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Diffstat (limited to '')
| -rw-r--r-- | vendor/compiler_builtins/libm/src/math/erff.rs | 229 |
1 files changed, 229 insertions, 0 deletions
diff --git a/vendor/compiler_builtins/libm/src/math/erff.rs b/vendor/compiler_builtins/libm/src/math/erff.rs new file mode 100644 index 000000000..384052293 --- /dev/null +++ b/vendor/compiler_builtins/libm/src/math/erff.rs @@ -0,0 +1,229 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.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::{expf, fabsf}; + +const ERX: f32 = 8.4506291151e-01; /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +const EFX8: f32 = 1.0270333290e+00; /* 0x3f8375d4 */ +const PP0: f32 = 1.2837916613e-01; /* 0x3e0375d4 */ +const PP1: f32 = -3.2504209876e-01; /* 0xbea66beb */ +const PP2: f32 = -2.8481749818e-02; /* 0xbce9528f */ +const PP3: f32 = -5.7702702470e-03; /* 0xbbbd1489 */ +const PP4: f32 = -2.3763017452e-05; /* 0xb7c756b1 */ +const QQ1: f32 = 3.9791721106e-01; /* 0x3ecbbbce */ +const QQ2: f32 = 6.5022252500e-02; /* 0x3d852a63 */ +const QQ3: f32 = 5.0813062117e-03; /* 0x3ba68116 */ +const QQ4: f32 = 1.3249473704e-04; /* 0x390aee49 */ +const QQ5: f32 = -3.9602282413e-06; /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +const PA0: f32 = -2.3621185683e-03; /* 0xbb1acdc6 */ +const PA1: f32 = 4.1485610604e-01; /* 0x3ed46805 */ +const PA2: f32 = -3.7220788002e-01; /* 0xbebe9208 */ +const PA3: f32 = 3.1834661961e-01; /* 0x3ea2fe54 */ +const PA4: f32 = -1.1089469492e-01; /* 0xbde31cc2 */ +const PA5: f32 = 3.5478305072e-02; /* 0x3d1151b3 */ +const PA6: f32 = -2.1663755178e-03; /* 0xbb0df9c0 */ +const QA1: f32 = 1.0642088205e-01; /* 0x3dd9f331 */ +const QA2: f32 = 5.4039794207e-01; /* 0x3f0a5785 */ +const QA3: f32 = 7.1828655899e-02; /* 0x3d931ae7 */ +const QA4: f32 = 1.2617121637e-01; /* 0x3e013307 */ +const QA5: f32 = 1.3637083583e-02; /* 0x3c5f6e13 */ +const QA6: f32 = 1.1984500103e-02; /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +const RA0: f32 = -9.8649440333e-03; /* 0xbc21a093 */ +const RA1: f32 = -6.9385856390e-01; /* 0xbf31a0b7 */ +const RA2: f32 = -1.0558626175e+01; /* 0xc128f022 */ +const RA3: f32 = -6.2375331879e+01; /* 0xc2798057 */ +const RA4: f32 = -1.6239666748e+02; /* 0xc322658c */ +const RA5: f32 = -1.8460508728e+02; /* 0xc3389ae7 */ +const RA6: f32 = -8.1287437439e+01; /* 0xc2a2932b */ +const RA7: f32 = -9.8143291473e+00; /* 0xc11d077e */ +const SA1: f32 = 1.9651271820e+01; /* 0x419d35ce */ +const SA2: f32 = 1.3765776062e+02; /* 0x4309a863 */ +const SA3: f32 = 4.3456588745e+02; /* 0x43d9486f */ +const SA4: f32 = 6.4538726807e+02; /* 0x442158c9 */ +const SA5: f32 = 4.2900814819e+02; /* 0x43d6810b */ +const SA6: f32 = 1.0863500214e+02; /* 0x42d9451f */ +const SA7: f32 = 6.5702495575e+00; /* 0x40d23f7c */ +const SA8: f32 = -6.0424413532e-02; /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +const RB0: f32 = -9.8649431020e-03; /* 0xbc21a092 */ +const RB1: f32 = -7.9928326607e-01; /* 0xbf4c9dd4 */ +const RB2: f32 = -1.7757955551e+01; /* 0xc18e104b */ +const RB3: f32 = -1.6063638306e+02; /* 0xc320a2ea */ +const RB4: f32 = -6.3756646729e+02; /* 0xc41f6441 */ +const RB5: f32 = -1.0250950928e+03; /* 0xc480230b */ +const RB6: f32 = -4.8351919556e+02; /* 0xc3f1c275 */ +const SB1: f32 = 3.0338060379e+01; /* 0x41f2b459 */ +const SB2: f32 = 3.2579251099e+02; /* 0x43a2e571 */ +const SB3: f32 = 1.5367296143e+03; /* 0x44c01759 */ +const SB4: f32 = 3.1998581543e+03; /* 0x4547fdbb */ +const SB5: f32 = 2.5530502930e+03; /* 0x451f90ce */ +const SB6: f32 = 4.7452853394e+02; /* 0x43ed43a7 */ +const SB7: f32 = -2.2440952301e+01; /* 0xc1b38712 */ + +fn erfc1(x: f32) -> f32 { + let s: f32; + let p: f32; + let q: f32; + + s = fabsf(x) - 1.0; + p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6))))); + q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6))))); + return 1.0 - ERX - p / q; +} + +fn erfc2(mut ix: u32, mut x: f32) -> f32 { + let s: f32; + let r: f32; + let big_s: f32; + let z: f32; + + if ix < 0x3fa00000 { + /* |x| < 1.25 */ + return erfc1(x); + } + + x = fabsf(x); + s = 1.0 / (x * x); + if ix < 0x4036db6d { + /* |x| < 1/0.35 */ + r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7)))))); + big_s = 1.0 + + s * (SA1 + + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8))))))); + } else { + /* |x| >= 1/0.35 */ + r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6))))); + big_s = + 1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7)))))); + } + ix = x.to_bits(); + z = f32::from_bits(ix & 0xffffe000); + + expf(-z * z - 0.5625) * expf((z - x) * (z + x) + r / big_s) / x +} + +/// Error function (f32) +/// +/// Calculates an approximation to the “error function”, which estimates +/// the probability that an observation will fall within x standard +/// deviations of the mean (assuming a normal distribution). +pub fn erff(x: f32) -> f32 { + let r: f32; + let s: f32; + let z: f32; + let y: f32; + let mut ix: u32; + let sign: usize; + + ix = x.to_bits(); + sign = (ix >> 31) as usize; + ix &= 0x7fffffff; + if ix >= 0x7f800000 { + /* erf(nan)=nan, erf(+-inf)=+-1 */ + return 1.0 - 2.0 * (sign as f32) + 1.0 / x; + } + if ix < 0x3f580000 { + /* |x| < 0.84375 */ + if ix < 0x31800000 { + /* |x| < 2**-28 */ + /*avoid underflow */ + return 0.125 * (8.0 * x + EFX8 * x); + } + z = x * x; + r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4))); + s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5)))); + y = r / s; + return x + x * y; + } + if ix < 0x40c00000 { + /* |x| < 6 */ + y = 1.0 - erfc2(ix, x); + } else { + let x1p_120 = f32::from_bits(0x03800000); + y = 1.0 - x1p_120; + } + + if sign != 0 { + -y + } else { + y + } +} + +/// Error function (f32) +/// +/// Calculates the complementary probability. +/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid +/// the loss of precision that would result from subtracting +/// large probabilities (on large `x`) from 1. +pub fn erfcf(x: f32) -> f32 { + let r: f32; + let s: f32; + let z: f32; + let y: f32; + let mut ix: u32; + let sign: usize; + + ix = x.to_bits(); + sign = (ix >> 31) as usize; + ix &= 0x7fffffff; + if ix >= 0x7f800000 { + /* erfc(nan)=nan, erfc(+-inf)=0,2 */ + return 2.0 * (sign as f32) + 1.0 / x; + } + + if ix < 0x3f580000 { + /* |x| < 0.84375 */ + if ix < 0x23800000 { + /* |x| < 2**-56 */ + return 1.0 - x; + } + z = x * x; + r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4))); + s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5)))); + y = r / s; + if sign != 0 || ix < 0x3e800000 { + /* x < 1/4 */ + return 1.0 - (x + x * y); + } + return 0.5 - (x - 0.5 + x * y); + } + if ix < 0x41e00000 { + /* |x| < 28 */ + if sign != 0 { + return 2.0 - erfc2(ix, x); + } else { + return erfc2(ix, x); + } + } + + let x1p_120 = f32::from_bits(0x03800000); + if sign != 0 { + 2.0 - x1p_120 + } else { + x1p_120 * x1p_120 + } +} |