| <!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 `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.7/src/math/rem_pio2.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>rem_pio2.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.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"><a class="sidebar-logo" href="../../../libm/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../libm/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" 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="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c |
| // |
| // ==================================================== |
| // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| // |
| // Developed at SunPro, a Sun Microsystems, Inc. business. |
| // Permission to use, copy, modify, and distribute this |
| // software is freely granted, provided that this notice |
| // is preserved. |
| // ==================================================== |
| // |
| // Optimized by Bruce D. Evans. */ |
| </span><span class="kw">use </span><span class="kw">super</span>::rem_pio2_large; |
| |
| <span class="comment">// #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 |
| // #define EPS DBL_EPSILON |
| </span><span class="kw">const </span>EPS: f64 = <span class="number">2.2204460492503131e-16</span>; |
| <span class="comment">// #elif FLT_EVAL_METHOD==2 |
| // #define EPS LDBL_EPSILON |
| // #endif |
| |
| // TODO: Support FLT_EVAL_METHOD? |
| |
| </span><span class="kw">const </span>TO_INT: f64 = <span class="number">1.5 </span>/ EPS; |
| <span class="doccomment">/// 53 bits of 2/pi |
| </span><span class="kw">const </span>INV_PIO2: f64 = <span class="number">6.36619772367581382433e-01</span>; <span class="comment">/* 0x3FE45F30, 0x6DC9C883 */ |
| </span><span class="doccomment">/// first 33 bits of pi/2 |
| </span><span class="kw">const </span>PIO2_1: f64 = <span class="number">1.57079632673412561417e+00</span>; <span class="comment">/* 0x3FF921FB, 0x54400000 */ |
| </span><span class="doccomment">/// pi/2 - PIO2_1 |
| </span><span class="kw">const </span>PIO2_1T: f64 = <span class="number">6.07710050650619224932e-11</span>; <span class="comment">/* 0x3DD0B461, 0x1A626331 */ |
| </span><span class="doccomment">/// second 33 bits of pi/2 |
| </span><span class="kw">const </span>PIO2_2: f64 = <span class="number">6.07710050630396597660e-11</span>; <span class="comment">/* 0x3DD0B461, 0x1A600000 */ |
| </span><span class="doccomment">/// pi/2 - (PIO2_1+PIO2_2) |
| </span><span class="kw">const </span>PIO2_2T: f64 = <span class="number">2.02226624879595063154e-21</span>; <span class="comment">/* 0x3BA3198A, 0x2E037073 */ |
| </span><span class="doccomment">/// third 33 bits of pi/2 |
| </span><span class="kw">const </span>PIO2_3: f64 = <span class="number">2.02226624871116645580e-21</span>; <span class="comment">/* 0x3BA3198A, 0x2E000000 */ |
| </span><span class="doccomment">/// pi/2 - (PIO2_1+PIO2_2+PIO2_3) |
| </span><span class="kw">const </span>PIO2_3T: f64 = <span class="number">8.47842766036889956997e-32</span>; <span class="comment">/* 0x397B839A, 0x252049C1 */ |
| |
| // return the remainder of x rem pi/2 in y[0]+y[1] |
| // use rem_pio2_large() for large x |
| // |
| // caller must handle the case when reduction is not needed: |x| ~<= pi/4 */ |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn </span>rem_pio2(x: f64) -> (i32, f64, f64) { |
| <span class="kw">let </span>x1p24 = f64::from_bits(<span class="number">0x4170000000000000</span>); |
| |
| <span class="kw">let </span>sign = (f64::to_bits(x) >> <span class="number">63</span>) <span class="kw">as </span>i32; |
| <span class="kw">let </span>ix = (f64::to_bits(x) >> <span class="number">32</span>) <span class="kw">as </span>u32 & <span class="number">0x7fffffff</span>; |
| |
| <span class="kw">fn </span>medium(x: f64, ix: u32) -> (i32, f64, f64) { |
| <span class="comment">/* rint(x/(pi/2)), Assume round-to-nearest. */ |
| </span><span class="kw">let </span>tmp = x <span class="kw">as </span>f64 * INV_PIO2 + TO_INT; |
| <span class="comment">// force rounding of tmp to it's storage format on x87 to avoid |
| // excess precision issues. |
| </span><span class="attribute">#[cfg(all(target_arch = <span class="string">"x86"</span>, not(target_feature = <span class="string">"sse2"</span>)))] |
| </span><span class="kw">let </span>tmp = <span class="macro">force_eval!</span>(tmp); |
| <span class="kw">let </span>f_n = tmp - TO_INT; |
| <span class="kw">let </span>n = f_n <span class="kw">as </span>i32; |
| <span class="kw">let </span><span class="kw-2">mut </span>r = x - f_n * PIO2_1; |
| <span class="kw">let </span><span class="kw-2">mut </span>w = f_n * PIO2_1T; <span class="comment">/* 1st round, good to 85 bits */ |
| </span><span class="kw">let </span><span class="kw-2">mut </span>y0 = r - w; |
| <span class="kw">let </span>ui = f64::to_bits(y0); |
