rm asine, mv lgamma
This commit is contained in:
Andrey Zgarbul
@@ -41,17 +41,16 @@ mod musl_reference_tests {
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"rem_pio2.rs",
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"rem_pio2_large.rs",
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"rem_pio2f.rs",
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"remquo.rs",
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"remquof.rs",
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"lgamma.rs", // lgamma passed, lgamma_r has more than 1 result
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"lgammaf.rs", // lgammaf passed, lgammaf_r has more than 1 result
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"remquo.rs", // more than 1 result
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"remquof.rs", // more than 1 result
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"lgamma_r.rs", // more than 1 result
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"lgammaf_r.rs", // more than 1 result
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"frexp.rs", // more than 1 result
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"frexpf.rs", // more than 1 result
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"sincos.rs", // more than 1 result
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"sincosf.rs", // more than 1 result
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"modf.rs", // more than 1 result
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"modff.rs", // more than 1 result
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"asinef.rs", // not exists
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"jn.rs", // passed, but very slow
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"jnf.rs", // passed, but very slow
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];
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@@ -1,93 +0,0 @@
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/* @(#)z_asinef.c 1.0 98/08/13 */
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/******************************************************************
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* The following routines are coded directly from the algorithms
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* and coefficients given in "Software Manual for the Elementary
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* Functions" by William J. Cody, Jr. and William Waite, Prentice
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* Hall, 1980.
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******************************************************************/
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/******************************************************************
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* Arcsine
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*
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* Input:
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* x - floating point value
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* acosine - indicates acos calculation
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*
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* Output:
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* Arcsine of x.
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*
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* Description:
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* This routine calculates arcsine / arccosine.
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*
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*****************************************************************/
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use super::{fabsf, sqrtf};
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const P: [f32; 2] = [ 0.933935835, -0.504400557 ];
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const Q: [f32; 2] = [ 0.560363004e+1, -0.554846723e+1 ];
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const A: [f32; 2] = [ 0.0, 0.785398163 ];
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const B: [f32; 2] = [ 1.570796326, 0.785398163 ];
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const Z_ROOTEPS_F: f32 = 1.7263349182589107e-4;
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pub fn asinef(x: f32, acosine: bool) -> f32 {
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let i: usize;
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let mut branch: bool = false;
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let g: f32;
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let mut res: f32 = 0.0;
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let mut y: f32;
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/* Check for special values. */
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//i = numtestf (x);
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if x.is_nan() || x.is_infinite() {
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force_eval!(x);
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return x;
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}
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y = fabsf(x);
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let flag = acosine;
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if y > 0.5 {
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i = (!flag) as usize;
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/* Check for range error. */
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if y > 1.0 {
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return 0.0 / 0.0;
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}
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g = (1.0 - y) / 2.0;
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y = -2.0 * sqrtf(g);
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branch = true;
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} else {
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i = flag;
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if y < Z_ROOTEPS_F {
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res = y;
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g = 0.0; // pleasing the uninitialized variable
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} else {
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g = y * y;
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}
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}
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if y >= Z_ROOTEPS_F || branch {
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/* Calculate the Taylor series. */
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let p = (P[1] * g + P[0]) * g;
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let q = (g + Q[1]) * g + Q[0];
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let r = p / q;
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res = y + y * r;
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}
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/* Calculate asine or acose. */
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if flag == 0 {
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res = (A[i] + res) + A[i];
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if x < 0.0 {
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res = -res;
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}
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} else {
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if x < 0.0 {
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res = (B[i] + res) + B[i];
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} else {
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res = (A[i] - res) + A[i];
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}
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}
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return res;
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}
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+1
-319
@@ -1,323 +1,5 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/e_lgamma_r.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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/* lgamma_r(x, signgamp)
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* Reentrant version of the logarithm of the Gamma function
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* with user provide pointer for the sign of Gamma(x).
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*
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* Method:
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* 1. Argument Reduction for 0 < x <= 8
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* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
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* reduce x to a number in [1.5,2.5] by
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* lgamma(1+s) = log(s) + lgamma(s)
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* for example,
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* lgamma(7.3) = log(6.3) + lgamma(6.3)
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* = log(6.3*5.3) + lgamma(5.3)
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* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
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* 2. Polynomial approximation of lgamma around its
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* minimun ymin=1.461632144968362245 to maintain monotonicity.
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* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
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* Let z = x-ymin;
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* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
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* where
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* poly(z) is a 14 degree polynomial.
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* 2. Rational approximation in the primary interval [2,3]
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* We use the following approximation:
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* s = x-2.0;
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* lgamma(x) = 0.5*s + s*P(s)/Q(s)
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* with accuracy
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* |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
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* Our algorithms are based on the following observation
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*
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* zeta(2)-1 2 zeta(3)-1 3
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* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
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* 2 3
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*
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* where Euler = 0.5771... is the Euler constant, which is very
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* close to 0.5.
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*
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* 3. For x>=8, we have
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* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
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* (better formula:
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* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
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* Let z = 1/x, then we approximation
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* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
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* by
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* 3 5 11
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* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
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* where
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* |w - f(z)| < 2**-58.74
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*
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* 4. For negative x, since (G is gamma function)
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* -x*G(-x)*G(x) = PI/sin(PI*x),
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* we have
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* G(x) = PI/(sin(PI*x)*(-x)*G(-x))
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* since G(-x) is positive, sign(G(x)) = sign(sin(PI*x)) for x<0
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* Hence, for x<0, signgam = sign(sin(PI*x)) and
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* lgamma(x) = log(|Gamma(x)|)
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* = log(PI/(|x*sin(PI*x)|)) - lgamma(-x);
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* Note: one should avoid compute PI*(-x) directly in the
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* computation of sin(PI*(-x)).
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*
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* 5. Special Cases
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* lgamma(2+s) ~ s*(1-Euler) for tiny s
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* lgamma(1) = lgamma(2) = 0
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* lgamma(x) ~ -log(|x|) for tiny x
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* lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero
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* lgamma(inf) = inf
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* lgamma(-inf) = inf (bug for bug compatible with C99!?)
