<!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/m018/.cargo/registry/src/github.com-1ecc6299db9ec823/num-traits-0.2.16/src/float.rs`."><title>float.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceSerif4-Regular-46f98efaafac5295.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-a2c9cd1067f8b328.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-c4dbdcde0fbd8430.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../static.files/light-db279b6232be9c13.css"><link rel="stylesheet" disabled href="../../static.files/dark-cf923f49f397b216.css"><link rel="stylesheet" disabled href="../../static.files/ayu-be46fdc453a55015.css"><script src="../../static.files/storage-3891ce972e3a2bf8.js"></script><script defer src="../../static.files/source-script-1b95b7cca98b26e5.js"></script><script defer src="../../source-files.js"></script><script defer src="../../static.files/main-98a684e84ae5b08b.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><nav class="sub"><a class="sub-logo-container" href="../../num_traits/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-7b819b6101059cd0.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="#934" id="934">934</a>
<a href="#935" id="935">935</a>
<a href="#936" id="936">936</a>
<a href="#937" id="937">937</a>
<a href="#938" id="938">938</a>
<a href="#939" id="939">939</a>
<a href="#940" id="940">940</a>
<a href="#941" id="941">941</a>
<a href="#942" id="942">942</a>
<a href="#943" id="943">943</a>
<a href="#944" id="944">944</a>
<a href="#945" id="945">945</a>
<a href="#946" id="946">946</a>
<a href="#947" id="947">947</a>
<a href="#948" id="948">948</a>
<a href="#949" id="949">949</a>
<a href="#950" id="950">950</a>
<a href="#951" id="951">951</a>
<a href="#952" id="952">952</a>
<a href="#953" id="953">953</a>
<a href="#954" id="954">954</a>
<a href="#955" id="955">955</a>
<a href="#956" id="956">956</a>
<a href="#957" id="957">957</a>
<a href="#958" id="958">958</a>
<a href="#959" id="959">959</a>
<a href="#960" id="960">960</a>
<a href="#961" id="961">961</a>
<a href="#962" id="962">962</a>
<a href="#963" id="963">963</a>
<a href="#964" id="964">964</a>
<a href="#965" id="965">965</a>
<a href="#966" id="966">966</a>
<a href="#967" id="967">967</a>
<a href="#968" id="968">968</a>
<a href="#969" id="969">969</a>
<a href="#970" id="970">970</a>
<a href="#971" id="971">971</a>
<a href="#972" id="972">972</a>
<a href="#973" id="973">973</a>
<a href="#974" id="974">974</a>
<a href="#975" id="975">975</a>
<a href="#976" id="976">976</a>
<a href="#977" id="977">977</a>
<a href="#978" id="978">978</a>
<a href="#979" id="979">979</a>
<a href="#980" id="980">980</a>
<a href="#981" id="981">981</a>
<a href="#982" id="982">982</a>
<a href="#983" id="983">983</a>
<a href="#984" id="984">984</a>
<a href="#985" id="985">985</a>
<a href="#986" id="986">986</a>
<a href="#987" id="987">987</a>
<a href="#988" id="988">988</a>
<a href="#989" id="989">989</a>
<a href="#990" id="990">990</a>
<a href="#991" id="991">991</a>
<a href="#992" id="992">992</a>
<a href="#993" id="993">993</a>
<a href="#994" id="994">994</a>
<a href="#995" id="995">995</a>
<a href="#996" id="996">996</a>
<a href="#997" id="997">997</a>
<a href="#998" id="998">998</a>
<a href="#999" id="999">999</a>
<a href="#1000" id="1000">1000</a>
<a href="#1001" id="1001">1001</a>
<a href="#1002" id="1002">1002</a>
<a href="#1003" id="1003">1003</a>
<a href="#1004" id="1004">1004</a>
<a href="#1005" id="1005">1005</a>
<a href="#1006" id="1006">1006</a>
<a href="#1007" id="1007">1007</a>
<a href="#1008" id="1008">1008</a>
<a href="#1009" id="1009">1009</a>
<a href="#1010" id="1010">1010</a>
<a href="#1011" id="1011">1011</a>
<a href="#1012" id="1012">1012</a>
<a href="#1013" id="1013">1013</a>
<a href="#1014" id="1014">1014</a>
<a href="#1015" id="1015">1015</a>
<a href="#1016" id="1016">1016</a>
<a href="#1017" id="1017">1017</a>
<a href="#1018" id="1018">1018</a>
<a href="#1019" id="1019">1019</a>
<a href="#1020" id="1020">1020</a>
<a href="#1021" id="1021">1021</a>
<a href="#1022" id="1022">1022</a>
<a href="#1023" id="1023">1023</a>
<a href="#1024" id="1024">1024</a>
<a href="#1025" id="1025">1025</a>
<a href="#1026" id="1026">1026</a>
<a href="#1027" id="1027">1027</a>
<a href="#1028" id="1028">1028</a>
<a href="#1029" id="1029">1029</a>
<a href="#1030" id="1030">1030</a>
<a href="#1031" id="1031">1031</a>
<a href="#1032" id="1032">1032</a>
<a href="#1033" id="1033">1033</a>
<a href="#1034" id="1034">1034</a>
<a href="#1035" id="1035">1035</a>
<a href="#1036" id="1036">1036</a>
<a href="#1037" id="1037">1037</a>
<a href="#1038" id="1038">1038</a>
<a href="#1039" id="1039">1039</a>
<a href="#1040" id="1040">1040</a>
<a href="#1041" id="1041">1041</a>
<a href="#1042" id="1042">1042</a>
<a href="#1043" id="1043">1043</a>
<a href="#1044" id="1044">1044</a>
<a href="#1045" id="1045">1045</a>
<a href="#1046" id="1046">1046</a>
<a href="#1047" id="1047">1047</a>
<a href="#1048" id="1048">1048</a>
<a href="#1049" id="1049">1049</a>
<a href="#1050" id="1050">1050</a>
<a href="#1051" id="1051">1051</a>
<a href="#1052" id="1052">1052</a>
<a href="#1053" id="1053">1053</a>
<a href="#1054" id="1054">1054</a>
<a href="#1055" id="1055">1055</a>
<a href="#1056" id="1056">1056</a>
<a href="#1057" id="1057">1057</a>
<a href="#1058" id="1058">1058</a>
<a href="#1059" id="1059">1059</a>
<a href="#1060" id="1060">1060</a>
<a href="#1061" id="1061">1061</a>
<a href="#1062" id="1062">1062</a>
<a href="#1063" id="1063">1063</a>
<a href="#1064" id="1064">1064</a>
<a href="#1065" id="1065">1065</a>
<a href="#1066" id="1066">1066</a>
<a href="#1067" id="1067">1067</a>
<a href="#1068" id="1068">1068</a>
<a href="#1069" id="1069">1069</a>
<a href="#1070" id="1070">1070</a>
<a href="#1071" id="1071">1071</a>
<a href="#1072" id="1072">1072</a>
<a href="#1073" id="1073">1073</a>
<a href="#1074" id="1074">1074</a>
<a href="#1075" id="1075">1075</a>
<a href="#1076" id="1076">1076</a>
<a href="#1077" id="1077">1077</a>
<a href="#1078" id="1078">1078</a>
<a href="#1079" id="1079">1079</a>
<a href="#1080" id="1080">1080</a>
<a href="#1081" id="1081">1081</a>
<a href="#1082" id="1082">1082</a>
<a href="#1083" id="1083">1083</a>
<a href="#1084" id="1084">1084</a>
<a href="#1085" id="1085">1085</a>
<a href="#1086" id="1086">1086</a>
<a href="#1087" id="1087">1087</a>
<a href="#1088" id="1088">1088</a>
<a href="#1089" id="1089">1089</a>
<a href="#1090" id="1090">1090</a>
<a href="#1091" id="1091">1091</a>
<a href="#1092" id="1092">1092</a>
<a href="#1093" id="1093">1093</a>
<a href="#1094" id="1094">1094</a>
<a href="#1095" id="1095">1095</a>
<a href="#1096" id="1096">1096</a>
<a href="#1097" id="1097">1097</a>
<a href="#1098" id="1098">1098</a>
<a href="#1099" id="1099">1099</a>
<a href="#1100" id="1100">1100</a>
<a href="#1101" id="1101">1101</a>
<a href="#1102" id="1102">1102</a>
<a href="#1103" id="1103">1103</a>
<a href="#1104" id="1104">1104</a>
<a href="#1105" id="1105">1105</a>
<a href="#1106" id="1106">1106</a>
<a href="#1107" id="1107">1107</a>
<a href="#1108" id="1108">1108</a>
<a href="#1109" id="1109">1109</a>
<a href="#1110" id="1110">1110</a>
<a href="#1111" id="1111">1111</a>
<a href="#1112" id="1112">1112</a>
<a href="#1113" id="1113">1113</a>
<a href="#1114" id="1114">1114</a>
<a href="#1115" id="1115">1115</a>
<a href="#1116" id="1116">1116</a>
<a href="#1117" id="1117">1117</a>
<a href="#1118" id="1118">1118</a>
<a href="#1119" id="1119">1119</a>
<a href="#1120" id="1120">1120</a>
<a href="#1121" id="1121">1121</a>
<a href="#1122" id="1122">1122</a>
<a href="#1123" id="1123">1123</a>
<a href="#1124" id="1124">1124</a>
<a href="#1125" id="1125">1125</a>
<a href="#1126" id="1126">1126</a>
<a href="#1127" id="1127">1127</a>
<a href="#1128" id="1128">1128</a>
<a href="#1129" id="1129">1129</a>
<a href="#1130" id="1130">1130</a>
<a href="#1131" id="1131">1131</a>
<a href="#1132" id="1132">1132</a>
<a href="#1133" id="1133">1133</a>
<a href="#1134" id="1134">1134</a>
<a href="#1135" id="1135">1135</a>
<a href="#1136" id="1136">1136</a>
<a href="#1137" id="1137">1137</a>
<a href="#1138" id="1138">1138</a>
<a href="#1139" id="1139">1139</a>
<a href="#1140" id="1140">1140</a>
<a href="#1141" id="1141">1141</a>
<a href="#1142" id="1142">1142</a>
<a href="#1143" id="1143">1143</a>
<a href="#1144" id="1144">1144</a>
<a href="#1145" id="1145">1145</a>
<a href="#1146" id="1146">1146</a>
<a href="#1147" id="1147">1147</a>
<a href="#1148" id="1148">1148</a>
<a href="#1149" id="1149">1149</a>
<a href="#1150" id="1150">1150</a>
<a href="#1151" id="1151">1151</a>
<a href="#1152" id="1152">1152</a>
<a href="#1153" id="1153">1153</a>
<a href="#1154" id="1154">1154</a>
<a href="#1155" id="1155">1155</a>
<a href="#1156" id="1156">1156</a>
<a href="#1157" id="1157">1157</a>
<a href="#1158" id="1158">1158</a>
<a href="#1159" id="1159">1159</a>
<a href="#1160" id="1160">1160</a>
<a href="#1161" id="1161">1161</a>
<a href="#1162" id="1162">1162</a>
<a href="#1163" id="1163">1163</a>
<a href="#1164" id="1164">1164</a>
<a href="#1165" id="1165">1165</a>
<a href="#1166" id="1166">1166</a>
<a href="#1167" id="1167">1167</a>
<a href="#1168" id="1168">1168</a>
<a href="#1169" id="1169">1169</a>
<a href="#1170" id="1170">1170</a>
<a href="#1171" id="1171">1171</a>
<a href="#1172" id="1172">1172</a>
<a href="#1173" id="1173">1173</a>
<a href="#1174" id="1174">1174</a>
<a href="#1175" id="1175">1175</a>
<a href="#1176" id="1176">1176</a>
<a href="#1177" id="1177">1177</a>
<a href="#1178" id="1178">1178</a>
<a href="#1179" id="1179">1179</a>
<a href="#1180" id="1180">1180</a>
<a href="#1181" id="1181">1181</a>
<a href="#1182" id="1182">1182</a>
<a href="#1183" id="1183">1183</a>
<a href="#1184" id="1184">1184</a>
<a href="#1185" id="1185">1185</a>
<a href="#1186" id="1186">1186</a>
<a href="#1187" id="1187">1187</a>
<a href="#1188" id="1188">1188</a>
<a href="#1189" id="1189">1189</a>
<a href="#1190" id="1190">1190</a>
<a href="#1191" id="1191">1191</a>
<a href="#1192" id="1192">1192</a>
<a href="#1193" id="1193">1193</a>
<a href="#1194" id="1194">1194</a>
<a href="#1195" id="1195">1195</a>
<a href="#1196" id="1196">1196</a>
<a href="#1197" id="1197">1197</a>
<a href="#1198" id="1198">1198</a>
<a href="#1199" id="1199">1199</a>
<a href="#1200" id="1200">1200</a>
<a href="#1201" id="1201">1201</a>
<a href="#1202" id="1202">1202</a>
<a href="#1203" id="1203">1203</a>
<a href="#1204" id="1204">1204</a>
<a href="#1205" id="1205">1205</a>
<a href="#1206" id="1206">1206</a>
<a href="#1207" id="1207">1207</a>
<a href="#1208" id="1208">1208</a>
<a href="#1209" id="1209">1209</a>
<a href="#1210" id="1210">1210</a>
<a href="#1211" id="1211">1211</a>
<a href="#1212" id="1212">1212</a>
<a href="#1213" id="1213">1213</a>
<a href="#1214" id="1214">1214</a>
<a href="#1215" id="1215">1215</a>
<a href="#1216" id="1216">1216</a>
<a href="#1217" id="1217">1217</a>
<a href="#1218" id="1218">1218</a>
<a href="#1219" id="1219">1219</a>
<a href="#1220" id="1220">1220</a>
<a href="#1221" id="1221">1221</a>
<a href="#1222" id="1222">1222</a>
<a href="#1223" id="1223">1223</a>
<a href="#1224" id="1224">1224</a>
<a href="#1225" id="1225">1225</a>
<a href="#1226" id="1226">1226</a>
<a href="#1227" id="1227">1227</a>
<a href="#1228" id="1228">1228</a>
<a href="#1229" id="1229">1229</a>
<a href="#1230" id="1230">1230</a>
<a href="#1231" id="1231">1231</a>
<a href="#1232" id="1232">1232</a>
<a href="#1233" id="1233">1233</a>
<a href="#1234" id="1234">1234</a>
<a href="#1235" id="1235">1235</a>
<a href="#1236" id="1236">1236</a>
<a href="#1237" id="1237">1237</a>
<a href="#1238" id="1238">1238</a>
<a href="#1239" id="1239">1239</a>
<a href="#1240" id="1240">1240</a>
<a href="#1241" id="1241">1241</a>
<a href="#1242" id="1242">1242</a>
<a href="#1243" id="1243">1243</a>
<a href="#1244" id="1244">1244</a>
