diff --git a/build.rs b/build.rs index 29521ab..4d739a1 100644 --- a/build.rs +++ b/build.rs @@ -41,17 +41,16 @@ mod musl_reference_tests { "rem_pio2.rs", "rem_pio2_large.rs", "rem_pio2f.rs", - "remquo.rs", - "remquof.rs", - "lgamma.rs", // lgamma passed, lgamma_r has more than 1 result - "lgammaf.rs", // lgammaf passed, lgammaf_r has more than 1 result + "remquo.rs", // more than 1 result + "remquof.rs", // more than 1 result + "lgamma_r.rs", // more than 1 result + "lgammaf_r.rs", // more than 1 result "frexp.rs", // more than 1 result "frexpf.rs", // more than 1 result "sincos.rs", // more than 1 result "sincosf.rs", // more than 1 result "modf.rs", // more than 1 result "modff.rs", // more than 1 result - "asinef.rs", // not exists "jn.rs", // passed, but very slow "jnf.rs", // passed, but very slow ]; diff --git a/src/math/asinef.rs b/src/math/asinef.rs deleted file mode 100644 index cd1428b..0000000 --- a/src/math/asinef.rs +++ /dev/null @@ -1,93 +0,0 @@ -/* @(#)z_asinef.c 1.0 98/08/13 */ -/****************************************************************** - * The following routines are coded directly from the algorithms - * and coefficients given in "Software Manual for the Elementary - * Functions" by William J. Cody, Jr. and William Waite, Prentice - * Hall, 1980. - ******************************************************************/ -/****************************************************************** - * Arcsine - * - * Input: - * x - floating point value - * acosine - indicates acos calculation - * - * Output: - * Arcsine of x. - * - * Description: - * This routine calculates arcsine / arccosine. - * - *****************************************************************/ - -use super::{fabsf, sqrtf}; - -const P: [f32; 2] = [ 0.933935835, -0.504400557 ]; -const Q: [f32; 2] = [ 0.560363004e+1, -0.554846723e+1 ]; -const A: [f32; 2] = [ 0.0, 0.785398163 ]; -const B: [f32; 2] = [ 1.570796326, 0.785398163 ]; -const Z_ROOTEPS_F: f32 = 1.7263349182589107e-4; - -pub fn asinef(x: f32, acosine: bool) -> f32 { - let i: usize; - let mut branch: bool = false; - let g: f32; - let mut res: f32 = 0.0; - let mut y: f32; - - /* Check for special values. */ - //i = numtestf (x); - if x.is_nan() || x.is_infinite() { - force_eval!(x); - return x; - } - - y = fabsf(x); - let flag = acosine; - - if y > 0.5 { - i = (!flag) as usize; - - /* Check for range error. */ - if y > 1.0 { - return 0.0 / 0.0; - } - - g = (1.0 - y) / 2.0; - y = -2.0 * sqrtf(g); - branch = true; - } else { - i = flag; - if y < Z_ROOTEPS_F { - res = y; - g = 0.0; // pleasing the uninitialized variable - } else { - g = y * y; - } - } - - if y >= Z_ROOTEPS_F || branch { - /* Calculate the Taylor series. */ - let p = (P[1] * g + P[0]) * g; - let q = (g + Q[1]) * g + Q[0]; - let r = p / q; - - res = y + y * r; - } - - /* Calculate asine or acose. */ - if flag == 0 { - res = (A[i] + res) + A[i]; - if x < 0.0 { - res = -res; - } - } else { - if x < 0.0 { - res = (B[i] + res) + B[i]; - } else { - res = (A[i] - res) + A[i]; - } - } - - return res; -} diff --git a/src/math/lgamma.rs b/src/math/lgamma.rs index b1a321e..5bc87e8 100644 --- a/src/math/lgamma.rs +++ b/src/math/lgamma.rs @@ -1,323 +1,5 @@ -/* 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), - } -} +use super::lgamma_r; pub fn lgamma(x: f64) -> f64 { lgamma_r(x).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); -} diff --git a/src/math/lgamma_r.rs b/src/math/lgamma_r.rs new file mode 100644 index 0000000..382a501 --- /dev/null +++ b/src/math/lgamma_r.rs @@ -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); +} diff --git a/src/math/lgammaf.rs b/src/math/lgammaf.rs index 8fe8060..dfdc87f 100644 --- a/src/math/lgammaf.rs +++ b/src/math/lgammaf.rs @@ -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); -} diff --git a/src/math/lgammaf_r.rs b/src/math/lgammaf_r.rs new file mode 100644 index 0000000..0745359 --- /dev/null +++ b/src/math/lgammaf_r.rs @@ -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); +} diff --git a/src/math/mod.rs b/src/math/mod.rs index b70b0cd..c4d2474 100644 --- a/src/math/mod.rs +++ b/src/math/mod.rs @@ -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; diff --git a/src/math/modf.rs b/src/math/modf.rs index a37f8b9..bcab33a 100644 --- a/src/math/modf.rs +++ b/src/math/modf.rs @@ -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 { diff --git a/src/math/modff.rs b/src/math/modff.rs index 4ce9052..56ece12 100644 --- a/src/math/modff.rs +++ b/src/math/modff.rs @@ -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 { diff --git a/src/math/remquo.rs b/src/math/remquo.rs index 3681b94..507f8db 100644 --- a/src/math/remquo.rs +++ b/src/math/remquo.rs @@ -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 { diff --git a/src/math/remquof.rs b/src/math/remquof.rs index 40ded5d..6aa4974 100644 --- a/src/math/remquof.rs +++ b/src/math/remquof.rs @@ -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 {