| <span class="kw">let </span>ey = (ui >> <span class="number">52</span>) <span class="kw">as </span>i32 & <span class="number">0x7ff</span>; |
| <span class="kw">let </span>ex = (ix >> <span class="number">20</span>) <span class="kw">as </span>i32; |
| <span class="kw">if </span>ex - ey > <span class="number">16 </span>{ |
| <span class="comment">/* 2nd round, good to 118 bits */ |
| </span><span class="kw">let </span>t = r; |
| w = f_n * PIO2_2; |
| r = t - w; |
| w = f_n * PIO2_2T - ((t - r) - w); |
| y0 = r - w; |
| <span class="kw">let </span>ey = (f64::to_bits(y0) >> <span class="number">52</span>) <span class="kw">as </span>i32 & <span class="number">0x7ff</span>; |
| <span class="kw">if </span>ex - ey > <span class="number">49 </span>{ |
| <span class="comment">/* 3rd round, good to 151 bits, covers all cases */ |
| </span><span class="kw">let </span>t = r; |
| w = f_n * PIO2_3; |
| r = t - w; |
| w = f_n * PIO2_3T - ((t - r) - w); |
| y0 = r - w; |
| } |
| } |
| <span class="kw">let </span>y1 = (r - y0) - w; |
| (n, y0, y1) |
| } |
| |
| <span class="kw">if </span>ix <= <span class="number">0x400f6a7a </span>{ |
| <span class="comment">/* |x| ~<= 5pi/4 */ |
| </span><span class="kw">if </span>(ix & <span class="number">0xfffff</span>) == <span class="number">0x921fb </span>{ |
| <span class="comment">/* |x| ~= pi/2 or 2pi/2 */ |
| </span><span class="kw">return </span>medium(x, ix); <span class="comment">/* cancellation -- use medium case */ |
| </span>} |
| <span class="kw">if </span>ix <= <span class="number">0x4002d97c </span>{ |
| <span class="comment">/* |x| ~<= 3pi/4 */ |
| </span><span class="kw">if </span>sign == <span class="number">0 </span>{ |
| <span class="kw">let </span>z = x - PIO2_1; <span class="comment">/* one round good to 85 bits */ |
| </span><span class="kw">let </span>y0 = z - PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) - PIO2_1T; |
| <span class="kw">return </span>(<span class="number">1</span>, y0, y1); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>z = x + PIO2_1; |
| <span class="kw">let </span>y0 = z + PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) + PIO2_1T; |
| <span class="kw">return </span>(-<span class="number">1</span>, y0, y1); |
| } |
| } <span class="kw">else if </span>sign == <span class="number">0 </span>{ |
| <span class="kw">let </span>z = x - <span class="number">2.0 </span>* PIO2_1; |
| <span class="kw">let </span>y0 = z - <span class="number">2.0 </span>* PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) - <span class="number">2.0 </span>* PIO2_1T; |
| <span class="kw">return </span>(<span class="number">2</span>, y0, y1); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>z = x + <span class="number">2.0 </span>* PIO2_1; |
| <span class="kw">let </span>y0 = z + <span class="number">2.0 </span>* PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) + <span class="number">2.0 </span>* PIO2_1T; |
| <span class="kw">return </span>(-<span class="number">2</span>, y0, y1); |
| } |
| } |
| <span class="kw">if </span>ix <= <span class="number">0x401c463b </span>{ |
| <span class="comment">/* |x| ~<= 9pi/4 */ |
| </span><span class="kw">if </span>ix <= <span class="number">0x4015fdbc </span>{ |
| <span class="comment">/* |x| ~<= 7pi/4 */ |
| </span><span class="kw">if </span>ix == <span class="number">0x4012d97c </span>{ |
| <span class="comment">/* |x| ~= 3pi/2 */ |
| </span><span class="kw">return </span>medium(x, ix); |
| } |
| <span class="kw">if </span>sign == <span class="number">0 </span>{ |
| <span class="kw">let </span>z = x - <span class="number">3.0 </span>* PIO2_1; |
| <span class="kw">let </span>y0 = z - <span class="number">3.0 </span>* PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) - <span class="number">3.0 </span>* PIO2_1T; |
| <span class="kw">return </span>(<span class="number">3</span>, y0, y1); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>z = x + <span class="number">3.0 </span>* PIO2_1; |
| <span class="kw">let </span>y0 = z + <span class="number">3.0 </span>* PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) + <span class="number">3.0 </span>* PIO2_1T; |
| <span class="kw">return </span>(-<span class="number">3</span>, y0, y1); |
| } |
| } <span class="kw">else </span>{ |
| <span class="kw">if </span>ix == <span class="number">0x401921fb </span>{ |
| <span class="comment">/* |x| ~= 4pi/2 */ |
| </span><span class="kw">return </span>medium(x, ix); |
| } |
| <span class="kw">if </span>sign == <span class="number">0 </span>{ |
| <span class="kw">let </span>z = x - <span class="number">4.0 </span>* PIO2_1; |
| <span class="kw">let </span>y0 = z - <span class="number">4.0 </span>* PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) - <span class="number">4.0 </span>* PIO2_1T; |
| <span class="kw">return </span>(<span class="number">4</span>, y0, y1); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>z = x + <span class="number">4.0 </span>* PIO2_1; |