<a href="#1245" id="1245">1245</a>
<a href="#1246" id="1246">1246</a>
<a href="#1247" id="1247">1247</a>
<a href="#1248" id="1248">1248</a>
<a href="#1249" id="1249">1249</a>
<a href="#1250" id="1250">1250</a>
<a href="#1251" id="1251">1251</a>
<a href="#1252" id="1252">1252</a>
<a href="#1253" id="1253">1253</a>
<a href="#1254" id="1254">1254</a>
<a href="#1255" id="1255">1255</a>
<a href="#1256" id="1256">1256</a>
<a href="#1257" id="1257">1257</a>
<a href="#1258" id="1258">1258</a>
<a href="#1259" id="1259">1259</a>
<a href="#1260" id="1260">1260</a>
<a href="#1261" id="1261">1261</a>
<a href="#1262" id="1262">1262</a>
<a href="#1263" id="1263">1263</a>
<a href="#1264" id="1264">1264</a>
<a href="#1265" id="1265">1265</a>
<a href="#1266" id="1266">1266</a>
<a href="#1267" id="1267">1267</a>
<a href="#1268" id="1268">1268</a>
<a href="#1269" id="1269">1269</a>
<a href="#1270" id="1270">1270</a>
<a href="#1271" id="1271">1271</a>
<a href="#1272" id="1272">1272</a>
<a href="#1273" id="1273">1273</a>
<a href="#1274" id="1274">1274</a>
<a href="#1275" id="1275">1275</a>
<a href="#1276" id="1276">1276</a>
<a href="#1277" id="1277">1277</a>
<a href="#1278" id="1278">1278</a>
<a href="#1279" id="1279">1279</a>
<a href="#1280" id="1280">1280</a>
<a href="#1281" id="1281">1281</a>
<a href="#1282" id="1282">1282</a>
<a href="#1283" id="1283">1283</a>
<a href="#1284" id="1284">1284</a>
<a href="#1285" id="1285">1285</a>
<a href="#1286" id="1286">1286</a>
<a href="#1287" id="1287">1287</a>
<a href="#1288" id="1288">1288</a>
<a href="#1289" id="1289">1289</a>
<a href="#1290" id="1290">1290</a>
<a href="#1291" id="1291">1291</a>
<a href="#1292" id="1292">1292</a>
<a href="#1293" id="1293">1293</a>
<a href="#1294" id="1294">1294</a>
<a href="#1295" id="1295">1295</a>
<a href="#1296" id="1296">1296</a>
<a href="#1297" id="1297">1297</a>
<a href="#1298" id="1298">1298</a>
<a href="#1299" id="1299">1299</a>
<a href="#1300" id="1300">1300</a>
<a href="#1301" id="1301">1301</a>
<a href="#1302" id="1302">1302</a>
<a href="#1303" id="1303">1303</a>
<a href="#1304" id="1304">1304</a>
<a href="#1305" id="1305">1305</a>
<a href="#1306" id="1306">1306</a>
<a href="#1307" id="1307">1307</a>
<a href="#1308" id="1308">1308</a>
<a href="#1309" id="1309">1309</a>
<a href="#1310" id="1310">1310</a>
<a href="#1311" id="1311">1311</a>
<a href="#1312" id="1312">1312</a>
<a href="#1313" id="1313">1313</a>
<a href="#1314" id="1314">1314</a>
<a href="#1315" id="1315">1315</a>
<a href="#1316" id="1316">1316</a>
<a href="#1317" id="1317">1317</a>
<a href="#1318" id="1318">1318</a>
<a href="#1319" id="1319">1319</a>
<a href="#1320" id="1320">1320</a>
<a href="#1321" id="1321">1321</a>
<a href="#1322" id="1322">1322</a>
<a href="#1323" id="1323">1323</a>
<a href="#1324" id="1324">1324</a>
<a href="#1325" id="1325">1325</a>
<a href="#1326" id="1326">1326</a>
<a href="#1327" id="1327">1327</a>
<a href="#1328" id="1328">1328</a>
<a href="#1329" id="1329">1329</a>
<a href="#1330" id="1330">1330</a>
<a href="#1331" id="1331">1331</a>
<a href="#1332" id="1332">1332</a>
<a href="#1333" id="1333">1333</a>
<a href="#1334" id="1334">1334</a>
<a href="#1335" id="1335">1335</a>
<a href="#1336" id="1336">1336</a>
<a href="#1337" id="1337">1337</a>
<a href="#1338" id="1338">1338</a>
<a href="#1339" id="1339">1339</a>
<a href="#1340" id="1340">1340</a>
<a href="#1341" id="1341">1341</a>
<a href="#1342" id="1342">1342</a>
<a href="#1343" id="1343">1343</a>
<a href="#1344" id="1344">1344</a>
<a href="#1345" id="1345">1345</a>
<a href="#1346" id="1346">1346</a>
<a href="#1347" id="1347">1347</a>
<a href="#1348" id="1348">1348</a>
<a href="#1349" id="1349">1349</a>
<a href="#1350" id="1350">1350</a>
<a href="#1351" id="1351">1351</a>
<a href="#1352" id="1352">1352</a>
<a href="#1353" id="1353">1353</a>
<a href="#1354" id="1354">1354</a>
<a href="#1355" id="1355">1355</a>
<a href="#1356" id="1356">1356</a>
<a href="#1357" id="1357">1357</a>
<a href="#1358" id="1358">1358</a>
<a href="#1359" id="1359">1359</a>
<a href="#1360" id="1360">1360</a>
<a href="#1361" id="1361">1361</a>
<a href="#1362" id="1362">1362</a>
<a href="#1363" id="1363">1363</a>
<a href="#1364" id="1364">1364</a>
<a href="#1365" id="1365">1365</a>
<a href="#1366" id="1366">1366</a>
<a href="#1367" id="1367">1367</a>
<a href="#1368" id="1368">1368</a>
<a href="#1369" id="1369">1369</a>
<a href="#1370" id="1370">1370</a>
<a href="#1371" id="1371">1371</a>
<a href="#1372" id="1372">1372</a>
<a href="#1373" id="1373">1373</a>
<a href="#1374" id="1374">1374</a>
<a href="#1375" id="1375">1375</a>
<a href="#1376" id="1376">1376</a>
<a href="#1377" id="1377">1377</a>
<a href="#1378" id="1378">1378</a>
<a href="#1379" id="1379">1379</a>
<a href="#1380" id="1380">1380</a>
<a href="#1381" id="1381">1381</a>
<a href="#1382" id="1382">1382</a>
<a href="#1383" id="1383">1383</a>
<a href="#1384" id="1384">1384</a>
<a href="#1385" id="1385">1385</a>
<a href="#1386" id="1386">1386</a>
<a href="#1387" id="1387">1387</a>
<a href="#1388" id="1388">1388</a>
<a href="#1389" id="1389">1389</a>
<a href="#1390" id="1390">1390</a>
<a href="#1391" id="1391">1391</a>
<a href="#1392" id="1392">1392</a>
<a href="#1393" id="1393">1393</a>
<a href="#1394" id="1394">1394</a>
<a href="#1395" id="1395">1395</a>
<a href="#1396" id="1396">1396</a>
<a href="#1397" id="1397">1397</a>
<a href="#1398" id="1398">1398</a>
<a href="#1399" id="1399">1399</a>
<a href="#1400" id="1400">1400</a>
<a href="#1401" id="1401">1401</a>
<a href="#1402" id="1402">1402</a>
<a href="#1403" id="1403">1403</a>
<a href="#1404" id="1404">1404</a>
<a href="#1405" id="1405">1405</a>
<a href="#1406" id="1406">1406</a>
<a href="#1407" id="1407">1407</a>
<a href="#1408" id="1408">1408</a>
<a href="#1409" id="1409">1409</a>
<a href="#1410" id="1410">1410</a>
<a href="#1411" id="1411">1411</a>
<a href="#1412" id="1412">1412</a>
<a href="#1413" id="1413">1413</a>
<a href="#1414" id="1414">1414</a>
<a href="#1415" id="1415">1415</a>
<a href="#1416" id="1416">1416</a>
<a href="#1417" id="1417">1417</a>
<a href="#1418" id="1418">1418</a>
<a href="#1419" id="1419">1419</a>
<a href="#1420" id="1420">1420</a>
<a href="#1421" id="1421">1421</a>
<a href="#1422" id="1422">1422</a>
<a href="#1423" id="1423">1423</a>
<a href="#1424" id="1424">1424</a>
<a href="#1425" id="1425">1425</a>
<a href="#1426" id="1426">1426</a>
<a href="#1427" id="1427">1427</a>
<a href="#1428" id="1428">1428</a>
<a href="#1429" id="1429">1429</a>
<a href="#1430" id="1430">1430</a>
<a href="#1431" id="1431">1431</a>
<a href="#1432" id="1432">1432</a>
<a href="#1433" id="1433">1433</a>
<a href="#1434" id="1434">1434</a>
<a href="#1435" id="1435">1435</a>
<a href="#1436" id="1436">1436</a>
<a href="#1437" id="1437">1437</a>
<a href="#1438" id="1438">1438</a>
<a href="#1439" id="1439">1439</a>
<a href="#1440" id="1440">1440</a>
<a href="#1441" id="1441">1441</a>
<a href="#1442" id="1442">1442</a>
<a href="#1443" id="1443">1443</a>
<a href="#1444" id="1444">1444</a>
<a href="#1445" id="1445">1445</a>
<a href="#1446" id="1446">1446</a>
<a href="#1447" id="1447">1447</a>
<a href="#1448" id="1448">1448</a>
<a href="#1449" id="1449">1449</a>
<a href="#1450" id="1450">1450</a>
<a href="#1451" id="1451">1451</a>
<a href="#1452" id="1452">1452</a>
<a href="#1453" id="1453">1453</a>
<a href="#1454" id="1454">1454</a>
<a href="#1455" id="1455">1455</a>
<a href="#1456" id="1456">1456</a>
<a href="#1457" id="1457">1457</a>
<a href="#1458" id="1458">1458</a>
<a href="#1459" id="1459">1459</a>
<a href="#1460" id="1460">1460</a>
<a href="#1461" id="1461">1461</a>
<a href="#1462" id="1462">1462</a>
<a href="#1463" id="1463">1463</a>
<a href="#1464" id="1464">1464</a>
<a href="#1465" id="1465">1465</a>
<a href="#1466" id="1466">1466</a>
<a href="#1467" id="1467">1467</a>
<a href="#1468" id="1468">1468</a>
<a href="#1469" id="1469">1469</a>
<a href="#1470" id="1470">1470</a>
<a href="#1471" id="1471">1471</a>
<a href="#1472" id="1472">1472</a>
<a href="#1473" id="1473">1473</a>
<a href="#1474" id="1474">1474</a>
<a href="#1475" id="1475">1475</a>
<a href="#1476" id="1476">1476</a>
<a href="#1477" id="1477">1477</a>
<a href="#1478" id="1478">1478</a>
<a href="#1479" id="1479">1479</a>
<a href="#1480" id="1480">1480</a>
<a href="#1481" id="1481">1481</a>
<a href="#1482" id="1482">1482</a>
<a href="#1483" id="1483">1483</a>
<a href="#1484" id="1484">1484</a>
<a href="#1485" id="1485">1485</a>
<a href="#1486" id="1486">1486</a>
<a href="#1487" id="1487">1487</a>
<a href="#1488" id="1488">1488</a>
<a href="#1489" id="1489">1489</a>
<a href="#1490" id="1490">1490</a>
<a href="#1491" id="1491">1491</a>
<a href="#1492" id="1492">1492</a>
<a href="#1493" id="1493">1493</a>
<a href="#1494" id="1494">1494</a>
<a href="#1495" id="1495">1495</a>
<a href="#1496" id="1496">1496</a>
<a href="#1497" id="1497">1497</a>
<a href="#1498" id="1498">1498</a>
<a href="#1499" id="1499">1499</a>
<a href="#1500" id="1500">1500</a>
<a href="#1501" id="1501">1501</a>
<a href="#1502" id="1502">1502</a>
<a href="#1503" id="1503">1503</a>
<a href="#1504" id="1504">1504</a>
<a href="#1505" id="1505">1505</a>
<a href="#1506" id="1506">1506</a>
<a href="#1507" id="1507">1507</a>
<a href="#1508" id="1508">1508</a>
<a href="#1509" id="1509">1509</a>
<a href="#1510" id="1510">1510</a>
<a href="#1511" id="1511">1511</a>
<a href="#1512" id="1512">1512</a>
<a href="#1513" id="1513">1513</a>
<a href="#1514" id="1514">1514</a>
<a href="#1515" id="1515">1515</a>
<a href="#1516" id="1516">1516</a>
<a href="#1517" id="1517">1517</a>
<a href="#1518" id="1518">1518</a>
<a href="#1519" id="1519">1519</a>
<a href="#1520" id="1520">1520</a>
<a href="#1521" id="1521">1521</a>
<a href="#1522" id="1522">1522</a>
<a href="#1523" id="1523">1523</a>
<a href="#1524" id="1524">1524</a>
<a href="#1525" id="1525">1525</a>
<a href="#1526" id="1526">1526</a>
<a href="#1527" id="1527">1527</a>
<a href="#1528" id="1528">1528</a>
<a href="#1529" id="1529">1529</a>
<a href="#1530" id="1530">1530</a>
<a href="#1531" id="1531">1531</a>
<a href="#1532" id="1532">1532</a>
<a href="#1533" id="1533">1533</a>
<a href="#1534" id="1534">1534</a>
<a href="#1535" id="1535">1535</a>
<a href="#1536" id="1536">1536</a>
<a href="#1537" id="1537">1537</a>
<a href="#1538" id="1538">1538</a>
<a href="#1539" id="1539">1539</a>
<a href="#1540" id="1540">1540</a>
<a href="#1541" id="1541">1541</a>
<a href="#1542" id="1542">1542</a>
<a href="#1543" id="1543">1543</a>
<a href="#1544" id="1544">1544</a>
<a href="#1545" id="1545">1545</a>
<a href="#1546" id="1546">1546</a>
<a href="#1547" id="1547">1547</a>
<a href="#1548" id="1548">1548</a>
<a href="#1549" id="1549">1549</a>
<a href="#1550" id="1550">1550</a>
<a href="#1551" id="1551">1551</a>
<a href="#1552" id="1552">1552</a>
<a href="#1553" id="1553">1553</a>
<a href="#1554" id="1554">1554</a>
<a href="#1555" id="1555">1555</a>
<a href="#1556" id="1556">1556</a>
<a href="#1557" id="1557">1557</a>
<a href="#1558" id="1558">1558</a>
<a href="#1559" id="1559">1559</a>
<a href="#1560" id="1560">1560</a>
<a href="#1561" id="1561">1561</a>
<a href="#1562" id="1562">1562</a>
<a href="#1563" id="1563">1563</a>
<a href="#1564" id="1564">1564</a>
<a href="#1565" id="1565">1565</a>
<a href="#1566" id="1566">1566</a>
<a href="#1567" id="1567">1567</a>
<a href="#1568" id="1568">1568</a>
<a href="#1569" id="1569">1569</a>
<a href="#1570" id="1570">1570</a>
<a href="#1571" id="1571">1571</a>
<a href="#1572" id="1572">1572</a>
<a href="#1573" id="1573">1573</a>
<a href="#1574" id="1574">1574</a>
<a href="#1575" id="1575">1575</a>
<a href="#1576" id="1576">1576</a>
<a href="#1577" id="1577">1577</a>
<a href="#1578" id="1578">1578</a>
<a href="#1579" id="1579">1579</a>
<a href="#1580" id="1580">1580</a>
<a href="#1581" id="1581">1581</a>
<a href="#1582" id="1582">1582</a>
