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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_lgamma_r.c */</span> |
| <span class="comment">/* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| * |
| */</span> |
| <span class="comment">/* lgamma_r(x, signgamp) |
| * Reentrant version of the logarithm of the Gamma function |
| * with user provide pointer for the sign of Gamma(x). |
| * |
| * Method: |
| * 1. Argument Reduction for 0 < x <= 8 |
| * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may |
| * reduce x to a number in [1.5,2.5] by |
| * lgamma(1+s) = log(s) + lgamma(s) |
| * for example, |
| * lgamma(7.3) = log(6.3) + lgamma(6.3) |
| * = log(6.3*5.3) + lgamma(5.3) |
| * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) |
| * 2. Polynomial approximation of lgamma around its |
| * minimun ymin=1.461632144968362245 to maintain monotonicity. |
| * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use |
| * Let z = x-ymin; |
| * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) |
| * where |
| * poly(z) is a 14 degree polynomial. |
| * 2. Rational approximation in the primary interval [2,3] |
| * We use the following approximation: |
| * s = x-2.0; |
| * lgamma(x) = 0.5*s + s*P(s)/Q(s) |
| * with accuracy |
| * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 |
| * Our algorithms are based on the following observation |
| * |
| * zeta(2)-1 2 zeta(3)-1 3 |
| * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... |
| * 2 3 |
| * |
| * where Euler = 0.5771... is the Euler constant, which is very |
| * close to 0.5. |
| * |
| * 3. For x>=8, we have |
| * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... |
| * (better formula: |
| * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) |
| * Let z = 1/x, then we approximation |
| * f(z) = lgamma(x) - (x-0.5)(log(x)-1) |
| * by |
| * 3 5 11 |
| * w = w0 + w1*z + w2*z + w3*z + ... + w6*z |
| * where |
| * |w - f(z)| < 2**-58.74 |
| * |
| * 4. For negative x, since (G is gamma function) |
| * -x*G(-x)*G(x) = PI/sin(PI*x), |
| * we have |
| * G(x) = PI/(sin(PI*x)*(-x)*G(-x)) |
| * since G(-x) is positive, sign(G(x)) = sign(sin(PI*x)) for x<0 |
| * Hence, for x<0, signgam = sign(sin(PI*x)) and |
| * lgamma(x) = log(|Gamma(x)|) |
| * = log(PI/(|x*sin(PI*x)|)) - lgamma(-x); |
| * Note: one should avoid compute PI*(-x) directly in the |
| * computation of sin(PI*(-x)). |
| * |
| * 5. Special Cases |
| * lgamma(2+s) ~ s*(1-Euler) for tiny s |
| * lgamma(1) = lgamma(2) = 0 |
| * lgamma(x) ~ -log(|x|) for tiny x |
| * lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero |
| * lgamma(inf) = inf |
| * lgamma(-inf) = inf (bug for bug compatible with C99!?) |
| * |
| */</span> |
| |
| <span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">floor</span>, <span class="ident">k_cos</span>, <span class="ident">k_sin</span>, <span class="ident">log</span>}; |
| |
| <span class="kw">const</span> <span class="ident">PI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.14159265358979311600e+00</span>; <span class="comment">/* 0x400921FB, 0x54442D18 */</span> |
| <span class="kw">const</span> <span class="ident">A0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.72156649015328655494e-02</span>; <span class="comment">/* 0x3FB3C467, 0xE37DB0C8 */</span> |
| <span class="kw">const</span> <span class="ident">A1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.22467033424113591611e-01</span>; <span class="comment">/* 0x3FD4A34C, 0xC4A60FAD */</span> |
| <span class="kw">const</span> <span class="ident">A2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.73523010531292681824e-02</span>; <span class="comment">/* 0x3FB13E00, 0x1A5562A7 */</span> |
| <span class="kw">const</span> <span class="ident">A3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.05808084325167332806e-02</span>; <span class="comment">/* 0x3F951322, 0xAC92547B */</span> |
| <span class="kw">const</span> <span class="ident">A4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.38555086081402883957e-03</span>; <span class="comment">/* 0x3F7E404F, 0xB68FEFE8 */</span> |
| <span class="kw">const</span> <span class="ident">A5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.89051383673415629091e-03</span>; <span class="comment">/* 0x3F67ADD8, 0xCCB7926B */</span> |
| <span class="kw">const</span> <span class="ident">A6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.19270763183362067845e-03</span>; <span class="comment">/* 0x3F538A94, 0x116F3F5D */</span> |
| <span class="kw">const</span> <span class="ident">A7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.10069792153511336608e-04</span>; <span class="comment">/* 0x3F40B6C6, 0x89B99C00 */</span> |
| <span class="kw">const</span> <span class="ident">A8</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.20862790713908385557e-04</span>; <span class="comment">/* 0x3F2CF2EC, 0xED10E54D */</span> |
| <span class="kw">const</span> <span class="ident">A9</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.08011567247583939954e-04</span>; <span class="comment">/* 0x3F1C5088, 0x987DFB07 */</span> |
| <span class="kw">const</span> <span class="ident">A10</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.52144565451257326939e-05</span>; <span class="comment">/* 0x3EFA7074, 0x428CFA52 */</span> |
| <span class="kw">const</span> <span class="ident">A11</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.48640949618915160150e-05</span>; <span class="comment">/* 0x3F07858E, 0x90A45837 */</span> |