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*
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*/
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use super::{floor, k_cos, k_sin, log};
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const PI: f64 = 3.14159265358979311600e+00; /* 0x400921FB, 0x54442D18 */
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const A0: f64 = 7.72156649015328655494e-02; /* 0x3FB3C467, 0xE37DB0C8 */
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const A1: f64 = 3.22467033424113591611e-01; /* 0x3FD4A34C, 0xC4A60FAD */
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const A2: f64 = 6.73523010531292681824e-02; /* 0x3FB13E00, 0x1A5562A7 */
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const A3: f64 = 2.05808084325167332806e-02; /* 0x3F951322, 0xAC92547B */
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const A4: f64 = 7.38555086081402883957e-03; /* 0x3F7E404F, 0xB68FEFE8 */
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const A5: f64 = 2.89051383673415629091e-03; /* 0x3F67ADD8, 0xCCB7926B */
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const A6: f64 = 1.19270763183362067845e-03; /* 0x3F538A94, 0x116F3F5D */
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const A7: f64 = 5.10069792153511336608e-04; /* 0x3F40B6C6, 0x89B99C00 */
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const A8: f64 = 2.20862790713908385557e-04; /* 0x3F2CF2EC, 0xED10E54D */
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const A9: f64 = 1.08011567247583939954e-04; /* 0x3F1C5088, 0x987DFB07 */
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const A10: f64 = 2.52144565451257326939e-05; /* 0x3EFA7074, 0x428CFA52 */
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const A11: f64 = 4.48640949618915160150e-05; /* 0x3F07858E, 0x90A45837 */
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const TC: f64 = 1.46163214496836224576e+00; /* 0x3FF762D8, 0x6356BE3F */
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const TF: f64 = -1.21486290535849611461e-01; /* 0xBFBF19B9, 0xBCC38A42 */
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/* tt = -(tail of TF) */
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const TT: f64 = -3.63867699703950536541e-18; /* 0xBC50C7CA, 0xA48A971F */
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const T0: f64 = 4.83836122723810047042e-01; /* 0x3FDEF72B, 0xC8EE38A2 */
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const T1: f64 = -1.47587722994593911752e-01; /* 0xBFC2E427, 0x8DC6C509 */
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const T2: f64 = 6.46249402391333854778e-02; /* 0x3FB08B42, 0x94D5419B */
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const T3: f64 = -3.27885410759859649565e-02; /* 0xBFA0C9A8, 0xDF35B713 */
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const T4: f64 = 1.79706750811820387126e-02; /* 0x3F9266E7, 0x970AF9EC */
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const T5: f64 = -1.03142241298341437450e-02; /* 0xBF851F9F, 0xBA91EC6A */
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const T6: f64 = 6.10053870246291332635e-03; /* 0x3F78FCE0, 0xE370E344 */
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const T7: f64 = -3.68452016781138256760e-03; /* 0xBF6E2EFF, 0xB3E914D7 */
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const T8: f64 = 2.25964780900612472250e-03; /* 0x3F6282D3, 0x2E15C915 */
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const T9: f64 = -1.40346469989232843813e-03; /* 0xBF56FE8E, 0xBF2D1AF1 */
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const T10: f64 = 8.81081882437654011382e-04; /* 0x3F4CDF0C, 0xEF61A8E9 */
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const T11: f64 = -5.38595305356740546715e-04; /* 0xBF41A610, 0x9C73E0EC */
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const T12: f64 = 3.15632070903625950361e-04; /* 0x3F34AF6D, 0x6C0EBBF7 */
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const T13: f64 = -3.12754168375120860518e-04; /* 0xBF347F24, 0xECC38C38 */
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const T14: f64 = 3.35529192635519073543e-04; /* 0x3F35FD3E, 0xE8C2D3F4 */
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const U0: f64 = -7.72156649015328655494e-02; /* 0xBFB3C467, 0xE37DB0C8 */
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const U1: f64 = 6.32827064025093366517e-01; /* 0x3FE4401E, 0x8B005DFF */
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const U2: f64 = 1.45492250137234768737e+00; /* 0x3FF7475C, 0xD119BD6F */
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const U3: f64 = 9.77717527963372745603e-01; /* 0x3FEF4976, 0x44EA8450 */
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const U4: f64 = 2.28963728064692451092e-01; /* 0x3FCD4EAE, 0xF6010924 */
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const U5: f64 = 1.33810918536787660377e-02; /* 0x3F8B678B, 0xBF2BAB09 */
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const V1: f64 = 2.45597793713041134822e+00; /* 0x4003A5D7, 0xC2BD619C */
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const V2: f64 = 2.12848976379893395361e+00; /* 0x40010725, 0xA42B18F5 */
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const V3: f64 = 7.69285150456672783825e-01; /* 0x3FE89DFB, 0xE45050AF */
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const V4: f64 = 1.04222645593369134254e-01; /* 0x3FBAAE55, 0xD6537C88 */
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const V5: f64 = 3.21709242282423911810e-03; /* 0x3F6A5ABB, 0x57D0CF61 */
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const S0: f64 = -7.72156649015328655494e-02; /* 0xBFB3C467, 0xE37DB0C8 */
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const S1: f64 = 2.14982415960608852501e-01; /* 0x3FCB848B, 0x36E20878 */
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const S2: f64 = 3.25778796408930981787e-01; /* 0x3FD4D98F, 0x4F139F59 */
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const S3: f64 = 1.46350472652464452805e-01; /* 0x3FC2BB9C, 0xBEE5F2F7 */
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const S4: f64 = 2.66422703033638609560e-02; /* 0x3F9B481C, 0x7E939961 */
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const S5: f64 = 1.84028451407337715652e-03; /* 0x3F5E26B6, 0x7368F239 */
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const S6: f64 = 3.19475326584100867617e-05; /* 0x3F00BFEC, 0xDD17E945 */
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const R1: f64 = 1.39200533467621045958e+00; /* 0x3FF645A7, 0x62C4AB74 */
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const R2: f64 = 7.21935547567138069525e-01; /* 0x3FE71A18, 0x93D3DCDC */
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const R3: f64 = 1.71933865632803078993e-01; /* 0x3FC601ED, 0xCCFBDF27 */
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const R4: f64 = 1.86459191715652901344e-02; /* 0x3F9317EA, 0x742ED475 */
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const R5: f64 = 7.77942496381893596434e-04; /* 0x3F497DDA, 0xCA41A95B */
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const R6: f64 = 7.32668430744625636189e-06; /* 0x3EDEBAF7, 0xA5B38140 */
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const W0: f64 = 4.18938533204672725052e-01; /* 0x3FDACFE3, 0x90C97D69 */
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const W1: f64 = 8.33333333333329678849e-02; /* 0x3FB55555, 0x5555553B */
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const W2: f64 = -2.77777777728775536470e-03; /* 0xBF66C16C, 0x16B02E5C */
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const W3: f64 = 7.93650558643019558500e-04; /* 0x3F4A019F, 0x98CF38B6 */
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const W4: f64 = -5.95187557450339963135e-04; /* 0xBF4380CB, 0x8C0FE741 */
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const W5: f64 = 8.36339918996282139126e-04; /* 0x3F4B67BA, 0x4CDAD5D1 */
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const W6: f64 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
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/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
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fn sin_pi(mut x: f64) -> f64 {
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let mut n: i32;
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/* spurious inexact if odd int */
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x = 2.0 * (x * 0.5 - floor(x * 0.5)); /* x mod 2.0 */
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n = (x * 4.0) as i32;
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n = (n + 1) / 2;
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x -= (n as f64) * 0.5;
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x *= PI;
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match n {
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1 => k_cos(x, 0.0),
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2 => k_sin(-x, 0.0, 0),
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3 => -k_cos(x, 0.0),
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0 | _ => k_sin(x, 0.0, 0),
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}
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}
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use super::lgamma_r;
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pub fn lgamma(x: f64) -> f64 {
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lgamma_r(x).0
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}
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pub fn lgamma_r(mut x: f64) -> (f64, i32) {
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let u: u64 = x.to_bits();
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let mut t: f64;
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let y: f64;
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let mut z: f64;
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let nadj: f64;
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let p: f64;
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let p1: f64;
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let p2: f64;
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let p3: f64;
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let q: f64;
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let mut r: f64;
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let w: f64;
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let ix: u32;
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let sign: bool;
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let i: i32;
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let mut signgam: i32;
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/* purge off +-inf, NaN, +-0, tiny and negative arguments */
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signgam = 1;
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sign = (u >> 63) != 0;
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ix = ((u >> 32) as u32) & 0x7fffffff;
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if ix >= 0x7ff00000 {
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return (x * x, signgam);
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}
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if ix < (0x3ff - 70) << 20 {
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/* |x|<2**-70, return -log(|x|) */
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if sign {
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x = -x;
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signgam = -1;
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}
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return (-log(x), signgam);
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}
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if sign {
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x = -x;
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t = sin_pi(x);
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if t == 0.0 {
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/* -integer */
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return (1.0 / (x - x), signgam);
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}
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if t > 0.0 {
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signgam = -1;
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} else {
|
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t = -t;
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}
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nadj = log(PI / (t * x));
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} else {
|
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nadj = 0.0;
|
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}
|
||||
|
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/* purge off 1 and 2 */
|
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if (ix == 0x3ff00000 || ix == 0x40000000) && (u & 0xffffffff) == 0 {
|
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r = 0.0;
|
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}
|
||||
/* for x < 2.0 */
|
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else if ix < 0x40000000 {
|
||||
if ix <= 0x3feccccc {
|
||||
/* lgamma(x) = lgamma(x+1)-log(x) */
|
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r = -log(x);
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if ix >= 0x3FE76944 {
|
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y = 1.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3FCDA661 {
|
||||
y = x - (TC - 1.0);
|
||||
i = 1;
|
||||
} else {
|
||||
y = x;
|
||||
i = 2;
|
||||
}
|
||||
} else {
|
||||
r = 0.0;
|
||||
if ix >= 0x3FFBB4C3 {
|
||||
/* [1.7316,2] */
|
||||
y = 2.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3FF3B4C4 {
|
||||
/* [1.23,1.73] */
|
||||
y = x - TC;
|
||||
i = 1;
|
||||
} else {
|
||||
y = x - 1.0;
|
||||
i = 2;
|
||||
}
|
||||
}
|
||||
match i {
|
||||
0 => {
|
||||
z = y * y;
|
||||
p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10))));
|
||||
p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11)))));
|
||||
p = y * p1 + p2;
|
||||
r += p - 0.5 * y;
|
||||
}
|
||||
1 => {
|
||||
z = y * y;
|
||||
w = z * y;
|
||||
p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */
|
||||
p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13)));
|
||||
p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14)));
|
||||
p = z * p1 - (TT - w * (p2 + y * p3));
|
||||
r += TF + p;
|
||||
}
|
||||
2 => {
|
||||
p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5)))));
|
||||
p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5))));
|
||||
r += -0.5 * y + p1 / p2;
|
||||
}
|
||||
#[cfg(feature = "checked")]
|
||||
_ => unreachable!(),
|
||||
#[cfg(not(feature = "checked"))]
|
||||
_ => {}
|
||||
}
|
||||
} else if ix < 0x40200000 {
|
||||
/* x < 8.0 */
|
||||
i = x as i32;
|
||||
y = x - (i as f64);
|
||||
p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6))))));
|
||||
q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6)))));
|
||||
r = 0.5 * y + p / q;
|
||||
z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
// TODO: In C, this was implemented using switch jumps with fallthrough.
|
||||
// Does this implementation have performance problems?
|
||||
if i >= 7 {
|
||||
z *= y + 6.0;
|
||||
}
|
||||
if i >= 6 {
|
||||
z *= y + 5.0;
|
||||
}
|
||||
if i >= 5 {
|
||||
z *= y + 4.0;
|
||||
}
|
||||
if i >= 4 {
|
||||
z *= y + 3.0;
|
||||
}
|
||||
if i >= 3 {
|
||||
z *= y + 2.0;
|
||||
r += log(z);
|
||||
}
|
||||
} else if ix < 0x43900000 {
|
||||
/* 8.0 <= x < 2**58 */
|
||||
t = log(x);
|
||||
z = 1.0 / x;
|
||||
y = z * z;
|
||||
w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6)))));
|
||||
r = (x - 0.5) * (t - 1.0) + w;
|
||||
} else {
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x * (log(x) - 1.0);
|
||||
}
|
||||
if sign {
|
||||
r = nadj - r;
|
||||
}
|
||||
return (r, signgam);
|
||||
}
|
||||
|
||||
@@ -0,0 +1,319 @@
|
||||
/* origin: FreeBSD /usr/src/lib/msun/src/e_lgamma_r.c */
|
||||
/*
|
||||
* ====================================================
|
||||
* 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.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
/* 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!?)
|
||||
*
|
||||
*/
|
||||
|
||||
use super::{floor, k_cos, k_sin, log};
|
||||
|
||||
const PI: f64 = 3.14159265358979311600e+00; /* 0x400921FB, 0x54442D18 */
|
||||
const A0: f64 = 7.72156649015328655494e-02; /* 0x3FB3C467, 0xE37DB0C8 */
|
||||
const A1: f64 = 3.22467033424113591611e-01; /* 0x3FD4A34C, 0xC4A60FAD */
|
||||
const A2: f64 = 6.73523010531292681824e-02; /* 0x3FB13E00, 0x1A5562A7 */
|
||||
const A3: f64 = 2.05808084325167332806e-02; /* 0x3F951322, 0xAC92547B */
|
||||
const A4: f64 = 7.38555086081402883957e-03; /* 0x3F7E404F, 0xB68FEFE8 */
|
||||
const A5: f64 = 2.89051383673415629091e-03; /* 0x3F67ADD8, 0xCCB7926B */
|
||||
const A6: f64 = 1.19270763183362067845e-03; /* 0x3F538A94, 0x116F3F5D */
|
||||
const A7: f64 = 5.10069792153511336608e-04; /* 0x3F40B6C6, 0x89B99C00 */
|
||||
const A8: f64 = 2.20862790713908385557e-04; /* 0x3F2CF2EC, 0xED10E54D */
|
||||
const A9: f64 = 1.08011567247583939954e-04; /* 0x3F1C5088, 0x987DFB07 */
|
||||
const A10: f64 = 2.52144565451257326939e-05; /* 0x3EFA7074, 0x428CFA52 */
|
||||
const A11: f64 = 4.48640949618915160150e-05; /* 0x3F07858E, 0x90A45837 */
|
||||
const TC: f64 = 1.46163214496836224576e+00; /* 0x3FF762D8, 0x6356BE3F */
|
||||
const TF: f64 = -1.21486290535849611461e-01; /* 0xBFBF19B9, 0xBCC38A42 */
|
||||
/* tt = -(tail of TF) */
|
||||
const TT: f64 = -3.63867699703950536541e-18; /* 0xBC50C7CA, 0xA48A971F */
|
||||
const T0: f64 = 4.83836122723810047042e-01; /* 0x3FDEF72B, 0xC8EE38A2 */
|
||||
const T1: f64 = -1.47587722994593911752e-01; /* 0xBFC2E427, 0x8DC6C509 */
|
||||
const T2: f64 = 6.46249402391333854778e-02; /* 0x3FB08B42, 0x94D5419B */
|
||||
const T3: f64 = -3.27885410759859649565e-02; /* 0xBFA0C9A8, 0xDF35B713 */
|
||||
const T4: f64 = 1.79706750811820387126e-02; /* 0x3F9266E7, 0x970AF9EC */
|
||||
const T5: f64 = -1.03142241298341437450e-02; /* 0xBF851F9F, 0xBA91EC6A */
|
||||
const T6: f64 = 6.10053870246291332635e-03; /* 0x3F78FCE0, 0xE370E344 */
|
||||
const T7: f64 = -3.68452016781138256760e-03; /* 0xBF6E2EFF, 0xB3E914D7 */
|
||||
const T8: f64 = 2.25964780900612472250e-03; /* 0x3F6282D3, 0x2E15C915 */
|
||||
const T9: f64 = -1.40346469989232843813e-03; /* 0xBF56FE8E, 0xBF2D1AF1 */
|
||||
const T10: f64 = 8.81081882437654011382e-04; /* 0x3F4CDF0C, 0xEF61A8E9 */
|
||||
const T11: f64 = -5.38595305356740546715e-04; /* 0xBF41A610, 0x9C73E0EC */
|
||||
const T12: f64 = 3.15632070903625950361e-04; /* 0x3F34AF6D, 0x6C0EBBF7 */
|
||||
const T13: f64 = -3.12754168375120860518e-04; /* 0xBF347F24, 0xECC38C38 */
|
||||
const T14: f64 = 3.35529192635519073543e-04; /* 0x3F35FD3E, 0xE8C2D3F4 */
|
||||
const U0: f64 = -7.72156649015328655494e-02; /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
const U1: f64 = 6.32827064025093366517e-01; /* 0x3FE4401E, 0x8B005DFF */
|
||||
const U2: f64 = 1.45492250137234768737e+00; /* 0x3FF7475C, 0xD119BD6F */
|
||||
const U3: f64 = 9.77717527963372745603e-01; /* 0x3FEF4976, 0x44EA8450 */
|
||||
const U4: f64 = 2.28963728064692451092e-01; /* 0x3FCD4EAE, 0xF6010924 */
|
||||
const U5: f64 = 1.33810918536787660377e-02; /* 0x3F8B678B, 0xBF2BAB09 */
|
||||
const V1: f64 = 2.45597793713041134822e+00; /* 0x4003A5D7, 0xC2BD619C */
|
||||
const V2: f64 = 2.12848976379893395361e+00; /* 0x40010725, 0xA42B18F5 */
|
||||
const V3: f64 = 7.69285150456672783825e-01; /* 0x3FE89DFB, 0xE45050AF */
|
||||
const V4: f64 = 1.04222645593369134254e-01; /* 0x3FBAAE55, 0xD6537C88 */
|
||||
const V5: f64 = 3.21709242282423911810e-03; /* 0x3F6A5ABB, 0x57D0CF61 */
|
||||
const S0: f64 = -7.72156649015328655494e-02; /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
const S1: f64 = 2.14982415960608852501e-01; /* 0x3FCB848B, 0x36E20878 */
|
||||
const S2: f64 = 3.25778796408930981787e-01; /* 0x3FD4D98F, 0x4F139F59 */
|
||||
const S3: f64 = 1.46350472652464452805e-01; /* 0x3FC2BB9C, 0xBEE5F2F7 */
|
||||
const S4: f64 = 2.66422703033638609560e-02; /* 0x3F9B481C, 0x7E939961 */
|
||||
const S5: f64 = 1.84028451407337715652e-03; /* 0x3F5E26B6, 0x7368F239 */
|
||||
const S6: f64 = 3.19475326584100867617e-05; /* 0x3F00BFEC, 0xDD17E945 */
|
||||
const R1: f64 = 1.39200533467621045958e+00; /* 0x3FF645A7, 0x62C4AB74 */
|
||||
const R2: f64 = 7.21935547567138069525e-01; /* 0x3FE71A18, 0x93D3DCDC */
|
||||
const R3: f64 = 1.71933865632803078993e-01; /* 0x3FC601ED, 0xCCFBDF27 */
|
||||
const R4: f64 = 1.86459191715652901344e-02; /* 0x3F9317EA, 0x742ED475 */
|
||||
const R5: f64 = 7.77942496381893596434e-04; /* 0x3F497DDA, 0xCA41A95B */
|
||||
const R6: f64 = 7.32668430744625636189e-06; /* 0x3EDEBAF7, 0xA5B38140 */
|
||||
const W0: f64 = 4.18938533204672725052e-01; /* 0x3FDACFE3, 0x90C97D69 */
|
||||
const W1: f64 = 8.33333333333329678849e-02; /* 0x3FB55555, 0x5555553B */
|
||||
const W2: f64 = -2.77777777728775536470e-03; /* 0xBF66C16C, 0x16B02E5C */
|
||||
const W3: f64 = 7.93650558643019558500e-04; /* 0x3F4A019F, 0x98CF38B6 */
|
||||
const W4: f64 = -5.95187557450339963135e-04; /* 0xBF4380CB, 0x8C0FE741 */
|
||||
const W5: f64 = 8.36339918996282139126e-04; /* 0x3F4B67BA, 0x4CDAD5D1 */
|
||||
const W6: f64 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
|
||||
|
||||
/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
|
||||
fn sin_pi(mut x: f64) -> f64 {
|
||||
let mut n: i32;
|
||||
|
||||
/* spurious inexact if odd int */
|
||||
x = 2.0 * (x * 0.5 - floor(x * 0.5)); /* x mod 2.0 */
|
||||
|
||||
n = (x * 4.0) as i32;
|
||||
n = (n + 1) / 2;
|
||||
x -= (n as f64) * 0.5;
|
||||
x *= PI;
|
||||
|
||||
match n {
|
||||
1 => k_cos(x, 0.0),
|
||||
2 => k_sin(-x, 0.0, 0),
|
||||
3 => -k_cos(x, 0.0),
|
||||
0 | _ => k_sin(x, 0.0, 0),
|
||||
}
|
||||
}
|
||||
|
||||
pub fn lgamma_r(mut x: f64) -> (f64, i32) {
|
||||
let u: u64 = x.to_bits();
|
||||
let mut t: f64;
|
||||
let y: f64;
|
||||
let mut z: f64;
|
||||
let nadj: f64;
|
||||
let p: f64;
|
||||
let p1: f64;
|
||||
let p2: f64;
|
||||
let p3: f64;
|
||||
let q: f64;
|
||||
let mut r: f64;
|
||||
let w: f64;
|
||||
let ix: u32;
|
||||
let sign: bool;
|
||||
let i: i32;
|
||||
let mut signgam: i32;
|
||||
|
||||
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
|
||||
signgam = 1;
|
||||
sign = (u >> 63) != 0;
|
||||
ix = ((u >> 32) as u32) & 0x7fffffff;
|
||||
if ix >= 0x7ff00000 {
|
||||
return (x * x, signgam);
|
||||
}
|
||||
if ix < (0x3ff - 70) << 20 {
|
||||
/* |x|<2**-70, return -log(|x|) */
|
||||
if sign {
|
||||
x = -x;
|
||||
signgam = -1;
|
||||
}
|
||||
return (-log(x), signgam);
|
||||
}
|
||||
if sign {
|
||||
x = -x;
|
||||
t = sin_pi(x);
|
||||
if t == 0.0 {
|
||||
/* -integer */
|
||||
return (1.0 / (x - x), signgam);
|
||||
}
|
||||
if t > 0.0 {
|
||||
signgam = -1;
|
||||
} else {
|
||||
t = -t;
|
||||
}
|
||||
nadj = log(PI / (t * x));
|
||||
} else {
|
||||
nadj = 0.0;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if (ix == 0x3ff00000 || ix == 0x40000000) && (u & 0xffffffff) == 0 {
|
||||
r = 0.0;
|
||||
}
|
||||
/* for x < 2.0 */
|
||||
else if ix < 0x40000000 {
|
||||
if ix <= 0x3feccccc {
|
||||
/* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -log(x);
|
||||
if ix >= 0x3FE76944 {
|
||||
y = 1.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3FCDA661 {
|
||||
y = x - (TC - 1.0);
|
||||
i = 1;
|
||||
} else {
|
||||
y = x;
|
||||
i = 2;
|
||||
}
|
||||
} else {
|
||||
r = 0.0;
|
||||
if ix >= 0x3FFBB4C3 {
|
||||
/* [1.7316,2] */
|
||||
y = 2.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3FF3B4C4 {
|
||||
/* [1.23,1.73] */
|
||||
y = x - TC;
|
||||
i = 1;
|
||||
} else {
|
||||
y = x - 1.0;
|
||||
i = 2;
|
||||
}
|
||||
}
|
||||
match i {
|
||||
0 => {
|
||||
z = y * y;
|
||||
p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10))));
|
||||
p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11)))));
|
||||
p = y * p1 + p2;
|
||||
r += p - 0.5 * y;
|
||||
}
|
||||
1 => {
|
||||
z = y * y;
|
||||
w = z * y;
|
||||
p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */
|
||||
p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13)));
|
||||
p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14)));
|
||||
p = z * p1 - (TT - w * (p2 + y * p3));
|
||||
r += TF + p;
|
||||
}
|
||||
2 => {
|
||||
p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5)))));
|
||||
p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5))));
|
||||
r += -0.5 * y + p1 / p2;
|
||||
}
|
||||
#[cfg(feature = "checked")]
|
||||
_ => unreachable!(),
|
||||
#[cfg(not(feature = "checked"))]
|
||||
_ => {}
|
||||
}
|
||||
} else if ix < 0x40200000 {
|
||||
/* x < 8.0 */
|
||||
i = x as i32;
|
||||
y = x - (i as f64);
|
||||
p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6))))));
|
||||
q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6)))));
|
||||
r = 0.5 * y + p / q;
|
||||
z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
// TODO: In C, this was implemented using switch jumps with fallthrough.