<a href="#1583" id="1583">1583</a>
<a href="#1584" id="1584">1584</a>
<a href="#1585" id="1585">1585</a>
<a href="#1586" id="1586">1586</a>
<a href="#1587" id="1587">1587</a>
<a href="#1588" id="1588">1588</a>
<a href="#1589" id="1589">1589</a>
<a href="#1590" id="1590">1590</a>
<a href="#1591" id="1591">1591</a>
<a href="#1592" id="1592">1592</a>
<a href="#1593" id="1593">1593</a>
<a href="#1594" id="1594">1594</a>
<a href="#1595" id="1595">1595</a>
<a href="#1596" id="1596">1596</a>
<a href="#1597" id="1597">1597</a>
<a href="#1598" id="1598">1598</a>
<a href="#1599" id="1599">1599</a>
<a href="#1600" id="1600">1600</a>
<a href="#1601" id="1601">1601</a>
<a href="#1602" id="1602">1602</a>
<a href="#1603" id="1603">1603</a>
<a href="#1604" id="1604">1604</a>
<a href="#1605" id="1605">1605</a>
<a href="#1606" id="1606">1606</a>
<a href="#1607" id="1607">1607</a>
<a href="#1608" id="1608">1608</a>
<a href="#1609" id="1609">1609</a>
<a href="#1610" id="1610">1610</a>
<a href="#1611" id="1611">1611</a>
<a href="#1612" id="1612">1612</a>
<a href="#1613" id="1613">1613</a>
<a href="#1614" id="1614">1614</a>
<a href="#1615" id="1615">1615</a>
<a href="#1616" id="1616">1616</a>
<a href="#1617" id="1617">1617</a>
<a href="#1618" id="1618">1618</a>
<a href="#1619" id="1619">1619</a>
<a href="#1620" id="1620">1620</a>
<a href="#1621" id="1621">1621</a>
<a href="#1622" id="1622">1622</a>
<a href="#1623" id="1623">1623</a>
<a href="#1624" id="1624">1624</a>
<a href="#1625" id="1625">1625</a>
<a href="#1626" id="1626">1626</a>
<a href="#1627" id="1627">1627</a>
<a href="#1628" id="1628">1628</a>
<a href="#1629" id="1629">1629</a>
<a href="#1630" id="1630">1630</a>
<a href="#1631" id="1631">1631</a>
<a href="#1632" id="1632">1632</a>
<a href="#1633" id="1633">1633</a>
<a href="#1634" id="1634">1634</a>
<a href="#1635" id="1635">1635</a>
<a href="#1636" id="1636">1636</a>
<a href="#1637" id="1637">1637</a>
<a href="#1638" id="1638">1638</a>
<a href="#1639" id="1639">1639</a>
<a href="#1640" id="1640">1640</a>
<a href="#1641" id="1641">1641</a>
<a href="#1642" id="1642">1642</a>
<a href="#1643" id="1643">1643</a>
<a href="#1644" id="1644">1644</a>
<a href="#1645" id="1645">1645</a>
<a href="#1646" id="1646">1646</a>
<a href="#1647" id="1647">1647</a>
<a href="#1648" id="1648">1648</a>
<a href="#1649" id="1649">1649</a>
<a href="#1650" id="1650">1650</a>
<a href="#1651" id="1651">1651</a>
<a href="#1652" id="1652">1652</a>
<a href="#1653" id="1653">1653</a>
<a href="#1654" id="1654">1654</a>
<a href="#1655" id="1655">1655</a>
<a href="#1656" id="1656">1656</a>
<a href="#1657" id="1657">1657</a>
<a href="#1658" id="1658">1658</a>
<a href="#1659" id="1659">1659</a>
<a href="#1660" id="1660">1660</a>
<a href="#1661" id="1661">1661</a>
<a href="#1662" id="1662">1662</a>
<a href="#1663" id="1663">1663</a>
<a href="#1664" id="1664">1664</a>
<a href="#1665" id="1665">1665</a>
<a href="#1666" id="1666">1666</a>
<a href="#1667" id="1667">1667</a>
<a href="#1668" id="1668">1668</a>
<a href="#1669" id="1669">1669</a>
<a href="#1670" id="1670">1670</a>
<a href="#1671" id="1671">1671</a>
<a href="#1672" id="1672">1672</a>
<a href="#1673" id="1673">1673</a>
<a href="#1674" id="1674">1674</a>
<a href="#1675" id="1675">1675</a>
<a href="#1676" id="1676">1676</a>
<a href="#1677" id="1677">1677</a>
<a href="#1678" id="1678">1678</a>
<a href="#1679" id="1679">1679</a>
<a href="#1680" id="1680">1680</a>
<a href="#1681" id="1681">1681</a>
<a href="#1682" id="1682">1682</a>
<a href="#1683" id="1683">1683</a>
<a href="#1684" id="1684">1684</a>
<a href="#1685" id="1685">1685</a>
<a href="#1686" id="1686">1686</a>
<a href="#1687" id="1687">1687</a>
<a href="#1688" id="1688">1688</a>
<a href="#1689" id="1689">1689</a>
<a href="#1690" id="1690">1690</a>
<a href="#1691" id="1691">1691</a>
<a href="#1692" id="1692">1692</a>
<a href="#1693" id="1693">1693</a>
<a href="#1694" id="1694">1694</a>
<a href="#1695" id="1695">1695</a>
<a href="#1696" id="1696">1696</a>
<a href="#1697" id="1697">1697</a>
<a href="#1698" id="1698">1698</a>
<a href="#1699" id="1699">1699</a>
<a href="#1700" id="1700">1700</a>
<a href="#1701" id="1701">1701</a>
<a href="#1702" id="1702">1702</a>
<a href="#1703" id="1703">1703</a>
<a href="#1704" id="1704">1704</a>
<a href="#1705" id="1705">1705</a>
<a href="#1706" id="1706">1706</a>
<a href="#1707" id="1707">1707</a>
<a href="#1708" id="1708">1708</a>
<a href="#1709" id="1709">1709</a>
<a href="#1710" id="1710">1710</a>
<a href="#1711" id="1711">1711</a>
<a href="#1712" id="1712">1712</a>
<a href="#1713" id="1713">1713</a>
<a href="#1714" id="1714">1714</a>
<a href="#1715" id="1715">1715</a>
<a href="#1716" id="1716">1716</a>
<a href="#1717" id="1717">1717</a>
<a href="#1718" id="1718">1718</a>
<a href="#1719" id="1719">1719</a>
<a href="#1720" id="1720">1720</a>
<a href="#1721" id="1721">1721</a>
<a href="#1722" id="1722">1722</a>
<a href="#1723" id="1723">1723</a>
<a href="#1724" id="1724">1724</a>
<a href="#1725" id="1725">1725</a>
<a href="#1726" id="1726">1726</a>
<a href="#1727" id="1727">1727</a>
<a href="#1728" id="1728">1728</a>
<a href="#1729" id="1729">1729</a>
<a href="#1730" id="1730">1730</a>
<a href="#1731" id="1731">1731</a>
<a href="#1732" id="1732">1732</a>
<a href="#1733" id="1733">1733</a>
<a href="#1734" id="1734">1734</a>
<a href="#1735" id="1735">1735</a>
<a href="#1736" id="1736">1736</a>
<a href="#1737" id="1737">1737</a>
<a href="#1738" id="1738">1738</a>
<a href="#1739" id="1739">1739</a>
<a href="#1740" id="1740">1740</a>
<a href="#1741" id="1741">1741</a>
<a href="#1742" id="1742">1742</a>
<a href="#1743" id="1743">1743</a>
<a href="#1744" id="1744">1744</a>
<a href="#1745" id="1745">1745</a>
<a href="#1746" id="1746">1746</a>
<a href="#1747" id="1747">1747</a>
<a href="#1748" id="1748">1748</a>
<a href="#1749" id="1749">1749</a>
<a href="#1750" id="1750">1750</a>
<a href="#1751" id="1751">1751</a>
<a href="#1752" id="1752">1752</a>
<a href="#1753" id="1753">1753</a>
<a href="#1754" id="1754">1754</a>
<a href="#1755" id="1755">1755</a>
<a href="#1756" id="1756">1756</a>
<a href="#1757" id="1757">1757</a>
<a href="#1758" id="1758">1758</a>
<a href="#1759" id="1759">1759</a>
<a href="#1760" id="1760">1760</a>
<a href="#1761" id="1761">1761</a>
<a href="#1762" id="1762">1762</a>
<a href="#1763" id="1763">1763</a>
<a href="#1764" id="1764">1764</a>
<a href="#1765" id="1765">1765</a>
<a href="#1766" id="1766">1766</a>
<a href="#1767" id="1767">1767</a>
<a href="#1768" id="1768">1768</a>
<a href="#1769" id="1769">1769</a>
<a href="#1770" id="1770">1770</a>
<a href="#1771" id="1771">1771</a>
<a href="#1772" id="1772">1772</a>
<a href="#1773" id="1773">1773</a>
<a href="#1774" id="1774">1774</a>
<a href="#1775" id="1775">1775</a>
<a href="#1776" id="1776">1776</a>
<a href="#1777" id="1777">1777</a>
<a href="#1778" id="1778">1778</a>
<a href="#1779" id="1779">1779</a>
<a href="#1780" id="1780">1780</a>
<a href="#1781" id="1781">1781</a>
<a href="#1782" id="1782">1782</a>
<a href="#1783" id="1783">1783</a>
<a href="#1784" id="1784">1784</a>
<a href="#1785" id="1785">1785</a>
<a href="#1786" id="1786">1786</a>
<a href="#1787" id="1787">1787</a>
<a href="#1788" id="1788">1788</a>
<a href="#1789" id="1789">1789</a>
<a href="#1790" id="1790">1790</a>
<a href="#1791" id="1791">1791</a>
<a href="#1792" id="1792">1792</a>
<a href="#1793" id="1793">1793</a>
<a href="#1794" id="1794">1794</a>
<a href="#1795" id="1795">1795</a>
<a href="#1796" id="1796">1796</a>
<a href="#1797" id="1797">1797</a>
<a href="#1798" id="1798">1798</a>
<a href="#1799" id="1799">1799</a>
<a href="#1800" id="1800">1800</a>
<a href="#1801" id="1801">1801</a>
<a href="#1802" id="1802">1802</a>
<a href="#1803" id="1803">1803</a>
<a href="#1804" id="1804">1804</a>
<a href="#1805" id="1805">1805</a>
<a href="#1806" id="1806">1806</a>
<a href="#1807" id="1807">1807</a>
<a href="#1808" id="1808">1808</a>
<a href="#1809" id="1809">1809</a>
<a href="#1810" id="1810">1810</a>
<a href="#1811" id="1811">1811</a>
<a href="#1812" id="1812">1812</a>
<a href="#1813" id="1813">1813</a>
<a href="#1814" id="1814">1814</a>
<a href="#1815" id="1815">1815</a>
<a href="#1816" id="1816">1816</a>
<a href="#1817" id="1817">1817</a>
<a href="#1818" id="1818">1818</a>
<a href="#1819" id="1819">1819</a>
<a href="#1820" id="1820">1820</a>
<a href="#1821" id="1821">1821</a>
<a href="#1822" id="1822">1822</a>
<a href="#1823" id="1823">1823</a>
<a href="#1824" id="1824">1824</a>
<a href="#1825" id="1825">1825</a>
<a href="#1826" id="1826">1826</a>
<a href="#1827" id="1827">1827</a>
<a href="#1828" id="1828">1828</a>
<a href="#1829" id="1829">1829</a>
<a href="#1830" id="1830">1830</a>
<a href="#1831" id="1831">1831</a>
<a href="#1832" id="1832">1832</a>
<a href="#1833" id="1833">1833</a>
<a href="#1834" id="1834">1834</a>
<a href="#1835" id="1835">1835</a>
<a href="#1836" id="1836">1836</a>
<a href="#1837" id="1837">1837</a>
<a href="#1838" id="1838">1838</a>
<a href="#1839" id="1839">1839</a>
<a href="#1840" id="1840">1840</a>
<a href="#1841" id="1841">1841</a>
<a href="#1842" id="1842">1842</a>
<a href="#1843" id="1843">1843</a>
<a href="#1844" id="1844">1844</a>
<a href="#1845" id="1845">1845</a>
<a href="#1846" id="1846">1846</a>
<a href="#1847" id="1847">1847</a>
<a href="#1848" id="1848">1848</a>
<a href="#1849" id="1849">1849</a>
<a href="#1850" id="1850">1850</a>
<a href="#1851" id="1851">1851</a>
<a href="#1852" id="1852">1852</a>
<a href="#1853" id="1853">1853</a>
<a href="#1854" id="1854">1854</a>
<a href="#1855" id="1855">1855</a>
<a href="#1856" id="1856">1856</a>
<a href="#1857" id="1857">1857</a>
<a href="#1858" id="1858">1858</a>
<a href="#1859" id="1859">1859</a>
<a href="#1860" id="1860">1860</a>
<a href="#1861" id="1861">1861</a>
<a href="#1862" id="1862">1862</a>
<a href="#1863" id="1863">1863</a>
<a href="#1864" id="1864">1864</a>
<a href="#1865" id="1865">1865</a>
<a href="#1866" id="1866">1866</a>
<a href="#1867" id="1867">1867</a>
<a href="#1868" id="1868">1868</a>
<a href="#1869" id="1869">1869</a>
<a href="#1870" id="1870">1870</a>
<a href="#1871" id="1871">1871</a>
<a href="#1872" id="1872">1872</a>
<a href="#1873" id="1873">1873</a>
<a href="#1874" id="1874">1874</a>
<a href="#1875" id="1875">1875</a>
<a href="#1876" id="1876">1876</a>
<a href="#1877" id="1877">1877</a>
<a href="#1878" id="1878">1878</a>
<a href="#1879" id="1879">1879</a>
<a href="#1880" id="1880">1880</a>
<a href="#1881" id="1881">1881</a>
<a href="#1882" id="1882">1882</a>
<a href="#1883" id="1883">1883</a>
<a href="#1884" id="1884">1884</a>
<a href="#1885" id="1885">1885</a>
<a href="#1886" id="1886">1886</a>
<a href="#1887" id="1887">1887</a>
<a href="#1888" id="1888">1888</a>
<a href="#1889" id="1889">1889</a>
<a href="#1890" id="1890">1890</a>
<a href="#1891" id="1891">1891</a>
<a href="#1892" id="1892">1892</a>
<a href="#1893" id="1893">1893</a>
<a href="#1894" id="1894">1894</a>
<a href="#1895" id="1895">1895</a>
<a href="#1896" id="1896">1896</a>
<a href="#1897" id="1897">1897</a>
<a href="#1898" id="1898">1898</a>
<a href="#1899" id="1899">1899</a>
<a href="#1900" id="1900">1900</a>
<a href="#1901" id="1901">1901</a>
<a href="#1902" id="1902">1902</a>
<a href="#1903" id="1903">1903</a>
<a href="#1904" id="1904">1904</a>
<a href="#1905" id="1905">1905</a>
<a href="#1906" id="1906">1906</a>
<a href="#1907" id="1907">1907</a>
<a href="#1908" id="1908">1908</a>
<a href="#1909" id="1909">1909</a>
<a href="#1910" id="1910">1910</a>
<a href="#1911" id="1911">1911</a>
<a href="#1912" id="1912">1912</a>
<a href="#1913" id="1913">1913</a>
<a href="#1914" id="1914">1914</a>
<a href="#1915" id="1915">1915</a>
<a href="#1916" id="1916">1916</a>
<a href="#1917" id="1917">1917</a>
<a href="#1918" id="1918">1918</a>
<a href="#1919" id="1919">1919</a>
<a href="#1920" id="1920">1920</a>
<a href="#1921" id="1921">1921</a>