| <span class="kw">let </span>y0 = z + <span class="number">4.0 </span>* PIO2_1T; |
| <span class="kw">let </span>y1 = (z - y0) + <span class="number">4.0 </span>* PIO2_1T; |
| <span class="kw">return </span>(-<span class="number">4</span>, y0, y1); |
| } |
| } |
| } |
| <span class="kw">if </span>ix < <span class="number">0x413921fb </span>{ |
| <span class="comment">/* |x| ~< 2^20*(pi/2), medium size */ |
| </span><span class="kw">return </span>medium(x, ix); |
| } |
| <span class="comment">/* |
| * all other (large) arguments |
| */ |
| </span><span class="kw">if </span>ix >= <span class="number">0x7ff00000 </span>{ |
| <span class="comment">/* x is inf or NaN */ |
| </span><span class="kw">let </span>y0 = x - x; |
| <span class="kw">let </span>y1 = y0; |
| <span class="kw">return </span>(<span class="number">0</span>, y0, y1); |
| } |
| <span class="comment">/* set z = scalbn(|x|,-ilogb(x)+23) */ |
| </span><span class="kw">let </span><span class="kw-2">mut </span>ui = f64::to_bits(x); |
| ui &= (!<span class="number">1</span>) >> <span class="number">12</span>; |
| ui |= (<span class="number">0x3ff </span>+ <span class="number">23</span>) << <span class="number">52</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>z = f64::from_bits(ui); |
| <span class="kw">let </span><span class="kw-2">mut </span>tx = [<span class="number">0.0</span>; <span class="number">3</span>]; |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">2 </span>{ |
| <span class="macro">i!</span>(tx,i, =, z <span class="kw">as </span>i32 <span class="kw">as </span>f64); |
| z = (z - <span class="macro">i!</span>(tx, i)) * x1p24; |
| } |
| <span class="macro">i!</span>(tx,<span class="number">2</span>, =, z); |
| <span class="comment">/* skip zero terms, first term is non-zero */ |
| </span><span class="kw">let </span><span class="kw-2">mut </span>i = <span class="number">2</span>; |
| <span class="kw">while </span>i != <span class="number">0 </span>&& <span class="macro">i!</span>(tx, i) == <span class="number">0.0 </span>{ |
| i -= <span class="number">1</span>; |
| } |
| <span class="kw">let </span><span class="kw-2">mut </span>ty = [<span class="number">0.0</span>; <span class="number">3</span>]; |
| <span class="kw">let </span>n = rem_pio2_large(<span class="kw-2">&</span>tx[..=i], <span class="kw-2">&mut </span>ty, ((ix <span class="kw">as </span>i32) >> <span class="number">20</span>) - (<span class="number">0x3ff </span>+ <span class="number">23</span>), <span class="number">1</span>); |
| <span class="kw">if </span>sign != <span class="number">0 </span>{ |
| <span class="kw">return </span>(-n, -<span class="macro">i!</span>(ty, <span class="number">0</span>), -<span class="macro">i!</span>(ty, <span class="number">1</span>)); |
| } |
| (n, <span class="macro">i!</span>(ty, <span class="number">0</span>), <span class="macro">i!</span>(ty, <span class="number">1</span>)) |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span><span class="kw">super</span>::rem_pio2; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_near_pi() { |
| <span class="kw">let </span>arg = <span class="number">3.141592025756836</span>; |
| <span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg); |
| <span class="macro">assert_eq!</span>( |
| rem_pio2(arg), |
| (<span class="number">2</span>, -<span class="number">6.278329573009626e-7</span>, -<span class="number">2.1125998133974653e-23</span>) |
| ); |
| <span class="kw">let </span>arg = <span class="number">3.141592033207416</span>; |
| <span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg); |
| <span class="macro">assert_eq!</span>( |
| rem_pio2(arg), |
| (<span class="number">2</span>, -<span class="number">6.20382377148128e-7</span>, -<span class="number">2.1125998133974653e-23</span>) |
| ); |
| <span class="kw">let </span>arg = <span class="number">3.141592144966125</span>; |
| <span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg); |
| <span class="macro">assert_eq!</span>( |
| rem_pio2(arg), |
| (<span class="number">2</span>, -<span class="number">5.086236681942706e-7</span>, -<span class="number">2.1125998133974653e-23</span>) |
| ); |
| <span class="kw">let </span>arg = <span class="number">3.141592979431152</span>; |
| <span class="kw">let </span>arg = <span class="macro">force_eval!</span>(arg); |
| <span class="macro">assert_eq!</span>( |
| rem_pio2(arg), |
| (<span class="number">2</span>, <span class="number">3.2584135866119817e-7</span>, -<span class="number">2.1125998133974653e-23</span>) |
| ); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_overflow_b9b847() { |
| <span class="kw">let _ </span>= rem_pio2(-<span class="number">3054214.5490637687</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_overflow_4747b9() { |
| <span class="kw">let _ </span>= rem_pio2(<span class="number">917340800458.2274</span>); |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="libm" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |