multinomial!</span>(u64, <span class="kw-2">&</span>[<span class="number">12345</span>], <span class="number">1</span>);
}
</code></pre></div>
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