<a href="#1922" id="1922">1922</a>
<a href="#1923" id="1923">1923</a>
<a href="#1924" id="1924">1924</a>
<a href="#1925" id="1925">1925</a>
<a href="#1926" id="1926">1926</a>
<a href="#1927" id="1927">1927</a>
<a href="#1928" id="1928">1928</a>
<a href="#1929" id="1929">1929</a>
<a href="#1930" id="1930">1930</a>
<a href="#1931" id="1931">1931</a>
<a href="#1932" id="1932">1932</a>
<a href="#1933" id="1933">1933</a>
<a href="#1934" id="1934">1934</a>
<a href="#1935" id="1935">1935</a>
<a href="#1936" id="1936">1936</a>
<a href="#1937" id="1937">1937</a>
<a href="#1938" id="1938">1938</a>
<a href="#1939" id="1939">1939</a>
<a href="#1940" id="1940">1940</a>
<a href="#1941" id="1941">1941</a>
<a href="#1942" id="1942">1942</a>
<a href="#1943" id="1943">1943</a>
<a href="#1944" id="1944">1944</a>
<a href="#1945" id="1945">1945</a>
<a href="#1946" id="1946">1946</a>
<a href="#1947" id="1947">1947</a>
<a href="#1948" id="1948">1948</a>
<a href="#1949" id="1949">1949</a>
<a href="#1950" id="1950">1950</a>
<a href="#1951" id="1951">1951</a>
<a href="#1952" id="1952">1952</a>
<a href="#1953" id="1953">1953</a>
<a href="#1954" id="1954">1954</a>
<a href="#1955" id="1955">1955</a>
<a href="#1956" id="1956">1956</a>
<a href="#1957" id="1957">1957</a>
<a href="#1958" id="1958">1958</a>
<a href="#1959" id="1959">1959</a>
<a href="#1960" id="1960">1960</a>
<a href="#1961" id="1961">1961</a>
<a href="#1962" id="1962">1962</a>
<a href="#1963" id="1963">1963</a>
<a href="#1964" id="1964">1964</a>
<a href="#1965" id="1965">1965</a>
<a href="#1966" id="1966">1966</a>
<a href="#1967" id="1967">1967</a>
<a href="#1968" id="1968">1968</a>
<a href="#1969" id="1969">1969</a>
<a href="#1970" id="1970">1970</a>
<a href="#1971" id="1971">1971</a>
<a href="#1972" id="1972">1972</a>
<a href="#1973" id="1973">1973</a>
<a href="#1974" id="1974">1974</a>
<a href="#1975" id="1975">1975</a>
<a href="#1976" id="1976">1976</a>
<a href="#1977" id="1977">1977</a>
<a href="#1978" id="1978">1978</a>
<a href="#1979" id="1979">1979</a>
<a href="#1980" id="1980">1980</a>
<a href="#1981" id="1981">1981</a>
<a href="#1982" id="1982">1982</a>
<a href="#1983" id="1983">1983</a>
<a href="#1984" id="1984">1984</a>
<a href="#1985" id="1985">1985</a>
<a href="#1986" id="1986">1986</a>
<a href="#1987" id="1987">1987</a>
<a href="#1988" id="1988">1988</a>
<a href="#1989" id="1989">1989</a>
<a href="#1990" id="1990">1990</a>
<a href="#1991" id="1991">1991</a>
<a href="#1992" id="1992">1992</a>
<a href="#1993" id="1993">1993</a>
<a href="#1994" id="1994">1994</a>
<a href="#1995" id="1995">1995</a>
<a href="#1996" id="1996">1996</a>
<a href="#1997" id="1997">1997</a>
<a href="#1998" id="1998">1998</a>
<a href="#1999" id="1999">1999</a>
<a href="#2000" id="2000">2000</a>
<a href="#2001" id="2001">2001</a>
<a href="#2002" id="2002">2002</a>
<a href="#2003" id="2003">2003</a>
<a href="#2004" id="2004">2004</a>
<a href="#2005" id="2005">2005</a>
<a href="#2006" id="2006">2006</a>
<a href="#2007" id="2007">2007</a>
<a href="#2008" id="2008">2008</a>
<a href="#2009" id="2009">2009</a>
<a href="#2010" id="2010">2010</a>
<a href="#2011" id="2011">2011</a>
<a href="#2012" id="2012">2012</a>
<a href="#2013" id="2013">2013</a>
<a href="#2014" id="2014">2014</a>
<a href="#2015" id="2015">2015</a>
<a href="#2016" id="2016">2016</a>
<a href="#2017" id="2017">2017</a>
<a href="#2018" id="2018">2018</a>
<a href="#2019" id="2019">2019</a>
<a href="#2020" id="2020">2020</a>
<a href="#2021" id="2021">2021</a>
<a href="#2022" id="2022">2022</a>
<a href="#2023" id="2023">2023</a>
<a href="#2024" id="2024">2024</a>
<a href="#2025" id="2025">2025</a>
<a href="#2026" id="2026">2026</a>
<a href="#2027" id="2027">2027</a>
<a href="#2028" id="2028">2028</a>
<a href="#2029" id="2029">2029</a>
<a href="#2030" id="2030">2030</a>
<a href="#2031" id="2031">2031</a>
<a href="#2032" id="2032">2032</a>
<a href="#2033" id="2033">2033</a>
<a href="#2034" id="2034">2034</a>
<a href="#2035" id="2035">2035</a>
<a href="#2036" id="2036">2036</a>
<a href="#2037" id="2037">2037</a>
<a href="#2038" id="2038">2038</a>
<a href="#2039" id="2039">2039</a>
<a href="#2040" id="2040">2040</a>
<a href="#2041" id="2041">2041</a>
<a href="#2042" id="2042">2042</a>
<a href="#2043" id="2043">2043</a>
<a href="#2044" id="2044">2044</a>
<a href="#2045" id="2045">2045</a>
<a href="#2046" id="2046">2046</a>
<a href="#2047" id="2047">2047</a>
<a href="#2048" id="2048">2048</a>
<a href="#2049" id="2049">2049</a>
<a href="#2050" id="2050">2050</a>
<a href="#2051" id="2051">2051</a>
<a href="#2052" id="2052">2052</a>
<a href="#2053" id="2053">2053</a>
<a href="#2054" id="2054">2054</a>
<a href="#2055" id="2055">2055</a>
<a href="#2056" id="2056">2056</a>
<a href="#2057" id="2057">2057</a>
<a href="#2058" id="2058">2058</a>
<a href="#2059" id="2059">2059</a>
<a href="#2060" id="2060">2060</a>
<a href="#2061" id="2061">2061</a>
<a href="#2062" id="2062">2062</a>
<a href="#2063" id="2063">2063</a>
<a href="#2064" id="2064">2064</a>
<a href="#2065" id="2065">2065</a>
<a href="#2066" id="2066">2066</a>
<a href="#2067" id="2067">2067</a>
<a href="#2068" id="2068">2068</a>
<a href="#2069" id="2069">2069</a>
<a href="#2070" id="2070">2070</a>
<a href="#2071" id="2071">2071</a>
<a href="#2072" id="2072">2072</a>
<a href="#2073" id="2073">2073</a>
<a href="#2074" id="2074">2074</a>
<a href="#2075" id="2075">2075</a>
<a href="#2076" id="2076">2076</a>
<a href="#2077" id="2077">2077</a>
<a href="#2078" id="2078">2078</a>
<a href="#2079" id="2079">2079</a>
<a href="#2080" id="2080">2080</a>
<a href="#2081" id="2081">2081</a>
<a href="#2082" id="2082">2082</a>
<a href="#2083" id="2083">2083</a>
<a href="#2084" id="2084">2084</a>
<a href="#2085" id="2085">2085</a>
<a href="#2086" id="2086">2086</a>
<a href="#2087" id="2087">2087</a>
<a href="#2088" id="2088">2088</a>
<a href="#2089" id="2089">2089</a>
<a href="#2090" id="2090">2090</a>
<a href="#2091" id="2091">2091</a>
<a href="#2092" id="2092">2092</a>
<a href="#2093" id="2093">2093</a>
<a href="#2094" id="2094">2094</a>
<a href="#2095" id="2095">2095</a>
<a href="#2096" id="2096">2096</a>
<a href="#2097" id="2097">2097</a>
<a href="#2098" id="2098">2098</a>
<a href="#2099" id="2099">2099</a>
<a href="#2100" id="2100">2100</a>
<a href="#2101" id="2101">2101</a>
<a href="#2102" id="2102">2102</a>
<a href="#2103" id="2103">2103</a>
<a href="#2104" id="2104">2104</a>
<a href="#2105" id="2105">2105</a>
<a href="#2106" id="2106">2106</a>
<a href="#2107" id="2107">2107</a>
<a href="#2108" id="2108">2108</a>
<a href="#2109" id="2109">2109</a>
<a href="#2110" id="2110">2110</a>
<a href="#2111" id="2111">2111</a>
<a href="#2112" id="2112">2112</a>
<a href="#2113" id="2113">2113</a>
<a href="#2114" id="2114">2114</a>
<a href="#2115" id="2115">2115</a>
<a href="#2116" id="2116">2116</a>
<a href="#2117" id="2117">2117</a>
<a href="#2118" id="2118">2118</a>
<a href="#2119" id="2119">2119</a>
<a href="#2120" id="2120">2120</a>
<a href="#2121" id="2121">2121</a>
<a href="#2122" id="2122">2122</a>
<a href="#2123" id="2123">2123</a>
<a href="#2124" id="2124">2124</a>
<a href="#2125" id="2125">2125</a>
<a href="#2126" id="2126">2126</a>
<a href="#2127" id="2127">2127</a>
<a href="#2128" id="2128">2128</a>
<a href="#2129" id="2129">2129</a>
<a href="#2130" id="2130">2130</a>
<a href="#2131" id="2131">2131</a>
<a href="#2132" id="2132">2132</a>
<a href="#2133" id="2133">2133</a>
<a href="#2134" id="2134">2134</a>
<a href="#2135" id="2135">2135</a>
<a href="#2136" id="2136">2136</a>
<a href="#2137" id="2137">2137</a>
<a href="#2138" id="2138">2138</a>
<a href="#2139" id="2139">2139</a>
<a href="#2140" id="2140">2140</a>
<a href="#2141" id="2141">2141</a>
<a href="#2142" id="2142">2142</a>
<a href="#2143" id="2143">2143</a>
<a href="#2144" id="2144">2144</a>
<a href="#2145" id="2145">2145</a>
<a href="#2146" id="2146">2146</a>
<a href="#2147" id="2147">2147</a>
<a href="#2148" id="2148">2148</a>
<a href="#2149" id="2149">2149</a>
<a href="#2150" id="2150">2150</a>
<a href="#2151" id="2151">2151</a>
<a href="#2152" id="2152">2152</a>
<a href="#2153" id="2153">2153</a>
<a href="#2154" id="2154">2154</a>
<a href="#2155" id="2155">2155</a>
<a href="#2156" id="2156">2156</a>
<a href="#2157" id="2157">2157</a>
<a href="#2158" id="2158">2158</a>
<a href="#2159" id="2159">2159</a>
<a href="#2160" id="2160">2160</a>
<a href="#2161" id="2161">2161</a>
<a href="#2162" id="2162">2162</a>
<a href="#2163" id="2163">2163</a>
<a href="#2164" id="2164">2164</a>
<a href="#2165" id="2165">2165</a>
<a href="#2166" id="2166">2166</a>
<a href="#2167" id="2167">2167</a>
<a href="#2168" id="2168">2168</a>
<a href="#2169" id="2169">2169</a>
<a href="#2170" id="2170">2170</a>
<a href="#2171" id="2171">2171</a>
<a href="#2172" id="2172">2172</a>
<a href="#2173" id="2173">2173</a>
<a href="#2174" id="2174">2174</a>
<a href="#2175" id="2175">2175</a>
<a href="#2176" id="2176">2176</a>
<a href="#2177" id="2177">2177</a>
<a href="#2178" id="2178">2178</a>
<a href="#2179" id="2179">2179</a>
<a href="#2180" id="2180">2180</a>
<a href="#2181" id="2181">2181</a>
<a href="#2182" id="2182">2182</a>
<a href="#2183" id="2183">2183</a>
<a href="#2184" id="2184">2184</a>
<a href="#2185" id="2185">2185</a>
<a href="#2186" id="2186">2186</a>
<a href="#2187" id="2187">2187</a>
<a href="#2188" id="2188">2188</a>
<a href="#2189" id="2189">2189</a>
<a href="#2190" id="2190">2190</a>
<a href="#2191" id="2191">2191</a>
<a href="#2192" id="2192">2192</a>
<a href="#2193" id="2193">2193</a>
<a href="#2194" id="2194">2194</a>
<a href="#2195" id="2195">2195</a>
<a href="#2196" id="2196">2196</a>
<a href="#2197" id="2197">2197</a>
<a href="#2198" id="2198">2198</a>
<a href="#2199" id="2199">2199</a>
<a href="#2200" id="2200">2200</a>
<a href="#2201" id="2201">2201</a>
<a href="#2202" id="2202">2202</a>
<a href="#2203" id="2203">2203</a>
<a href="#2204" id="2204">2204</a>
<a href="#2205" id="2205">2205</a>
<a href="#2206" id="2206">2206</a>
<a href="#2207" id="2207">2207</a>
<a href="#2208" id="2208">2208</a>
<a href="#2209" id="2209">2209</a>
<a href="#2210" id="2210">2210</a>
<a href="#2211" id="2211">2211</a>
<a href="#2212" id="2212">2212</a>
<a href="#2213" id="2213">2213</a>
<a href="#2214" id="2214">2214</a>
<a href="#2215" id="2215">2215</a>
<a href="#2216" id="2216">2216</a>
<a href="#2217" id="2217">2217</a>
<a href="#2218" id="2218">2218</a>
<a href="#2219" id="2219">2219</a>
<a href="#2220" id="2220">2220</a>
<a href="#2221" id="2221">2221</a>
<a href="#2222" id="2222">2222</a>
<a href="#2223" id="2223">2223</a>
<a href="#2224" id="2224">2224</a>
<a href="#2225" id="2225">2225</a>
<a href="#2226" id="2226">2226</a>
<a href="#2227" id="2227">2227</a>
<a href="#2228" id="2228">2228</a>
<a href="#2229" id="2229">2229</a>
<a href="#2230" id="2230">2230</a>
<a href="#2231" id="2231">2231</a>
<a href="#2232" id="2232">2232</a>
<a href="#2233" id="2233">2233</a>
<a href="#2234" id="2234">2234</a>
<a href="#2235" id="2235">2235</a>
<a href="#2236" id="2236">2236</a>
<a href="#2237" id="2237">2237</a>
<a href="#2238" id="2238">2238</a>
<a href="#2239" id="2239">2239</a>
<a href="#2240" id="2240">2240</a>
<a href="#2241" id="2241">2241</a>
<a href="#2242" id="2242">2242</a>
<a href="#2243" id="2243">2243</a>
<a href="#2244" id="2244">2244</a>
<a href="#2245" id="2245">2245</a>
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</pre><pre class="rust"><code><span class="kw">use </span>core::num::FpCategory;
<span class="kw">use </span>core::ops::{Add, Div, Neg};
<span class="kw">use </span>core::f32;
<span class="kw">use </span>core::f64;
<span class="kw">use crate</span>::{Num, NumCast, ToPrimitive};
<span class="doccomment">/// Generic trait for floating point numbers that works with `no_std`.
///
/// This trait implements a subset of the `Float` trait.
