| /* 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 = div!(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), |
| } |
| } |
| |
| #[cfg_attr(assert_no_panic, no_panic::no_panic)] |
| 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(debug_assertions)] |
| _ => unreachable!(), |
| #[cfg(not(debug_assertions))] |
| _ => {} |
| } |
| } 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); |
| } |