|
||||
// Does this implementation have performance problems?
|
||||
if i >= 7 {
|
||||
z *= y + 6.0;
|
||||
}
|
||||
if i >= 6 {
|
||||
z *= y + 5.0;
|
||||
}
|
||||
if i >= 5 {
|
||||
z *= y + 4.0;
|
||||
}
|
||||
if i >= 4 {
|
||||
z *= y + 3.0;
|
||||
}
|
||||
if i >= 3 {
|
||||
z *= y + 2.0;
|
||||
r += log(z);
|
||||
}
|
||||
} else if ix < 0x43900000 {
|
||||
/* 8.0 <= x < 2**58 */
|
||||
t = log(x);
|
||||
z = 1.0 / x;
|
||||
y = z * z;
|
||||
w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6)))));
|
||||
r = (x - 0.5) * (t - 1.0) + w;
|
||||
} else {
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x * (log(x) - 1.0);
|
||||
}
|
||||
if sign {
|
||||
r = nadj - r;
|
||||
}
|
||||
return (r, signgam);
|
||||
}
|
||||
+1
-254
@@ -1,258 +1,5 @@
|
||||
/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
|
||||
/*
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
/*
|
||||
* ====================================================
|
||||
* 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.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
use super::{floorf, k_cosf, k_sinf, logf};
|
||||
|
||||
const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */
|
||||
const A0: f32 = 7.7215664089e-02; /* 0x3d9e233f */
|
||||
const A1: f32 = 3.2246702909e-01; /* 0x3ea51a66 */
|
||||
const A2: f32 = 6.7352302372e-02; /* 0x3d89f001 */
|
||||
const A3: f32 = 2.0580807701e-02; /* 0x3ca89915 */
|
||||
const A4: f32 = 7.3855509982e-03; /* 0x3bf2027e */
|
||||
const A5: f32 = 2.8905137442e-03; /* 0x3b3d6ec6 */
|
||||
const A6: f32 = 1.1927076848e-03; /* 0x3a9c54a1 */
|
||||
const A7: f32 = 5.1006977446e-04; /* 0x3a05b634 */
|
||||
const A8: f32 = 2.2086278477e-04; /* 0x39679767 */
|
||||
const A9: f32 = 1.0801156895e-04; /* 0x38e28445 */
|
||||
const A10: f32 = 2.5214456400e-05; /* 0x37d383a2 */
|
||||
const A11: f32 = 4.4864096708e-05; /* 0x383c2c75 */
|
||||
const TC: f32 = 1.4616321325e+00; /* 0x3fbb16c3 */
|
||||
const TF: f32 = -1.2148628384e-01; /* 0xbdf8cdcd */
|
||||
/* TT = -(tail of TF) */
|
||||
const TT: f32 = 6.6971006518e-09; /* 0x31e61c52 */
|
||||
const T0: f32 = 4.8383611441e-01; /* 0x3ef7b95e */
|
||||
const T1: f32 = -1.4758771658e-01; /* 0xbe17213c */
|
||||
const T2: f32 = 6.4624942839e-02; /* 0x3d845a15 */
|
||||
const T3: f32 = -3.2788541168e-02; /* 0xbd064d47 */
|
||||
const T4: f32 = 1.7970675603e-02; /* 0x3c93373d */
|
||||
const T5: f32 = -1.0314224288e-02; /* 0xbc28fcfe */
|
||||
const T6: f32 = 6.1005386524e-03; /* 0x3bc7e707 */
|
||||
const T7: f32 = -3.6845202558e-03; /* 0xbb7177fe */
|
||||
const T8: f32 = 2.2596477065e-03; /* 0x3b141699 */
|
||||
const T9: f32 = -1.4034647029e-03; /* 0xbab7f476 */
|
||||
const T10: f32 = 8.8108185446e-04; /* 0x3a66f867 */
|
||||
const T11: f32 = -5.3859531181e-04; /* 0xba0d3085 */
|
||||
const T12: f32 = 3.1563205994e-04; /* 0x39a57b6b */
|
||||
const T13: f32 = -3.1275415677e-04; /* 0xb9a3f927 */
|
||||
const T14: f32 = 3.3552918467e-04; /* 0x39afe9f7 */
|
||||
const U0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
|
||||
const U1: f32 = 6.3282704353e-01; /* 0x3f2200f4 */
|
||||
const U2: f32 = 1.4549225569e+00; /* 0x3fba3ae7 */
|
||||
const U3: f32 = 9.7771751881e-01; /* 0x3f7a4bb2 */
|
||||
const U4: f32 = 2.2896373272e-01; /* 0x3e6a7578 */
|
||||
const U5: f32 = 1.3381091878e-02; /* 0x3c5b3c5e */
|
||||
const V1: f32 = 2.4559779167e+00; /* 0x401d2ebe */
|
||||
const V2: f32 = 2.1284897327e+00; /* 0x4008392d */
|
||||
const V3: f32 = 7.6928514242e-01; /* 0x3f44efdf */
|
||||
const V4: f32 = 1.0422264785e-01; /* 0x3dd572af */
|
||||
const V5: f32 = 3.2170924824e-03; /* 0x3b52d5db */
|
||||
const S0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
|
||||
const S1: f32 = 2.1498242021e-01; /* 0x3e5c245a */
|
||||
const S2: f32 = 3.2577878237e-01; /* 0x3ea6cc7a */
|
||||
const S3: f32 = 1.4635047317e-01; /* 0x3e15dce6 */
|
||||
const S4: f32 = 2.6642270386e-02; /* 0x3cda40e4 */
|
||||
const S5: f32 = 1.8402845599e-03; /* 0x3af135b4 */
|
||||
const S6: f32 = 3.1947532989e-05; /* 0x3805ff67 */
|
||||
const R1: f32 = 1.3920053244e+00; /* 0x3fb22d3b */
|
||||
const R2: f32 = 7.2193557024e-01; /* 0x3f38d0c5 */
|
||||
const R3: f32 = 1.7193385959e-01; /* 0x3e300f6e */
|
||||
const R4: f32 = 1.8645919859e-02; /* 0x3c98bf54 */
|
||||
const R5: f32 = 7.7794247773e-04; /* 0x3a4beed6 */
|