| <span class="kw">const</span> <span class="ident">TC</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.46163214496836224576e+00</span>; <span class="comment">/* 0x3FF762D8, 0x6356BE3F */</span> |
| <span class="kw">const</span> <span class="ident">TF</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.21486290535849611461e-01</span>; <span class="comment">/* 0xBFBF19B9, 0xBCC38A42 */</span> |
| <span class="comment">/* tt = -(tail of TF) */</span> |
| <span class="kw">const</span> <span class="ident">TT</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.63867699703950536541e-18</span>; <span class="comment">/* 0xBC50C7CA, 0xA48A971F */</span> |
| <span class="kw">const</span> <span class="ident">T0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.83836122723810047042e-01</span>; <span class="comment">/* 0x3FDEF72B, 0xC8EE38A2 */</span> |
| <span class="kw">const</span> <span class="ident">T1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.47587722994593911752e-01</span>; <span class="comment">/* 0xBFC2E427, 0x8DC6C509 */</span> |
| <span class="kw">const</span> <span class="ident">T2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.46249402391333854778e-02</span>; <span class="comment">/* 0x3FB08B42, 0x94D5419B */</span> |
| <span class="kw">const</span> <span class="ident">T3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.27885410759859649565e-02</span>; <span class="comment">/* 0xBFA0C9A8, 0xDF35B713 */</span> |
| <span class="kw">const</span> <span class="ident">T4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.79706750811820387126e-02</span>; <span class="comment">/* 0x3F9266E7, 0x970AF9EC */</span> |
| <span class="kw">const</span> <span class="ident">T5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.03142241298341437450e-02</span>; <span class="comment">/* 0xBF851F9F, 0xBA91EC6A */</span> |
| <span class="kw">const</span> <span class="ident">T6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.10053870246291332635e-03</span>; <span class="comment">/* 0x3F78FCE0, 0xE370E344 */</span> |
| <span class="kw">const</span> <span class="ident">T7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.68452016781138256760e-03</span>; <span class="comment">/* 0xBF6E2EFF, 0xB3E914D7 */</span> |
| <span class="kw">const</span> <span class="ident">T8</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.25964780900612472250e-03</span>; <span class="comment">/* 0x3F6282D3, 0x2E15C915 */</span> |
| <span class="kw">const</span> <span class="ident">T9</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.40346469989232843813e-03</span>; <span class="comment">/* 0xBF56FE8E, 0xBF2D1AF1 */</span> |
| <span class="kw">const</span> <span class="ident">T10</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">8.81081882437654011382e-04</span>; <span class="comment">/* 0x3F4CDF0C, 0xEF61A8E9 */</span> |
| <span class="kw">const</span> <span class="ident">T11</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">5.38595305356740546715e-04</span>; <span class="comment">/* 0xBF41A610, 0x9C73E0EC */</span> |
| <span class="kw">const</span> <span class="ident">T12</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.15632070903625950361e-04</span>; <span class="comment">/* 0x3F34AF6D, 0x6C0EBBF7 */</span> |
| <span class="kw">const</span> <span class="ident">T13</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.12754168375120860518e-04</span>; <span class="comment">/* 0xBF347F24, 0xECC38C38 */</span> |
| <span class="kw">const</span> <span class="ident">T14</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.35529192635519073543e-04</span>; <span class="comment">/* 0x3F35FD3E, 0xE8C2D3F4 */</span> |
| <span class="kw">const</span> <span class="ident">U0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">7.72156649015328655494e-02</span>; <span class="comment">/* 0xBFB3C467, 0xE37DB0C8 */</span> |
| <span class="kw">const</span> <span class="ident">U1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.32827064025093366517e-01</span>; <span class="comment">/* 0x3FE4401E, 0x8B005DFF */</span> |
| <span class="kw">const</span> <span class="ident">U2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.45492250137234768737e+00</span>; <span class="comment">/* 0x3FF7475C, 0xD119BD6F */</span> |
| <span class="kw">const</span> <span class="ident">U3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">9.77717527963372745603e-01</span>; <span class="comment">/* 0x3FEF4976, 0x44EA8450 */</span> |
| <span class="kw">const</span> <span class="ident">U4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.28963728064692451092e-01</span>; <span class="comment">/* 0x3FCD4EAE, 0xF6010924 */</span> |
| <span class="kw">const</span> <span class="ident">U5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.33810918536787660377e-02</span>; <span class="comment">/* 0x3F8B678B, 0xBF2BAB09 */</span> |
| <span class="kw">const</span> <span class="ident">V1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.45597793713041134822e+00</span>; <span class="comment">/* 0x4003A5D7, 0xC2BD619C */</span> |
| <span class="kw">const</span> <span class="ident">V2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.12848976379893395361e+00</span>; <span class="comment">/* 0x40010725, 0xA42B18F5 */</span> |
| <span class="kw">const</span> <span class="ident">V3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.69285150456672783825e-01</span>; <span class="comment">/* 0x3FE89DFB, 0xE45050AF */</span> |
