| /* 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 |
| } |
| } |