||||
const R6: f32 = 7.3266842264e-06; /* 0x36f5d7bd */
|
||||
const W0: f32 = 4.1893854737e-01; /* 0x3ed67f1d */
|
||||
const W1: f32 = 8.3333335817e-02; /* 0x3daaaaab */
|
||||
const W2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
|
||||
const W3: f32 = 7.9365057172e-04; /* 0x3a500cfd */
|
||||
const W4: f32 = -5.9518753551e-04; /* 0xba1c065c */
|
||||
const W5: f32 = 8.3633989561e-04; /* 0x3a5b3dd2 */
|
||||
const W6: f32 = -1.6309292987e-03; /* 0xbad5c4e8 */
|
||||
|
||||
/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
|
||||
fn sin_pi(mut x: f32) -> f32 {
|
||||
let mut y: f64;
|
||||
let mut n: isize;
|
||||
|
||||
/* spurious inexact if odd int */
|
||||
x = 2.0 * (x * 0.5 - floorf(x * 0.5)); /* x mod 2.0 */
|
||||
|
||||
n = (x * 4.0) as isize;
|
||||
n = (n + 1) / 2;
|
||||
y = (x as f64) - (n as f64) * 0.5;
|
||||
y *= 3.14159265358979323846;
|
||||
match n {
|
||||
1 => k_cosf(y),
|
||||
2 => k_sinf(-y),
|
||||
3 => -k_cosf(y),
|
||||
0 | _ => k_sinf(y),
|
||||
}
|
||||
}
|
||||
use super::lgammaf_r;
|
||||
|
||||
pub fn lgammaf(x: f32) -> f32 {
|
||||
lgammaf_r(x).0
|
||||
}
|
||||
|
||||
pub fn lgammaf_r(mut x: f32) -> (f32, isize) {
|
||||
let u = x.to_bits();
|
||||
let mut t: f32;
|
||||
let y: f32;
|
||||
let mut z: f32;
|
||||
let nadj: f32;
|
||||
let p: f32;
|
||||
let p1: f32;
|
||||
let p2: f32;
|
||||
let p3: f32;
|
||||
let q: f32;
|
||||
let mut r: f32;
|
||||
let w: f32;
|
||||
let ix: u32;
|
||||
let i: isize;
|
||||
let sign: bool;
|
||||
let mut signgam: isize;
|
||||
|
||||
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
|
||||
signgam = 1;
|
||||
sign = (u >> 31) != 0;
|
||||
ix = u & 0x7fffffff;
|
||||
if ix >= 0x7f800000 {
|
||||
return (x * x, signgam);
|
||||
}
|
||||
if ix < 0x35000000 {
|
||||
/* |x| < 2**-21, return -log(|x|) */
|
||||
if sign {
|
||||
signgam = -1;
|
||||
x = -x;
|
||||
}
|
||||
return (-logf(x), signgam);
|
||||
}
|
||||
if sign {
|
||||
x = -x;
|
||||
t = sin_pi(x);
|
||||
if t == 0.0 {
|
||||
/* -integer */
|
||||
return (1.0 / (x - x), signgam);
|
||||
}
|
||||
if t > 0.0 {
|
||||
signgam = -1;
|
||||
} else {
|
||||
t = -t;
|
||||
}
|
||||
nadj = logf(PI / (t * x));
|
||||
} else {
|
||||
nadj = 0.0;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if ix == 0x3f800000 || ix == 0x40000000 {
|
||||
r = 0.0;
|
||||
}
|
||||
/* for x < 2.0 */
|
||||
else if ix < 0x40000000 {
|
||||
if ix <= 0x3f666666 {
|
||||
/* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -logf(x);
|
||||
if ix >= 0x3f3b4a20 {
|
||||
y = 1.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3e6d3308 {
|
||||
y = x - (TC - 1.0);
|
||||
i = 1;
|
||||
} else {
|
||||
y = x;
|
||||
i = 2;
|
||||
}
|
||||
} else {
|
||||
r = 0.0;
|
||||
if ix >= 0x3fdda618 {
|
||||
/* [1.7316,2] */
|
||||
y = 2.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3F9da620 {
|
||||
/* [1.23,1.73] */
|
||||
y = x - TC;
|
||||
i = 1;
|
||||
} else {
|
||||
y = x - 1.0;
|
||||
i = 2;
|
||||
}
|
||||
}
|
||||
match i {
|
||||
0 => {
|
||||
z = y * y;
|
||||
p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10))));
|
||||
p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11)))));
|
||||
p = y * p1 + p2;
|
||||
r += p - 0.5 * y;
|
||||
}
|
||||
1 => {
|
||||
z = y * y;
|
||||
w = z * y;
|
||||
p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */
|
||||
p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13)));
|
||||
p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14)));
|
||||
p = z * p1 - (TT - w * (p2 + y * p3));
|
||||
r += TF + p;
|
||||
}
|
||||
2 => {
|
||||
p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5)))));
|
||||
p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5))));
|
||||
r += -0.5 * y + p1 / p2;
|
||||
}
|
||||
#[cfg(feature = "checked")]
|
||||
_ => unreachable!(),
|
||||
#[cfg(not(feature = "checked"))]
|
||||
_ => {}
|
||||
}
|
||||
} else if ix < 0x41000000 {
|
||||
/* x < 8.0 */
|
||||
i = x as isize;
|
||||
y = x - (i as f32);
|
||||
p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6))))));
|
||||
q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6)))));
|
||||
r = 0.5 * y + p / q;
|
||||
z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
// TODO: In C, this was implemented using switch jumps with fallthrough.
|
||||
// Does this implementation have performance problems?
|
||||
if i >= 7 {
|
||||
z *= y + 6.0;
|
||||
}
|
||||
if i >= 6 {
|
||||
z *= y + 5.0;
|
||||
}
|
||||
if i >= 5 {
|
||||
z *= y + 4.0;
|
||||
}
|
||||
if i >= 4 {
|
||||
z *= y + 3.0;
|
||||
}
|
||||
if i >= 3 {
|
||||
z *= y + 2.0;
|
||||
r += logf(z);
|
||||
}
|
||||
} else if ix < 0x5c800000 {
|
||||
/* 8.0 <= x < 2**58 */
|
||||
t = logf(x);
|
||||
z = 1.0 / x;
|
||||
y = z * z;
|
||||
w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6)))));
|
||||
r = (x - 0.5) * (t - 1.0) + w;
|
||||
} else {
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x * (logf(x) - 1.0);
|
||||
}
|
||||
if sign {
|
||||
r = nadj - r;
|
||||
}
|
||||
return (r, signgam);
|
||||
}
|
||||
|
||||
@@ -0,0 +1,254 @@
|
||||
/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
|
||||
/*
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
/*
|
||||
* ====================================================
|
||||
* 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.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
use super::{floorf, k_cosf, k_sinf, logf};
|
||||
|
||||
const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */
|
||||
const A0: f32 = 7.7215664089e-02; /* 0x3d9e233f */
|
||||
const A1: f32 = 3.2246702909e-01; /* 0x3ea51a66 */
|
||||
const A2: f32 = 6.7352302372e-02; /* 0x3d89f001 */
|
||||
const A3: f32 = 2.0580807701e-02; /* 0x3ca89915 */
|
||||
const A4: f32 = 7.3855509982e-03; /* 0x3bf2027e */
|
||||
const A5: f32 = 2.8905137442e-03; /* 0x3b3d6ec6 */
|
||||
const A6: f32 = 1.1927076848e-03; /* 0x3a9c54a1 */
|
||||
const A7: f32 = 5.1006977446e-04; /* 0x3a05b634 */
|
||||
const A8: f32 = 2.2086278477e-04; /* 0x39679767 */
|
||||
const A9: f32 = 1.0801156895e-04; /* 0x38e28445 */
|
||||
const A10: f32 = 2.5214456400e-05; /* 0x37d383a2 */
|
||||
const A11: f32 = 4.4864096708e-05; /* 0x383c2c75 */
|
||||
const TC: f32 = 1.4616321325e+00; /* 0x3fbb16c3 */
|
||||
const TF: f32 = -1.2148628384e-01; /* 0xbdf8cdcd */
|
||||
/* TT = -(tail of TF) */
|
||||
const TT: f32 = 6.6971006518e-09; /* 0x31e61c52 */
|
||||
const T0: f32 = 4.8383611441e-01; /* 0x3ef7b95e */
|
||||
const T1: f32 = -1.4758771658e-01; /* 0xbe17213c */
|
||||
const T2: f32 = 6.4624942839e-02; /* 0x3d845a15 */
|
||||
const T3: f32 = -3.2788541168e-02; /* 0xbd064d47 */
|
||||
const T4: f32 = 1.7970675603e-02; /* 0x3c93373d */
|
||||
const T5: f32 = -1.0314224288e-02; /* 0xbc28fcfe */
|
||||
const T6: f32 = 6.1005386524e-03; /* 0x3bc7e707 */
|
||||
const T7: f32 = -3.6845202558e-03; /* 0xbb7177fe */
|
||||
const T8: f32 = 2.2596477065e-03; /* 0x3b141699 */
|
||||
const T9: f32 = -1.4034647029e-03; /* 0xbab7f476 */
|
||||
const T10: f32 = 8.8108185446e-04; /* 0x3a66f867 */
|
||||
const T11: f32 = -5.3859531181e-04; /* 0xba0d3085 */
|
||||
const T12: f32 = 3.1563205994e-04; /* 0x39a57b6b */
|
||||
const T13: f32 = -3.1275415677e-04; /* 0xb9a3f927 */
|
||||
const T14: f32 = 3.3552918467e-04; /* 0x39afe9f7 */
|
||||
const U0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
|
||||
const U1: f32 = 6.3282704353e-01; /* 0x3f2200f4 */
|
||||
const U2: f32 = 1.4549225569e+00; /* 0x3fba3ae7 */
|
||||
const U3: f32 = 9.7771751881e-01; /* 0x3f7a4bb2 */
|
||||
const U4: f32 = 2.2896373272e-01; /* 0x3e6a7578 */
|
||||
const U5: f32 = 1.3381091878e-02; /* 0x3c5b3c5e */
|
||||
const V1: f32 = 2.4559779167e+00; /* 0x401d2ebe */
|
||||
const V2: f32 = 2.1284897327e+00; /* 0x4008392d */
|
||||
const V3: f32 = 7.6928514242e-01; /* 0x3f44efdf */
|
||||
const V4: f32 = 1.0422264785e-01; /* 0x3dd572af */
|
||||
const V5: f32 = 3.2170924824e-03; /* 0x3b52d5db */
|
||||
const S0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
|
||||
const S1: f32 = 2.1498242021e-01; /* 0x3e5c245a */
|
||||
const S2: f32 = 3.2577878237e-01; /* 0x3ea6cc7a */
|
||||
const S3: f32 = 1.4635047317e-01; /* 0x3e15dce6 */
|
||||
const S4: f32 = 2.6642270386e-02; /* 0x3cda40e4 */
|
||||
const S5: f32 = 1.8402845599e-03; /* 0x3af135b4 */
|
||||
const S6: f32 = 3.1947532989e-05; /* 0x3805ff67 */
|
||||
const R1: f32 = 1.3920053244e+00; /* 0x3fb22d3b */
|
||||
const R2: f32 = 7.2193557024e-01; /* 0x3f38d0c5 */
|
||||
const R3: f32 = 1.7193385959e-01; /* 0x3e300f6e */
|
||||
const R4: f32 = 1.8645919859e-02; /* 0x3c98bf54 */
|
||||
const R5: f32 = 7.7794247773e-04; /* 0x3a4beed6 */
|
||||
const R6: f32 = 7.3266842264e-06; /* 0x36f5d7bd */
|
||||
const W0: f32 = 4.1893854737e-01; /* 0x3ed67f1d */
|
||||
const W1: f32 = 8.3333335817e-02; /* 0x3daaaaab */
|
||||
const W2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
|
||||
const W3: f32 = 7.9365057172e-04; /* 0x3a500cfd */
|
||||
const W4: f32 = -5.9518753551e-04; /* 0xba1c065c */
|
||||
const W5: f32 = 8.3633989561e-04; /* 0x3a5b3dd2 */
|
||||
const W6: f32 = -1.6309292987e-03; /* 0xbad5c4e8 */
|
||||
|
||||
/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
|
||||
fn sin_pi(mut x: f32) -> f32 {
|
||||
let mut y: f64;
|
||||
let mut n: isize;
|
||||
|
||||
/* spurious inexact if odd int */
|
||||
x = 2.0 * (x * 0.5 - floorf(x * 0.5)); /* x mod 2.0 */
|
||||
|
||||
n = (x * 4.0) as isize;
|
||||
n = (n + 1) / 2;
|
||||
y = (x as f64) - (n as f64) * 0.5;
|
||||
y *= 3.14159265358979323846;
|
||||
match n {
|
||||
1 => k_cosf(y),
|
||||
2 => k_sinf(-y),
|
||||
3 => -k_cosf(y),
|
||||
0 | _ => k_sinf(y),
|
||||
}
|
||||
}
|
||||
|
||||
pub fn lgammaf_r(mut x: f32) -> (f32, i32) {
|
||||
let u = x.to_bits();
|
||||
let mut t: f32;
|
||||
let y: f32;
|
||||
let mut z: f32;
|
||||
let nadj: f32;
|
||||
let p: f32;
|
||||
let p1: f32;
|
||||
let p2: f32;
|
||||
let p3: f32;
|
||||
let q: f32;
|
||||
let mut r: f32;
|
||||
let w: f32;
|
||||
let ix: u32;
|
||||
let i: i32;
|
||||
let sign: bool;
|
||||
let mut signgam: i32;
|
||||
|
||||
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
|
||||
signgam = 1;
|
||||
sign = (u >> 31) != 0;
|
||||
ix = u & 0x7fffffff;
|
||||
if ix >= 0x7f800000 {
|
||||
return (x * x, signgam);
|
||||
}
|
||||
if ix < 0x35000000 {
|
||||
/* |x| < 2**-21, return -log(|x|) */
|
||||
if sign {
|
||||
signgam = -1;
|
||||
x = -x;
|
||||
}
|
||||
return (-logf(x), signgam);
|
||||
}
|
||||
if sign {
|
||||
x = -x;
|
||||
t = sin_pi(x);
|
||||
if t == 0.0 {
|
||||
/* -integer */
|
||||
return (1.0 / (x - x), signgam);
|
||||
}
|
||||
if t > 0.0 {
|
||||
signgam = -1;
|
||||
} else {
|
||||
t = -t;
|
||||
}
|
||||
nadj = logf(PI / (t * x));
|
||||
} else {
|
||||
nadj = 0.0;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if ix == 0x3f800000 || ix == 0x40000000 {
|
||||
r = 0.0;
|
||||
}
|
||||
/* for x < 2.0 */
|
||||
else if ix < 0x40000000 {
|
||||
if ix <= 0x3f666666 {
|
||||
/* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -logf(x);
|
||||
if ix >= 0x3f3b4a20 {
|
||||
y = 1.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3e6d3308 {
|
||||
y = x - (TC - 1.0);
|
||||
i = 1;
|
||||
} else {
|
||||
y = x;
|
||||
i = 2;
|
||||
}
|
||||
} else {
|
||||
r = 0.0;
|
||||
if ix >= 0x3fdda618 {
|
||||
/* [1.7316,2] */
|
||||
y = 2.0 - x;
|
||||
i = 0;
|
||||
} else if ix >= 0x3F9da620 {
|
||||
/* [1.23,1.73] */
|
||||
y = x - TC;
|
||||
i = 1;
|
||||
} else {
|
||||
y = x - 1.0;
|
||||
i = 2;
|
||||
}
|
||||
}
|
||||
match i {
|
||||
0 => {
|
||||
z = y * y;
|
||||
p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10))));
|
||||
p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11)))));
|
||||
p = y * p1 + p2;
|
||||
r += p - 0.5 * y;
|
||||
}
|
||||
1 => {
|
||||
z = y * y;
|
||||
w = z * y;
|
||||
p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */
|
||||
p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13)));
|
||||
p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14)));
|
||||
p = z * p1 - (TT - w * (p2 + y * p3));
|
||||
r += TF + p;
|
||||
}
|
||||
2 => {
|
||||
p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5)))));
|
||||
p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5))));
|
||||
r += -0.5 * y + p1 / p2;
|
||||
}
|
||||
#[cfg(feature = "checked")]
|
||||
_ => unreachable!(),
|
||||
#[cfg(not(feature = "checked"))]
|
||||
_ => {}
|
||||
}
|
||||
} else if ix < 0x41000000 {
|
||||
/* x < 8.0 */
|
||||
i = x as i32;
|
||||
y = x - (i as f32);
|
||||
p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6))))));
|
||||
q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6)))));
|
||||
r = 0.5 * y + p / q;
|
||||
z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
// TODO: In C, this was implemented using switch jumps with fallthrough.
|
||||
// Does this implementation have performance problems?
|
||||
if i >= 7 {
|
||||
z *= y + 6.0;
|
||||
}
|
||||
if i >= 6 {
|
||||
z *= y + 5.0;
|
||||
}
|
||||
if i >= 5 {
|
||||
z *= y + 4.0;
|
||||
}
|
||||
if i >= 4 {
|
||||
z *= y + 3.0;
|
||||
}
|
||||
if i >= 3 {
|
||||
z *= y + 2.0;
|
||||
r += logf(z);
|
||||
}
|
||||
} else if ix < 0x5c800000 {
|
||||
/* 8.0 <= x < 2**58 */
|
||||
t = logf(x);
|
||||
z = 1.0 / x;
|
||||
y = z * z;
|
||||
w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6)))));
|
||||
r = (x - 0.5) * (t - 1.0) + w;
|
||||
} else {
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x * (logf(x) - 1.0);
|
||||
}
|
||||
if sign {
|
||||
r = nadj - r;
|
||||
}
|
||||
return (r, signgam);
|
||||
}
|
||||
+4
-2
@@ -129,7 +129,9 @@ mod jnf;
|
||||
mod ldexp;
|
||||
mod ldexpf;
|
||||
mod lgamma;
|
||||
mod lgamma_r;
|
||||
mod lgammaf;
|
||||
mod lgammaf_r;
|
||||
mod log;
|
||||
mod log10;
|
||||
mod log10f;
|
||||
@@ -233,9 +235,9 @@ pub use self::jnf::ynf;
|
||||
pub use self::ldexp::ldexp;
|
||||
pub use self::ldexpf::ldexpf;
|
||||
pub use self::lgamma::lgamma;
|
||||
pub use self::lgamma::lgamma_r;
|
||||
pub use self::lgamma_r::lgamma_r;
|
||||
pub use self::lgammaf::lgammaf;
|
||||
pub use self::lgammaf::lgammaf_r;
|
||||
pub use self::lgammaf_r::lgammaf_r;
|
||||
pub use self::log::log;
|
||||
pub use self::log10::log10;
|
||||
pub use self::log10f::log10f;
|
||||
|
||||
+1
-1
@@ -2,7 +2,7 @@ pub fn modf(x: f64) -> (f64, f64) {
|
||||
let rv2: f64;
|
||||
let mut u = x.to_bits();
|
||||
let mask: u64;
|
||||
let e = ((u >> 52 & 0x7ff) as isize) - 0x3ff;
|
||||
let e = ((u >> 52 & 0x7ff) as i32) - 0x3ff;
|
||||
|
||||
/* no fractional part */
|
||||
if e >= 52 {
|
||||
|
||||
+1
-1
@@ -2,7 +2,7 @@ pub fn modff(x: f32) -> (f32, f32) {
|
||||
let rv2: f32;
|
||||
let mut u: u32 = x.to_bits();
|
||||
let mask: u32;
|
||||
let e = ((u >> 23 & 0xff) as isize) - 0x7f;
|
||||
let e = ((u >> 23 & 0xff) as i32) - 0x7f;
|
||||
|
||||
/* no fractional part */
|
||||
if e >= 23 {
|
||||
|
||||
+4
-4
@@ -1,8 +1,8 @@
|
||||
pub fn remquo(mut x: f64, mut y: f64) -> (f64, isize) {
|
||||
pub fn remquo(mut x: f64, mut y: f64) -> (f64, i32) {
|
||||
let ux: u64 = x.to_bits();
|
||||
let mut uy: u64 = y.to_bits();
|
||||
let mut ex = ((ux >> 52) & 0x7ff) as isize;
|
||||
let mut ey = ((uy >> 52) & 0x7ff) as isize;
|
||||
let mut ex = ((ux >> 52) & 0x7ff) as i32;
|
||||
let mut ey = ((uy >> 52) & 0x7ff) as i32;
|
||||
let sx = (ux >> 63) != 0;
|
||||
let sy = (uy >> 63) != 0;
|
||||
let mut q: u32;
|
||||
@@ -88,7 +88,7 @@ pub fn remquo(mut x: f64, mut y: f64) -> (f64, isize) {
|
||||
q += 1;
|
||||
}
|
||||
q &= 0x7fffffff;
|
||||
let quo = if sx ^ sy { -(q as isize) } else { q as isize };
|
||||
let quo = if sx ^ sy { -(q as i32) } else { q as i32 };
|
||||
if sx {
|
||||
(-x, quo)
|
||||
} else {
|
||||
|
||||
+4
-4
@@ -1,8 +1,8 @@
|
||||
pub fn remquof(mut x: f32, mut y: f32) -> (f32, isize) {
|
||||
pub fn remquof(mut x: f32, mut y: f32) -> (f32, i32) {
|
||||
let ux: u32 = x.to_bits();
|
||||
let mut uy: u32 = y.to_bits();
|
||||
let mut ex = ((ux >> 23) & 0xff) as isize;
|
||||
let mut ey = ((uy >> 23) & 0xff) as isize;
|
||||
let mut ex = ((ux >> 23) & 0xff) as i32;
|
||||
let mut ey = ((uy >> 23) & 0xff) as i32;
|
||||
let sx = (ux >> 31) != 0;
|
||||
let sy = (uy >> 31) != 0;
|
||||
let mut q: u32;
|
||||
@@ -87,7 +87,7 @@ pub fn remquof(mut x: f32, mut y: f32) -> (f32, isize) {
|
||||
q += 1;
|
||||
}
|
||||
q &= 0x7fffffff;
|
||||
let quo = if sx ^ sy { -(q as isize) } else { q as isize };
|
||||
let quo = if sx ^ sy { -(q as i32) } else { q as i32 };
|
||||
if sx {
|
||||
(-x, quo)
|
||||
} else {
|
||||
|
||||
Reference in New Issue
Block a user