| <span class="kw">const</span> <span class="ident">V4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.04222645593369134254e-01</span>; <span class="comment">/* 0x3FBAAE55, 0xD6537C88 */</span> |
| <span class="kw">const</span> <span class="ident">V5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.21709242282423911810e-03</span>; <span class="comment">/* 0x3F6A5ABB, 0x57D0CF61 */</span> |
| <span class="kw">const</span> <span class="ident">S0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">7.72156649015328655494e-02</span>; <span class="comment">/* 0xBFB3C467, 0xE37DB0C8 */</span> |
| <span class="kw">const</span> <span class="ident">S1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.14982415960608852501e-01</span>; <span class="comment">/* 0x3FCB848B, 0x36E20878 */</span> |
| <span class="kw">const</span> <span class="ident">S2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.25778796408930981787e-01</span>; <span class="comment">/* 0x3FD4D98F, 0x4F139F59 */</span> |
| <span class="kw">const</span> <span class="ident">S3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.46350472652464452805e-01</span>; <span class="comment">/* 0x3FC2BB9C, 0xBEE5F2F7 */</span> |
| <span class="kw">const</span> <span class="ident">S4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.66422703033638609560e-02</span>; <span class="comment">/* 0x3F9B481C, 0x7E939961 */</span> |
| <span class="kw">const</span> <span class="ident">S5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.84028451407337715652e-03</span>; <span class="comment">/* 0x3F5E26B6, 0x7368F239 */</span> |
| <span class="kw">const</span> <span class="ident">S6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.19475326584100867617e-05</span>; <span class="comment">/* 0x3F00BFEC, 0xDD17E945 */</span> |
| <span class="kw">const</span> <span class="ident">R1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.39200533467621045958e+00</span>; <span class="comment">/* 0x3FF645A7, 0x62C4AB74 */</span> |
| <span class="kw">const</span> <span class="ident">R2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.21935547567138069525e-01</span>; <span class="comment">/* 0x3FE71A18, 0x93D3DCDC */</span> |
| <span class="kw">const</span> <span class="ident">R3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.71933865632803078993e-01</span>; <span class="comment">/* 0x3FC601ED, 0xCCFBDF27 */</span> |
| <span class="kw">const</span> <span class="ident">R4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.86459191715652901344e-02</span>; <span class="comment">/* 0x3F9317EA, 0x742ED475 */</span> |
| <span class="kw">const</span> <span class="ident">R5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.77942496381893596434e-04</span>; <span class="comment">/* 0x3F497DDA, 0xCA41A95B */</span> |
| <span class="kw">const</span> <span class="ident">R6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.32668430744625636189e-06</span>; <span class="comment">/* 0x3EDEBAF7, 0xA5B38140 */</span> |
| <span class="kw">const</span> <span class="ident">W0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.18938533204672725052e-01</span>; <span class="comment">/* 0x3FDACFE3, 0x90C97D69 */</span> |
| <span class="kw">const</span> <span class="ident">W1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">8.33333333333329678849e-02</span>; <span class="comment">/* 0x3FB55555, 0x5555553B */</span> |
| <span class="kw">const</span> <span class="ident">W2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.77777777728775536470e-03</span>; <span class="comment">/* 0xBF66C16C, 0x16B02E5C */</span> |
| <span class="kw">const</span> <span class="ident">W3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.93650558643019558500e-04</span>; <span class="comment">/* 0x3F4A019F, 0x98CF38B6 */</span> |
| <span class="kw">const</span> <span class="ident">W4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">5.95187557450339963135e-04</span>; <span class="comment">/* 0xBF4380CB, 0x8C0FE741 */</span> |
| <span class="kw">const</span> <span class="ident">W5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">8.36339918996282139126e-04</span>; <span class="comment">/* 0x3F4B67BA, 0x4CDAD5D1 */</span> |
| <span class="kw">const</span> <span class="ident">W6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.63092934096575273989e-03</span>; <span class="comment">/* 0xBF5AB89D, 0x0B9E43E4 */</span> |
| |
| <span class="comment">/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */</span> |
| <span class="kw">fn</span> <span class="ident">sin_pi</span>(<span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">n</span>: <span class="ident">i32</span>; |
| |
| <span class="comment">/* spurious inexact if odd int */</span> |
| <span class="ident">x</span> <span class="op">=</span> <span class="number">2.0</span> <span class="op">*</span> (<span class="ident">x</span> <span class="op">*</span> <span class="number">0.5</span> <span class="op">-</span> <span class="ident">floor</span>(<span class="ident">x</span> <span class="op">*</span> <span class="number">0.5</span>)); <span class="comment">/* x mod 2.0 */</span> |
| |
| <span class="ident">n</span> <span class="op">=</span> (<span class="ident">x</span> <span class="op">*</span> <span class="number">4.0</span>) <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="ident">n</span> <span class="op">=</span> (<span class="ident">n</span> <span class="op">+</span> <span class="number">1</span>) <span class="op">/</span> <span class="number">2</span>; |
