libm/math/
erff.rs

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1/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16use super::{expf, fabsf};
17
18const ERX: f32 = 8.4506291151e-01; /* 0x3f58560b */
19/*
20 * Coefficients for approximation to  erf on [0,0.84375]
21 */
22const EFX8: f32 = 1.0270333290e+00; /* 0x3f8375d4 */
23const PP0: f32 = 1.2837916613e-01; /* 0x3e0375d4 */
24const PP1: f32 = -3.2504209876e-01; /* 0xbea66beb */
25const PP2: f32 = -2.8481749818e-02; /* 0xbce9528f */
26const PP3: f32 = -5.7702702470e-03; /* 0xbbbd1489 */
27const PP4: f32 = -2.3763017452e-05; /* 0xb7c756b1 */
28const QQ1: f32 = 3.9791721106e-01; /* 0x3ecbbbce */
29const QQ2: f32 = 6.5022252500e-02; /* 0x3d852a63 */
30const QQ3: f32 = 5.0813062117e-03; /* 0x3ba68116 */
31const QQ4: f32 = 1.3249473704e-04; /* 0x390aee49 */
32const QQ5: f32 = -3.9602282413e-06; /* 0xb684e21a */
33/*
34 * Coefficients for approximation to  erf  in [0.84375,1.25]
35 */
36const PA0: f32 = -2.3621185683e-03; /* 0xbb1acdc6 */
37const PA1: f32 = 4.1485610604e-01; /* 0x3ed46805 */
38const PA2: f32 = -3.7220788002e-01; /* 0xbebe9208 */
39const PA3: f32 = 3.1834661961e-01; /* 0x3ea2fe54 */
40const PA4: f32 = -1.1089469492e-01; /* 0xbde31cc2 */
41const PA5: f32 = 3.5478305072e-02; /* 0x3d1151b3 */
42const PA6: f32 = -2.1663755178e-03; /* 0xbb0df9c0 */
43const QA1: f32 = 1.0642088205e-01; /* 0x3dd9f331 */
44const QA2: f32 = 5.4039794207e-01; /* 0x3f0a5785 */
45const QA3: f32 = 7.1828655899e-02; /* 0x3d931ae7 */
46const QA4: f32 = 1.2617121637e-01; /* 0x3e013307 */
47const QA5: f32 = 1.3637083583e-02; /* 0x3c5f6e13 */
48const QA6: f32 = 1.1984500103e-02; /* 0x3c445aa3 */
49/*
50 * Coefficients for approximation to  erfc in [1.25,1/0.35]
51 */
52const RA0: f32 = -9.8649440333e-03; /* 0xbc21a093 */
53const RA1: f32 = -6.9385856390e-01; /* 0xbf31a0b7 */
54const RA2: f32 = -1.0558626175e+01; /* 0xc128f022 */
55const RA3: f32 = -6.2375331879e+01; /* 0xc2798057 */
56const RA4: f32 = -1.6239666748e+02; /* 0xc322658c */
57const RA5: f32 = -1.8460508728e+02; /* 0xc3389ae7 */
58const RA6: f32 = -8.1287437439e+01; /* 0xc2a2932b */
59const RA7: f32 = -9.8143291473e+00; /* 0xc11d077e */
60const SA1: f32 = 1.9651271820e+01; /* 0x419d35ce */
61const SA2: f32 = 1.3765776062e+02; /* 0x4309a863 */
62const SA3: f32 = 4.3456588745e+02; /* 0x43d9486f */
63const SA4: f32 = 6.4538726807e+02; /* 0x442158c9 */
64const SA5: f32 = 4.2900814819e+02; /* 0x43d6810b */
65const SA6: f32 = 1.0863500214e+02; /* 0x42d9451f */
66const SA7: f32 = 6.5702495575e+00; /* 0x40d23f7c */
67const SA8: f32 = -6.0424413532e-02; /* 0xbd777f97 */
68/*
69 * Coefficients for approximation to  erfc in [1/.35,28]
70 */
71const RB0: f32 = -9.8649431020e-03; /* 0xbc21a092 */
72const RB1: f32 = -7.9928326607e-01; /* 0xbf4c9dd4 */
73const RB2: f32 = -1.7757955551e+01; /* 0xc18e104b */
74const RB3: f32 = -1.6063638306e+02; /* 0xc320a2ea */
75const RB4: f32 = -6.3756646729e+02; /* 0xc41f6441 */
76const RB5: f32 = -1.0250950928e+03; /* 0xc480230b */
77const RB6: f32 = -4.8351919556e+02; /* 0xc3f1c275 */
78const SB1: f32 = 3.0338060379e+01; /* 0x41f2b459 */
79const SB2: f32 = 3.2579251099e+02; /* 0x43a2e571 */
80const SB3: f32 = 1.5367296143e+03; /* 0x44c01759 */
81const SB4: f32 = 3.1998581543e+03; /* 0x4547fdbb */
82const SB5: f32 = 2.5530502930e+03; /* 0x451f90ce */
83const SB6: f32 = 4.7452853394e+02; /* 0x43ed43a7 */
84const SB7: f32 = -2.2440952301e+01; /* 0xc1b38712 */
85
86fn erfc1(x: f32) -> f32 {
87    let s: f32;
88    let p: f32;
89    let q: f32;
90
91    s = fabsf(x) - 1.0;
92    p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6)))));
93    q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6)))));
94    return 1.0 - ERX - p / q;
95}
96
97fn erfc2(mut ix: u32, mut x: f32) -> f32 {