</span><span class="kw">pub trait </span>FloatCore: Num + NumCast + Neg<Output = <span class="self">Self</span>> + PartialOrd + Copy {
<span class="doccomment">/// Returns positive infinity.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T) {
/// assert!(T::infinity() == x);
/// }
///
/// check(f32::INFINITY);
/// check(f64::INFINITY);
/// ```
</span><span class="kw">fn </span>infinity() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns negative infinity.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T) {
/// assert!(T::neg_infinity() == x);
/// }
///
/// check(f32::NEG_INFINITY);
/// check(f64::NEG_INFINITY);
/// ```
</span><span class="kw">fn </span>neg_infinity() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns NaN.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
///
/// fn check<T: FloatCore>() {
/// let n = T::nan();
/// assert!(n != n);
/// }
///
/// check::<f32>();
/// check::<f64>();
/// ```
</span><span class="kw">fn </span>nan() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `-0.0`.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(n: T) {
/// let z = T::neg_zero();
/// assert!(z.is_zero());
/// assert!(T::one() / z == n);
/// }
///
/// check(f32::NEG_INFINITY);
/// check(f64::NEG_INFINITY);
/// ```
</span><span class="kw">fn </span>neg_zero() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest finite value that this type can represent.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T) {
/// assert!(T::min_value() == x);
/// }
///
/// check(f32::MIN);
/// check(f64::MIN);
/// ```
</span><span class="kw">fn </span>min_value() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest positive, normalized value that this type can represent.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T) {
/// assert!(T::min_positive_value() == x);
/// }
///
/// check(f32::MIN_POSITIVE);
/// check(f64::MIN_POSITIVE);
/// ```
</span><span class="kw">fn </span>min_positive_value() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns epsilon, a small positive value.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T) {
/// assert!(T::epsilon() == x);
/// }
///
/// check(f32::EPSILON);
/// check(f64::EPSILON);
/// ```
</span><span class="kw">fn </span>epsilon() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the largest finite value that this type can represent.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T) {
/// assert!(T::max_value() == x);
/// }
///
/// check(f32::MAX);
/// check(f64::MAX);
/// ```
</span><span class="kw">fn </span>max_value() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `true` if the number is NaN.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, p: bool) {
/// assert!(x.is_nan() == p);
/// }
///
/// check(f32::NAN, true);
/// check(f32::INFINITY, false);
/// check(f64::NAN, true);
/// check(0.0f64, false);
/// ```
</span><span class="attr">#[inline]
#[allow(clippy::eq_op)]
</span><span class="kw">fn </span>is_nan(<span class="self">self</span>) -> bool {
<span class="self">self </span>!= <span class="self">self
</span>}
<span class="doccomment">/// Returns `true` if the number is infinite.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, p: bool) {
/// assert!(x.is_infinite() == p);
/// }
///
/// check(f32::INFINITY, true);
/// check(f32::NEG_INFINITY, true);
/// check(f32::NAN, false);
/// check(f64::INFINITY, true);
/// check(f64::NEG_INFINITY, true);
/// check(0.0f64, false);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_infinite(<span class="self">self</span>) -> bool {
<span class="self">self </span>== <span class="self">Self</span>::infinity() || <span class="self">self </span>== <span class="self">Self</span>::neg_infinity()
}
<span class="doccomment">/// Returns `true` if the number is neither infinite or NaN.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, p: bool) {
/// assert!(x.is_finite() == p);
/// }
///
/// check(f32::INFINITY, false);
/// check(f32::MAX, true);
/// check(f64::NEG_INFINITY, false);
/// check(f64::MIN_POSITIVE, true);
/// check(f64::NAN, false);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_finite(<span class="self">self</span>) -> bool {
!(<span class="self">self</span>.is_nan() || <span class="self">self</span>.is_infinite())
}
<span class="doccomment">/// Returns `true` if the number is neither zero, infinite, subnormal or NaN.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, p: bool) {
/// assert!(x.is_normal() == p);
/// }
///
/// check(f32::INFINITY, false);
/// check(f32::MAX, true);
/// check(f64::NEG_INFINITY, false);
/// check(f64::MIN_POSITIVE, true);
/// check(0.0f64, false);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_normal(<span class="self">self</span>) -> bool {
<span class="self">self</span>.classify() == FpCategory::Normal
}
<span class="doccomment">/// Returns `true` if the number is [subnormal].
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::f64;
///
/// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
/// let max = f64::MAX;
/// let lower_than_min = 1.0e-308_f64;
/// let zero = 0.0_f64;
///
/// assert!(!min.is_subnormal());
/// assert!(!max.is_subnormal());
///
/// assert!(!zero.is_subnormal());
/// assert!(!f64::NAN.is_subnormal());
/// assert!(!f64::INFINITY.is_subnormal());
/// // Values between `0` and `min` are Subnormal.
/// assert!(lower_than_min.is_subnormal());
/// ```
/// [subnormal]: https://en.wikipedia.org/wiki/Subnormal_number
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_subnormal(<span class="self">self</span>) -> bool {
<span class="self">self</span>.classify() == FpCategory::Subnormal
}
<span class="doccomment">/// Returns the floating point category of the number. If only one property
/// is going to be tested, it is generally faster to use the specific
/// predicate instead.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
/// use std::num::FpCategory;
///
/// fn check<T: FloatCore>(x: T, c: FpCategory) {
/// assert!(x.classify() == c);
/// }
///
/// check(f32::INFINITY, FpCategory::Infinite);
/// check(f32::MAX, FpCategory::Normal);
/// check(f64::NAN, FpCategory::Nan);
/// check(f64::MIN_POSITIVE, FpCategory::Normal);
/// check(f64::MIN_POSITIVE / 2.0, FpCategory::Subnormal);
/// check(0.0f64, FpCategory::Zero);
/// ```
</span><span class="kw">fn </span>classify(<span class="self">self</span>) -> FpCategory;
<span class="doccomment">/// Returns the largest integer less than or equal to a number.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.floor() == y);
/// }
///
/// check(f32::INFINITY, f32::INFINITY);
/// check(0.9f32, 0.0);
/// check(1.0f32, 1.0);
/// check(1.1f32, 1.0);
/// check(-0.0f64, 0.0);
/// check(-0.9f64, -1.0);
/// check(-1.0f64, -1.0);
/// check(-1.1f64, -2.0);
/// check(f64::MIN, f64::MIN);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>floor(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>f = <span class="self">self</span>.fract();
<span class="kw">if </span>f.is_nan() || f.is_zero() {
<span class="self">self
</span>} <span class="kw">else if </span><span class="self">self </span>< <span class="self">Self</span>::zero() {
<span class="self">self </span>- f - <span class="self">Self</span>::one()
} <span class="kw">else </span>{
<span class="self">self </span>- f
}
}
<span class="doccomment">/// Returns the smallest integer greater than or equal to a number.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.ceil() == y);
/// }
///
/// check(f32::INFINITY, f32::INFINITY);
/// check(0.9f32, 1.0);
/// check(1.0f32, 1.0);
/// check(1.1f32, 2.0);
/// check(-0.0f64, 0.0);
/// check(-0.9f64, -0.0);
/// check(-1.0f64, -1.0);
/// check(-1.1f64, -1.0);
/// check(f64::MIN, f64::MIN);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>ceil(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>f = <span class="self">self</span>.fract();
<span class="kw">if </span>f.is_nan() || f.is_zero() {
<span class="self">self
</span>} <span class="kw">else if </span><span class="self">self </span>> <span class="self">Self</span>::zero() {
<span class="self">self </span>- f + <span class="self">Self</span>::one()
} <span class="kw">else </span>{
<span class="self">self </span>- f
}
}
<span class="doccomment">/// Returns the nearest integer to a number. Round half-way cases away from `0.0`.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.round() == y);
/// }
///
/// check(f32::INFINITY, f32::INFINITY);
/// check(0.4f32, 0.0);
/// check(0.5f32, 1.0);
/// check(0.6f32, 1.0);
/// check(-0.4f64, 0.0);
/// check(-0.5f64, -1.0);
/// check(-0.6f64, -1.0);
/// check(f64::MIN, f64::MIN);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>round(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>one = <span class="self">Self</span>::one();
<span class="kw">let </span>h = <span class="self">Self</span>::from(<span class="number">0.5</span>).expect(<span class="string">"Unable to cast from 0.5"</span>);
<span class="kw">let </span>f = <span class="self">self</span>.fract();
<span class="kw">if </span>f.is_nan() || f.is_zero() {
<span class="self">self
</span>} <span class="kw">else if </span><span class="self">self </span>> <span class="self">Self</span>::zero() {
<span class="kw">if </span>f < h {
<span class="self">self </span>- f
} <span class="kw">else </span>{
<span class="self">self </span>- f + one
}
} <span class="kw">else if </span>-f < h {
<span class="self">self </span>- f
} <span class="kw">else </span>{
<span class="self">self </span>- f - one
}
}
<span class="doccomment">/// Return the integer part of a number.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.trunc() == y);
/// }
///
/// check(f32::INFINITY, f32::INFINITY);
/// check(0.9f32, 0.0);
/// check(1.0f32, 1.0);
/// check(1.1f32, 1.0);
/// check(-0.0f64, 0.0);
/// check(-0.9f64, -0.0);
/// check(-1.0f64, -1.0);
/// check(-1.1f64, -1.0);
/// check(f64::MIN, f64::MIN);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>trunc(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>f = <span class="self">self</span>.fract();
<span class="kw">if </span>f.is_nan() {
<span class="self">self
</span>} <span class="kw">else </span>{
<span class="self">self </span>- f
}
}
<span class="doccomment">/// Returns the fractional part of a number.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.fract() == y);
/// }
///
/// check(f32::MAX, 0.0);
/// check(0.75f32, 0.75);
/// check(1.0f32, 0.0);
/// check(1.25f32, 0.25);
/// check(-0.0f64, 0.0);
/// check(-0.75f64, -0.75);
/// check(-1.0f64, 0.0);
/// check(-1.25f64, -0.25);
/// check(f64::MIN, 0.0);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>fract(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">if </span><span class="self">self</span>.is_zero() {
<span class="self">Self</span>::zero()
} <span class="kw">else </span>{
<span class="self">self </span>% <span class="self">Self</span>::one()
}
}
<span class="doccomment">/// Computes the absolute value of `self`. Returns `FloatCore::nan()` if the
/// number is `FloatCore::nan()`.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.abs() == y);
/// }
///
/// check(f32::INFINITY, f32::INFINITY);
/// check(1.0f32, 1.0);
/// check(0.0f64, 0.0);
/// check(-0.0f64, 0.0);
/// check(-1.0f64, 1.0);
/// check(f64::MIN, f64::MAX);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>abs(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">if </span><span class="self">self</span>.is_sign_positive() {
<span class="kw">return </span><span class="self">self</span>;
}
<span class="kw">if </span><span class="self">self</span>.is_sign_negative() {
<span class="kw">return </span>-<span class="self">self</span>;
}
<span class="self">Self</span>::nan()
}
<span class="doccomment">/// Returns a number that represents the sign of `self`.
///
/// - `1.0` if the number is positive, `+0.0` or `FloatCore::infinity()`
/// - `-1.0` if the number is negative, `-0.0` or `FloatCore::neg_infinity()`
/// - `FloatCore::nan()` if the number is `FloatCore::nan()`
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.signum() == y);
/// }
///
/// check(f32::INFINITY, 1.0);
/// check(3.0f32, 1.0);
/// check(0.0f32, 1.0);
/// check(-0.0f64, -1.0);
/// check(-3.0f64, -1.0);
/// check(f64::MIN, -1.0);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>signum(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">if </span><span class="self">self</span>.is_nan() {
<span class="self">Self</span>::nan()
} <span class="kw">else if </span><span class="self">self</span>.is_sign_negative() {
-<span class="self">Self</span>::one()
} <span class="kw">else </span>{
<span class="self">Self</span>::one()
}
}
<span class="doccomment">/// Returns `true` if `self` is positive, including `+0.0` and
/// `FloatCore::infinity()`, and `FloatCore::nan()`.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, p: bool) {
/// assert!(x.is_sign_positive() == p);
/// }
///
/// check(f32::INFINITY, true);
/// check(f32::MAX, true);
/// check(0.0f32, true);
/// check(-0.0f64, false);
/// check(f64::NEG_INFINITY, false);
/// check(f64::MIN_POSITIVE, true);
/// check(f64::NAN, true);
/// check(-f64::NAN, false);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_sign_positive(<span class="self">self</span>) -> bool {
!<span class="self">self</span>.is_sign_negative()
}
<span class="doccomment">/// Returns `true` if `self` is negative, including `-0.0` and
/// `FloatCore::neg_infinity()`, and `-FloatCore::nan()`.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, p: bool) {
/// assert!(x.is_sign_negative() == p);
/// }
///
/// check(f32::INFINITY, false);
/// check(f32::MAX, false);
/// check(0.0f32, false);
/// check(-0.0f64, true);
/// check(f64::NEG_INFINITY, true);
/// check(f64::MIN_POSITIVE, false);
/// check(f64::NAN, false);
/// check(-f64::NAN, true);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_sign_negative(<span class="self">self</span>) -> bool {
<span class="kw">let </span>(<span class="kw">_</span>, <span class="kw">_</span>, sign) = <span class="self">self</span>.integer_decode();
sign < <span class="number">0
</span>}
<span class="doccomment">/// Returns the minimum of the two numbers.
///
/// If one of the arguments is NaN, then the other argument is returned.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T, min: T) {
/// assert!(x.min(y) == min);
/// }
///
/// check(1.0f32, 2.0, 1.0);
/// check(f32::NAN, 2.0, 2.0);
/// check(1.0f64, -2.0, -2.0);
/// check(1.0f64, f64::NAN, 1.0);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw">if </span><span class="self">self</span>.is_nan() {
<span class="kw">return </span>other;
}
<span class="kw">if </span>other.is_nan() {
<span class="kw">return </span><span class="self">self</span>;
}
<span class="kw">if </span><span class="self">self </span>< other {
<span class="self">self
</span>} <span class="kw">else </span>{
other
}
}
<span class="doccomment">/// Returns the maximum of the two numbers.
///
/// If one of the arguments is NaN, then the other argument is returned.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T, max: T) {
/// assert!(x.max(y) == max);
/// }
///
/// check(1.0f32, 2.0, 2.0);
/// check(1.0f32, f32::NAN, 1.0);
/// check(-1.0f64, 2.0, 2.0);
/// check(-1.0f64, f64::NAN, -1.0);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw">if </span><span class="self">self</span>.is_nan() {
<span class="kw">return </span>other;
}
<span class="kw">if </span>other.is_nan() {
<span class="kw">return </span><span class="self">self</span>;
}
<span class="kw">if </span><span class="self">self </span>> other {
<span class="self">self
</span>} <span class="kw">else </span>{
other
}
}
<span class="doccomment">/// Returns the reciprocal (multiplicative inverse) of the number.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, y: T) {
/// assert!(x.recip() == y);
/// assert!(y.recip() == x);
/// }
///
/// check(f32::INFINITY, 0.0);
/// check(2.0f32, 0.5);
/// check(-0.25f64, -4.0);
/// check(-0.0f64, f64::NEG_INFINITY);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>recip(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="self">Self</span>::one() / <span class="self">self
</span>}
<span class="doccomment">/// Raise a number to an integer power.
///
/// Using this function is generally faster than using `powf`
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
///
/// fn check<T: FloatCore>(x: T, exp: i32, powi: T) {
/// assert!(x.powi(exp) == powi);
/// }
///
/// check(9.0f32, 2, 81.0);
/// check(1.0f32, -2, 1.0);
/// check(10.0f64, 20, 1e20);
/// check(4.0f64, -2, 0.0625);
/// check(-1.0f64, std::i32::MIN, 1.0);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>powi(<span class="kw-2">mut </span><span class="self">self</span>, <span class="kw-2">mut </span>exp: i32) -> <span class="self">Self </span>{
<span class="kw">if </span>exp < <span class="number">0 </span>{
exp = exp.wrapping_neg();
<span class="self">self </span>= <span class="self">self</span>.recip();
}
<span class="comment">// It should always be possible to convert a positive `i32` to a `usize`.
// Note, `i32::MIN` will wrap and still be negative, so we need to convert
// to `u32` without sign-extension before growing to `usize`.
</span><span class="kw">super</span>::pow(<span class="self">self</span>, (exp <span class="kw">as </span>u32).to_usize().unwrap())
}
<span class="doccomment">/// Converts to degrees, assuming the number is in radians.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(rad: T, deg: T) {
/// assert!(rad.to_degrees() == deg);
/// }
///
/// check(0.0f32, 0.0);
/// check(f32::consts::PI, 180.0);
/// check(f64::consts::FRAC_PI_4, 45.0);
/// check(f64::INFINITY, f64::INFINITY);
/// ```
</span><span class="kw">fn </span>to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Converts to radians, assuming the number is in degrees.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(deg: T, rad: T) {
/// assert!(deg.to_radians() == rad);
/// }
///
/// check(0.0f32, 0.0);
/// check(180.0, f32::consts::PI);
/// check(45.0, f64::consts::FRAC_PI_4);
/// check(f64::INFINITY, f64::INFINITY);
/// ```
</span><span class="kw">fn </span>to_radians(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
/// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
///
/// # Examples
///
/// ```
/// use num_traits::float::FloatCore;
/// use std::{f32, f64};
///
/// fn check<T: FloatCore>(x: T, m: u64, e: i16, s:i8) {
/// let (mantissa, exponent, sign) = x.integer_decode();
/// assert_eq!(mantissa, m);
/// assert_eq!(exponent, e);
/// assert_eq!(sign, s);
/// }
///
/// check(2.0f32, 1 << 23, -22, 1);
/// check(-2.0f32, 1 << 23, -22, -1);
/// check(f32::INFINITY, 1 << 23, 105, 1);
/// check(f64::NEG_INFINITY, 1 << 52, 972, -1);
/// ```
</span><span class="kw">fn </span>integer_decode(<span class="self">self</span>) -> (u64, i16, i8);
}
<span class="kw">impl </span>FloatCore <span class="kw">for </span>f32 {
<span class="macro">constant! </span>{
infinity() -> f32::INFINITY;
neg_infinity() -> f32::NEG_INFINITY;
nan() -> f32::NAN;
neg_zero() -> -<span class="number">0.0</span>;
min_value() -> f32::MIN;
min_positive_value() -> f32::MIN_POSITIVE;
epsilon() -> f32::EPSILON;
max_value() -> f32::MAX;
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>integer_decode(<span class="self">self</span>) -> (u64, i16, i8) {
integer_decode_f32(<span class="self">self</span>)
}
<span class="macro">forward! </span>{
<span class="self">Self</span>::is_nan(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_infinite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_finite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_normal(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::classify(<span class="self">self</span>) -> FpCategory;
<span class="self">Self</span>::is_sign_positive(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_sign_negative(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::recip(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_radians(<span class="self">self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(has_is_subnormal)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::is_subnormal(<span class="self">self</span>) -> bool;
}
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::floor(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::round(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::fract(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::abs(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::signum(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
</span><span class="macro">forward! </span>{
libm::floorf <span class="kw">as </span>floor(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::ceilf <span class="kw">as </span>ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::roundf <span class="kw">as </span>round(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::truncf <span class="kw">as </span>trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::fabsf <span class="kw">as </span>abs(<span class="self">self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
#[inline]
</span><span class="kw">fn </span>fract(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="self">self </span>- libm::truncf(<span class="self">self</span>)
}
}
<span class="kw">impl </span>FloatCore <span class="kw">for </span>f64 {
<span class="macro">constant! </span>{
infinity() -> f64::INFINITY;
neg_infinity() -> f64::NEG_INFINITY;
nan() -> f64::NAN;
neg_zero() -> -<span class="number">0.0</span>;
min_value() -> f64::MIN;
min_positive_value() -> f64::MIN_POSITIVE;
epsilon() -> f64::EPSILON;
max_value() -> f64::MAX;
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>integer_decode(<span class="self">self</span>) -> (u64, i16, i8) {
integer_decode_f64(<span class="self">self</span>)
}
<span class="macro">forward! </span>{
<span class="self">Self</span>::is_nan(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_infinite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_finite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_normal(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::classify(<span class="self">self</span>) -> FpCategory;
<span class="self">Self</span>::is_sign_positive(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_sign_negative(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::recip(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_radians(<span class="self">self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(has_is_subnormal)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::is_subnormal(<span class="self">self</span>) -> bool;
}
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::floor(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::round(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::fract(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::abs(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::signum(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
</span><span class="macro">forward! </span>{
libm::floor <span class="kw">as </span>floor(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::ceil <span class="kw">as </span>ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::round <span class="kw">as </span>round(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::trunc <span class="kw">as </span>trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::fabs <span class="kw">as </span>abs(<span class="self">self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
#[inline]
</span><span class="kw">fn </span>fract(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="self">self </span>- libm::trunc(<span class="self">self</span>)
}
}
<span class="comment">// FIXME: these doctests aren't actually helpful, because they're using and
// testing the inherent methods directly, not going through `Float`.
</span><span class="doccomment">/// Generic trait for floating point numbers
///
/// This trait is only available with the `std` feature, or with the `libm` feature otherwise.
</span><span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">pub trait </span>Float: Num + Copy + NumCast + PartialOrd + Neg<Output = <span class="self">Self</span>> {
<span class="doccomment">/// Returns the `NaN` value.
///
/// ```
/// use num_traits::Float;
///
/// let nan: f32 = Float::nan();
///
/// assert!(nan.is_nan());
/// ```
</span><span class="kw">fn </span>nan() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the infinite value.
///
/// ```
/// use num_traits::Float;
/// use std::f32;
///
/// let infinity: f32 = Float::infinity();
///
/// assert!(infinity.is_infinite());
/// assert!(!infinity.is_finite());
/// assert!(infinity > f32::MAX);
/// ```
</span><span class="kw">fn </span>infinity() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the negative infinite value.
///
/// ```
/// use num_traits::Float;
/// use std::f32;
///
/// let neg_infinity: f32 = Float::neg_infinity();
///
/// assert!(neg_infinity.is_infinite());
/// assert!(!neg_infinity.is_finite());
/// assert!(neg_infinity < f32::MIN);
/// ```
</span><span class="kw">fn </span>neg_infinity() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `-0.0`.
///
/// ```
/// use num_traits::{Zero, Float};
///
/// let inf: f32 = Float::infinity();
/// let zero: f32 = Zero::zero();
/// let neg_zero: f32 = Float::neg_zero();
///
/// assert_eq!(zero, neg_zero);
/// assert_eq!(7.0f32/inf, zero);
/// assert_eq!(zero * 10.0, zero);
/// ```
</span><span class="kw">fn </span>neg_zero() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest finite value that this type can represent.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x: f64 = Float::min_value();
///
/// assert_eq!(x, f64::MIN);
/// ```
</span><span class="kw">fn </span>min_value() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest positive, normalized value that this type can represent.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x: f64 = Float::min_positive_value();
///
/// assert_eq!(x, f64::MIN_POSITIVE);
/// ```
</span><span class="kw">fn </span>min_positive_value() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns epsilon, a small positive value.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x: f64 = Float::epsilon();
///
/// assert_eq!(x, f64::EPSILON);
/// ```
///
/// # Panics
///
/// The default implementation will panic if `f32::EPSILON` cannot
/// be cast to `Self`.
</span><span class="kw">fn </span>epsilon() -> <span class="self">Self </span>{
<span class="self">Self</span>::from(f32::EPSILON).expect(<span class="string">"Unable to cast from f32::EPSILON"</span>)
}
<span class="doccomment">/// Returns the largest finite value that this type can represent.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x: f64 = Float::max_value();
/// assert_eq!(x, f64::MAX);
/// ```
</span><span class="kw">fn </span>max_value() -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `true` if this value is `NaN` and false otherwise.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let nan = f64::NAN;
/// let f = 7.0;
///
/// assert!(nan.is_nan());
/// assert!(!f.is_nan());
/// ```
</span><span class="kw">fn </span>is_nan(<span class="self">self</span>) -> bool;
<span class="doccomment">/// Returns `true` if this value is positive infinity or negative infinity and
/// false otherwise.
///
/// ```
/// use num_traits::Float;
/// use std::f32;
///
/// let f = 7.0f32;
/// let inf: f32 = Float::infinity();
/// let neg_inf: f32 = Float::neg_infinity();
/// let nan: f32 = f32::NAN;
///
/// assert!(!f.is_infinite());
/// assert!(!nan.is_infinite());
///
/// assert!(inf.is_infinite());
/// assert!(neg_inf.is_infinite());
/// ```
</span><span class="kw">fn </span>is_infinite(<span class="self">self</span>) -> bool;
<span class="doccomment">/// Returns `true` if this number is neither infinite nor `NaN`.
///
/// ```
/// use num_traits::Float;
/// use std::f32;
///
/// let f = 7.0f32;
/// let inf: f32 = Float::infinity();
/// let neg_inf: f32 = Float::neg_infinity();
/// let nan: f32 = f32::NAN;
///
/// assert!(f.is_finite());
///
/// assert!(!nan.is_finite());
/// assert!(!inf.is_finite());
/// assert!(!neg_inf.is_finite());
/// ```
</span><span class="kw">fn </span>is_finite(<span class="self">self</span>) -> bool;
<span class="doccomment">/// Returns `true` if the number is neither zero, infinite,
/// [subnormal][subnormal], or `NaN`.
///
/// ```
/// use num_traits::Float;
/// use std::f32;
///
/// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
/// let max = f32::MAX;
/// let lower_than_min = 1.0e-40_f32;
/// let zero = 0.0f32;
///
/// assert!(min.is_normal());
/// assert!(max.is_normal());
///
/// assert!(!zero.is_normal());
/// assert!(!f32::NAN.is_normal());
/// assert!(!f32::INFINITY.is_normal());
/// // Values between `0` and `min` are Subnormal.
/// assert!(!lower_than_min.is_normal());
/// ```
/// [subnormal]: http://en.wikipedia.org/wiki/Subnormal_number
</span><span class="kw">fn </span>is_normal(<span class="self">self</span>) -> bool;
<span class="doccomment">/// Returns `true` if the number is [subnormal].
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
/// let max = f64::MAX;
/// let lower_than_min = 1.0e-308_f64;
/// let zero = 0.0_f64;
///
/// assert!(!min.is_subnormal());
/// assert!(!max.is_subnormal());
///
/// assert!(!zero.is_subnormal());
/// assert!(!f64::NAN.is_subnormal());
/// assert!(!f64::INFINITY.is_subnormal());
/// // Values between `0` and `min` are Subnormal.
/// assert!(lower_than_min.is_subnormal());
/// ```
/// [subnormal]: https://en.wikipedia.org/wiki/Subnormal_number
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>is_subnormal(<span class="self">self</span>) -> bool {
<span class="self">self</span>.classify() == FpCategory::Subnormal
}
<span class="doccomment">/// Returns the floating point category of the number. If only one property
/// is going to be tested, it is generally faster to use the specific
/// predicate instead.
///
/// ```
/// use num_traits::Float;
/// use std::num::FpCategory;
/// use std::f32;
///
/// let num = 12.4f32;
/// let inf = f32::INFINITY;
///
/// assert_eq!(num.classify(), FpCategory::Normal);
/// assert_eq!(inf.classify(), FpCategory::Infinite);
/// ```
</span><span class="kw">fn </span>classify(<span class="self">self</span>) -> FpCategory;
<span class="doccomment">/// Returns the largest integer less than or equal to a number.
///
/// ```
/// use num_traits::Float;
///
/// let f = 3.99;
/// let g = 3.0;
///
/// assert_eq!(f.floor(), 3.0);
/// assert_eq!(g.floor(), 3.0);
/// ```
</span><span class="kw">fn </span>floor(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the smallest integer greater than or equal to a number.
///
/// ```
/// use num_traits::Float;
///
/// let f = 3.01;
/// let g = 4.0;
///
/// assert_eq!(f.ceil(), 4.0);
/// assert_eq!(g.ceil(), 4.0);
/// ```
</span><span class="kw">fn </span>ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the nearest integer to a number. Round half-way cases away from
/// `0.0`.
///
/// ```
/// use num_traits::Float;
///
/// let f = 3.3;
/// let g = -3.3;
///
/// assert_eq!(f.round(), 3.0);
/// assert_eq!(g.round(), -3.0);
/// ```
</span><span class="kw">fn </span>round(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Return the integer part of a number.
///
/// ```
/// use num_traits::Float;
///
/// let f = 3.3;
/// let g = -3.7;
///
/// assert_eq!(f.trunc(), 3.0);
/// assert_eq!(g.trunc(), -3.0);
/// ```
</span><span class="kw">fn </span>trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the fractional part of a number.
///
/// ```
/// use num_traits::Float;
///
/// let x = 3.5;
/// let y = -3.5;
/// let abs_difference_x = (x.fract() - 0.5).abs();
/// let abs_difference_y = (y.fract() - (-0.5)).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
</span><span class="kw">fn </span>fract(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the absolute value of `self`. Returns `Float::nan()` if the
/// number is `Float::nan()`.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x = 3.5;
/// let y = -3.5;
///
/// let abs_difference_x = (x.abs() - x).abs();
/// let abs_difference_y = (y.abs() - (-y)).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
///
/// assert!(f64::NAN.abs().is_nan());
/// ```
</span><span class="kw">fn </span>abs(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns a number that represents the sign of `self`.
///
/// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
/// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
/// - `Float::nan()` if the number is `Float::nan()`
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let f = 3.5;
///
/// assert_eq!(f.signum(), 1.0);
/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
///
/// assert!(f64::NAN.signum().is_nan());
/// ```
</span><span class="kw">fn </span>signum(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `true` if `self` is positive, including `+0.0`,
/// `Float::infinity()`, and `Float::nan()`.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let nan: f64 = f64::NAN;
/// let neg_nan: f64 = -f64::NAN;
///
/// let f = 7.0;
/// let g = -7.0;
///
/// assert!(f.is_sign_positive());
/// assert!(!g.is_sign_positive());
/// assert!(nan.is_sign_positive());
/// assert!(!neg_nan.is_sign_positive());
/// ```
</span><span class="kw">fn </span>is_sign_positive(<span class="self">self</span>) -> bool;
<span class="doccomment">/// Returns `true` if `self` is negative, including `-0.0`,
/// `Float::neg_infinity()`, and `-Float::nan()`.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let nan: f64 = f64::NAN;
/// let neg_nan: f64 = -f64::NAN;
///
/// let f = 7.0;
/// let g = -7.0;
///
/// assert!(!f.is_sign_negative());
/// assert!(g.is_sign_negative());
/// assert!(!nan.is_sign_negative());
/// assert!(neg_nan.is_sign_negative());
/// ```
</span><span class="kw">fn </span>is_sign_negative(<span class="self">self</span>) -> bool;
<span class="doccomment">/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
/// ```
/// use num_traits::Float;
///
/// let m = 10.0;
/// let x = 4.0;
/// let b = 60.0;
///
/// // 100.0
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>mul_add(<span class="self">self</span>, a: <span class="self">Self</span>, b: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Take the reciprocal (inverse) of a number, `1/x`.
///
/// ```
/// use num_traits::Float;
///
/// let x = 2.0;
/// let abs_difference = (x.recip() - (1.0/x)).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>recip(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Raise a number to an integer power.
///
/// Using this function is generally faster than using `powf`
///
/// ```
/// use num_traits::Float;
///
/// let x = 2.0;
/// let abs_difference = (x.powi(2) - x*x).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>;
<span class="doccomment">/// Raise a number to a floating point power.
///
/// ```
/// use num_traits::Float;
///
/// let x = 2.0;
/// let abs_difference = (x.powf(2.0) - x*x).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>powf(<span class="self">self</span>, n: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Take the square root of a number.
///
/// Returns NaN if `self` is a negative number.
///
/// ```
/// use num_traits::Float;
///
/// let positive = 4.0;
/// let negative = -4.0;
///
/// let abs_difference = (positive.sqrt() - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// assert!(negative.sqrt().is_nan());
/// ```
</span><span class="kw">fn </span>sqrt(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `e^(self)`, (the exponential function).
///
/// ```
/// use num_traits::Float;
///
/// let one = 1.0;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>exp(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `2^(self)`.
///
/// ```
/// use num_traits::Float;
///
/// let f = 2.0;
///
/// // 2^2 - 4 == 0
/// let abs_difference = (f.exp2() - 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>exp2(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the natural logarithm of the number.
///
/// ```
/// use num_traits::Float;
///
/// let one = 1.0;
/// // e^1
/// let e = one.exp();
///
/// // ln(e) - 1 == 0
/// let abs_difference = (e.ln() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>ln(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the logarithm of the number with respect to an arbitrary base.
///
/// ```
/// use num_traits::Float;
///
/// let ten = 10.0;
/// let two = 2.0;
///
/// // log10(10) - 1 == 0
/// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
///
/// // log2(2) - 1 == 0
/// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
///
/// assert!(abs_difference_10 < 1e-10);
/// assert!(abs_difference_2 < 1e-10);
/// ```
</span><span class="kw">fn </span>log(<span class="self">self</span>, base: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the base 2 logarithm of the number.
///
/// ```
/// use num_traits::Float;
///
/// let two = 2.0;
///
/// // log2(2) - 1 == 0
/// let abs_difference = (two.log2() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>log2(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the base 10 logarithm of the number.
///
/// ```
/// use num_traits::Float;
///
/// let ten = 10.0;
///
/// // log10(10) - 1 == 0
/// let abs_difference = (ten.log10() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>log10(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Converts radians to degrees.
///
/// ```
/// use std::f64::consts;
///
/// let angle = consts::PI;
///
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>to_degrees(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>halfpi = <span class="self">Self</span>::zero().acos();
<span class="kw">let </span>ninety = <span class="self">Self</span>::from(<span class="number">90u8</span>).unwrap();
<span class="self">self </span>* ninety / halfpi
}
<span class="doccomment">/// Converts degrees to radians.
///
/// ```
/// use std::f64::consts;
///
/// let angle = 180.0_f64;
///
/// let abs_difference = (angle.to_radians() - consts::PI).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>to_radians(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span>halfpi = <span class="self">Self</span>::zero().acos();
<span class="kw">let </span>ninety = <span class="self">Self</span>::from(<span class="number">90u8</span>).unwrap();
<span class="self">self </span>* halfpi / ninety
}
<span class="doccomment">/// Returns the maximum of the two numbers.
///
/// ```
/// use num_traits::Float;
///
/// let x = 1.0;
/// let y = 2.0;
///
/// assert_eq!(x.max(y), y);
/// ```
</span><span class="kw">fn </span>max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the minimum of the two numbers.
///
/// ```
/// use num_traits::Float;
///
/// let x = 1.0;
/// let y = 2.0;
///
/// assert_eq!(x.min(y), x);
/// ```
</span><span class="kw">fn </span>min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// The positive difference of two numbers.
///
/// * If `self <= other`: `0:0`
/// * Else: `self - other`
///
/// ```
/// use num_traits::Float;
///
/// let x = 3.0;
/// let y = -3.0;
///
/// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
/// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
///
/// assert!(abs_difference_x < 1e-10);
/// assert!(abs_difference_y < 1e-10);
/// ```
</span><span class="kw">fn </span>abs_sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Take the cubic root of a number.
///
/// ```
/// use num_traits::Float;
///
/// let x = 8.0;
///
/// // x^(1/3) - 2 == 0
/// let abs_difference = (x.cbrt() - 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>cbrt(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Calculate the length of the hypotenuse of a right-angle triangle given
/// legs of length `x` and `y`.
///
/// ```
/// use num_traits::Float;
///
/// let x = 2.0;
/// let y = 3.0;
///
/// // sqrt(x^2 + y^2)
/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>hypot(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the sine of a number (in radians).
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x = f64::consts::PI/2.0;
///
/// let abs_difference = (x.sin() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>sin(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the cosine of a number (in radians).
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x = 2.0*f64::consts::PI;
///
/// let abs_difference = (x.cos() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>cos(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the tangent of a number (in radians).
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x = f64::consts::PI/4.0;
/// let abs_difference = (x.tan() - 1.0).abs();
///
/// assert!(abs_difference < 1e-14);
/// ```
</span><span class="kw">fn </span>tan(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the arcsine of a number. Return value is in radians in
/// the range [-pi/2, pi/2] or NaN if the number is outside the range
/// [-1, 1].
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let f = f64::consts::PI / 2.0;
///
/// // asin(sin(pi/2))
/// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>asin(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the arccosine of a number. Return value is in radians in
/// the range [0, pi] or NaN if the number is outside the range
/// [-1, 1].
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let f = f64::consts::PI / 4.0;
///
/// // acos(cos(pi/4))
/// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>acos(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the arctangent of a number. Return value is in radians in the
/// range [-pi/2, pi/2];
///
/// ```
/// use num_traits::Float;
///
/// let f = 1.0;
///
/// // atan(tan(1))
/// let abs_difference = (f.tan().atan() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>atan(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
///
/// * `x = 0`, `y = 0`: `0`
/// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
/// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
/// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let pi = f64::consts::PI;
/// // All angles from horizontal right (+x)
/// // 45 deg counter-clockwise
/// let x1 = 3.0;
/// let y1 = -3.0;
///
/// // 135 deg clockwise
/// let x2 = -3.0;
/// let y2 = 3.0;
///
/// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
/// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
///
/// assert!(abs_difference_1 < 1e-10);
/// assert!(abs_difference_2 < 1e-10);
/// ```
</span><span class="kw">fn </span>atan2(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Simultaneously computes the sine and cosine of the number, `x`. Returns
/// `(sin(x), cos(x))`.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x = f64::consts::PI/4.0;
/// let f = x.sin_cos();
///
/// let abs_difference_0 = (f.0 - x.sin()).abs();
/// let abs_difference_1 = (f.1 - x.cos()).abs();
///
/// assert!(abs_difference_0 < 1e-10);
/// assert!(abs_difference_0 < 1e-10);
/// ```
</span><span class="kw">fn </span>sin_cos(<span class="self">self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>);
<span class="doccomment">/// Returns `e^(self) - 1` in a way that is accurate even if the
/// number is close to zero.
///
/// ```
/// use num_traits::Float;
///
/// let x = 7.0;
///
/// // e^(ln(7)) - 1
/// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>exp_m1(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns `ln(1+n)` (natural logarithm) more accurately than if
/// the operations were performed separately.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let x = f64::consts::E - 1.0;
///
/// // ln(1 + (e - 1)) == ln(e) == 1
/// let abs_difference = (x.ln_1p() - 1.0).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>ln_1p(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Hyperbolic sine function.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
///
/// let f = x.sinh();
/// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
/// let g = (e*e - 1.0)/(2.0*e);
/// let abs_difference = (f - g).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>sinh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Hyperbolic cosine function.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
/// let f = x.cosh();
/// // Solving cosh() at 1 gives this result
/// let g = (e*e + 1.0)/(2.0*e);
/// let abs_difference = (f - g).abs();
///
/// // Same result
/// assert!(abs_difference < 1.0e-10);
/// ```
</span><span class="kw">fn </span>cosh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Hyperbolic tangent function.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let x = 1.0;
///
/// let f = x.tanh();
/// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
/// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
/// let abs_difference = (f - g).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
</span><span class="kw">fn </span>tanh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Inverse hyperbolic sine function.
///
/// ```
/// use num_traits::Float;
///
/// let x = 1.0;
/// let f = x.sinh().asinh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
</span><span class="kw">fn </span>asinh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Inverse hyperbolic cosine function.
///
/// ```
/// use num_traits::Float;
///
/// let x = 1.0;
/// let f = x.cosh().acosh();
///
/// let abs_difference = (f - x).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
</span><span class="kw">fn </span>acosh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Inverse hyperbolic tangent function.
///
/// ```
/// use num_traits::Float;
/// use std::f64;
///
/// let e = f64::consts::E;
/// let f = e.tanh().atanh();
///
/// let abs_difference = (f - e).abs();
///
/// assert!(abs_difference < 1.0e-10);
/// ```
</span><span class="kw">fn </span>atanh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="doccomment">/// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
/// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
///
/// ```
/// use num_traits::Float;
///
/// let num = 2.0f32;
///
/// // (8388608, -22, 1)
/// let (mantissa, exponent, sign) = Float::integer_decode(num);
/// let sign_f = sign as f32;
/// let mantissa_f = mantissa as f32;
/// let exponent_f = num.powf(exponent as f32);
///
/// // 1 * 8388608 * 2^(-22) == 2
/// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
///
/// assert!(abs_difference < 1e-10);
/// ```
</span><span class="kw">fn </span>integer_decode(<span class="self">self</span>) -> (u64, i16, i8);
<span class="doccomment">/// Returns a number composed of the magnitude of `self` and the sign of
/// `sign`.
///
/// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
/// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
/// `sign` is returned.
///
/// # Examples
///
/// ```
/// use num_traits::Float;
///
/// let f = 3.5_f32;
///
/// assert_eq!(f.copysign(0.42), 3.5_f32);
/// assert_eq!(f.copysign(-0.42), -3.5_f32);
/// assert_eq!((-f).copysign(0.42), 3.5_f32);
/// assert_eq!((-f).copysign(-0.42), -3.5_f32);
///
/// assert!(f32::nan().copysign(1.0).is_nan());
/// ```
</span><span class="kw">fn </span>copysign(<span class="self">self</span>, sign: <span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="kw">if </span><span class="self">self</span>.is_sign_negative() == sign.is_sign_negative() {
<span class="self">self
</span>} <span class="kw">else </span>{
<span class="self">self</span>.neg()
}
}
}
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">macro_rules! </span>float_impl_std {
(<span class="macro-nonterminal">$T</span>:ident <span class="macro-nonterminal">$decode</span>:ident) => {
<span class="kw">impl </span>Float <span class="kw">for </span><span class="macro-nonterminal">$T </span>{
<span class="macro">constant! </span>{
nan() -> <span class="macro-nonterminal">$T::NAN</span>;
infinity() -> <span class="macro-nonterminal">$T::INFINITY</span>;
neg_infinity() -> <span class="macro-nonterminal">$T::NEG_INFINITY</span>;
neg_zero() -> -<span class="number">0.0</span>;
min_value() -> <span class="macro-nonterminal">$T::MIN</span>;
min_positive_value() -> <span class="macro-nonterminal">$T::MIN_POSITIVE</span>;
epsilon() -> <span class="macro-nonterminal">$T::EPSILON</span>;
max_value() -> <span class="macro-nonterminal">$T::MAX</span>;
}
<span class="attr">#[inline]
#[allow(deprecated)]
</span><span class="kw">fn </span>abs_sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self </span>{
<<span class="macro-nonterminal">$T</span>>::abs_sub(<span class="self">self</span>, other)
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>integer_decode(<span class="self">self</span>) -> (u64, i16, i8) {
<span class="macro-nonterminal">$decode</span>(<span class="self">self</span>)
}
<span class="macro">forward! </span>{
<span class="self">Self</span>::is_nan(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_infinite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_finite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_normal(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::classify(<span class="self">self</span>) -> FpCategory;
<span class="self">Self</span>::floor(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::round(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::fract(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::abs(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::signum(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::is_sign_positive(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_sign_negative(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::mul_add(<span class="self">self</span>, a: <span class="self">Self</span>, b: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::recip(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>;
<span class="self">Self</span>::powf(<span class="self">self</span>, n: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::sqrt(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::exp(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::exp2(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::ln(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::log(<span class="self">self</span>, base: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::log2(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::log10(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_radians(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::cbrt(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::hypot(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::sin(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::cos(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::tan(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::asin(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::acos(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::atan(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::atan2(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::sin_cos(<span class="self">self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>);
<span class="self">Self</span>::exp_m1(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::ln_1p(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::sinh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::cosh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::tanh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::asinh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::acosh(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::atanh(<span class="self">self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(has_copysign)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::copysign(<span class="self">self</span>, sign: <span class="self">Self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(has_is_subnormal)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::is_subnormal(<span class="self">self</span>) -> bool;
}
}
};
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
</span><span class="macro">macro_rules! </span>float_impl_libm {
(<span class="macro-nonterminal">$T</span>:ident <span class="macro-nonterminal">$decode</span>:ident) => {
<span class="macro">constant! </span>{
nan() -> <span class="macro-nonterminal">$T::NAN</span>;
infinity() -> <span class="macro-nonterminal">$T::INFINITY</span>;
neg_infinity() -> <span class="macro-nonterminal">$T::NEG_INFINITY</span>;
neg_zero() -> -<span class="number">0.0</span>;
min_value() -> <span class="macro-nonterminal">$T::MIN</span>;
min_positive_value() -> <span class="macro-nonterminal">$T::MIN_POSITIVE</span>;
epsilon() -> <span class="macro-nonterminal">$T::EPSILON</span>;
max_value() -> <span class="macro-nonterminal">$T::MAX</span>;
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>integer_decode(<span class="self">self</span>) -> (u64, i16, i8) {
<span class="macro-nonterminal">$decode</span>(<span class="self">self</span>)
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>fract(<span class="self">self</span>) -> <span class="self">Self </span>{
<span class="self">self </span>- Float::trunc(<span class="self">self</span>)
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>log(<span class="self">self</span>, base: <span class="self">Self</span>) -> <span class="self">Self </span>{
<span class="self">self</span>.ln() / base.ln()
}
<span class="macro">forward! </span>{
<span class="self">Self</span>::is_nan(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_infinite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_finite(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_normal(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::classify(<span class="self">self</span>) -> FpCategory;
<span class="self">Self</span>::is_sign_positive(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::is_sign_negative(<span class="self">self</span>) -> bool;
<span class="self">Self</span>::min(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::max(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::recip(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_degrees(<span class="self">self</span>) -> <span class="self">Self</span>;
<span class="self">Self</span>::to_radians(<span class="self">self</span>) -> <span class="self">Self</span>;
}
<span class="attr">#[cfg(has_is_subnormal)]
</span><span class="macro">forward! </span>{
<span class="self">Self</span>::is_subnormal(<span class="self">self</span>) -> bool;
}
<span class="macro">forward! </span>{
FloatCore::signum(<span class="self">self</span>) -> <span class="self">Self</span>;
FloatCore::powi(<span class="self">self</span>, n: i32) -> <span class="self">Self</span>;
}
};
}
<span class="kw">fn </span>integer_decode_f32(f: f32) -> (u64, i16, i8) {
<span class="kw">let </span>bits: u32 = f.to_bits();
<span class="kw">let </span>sign: i8 = <span class="kw">if </span>bits >> <span class="number">31 </span>== <span class="number">0 </span>{ <span class="number">1 </span>} <span class="kw">else </span>{ -<span class="number">1 </span>};
<span class="kw">let </span><span class="kw-2">mut </span>exponent: i16 = ((bits >> <span class="number">23</span>) & <span class="number">0xff</span>) <span class="kw">as </span>i16;
<span class="kw">let </span>mantissa = <span class="kw">if </span>exponent == <span class="number">0 </span>{
(bits & <span class="number">0x7fffff</span>) << <span class="number">1
</span>} <span class="kw">else </span>{
(bits & <span class="number">0x7fffff</span>) | <span class="number">0x800000
</span>};
<span class="comment">// Exponent bias + mantissa shift
</span>exponent -= <span class="number">127 </span>+ <span class="number">23</span>;
(mantissa <span class="kw">as </span>u64, exponent, sign)
}
<span class="kw">fn </span>integer_decode_f64(f: f64) -> (u64, i16, i8) {
<span class="kw">let </span>bits: u64 = f.to_bits();
<span class="kw">let </span>sign: i8 = <span class="kw">if </span>bits >> <span class="number">63 </span>== <span class="number">0 </span>{ <span class="number">1 </span>} <span class="kw">else </span>{ -<span class="number">1 </span>};
<span class="kw">let </span><span class="kw-2">mut </span>exponent: i16 = ((bits >> <span class="number">52</span>) & <span class="number">0x7ff</span>) <span class="kw">as </span>i16;
<span class="kw">let </span>mantissa = <span class="kw">if </span>exponent == <span class="number">0 </span>{
(bits & <span class="number">0xfffffffffffff</span>) << <span class="number">1
</span>} <span class="kw">else </span>{
(bits & <span class="number">0xfffffffffffff</span>) | <span class="number">0x10000000000000
</span>};
<span class="comment">// Exponent bias + mantissa shift
</span>exponent -= <span class="number">1023 </span>+ <span class="number">52</span>;
(mantissa, exponent, sign)
}
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">float_impl_std!</span>(f32 integer_decode_f32);
<span class="attr">#[cfg(feature = <span class="string">"std"</span>)]
</span><span class="macro">float_impl_std!</span>(f64 integer_decode_f64);
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
</span><span class="kw">impl </span>Float <span class="kw">for </span>f32 {
<span class="macro">float_impl_libm!</span>(f32 integer_decode_f32);
<span class="attr">#[inline]
#[allow(deprecated)]
</span><span class="kw">fn </span>abs_sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self </span>{
libm::fdimf(<span class="self">self</span>, other)
}
<span class="macro">forward! </span>{
libm::floorf <span class="kw">as </span>floor(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::ceilf <span class="kw">as </span>ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::roundf <span class="kw">as </span>round(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::truncf <span class="kw">as </span>trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::fabsf <span class="kw">as </span>abs(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::fmaf <span class="kw">as </span>mul_add(<span class="self">self</span>, a: <span class="self">Self</span>, b: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::powf <span class="kw">as </span>powf(<span class="self">self</span>, n: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::sqrtf <span class="kw">as </span>sqrt(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::expf <span class="kw">as </span>exp(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::exp2f <span class="kw">as </span>exp2(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::logf <span class="kw">as </span>ln(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log2f <span class="kw">as </span>log2(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log10f <span class="kw">as </span>log10(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::cbrtf <span class="kw">as </span>cbrt(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::hypotf <span class="kw">as </span>hypot(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::sinf <span class="kw">as </span>sin(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::cosf <span class="kw">as </span>cos(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::tanf <span class="kw">as </span>tan(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::asinf <span class="kw">as </span>asin(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::acosf <span class="kw">as </span>acos(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::atanf <span class="kw">as </span>atan(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::atan2f <span class="kw">as </span>atan2(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::sincosf <span class="kw">as </span>sin_cos(<span class="self">self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>);
libm::expm1f <span class="kw">as </span>exp_m1(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log1pf <span class="kw">as </span>ln_1p(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::sinhf <span class="kw">as </span>sinh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::coshf <span class="kw">as </span>cosh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::tanhf <span class="kw">as </span>tanh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::asinhf <span class="kw">as </span>asinh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::acoshf <span class="kw">as </span>acosh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::atanhf <span class="kw">as </span>atanh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::copysignf <span class="kw">as </span>copysign(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
}
}
<span class="attr">#[cfg(all(not(feature = <span class="string">"std"</span>), feature = <span class="string">"libm"</span>))]
</span><span class="kw">impl </span>Float <span class="kw">for </span>f64 {
<span class="macro">float_impl_libm!</span>(f64 integer_decode_f64);
<span class="attr">#[inline]
#[allow(deprecated)]
</span><span class="kw">fn </span>abs_sub(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self </span>{
libm::fdim(<span class="self">self</span>, other)
}
<span class="macro">forward! </span>{
libm::floor <span class="kw">as </span>floor(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::ceil <span class="kw">as </span>ceil(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::round <span class="kw">as </span>round(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::trunc <span class="kw">as </span>trunc(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::fabs <span class="kw">as </span>abs(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::fma <span class="kw">as </span>mul_add(<span class="self">self</span>, a: <span class="self">Self</span>, b: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::pow <span class="kw">as </span>powf(<span class="self">self</span>, n: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::sqrt <span class="kw">as </span>sqrt(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::exp <span class="kw">as </span>exp(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::exp2 <span class="kw">as </span>exp2(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log <span class="kw">as </span>ln(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log2 <span class="kw">as </span>log2(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log10 <span class="kw">as </span>log10(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::cbrt <span class="kw">as </span>cbrt(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::hypot <span class="kw">as </span>hypot(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::sin <span class="kw">as </span>sin(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::cos <span class="kw">as </span>cos(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::tan <span class="kw">as </span>tan(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::asin <span class="kw">as </span>asin(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::acos <span class="kw">as </span>acos(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::atan <span class="kw">as </span>atan(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::atan2 <span class="kw">as </span>atan2(<span class="self">self</span>, other: <span class="self">Self</span>) -> <span class="self">Self</span>;
libm::sincos <span class="kw">as </span>sin_cos(<span class="self">self</span>) -> (<span class="self">Self</span>, <span class="self">Self</span>);
libm::expm1 <span class="kw">as </span>exp_m1(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::log1p <span class="kw">as </span>ln_1p(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::sinh <span class="kw">as </span>sinh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::cosh <span class="kw">as </span>cosh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::tanh <span class="kw">as </span>tanh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::asinh <span class="kw">as </span>asinh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::acosh <span class="kw">as </span>acosh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::atanh <span class="kw">as </span>atanh(<span class="self">self</span>) -> <span class="self">Self</span>;
libm::copysign <span class="kw">as </span>copysign(<span class="self">self</span>, sign: <span class="self">Self</span>) -> <span class="self">Self</span>;
}
}
<span class="macro">macro_rules! </span>float_const_impl {
($(<span class="attr">#[<span class="macro-nonterminal">$doc</span>:meta] </span><span class="macro-nonterminal">$constant</span>:ident,)+) => (
<span class="attr">#[allow(non_snake_case)]
</span><span class="kw">pub trait </span>FloatConst {
$(<span class="attr">#[<span class="macro-nonterminal">$doc</span>] </span><span class="kw">fn </span><span class="macro-nonterminal">$constant</span>() -> <span class="self">Self</span>;)+
<span class="attr">#[doc = <span class="string">"Return the full circle constant `τ`."</span>]
#[inline]
</span><span class="kw">fn </span>TAU() -> <span class="self">Self </span><span class="kw">where </span><span class="self">Self</span>: Sized + Add<<span class="self">Self</span>, Output = <span class="self">Self</span>> {
<span class="self">Self</span>::PI() + <span class="self">Self</span>::PI()
}
<span class="attr">#[doc = <span class="string">"Return `log10(2.0)`."</span>]
#[inline]
</span><span class="kw">fn </span>LOG10_2() -> <span class="self">Self </span><span class="kw">where </span><span class="self">Self</span>: Sized + Div<<span class="self">Self</span>, Output = <span class="self">Self</span>> {
<span class="self">Self</span>::LN_2() / <span class="self">Self</span>::LN_10()
}
<span class="attr">#[doc = <span class="string">"Return `log2(10.0)`."</span>]
#[inline]
</span><span class="kw">fn </span>LOG2_10() -> <span class="self">Self </span><span class="kw">where </span><span class="self">Self</span>: Sized + Div<<span class="self">Self</span>, Output = <span class="self">Self</span>> {
<span class="self">Self</span>::LN_10() / <span class="self">Self</span>::LN_2()
}
}
<span class="macro">float_const_impl! </span>{ @float f32, $(<span class="macro-nonterminal">$constant</span>,)+ }
<span class="macro">float_const_impl! </span>{ @float f64, $(<span class="macro-nonterminal">$constant</span>,)+ }
);
(@float <span class="macro-nonterminal">$T</span>:ident, $(<span class="macro-nonterminal">$constant</span>:ident,)+) => (
<span class="kw">impl </span>FloatConst <span class="kw">for </span><span class="macro-nonterminal">$T </span>{
<span class="macro">constant! </span>{
$( <span class="macro-nonterminal">$constant</span>() -> <span class="macro-nonterminal">$T::consts</span>::<span class="macro-nonterminal">$constant</span>; )+
TAU() -> <span class="number">6.28318530717958647692528676655900577</span>;
LOG10_2() -> <span class="number">0.301029995663981195213738894724493027</span>;
LOG2_10() -> <span class="number">3.32192809488736234787031942948939018</span>;
}
}
);
}
<span class="macro">float_const_impl! </span>{
<span class="attr">#[doc = <span class="string">"Return Euler’s number."</span>]
</span>E,
<span class="attr">#[doc = <span class="string">"Return `1.0 / π`."</span>]
</span>FRAC_1_PI,
<span class="attr">#[doc = <span class="string">"Return `1.0 / sqrt(2.0)`."</span>]
</span>FRAC_1_SQRT_2,
<span class="attr">#[doc = <span class="string">"Return `2.0 / π`."</span>]
</span>FRAC_2_PI,
<span class="attr">#[doc = <span class="string">"Return `2.0 / sqrt(π)`."</span>]
</span>FRAC_2_SQRT_PI,
<span class="attr">#[doc = <span class="string">"Return `π / 2.0`."</span>]
</span>FRAC_PI_2,
<span class="attr">#[doc = <span class="string">"Return `π / 3.0`."</span>]
</span>FRAC_PI_3,
<span class="attr">#[doc = <span class="string">"Return `π / 4.0`."</span>]
</span>FRAC_PI_4,
<span class="attr">#[doc = <span class="string">"Return `π / 6.0`."</span>]
</span>FRAC_PI_6,
<span class="attr">#[doc = <span class="string">"Return `π / 8.0`."</span>]
</span>FRAC_PI_8,
<span class="attr">#[doc = <span class="string">"Return `ln(10.0)`."</span>]
</span>LN_10,
<span class="attr">#[doc = <span class="string">"Return `ln(2.0)`."</span>]
</span>LN_2,
<span class="attr">#[doc = <span class="string">"Return `log10(e)`."</span>]
</span>LOG10_E,
<span class="attr">#[doc = <span class="string">"Return `log2(e)`."</span>]
</span>LOG2_E,
<span class="attr">#[doc = <span class="string">"Return Archimedes’ constant `π`."</span>]
</span>PI,
<span class="attr">#[doc = <span class="string">"Return `sqrt(2.0)`."</span>]
</span>SQRT_2,
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use </span>core::f64::consts;
<span class="kw">const </span>DEG_RAD_PAIRS: [(f64, f64); <span class="number">7</span>] = [
(<span class="number">0.0</span>, <span class="number">0.</span>),
(<span class="number">22.5</span>, consts::FRAC_PI_8),
(<span class="number">30.0</span>, consts::FRAC_PI_6),
(<span class="number">45.0</span>, consts::FRAC_PI_4),
(<span class="number">60.0</span>, consts::FRAC_PI_3),
(<span class="number">90.0</span>, consts::FRAC_PI_2),
(<span class="number">180.0</span>, consts::PI),
];
<span class="attr">#[test]
</span><span class="kw">fn </span>convert_deg_rad() {
<span class="kw">use </span><span class="kw">crate</span>::float::FloatCore;
<span class="kw">for </span><span class="kw-2">&</span>(deg, rad) <span class="kw">in </span><span class="kw-2">&</span>DEG_RAD_PAIRS {
<span class="macro">assert!</span>((FloatCore::to_degrees(rad) - deg).abs() < <span class="number">1e-6</span>);
<span class="macro">assert!</span>((FloatCore::to_radians(deg) - rad).abs() < <span class="number">1e-6</span>);
<span class="kw">let </span>(deg, rad) = (deg <span class="kw">as </span>f32, rad <span class="kw">as </span>f32);
<span class="macro">assert!</span>((FloatCore::to_degrees(rad) - deg).abs() < <span class="number">1e-5</span>);
<span class="macro">assert!</span>((FloatCore::to_radians(deg) - rad).abs() < <span class="number">1e-5</span>);
}
}
<span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
#[test]
</span><span class="kw">fn </span>convert_deg_rad_std() {
<span class="kw">for </span><span class="kw-2">&</span>(deg, rad) <span class="kw">in </span><span class="kw-2">&</span>DEG_RAD_PAIRS {
<span class="kw">use </span><span class="kw">crate</span>::Float;
<span class="macro">assert!</span>((Float::to_degrees(rad) - deg).abs() < <span class="number">1e-6</span>);
<span class="macro">assert!</span>((Float::to_radians(deg) - rad).abs() < <span class="number">1e-6</span>);
<span class="kw">let </span>(deg, rad) = (deg <span class="kw">as </span>f32, rad <span class="kw">as </span>f32);
<span class="macro">assert!</span>((Float::to_degrees(rad) - deg).abs() < <span class="number">1e-5</span>);
<span class="macro">assert!</span>((Float::to_radians(deg) - rad).abs() < <span class="number">1e-5</span>);
}
}
<span class="attr">#[test]
</span><span class="kw">fn </span>to_degrees_rounding() {
<span class="kw">use </span><span class="kw">crate</span>::float::FloatCore;
<span class="macro">assert_eq!</span>(
FloatCore::to_degrees(<span class="number">1_f32</span>),
<span class="number">57.2957795130823208767981548141051703
</span>);
}
<span class="attr">#[test]
#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">fn </span>extra_logs() {
<span class="kw">use </span><span class="kw">crate</span>::float::{Float, FloatConst};
<span class="kw">fn </span>check<F: Float + FloatConst>(diff: F) {
<span class="kw">let </span>_2 = F::from(<span class="number">2.0</span>).unwrap();
<span class="macro">assert!</span>((F::LOG10_2() - F::log10(_2)).abs() < diff);
<span class="macro">assert!</span>((F::LOG10_2() - F::LN_2() / F::LN_10()).abs() < diff);
<span class="kw">let </span>_10 = F::from(<span class="number">10.0</span>).unwrap();
<span class="macro">assert!</span>((F::LOG2_10() - F::log2(_10)).abs() < diff);
<span class="macro">assert!</span>((F::LOG2_10() - F::LN_10() / F::LN_2()).abs() < diff);
}
check::<f32>(<span class="number">1e-6</span>);
check::<f64>(<span class="number">1e-12</span>);
}
<span class="attr">#[test]
#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">fn </span>copysign() {
<span class="kw">use </span><span class="kw">crate</span>::float::Float;
test_copysign_generic(<span class="number">2.0_f32</span>, -<span class="number">2.0_f32</span>, f32::nan());
test_copysign_generic(<span class="number">2.0_f64</span>, -<span class="number">2.0_f64</span>, f64::nan());
test_copysignf(<span class="number">2.0_f32</span>, -<span class="number">2.0_f32</span>, f32::nan());
}
<span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">fn </span>test_copysignf(p: f32, n: f32, nan: f32) {
<span class="kw">use </span><span class="kw">crate</span>::float::Float;
<span class="kw">use </span>core::ops::Neg;
<span class="macro">assert!</span>(p.is_sign_positive());
<span class="macro">assert!</span>(n.is_sign_negative());
<span class="macro">assert!</span>(nan.is_nan());
<span class="macro">assert_eq!</span>(p, Float::copysign(p, p));
<span class="macro">assert_eq!</span>(p.neg(), Float::copysign(p, n));
<span class="macro">assert_eq!</span>(n, Float::copysign(n, n));
<span class="macro">assert_eq!</span>(n.neg(), Float::copysign(n, p));
<span class="macro">assert!</span>(Float::copysign(nan, p).is_sign_positive());
<span class="macro">assert!</span>(Float::copysign(nan, n).is_sign_negative());
}
<span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">fn </span>test_copysign_generic<F: <span class="kw">crate</span>::float::Float + ::core::fmt::Debug>(p: F, n: F, nan: F) {
<span class="macro">assert!</span>(p.is_sign_positive());
<span class="macro">assert!</span>(n.is_sign_negative());
<span class="macro">assert!</span>(nan.is_nan());
<span class="macro">assert!</span>(!nan.is_subnormal());
<span class="macro">assert_eq!</span>(p, p.copysign(p));
<span class="macro">assert_eq!</span>(p.neg(), p.copysign(n));
<span class="macro">assert_eq!</span>(n, n.copysign(n));
<span class="macro">assert_eq!</span>(n.neg(), n.copysign(p));
<span class="macro">assert!</span>(nan.copysign(p).is_sign_positive());
<span class="macro">assert!</span>(nan.copysign(n).is_sign_negative());
}
<span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">fn </span>test_subnormal<F: <span class="kw">crate</span>::float::Float + ::core::fmt::Debug>() {
<span class="kw">let </span>min_positive = F::min_positive_value();
<span class="kw">let </span>lower_than_min = min_positive / F::from(<span class="number">2.0f32</span>).unwrap();
<span class="macro">assert!</span>(!min_positive.is_subnormal());
<span class="macro">assert!</span>(lower_than_min.is_subnormal());
}
<span class="attr">#[test]
#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">fn </span>subnormal() {
test_subnormal::<f64>();
test_subnormal::<f32>();
}
}
</code></pre></div>
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