| <span class="ident">x</span> <span class="op">-</span><span class="op">=</span> (<span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> <span class="number">0.5</span>; |
| <span class="ident">x</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">PI</span>; |
| |
| <span class="kw">match</span> <span class="ident">n</span> { |
| <span class="number">1</span> => <span class="ident">k_cos</span>(<span class="ident">x</span>, <span class="number">0.0</span>), |
| <span class="number">2</span> => <span class="ident">k_sin</span>(<span class="op">-</span><span class="ident">x</span>, <span class="number">0.0</span>, <span class="number">0</span>), |
| <span class="number">3</span> => <span class="op">-</span><span class="ident">k_cos</span>(<span class="ident">x</span>, <span class="number">0.0</span>), |
| <span class="number">0</span> <span class="op">|</span> <span class="kw">_</span> => <span class="ident">k_sin</span>(<span class="ident">x</span>, <span class="number">0.0</span>, <span class="number">0</span>), |
| } |
| } |
| |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">lgamma_r</span>(<span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f64</span>) -> (<span class="ident">f64</span>, <span class="ident">i32</span>) { |
| <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>(); |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">t</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">y</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">z</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">nadj</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">p</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">p1</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">p2</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">p3</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">q</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">w</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">bool</span>; |
| <span class="kw">let</span> <span class="ident">i</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">signgam</span>: <span class="ident">i32</span>; |
| |
| <span class="comment">/* purge off +-inf, NaN, +-0, tiny and negative arguments */</span> |
| <span class="ident">signgam</span> <span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">sign</span> <span class="op">=</span> (<span class="ident">u</span> <span class="op">></span><span class="op">></span> <span class="number">63</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span>; |
| <span class="ident">ix</span> <span class="op">=</span> ((<span class="ident">u</span> <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>) <span class="op">&</span> <span class="number">0x7fffffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7ff00000</span> { |
| <span class="kw">return</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>, <span class="ident">signgam</span>); |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> (<span class="number">0x3ff</span> <span class="op">-</span> <span class="number">70</span>) <span class="op"><</span><span class="op"><</span> <span class="number">20</span> { |
| <span class="comment">/* |x|<2**-70, return -log(|x|) */</span> |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="ident">x</span> <span class="op">=</span> <span class="op">-</span><span class="ident">x</span>; |
| <span class="ident">signgam</span> <span class="op">=</span> <span class="op">-</span><span class="number">1</span>; |
| } |
| <span class="kw">return</span> (<span class="op">-</span><span class="ident">log</span>(<span class="ident">x</span>), <span class="ident">signgam</span>); |
| } |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="ident">x</span> <span class="op">=</span> <span class="op">-</span><span class="ident">x</span>; |
| <span class="ident">t</span> <span class="op">=</span> <span class="ident">sin_pi</span>(<span class="ident">x</span>); |
| <span class="kw">if</span> <span class="ident">t</span> <span class="op">==</span> <span class="number">0.0</span> { |
| <span class="comment">/* -integer */</span> |
| <span class="kw">return</span> (<span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">x</span>), <span class="ident">signgam</span>); |
| } |
| <span class="kw">if</span> <span class="ident">t</span> <span class="op">></span> <span class="number">0.0</span> { |
| <span class="ident">signgam</span> <span class="op">=</span> <span class="op">-</span><span class="number">1</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">t</span> <span class="op">=</span> <span class="op">-</span><span class="ident">t</span>; |
| } |
| <span class="ident">nadj</span> <span class="op">=</span> <span class="ident">log</span>(<span class="ident">PI</span> <span class="op">/</span> (<span class="ident">t</span> <span class="op">*</span> <span class="ident">x</span>)); |
| } <span class="kw">else</span> { |
| <span class="ident">nadj</span> <span class="op">=</span> <span class="number">0.0</span>; |
| } |
| |
| <span class="comment">/* purge off 1 and 2 */</span> |
| <span class="kw">if</span> (<span class="ident">ix</span> <span class="op">==</span> <span class="number">0x3ff00000</span> <span class="op">|</span><span class="op">|</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0x40000000</span>) <span class="op">&&</span> (<span class="ident">u</span> <span class="op">&</span> <span class="number">0xffffffff</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="ident">r</span> <span class="op">=</span> <span class="number">0.0</span>; |