98    let s: f32;
99    let r: f32;
100    let big_s: f32;
101    let z: f32;
102
103    if ix < 0x3fa00000 {
104        /* |x| < 1.25 */
105        return erfc1(x);
106    }
107
108    x = fabsf(x);
109    s = 1.0 / (x * x);
110    if ix < 0x4036db6d {
111        /* |x| < 1/0.35 */
112        r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7))))));
113        big_s = 1.0
114            + s * (SA1
115                + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8)))))));
116    } else {
117        /* |x| >= 1/0.35 */
118        r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6)))));
119        big_s =
120            1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7))))));
121    }
122    ix = x.to_bits();
123    z = f32::from_bits(ix & 0xffffe000);
124
125    expf(-z * z - 0.5625) * expf((z - x) * (z + x) + r / big_s) / x
126}
127
128/// Error function (f32)
129///
130/// Calculates an approximation to the “error function”, which estimates
131/// the probability that an observation will fall within x standard
132/// deviations of the mean (assuming a normal distribution).
133#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
134pub fn erff(x: f32) -> f32 {
135    let r: f32;
136    let s: f32;
137    let z: f32;
138    let y: f32;
139    let mut ix: u32;
140    let sign: usize;
141
142    ix = x.to_bits();
143    sign = (ix >> 31) as usize;
144    ix &= 0x7fffffff;
145    if ix >= 0x7f800000 {
146        /* erf(nan)=nan, erf(+-inf)=+-1 */
147        return 1.0 - 2.0 * (sign as f32) + 1.0 / x;
148    }
149    if ix < 0x3f580000 {
150        /* |x| < 0.84375 */
151        if ix < 0x31800000 {
152            /* |x| < 2**-28 */
153            /*avoid underflow */
154            return 0.125 * (8.0 * x + EFX8 * x);
155        }
156        z = x * x;
157        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
158        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
159        y = r / s;
160        return x + x * y;
161    }
162    if ix < 0x40c00000 {
163        /* |x| < 6 */
164        y = 1.0 - erfc2(ix, x);
165    } else {
166        let x1p_120 = f32::from_bits(0x03800000);
167        y = 1.0 - x1p_120;
168    }
169
170    if sign != 0 { -y } else { y }
171}
172
173/// Complementary error function (f32)
174///
175/// Calculates the complementary probability.
176/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid
177/// the loss of precision that would result from subtracting
178/// large probabilities (on large `x`) from 1.
179pub fn erfcf(x: f32) -> f32 {
180    let r: f32;
181    let s: f32;
182    let z: f32;
183    let y: f32;
184    let mut ix: u32;
185    let sign: usize;
186
187    ix = x.to_bits();
188    sign = (ix >> 31) as usize;
189    ix &= 0x7fffffff;
190    if ix >= 0x7f800000 {
191        /* erfc(nan)=nan, erfc(+-inf)=0,2 */
192        return 2.0 * (sign as f32) + 1.0 / x;
193    }
194
195    if ix < 0x3f580000 {
196        /* |x| < 0.84375 */
197        if ix < 0x23800000 {
198            /* |x| < 2**-56 */
199            return 1.0 - x;
200        }
201        z = x * x;
202        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
203        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
204        y = r / s;
205        if sign != 0 || ix < 0x3e800000 {
206            /* x < 1/4 */
207            return 1.0 - (x + x * y);
208        }
209        return 0.5 - (x - 0.5 + x * y);
210    }
211    if ix < 0x41e00000 {
212        /* |x| < 28 */
213        if sign != 0 {
214            return 2.0 - erfc2(ix, x);
215        } else {
216            return erfc2(ix, x);
217        }
218    }
219
220    let x1p_120 = f32::from_bits(0x03800000);
221    if sign != 0 { 2.0 - x1p_120 } else { x1p_120 * x1p_120 }
222}
libm/math/erff.rs

libm/math/
erff.rs