| } |
| <span class="comment">/* for x < 2.0 */</span> |
| <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x40000000</span> { |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span><span class="op">=</span> <span class="number">0x3feccccc</span> { |
| <span class="comment">/* lgamma(x) = lgamma(x+1)-log(x) */</span> |
| <span class="ident">r</span> <span class="op">=</span> <span class="op">-</span><span class="ident">log</span>(<span class="ident">x</span>); |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3FE76944</span> { |
| <span class="ident">y</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">-</span> <span class="ident">x</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">0</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3FCDA661</span> { |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> (<span class="ident">TC</span> <span class="op">-</span> <span class="number">1.0</span>); |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">1</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">x</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">2</span>; |
| } |
| } <span class="kw">else</span> { |
| <span class="ident">r</span> <span class="op">=</span> <span class="number">0.0</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3FFBB4C3</span> { |
| <span class="comment">/* [1.7316,2] */</span> |
| <span class="ident">y</span> <span class="op">=</span> <span class="number">2.0</span> <span class="op">-</span> <span class="ident">x</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">0</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3FF3B4C4</span> { |
| <span class="comment">/* [1.23,1.73] */</span> |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">TC</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">1</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> <span class="number">1.0</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">2</span>; |
| } |
| } |
| <span class="kw">match</span> <span class="ident">i</span> { |
| <span class="number">0</span> => { |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">y</span>; |
| <span class="ident">p1</span> <span class="op">=</span> <span class="ident">A0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A4</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A6</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A8</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">A10</span>)))); |
| <span class="ident">p2</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A5</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A7</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">A9</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">A11</span>))))); |
| <span class="ident">p</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">p1</span> <span class="op">+</span> <span class="ident">p2</span>; |
| <span class="ident">r</span> <span class="op">+</span><span class="op">=</span> <span class="ident">p</span> <span class="op">-</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">y</span>; |
| } |
| <span class="number">1</span> => { |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">y</span>; |
| <span class="ident">w</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">y</span>; |
| <span class="ident">p1</span> <span class="op">=</span> <span class="ident">T0</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T3</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T6</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T9</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">T12</span>))); <span class="comment">/* parallel comp */</span> |
| <span class="ident">p2</span> <span class="op">=</span> <span class="ident">T1</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T4</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T7</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T10</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">T13</span>))); |
| <span class="ident">p3</span> <span class="op">=</span> <span class="ident">T2</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T5</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T8</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">T11</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">T14</span>))); |
| <span class="ident">p</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p1</span> <span class="op">-</span> (<span class="ident">TT</span> <span class="op">-</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">p2</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">p3</span>)); |
| <span class="ident">r</span> <span class="op">+</span><span class="op">=</span> <span class="ident">TF</span> <span class="op">+</span> <span class="ident">p</span>; |
| } |
| <span class="number">2</span> => { |
| <span class="ident">p1</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">U0</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">U1</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">U2</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">U3</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">U4</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">U5</span>))))); |
| <span class="ident">p2</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">V1</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">V2</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">V3</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">V4</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">V5</span>)))); |
| <span class="ident">r</span> <span class="op">+</span><span class="op">=</span> <span class="op">-</span><span class="number">0.5</span> <span class="op">*</span> <span class="ident">y</span> <span class="op">+</span> <span class="ident">p1</span> <span class="op">/</span> <span class="ident">p2</span>; |
| } |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">debug_assertions</span>)]</span> |
| <span class="kw">_</span> => <span class="macro">unreachable!</span>(), |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">debug_assertions</span>))]</span> |
| <span class="kw">_</span> => {} |
| } |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x40200000</span> { |
| <span class="comment">/* x < 8.0 */</span> |
| <span class="ident">i</span> <span class="op">=</span> <span class="ident">x</span> <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>); |
| <span class="ident">p</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">S0</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">S1</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">S2</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">S3</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">S4</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">S5</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">S6</span>)))))); |
| <span class="ident">q</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">R1</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">R2</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">R3</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">R4</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">R5</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">R6</span>))))); |
| <span class="ident">r</span> <span class="op">=</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">y</span> <span class="op">+</span> <span class="ident">p</span> <span class="op">/</span> <span class="ident">q</span>; |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span>; <span class="comment">/* lgamma(1+s) = log(s) + lgamma(s) */</span> |
| <span class="comment">// TODO: In C, this was implemented using switch jumps with fallthrough.</span> |
| <span class="comment">// Does this implementation have performance problems?</span> |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op">></span><span class="op">=</span> <span class="number">7</span> { |
| <span class="ident">z</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">6.0</span>; |
| } |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op">></span><span class="op">=</span> <span class="number">6</span> { |
| <span class="ident">z</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">5.0</span>; |
| } |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op">></span><span class="op">=</span> <span class="number">5</span> { |
| <span class="ident">z</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">4.0</span>; |
| } |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op">></span><span class="op">=</span> <span class="number">4</span> { |
| <span class="ident">z</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">3.0</span>; |
| } |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op">></span><span class="op">=</span> <span class="number">3</span> { |
| <span class="ident">z</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">2.0</span>; |
| <span class="ident">r</span> <span class="op">+</span><span class="op">=</span> <span class="ident">log</span>(<span class="ident">z</span>); |
| } |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x43900000</span> { |
| <span class="comment">/* 8.0 <= x < 2**58 */</span> |
| <span class="ident">t</span> <span class="op">=</span> <span class="ident">log</span>(<span class="ident">x</span>); |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">x</span>; |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">z</span>; |
| <span class="ident">w</span> <span class="op">=</span> <span class="ident">W0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">W1</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">W2</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">W3</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">W4</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> (<span class="ident">W5</span> <span class="op">+</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">W6</span>))))); |
| <span class="ident">r</span> <span class="op">=</span> (<span class="ident">x</span> <span class="op">-</span> <span class="number">0.5</span>) <span class="op">*</span> (<span class="ident">t</span> <span class="op">-</span> <span class="number">1.0</span>) <span class="op">+</span> <span class="ident">w</span>; |
| } <span class="kw">else</span> { |
| <span class="comment">/* 2**58 <= x <= inf */</span> |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> (<span class="ident">log</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="number">1.0</span>); |
| } |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">nadj</span> <span class="op">-</span> <span class="ident">r</span>; |
| } |
| <span class="kw">return</span> (<span class="ident">r</span>, <span class="ident">signgam</span>); |
| } |
| </code></pre></div> |
| </section><section id="search" class="content hidden"></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="1.60.0-nightly (1bd4fdc94 2022-01-12)" ></div> |
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