Jorge Aparicio
138 lines
3.8 KiB
Rust
138 lines
3.8 KiB
Rust
/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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use core::f64;
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const O_THRESHOLD: f64 = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
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const LN2_HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
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const LN2_LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
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const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
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/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
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const Q1: f64 = -3.33333333333331316428e-02; /* BFA11111 111110F4 */
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const Q2: f64 = 1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
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const Q3: f64 = -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
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const Q4: f64 = 4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
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const Q5: f64 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
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#[allow(warnings)]
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pub fn expm1(mut x: f64) -> f64 {
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let hi: f64;
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let lo: f64;
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let k: i32;
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let c: f64;
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let mut t: f64;
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let mut y: f64;
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let mut ui = x.to_bits();
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let hx = ((ui >> 32) & 0x7fffffff) as u32;
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let sign = (ui >> 63) as i32;
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/* filter out huge and non-finite argument */
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if hx >= 0x4043687A {
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/* if |x|>=56*ln2 */
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if x.is_nan() {
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return x;
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}
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if sign != 0 {
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return -1.0;
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}
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if x > O_THRESHOLD {
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x *= f64::from_bits(0x7fe0000000000000);
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return x;
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}
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}
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/* argument reduction */
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if hx > 0x3fd62e42 {
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/* if |x| > 0.5 ln2 */
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if hx < 0x3FF0A2B2 {
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/* and |x| < 1.5 ln2 */
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if sign == 0 {
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hi = x - LN2_HI;
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lo = LN2_LO;
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k = 1;
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} else {
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hi = x + LN2_HI;
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lo = -LN2_LO;
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k = -1;
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}
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} else {
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k = (INVLN2 * x + if sign != 0 { -0.5 } else { 0.5 }) as i32;
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t = k as f64;
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hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
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lo = t * LN2_LO;
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}
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x = hi - lo;
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c = (hi - x) - lo;
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} else if hx < 0x3c900000 {
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/* |x| < 2**-54, return x */
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if hx < 0x00100000 {
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force_eval!(x);
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}
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return x;
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} else {
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c = 0.0;
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k = 0;
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}
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/* x is now in primary range */
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let hfx = 0.5 * x;
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let hxs = x * hfx;
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let r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
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t = 3.0 - r1 * hfx;
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let mut e = hxs * ((r1 - t) / (6.0 - x * t));
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if k == 0 {
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/* c is 0 */
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return x - (x * e - hxs);
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}
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e = x * (e - c) - c;
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e -= hxs;
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/* exp(x) ~ 2^k (x_reduced - e + 1) */
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if k == -1 {
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return 0.5 * (x - e) - 0.5;
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}
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if k == 1 {
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if x < -0.25 {
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return -2.0 * (e - (x + 0.5));
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}
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return 1.0 + 2.0 * (x - e);
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}
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ui = ((0x3ff + k) as u64) << 52; /* 2^k */
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let twopk = f64::from_bits(ui);
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if k < 0 || k > 56 {
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/* suffice to return exp(x)-1 */
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y = x - e + 1.0;
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if k == 1024 {
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y = y * 2.0 * f64::from_bits(0x7fe0000000000000);
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} else {
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y = y * twopk;
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}
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return y - 1.0;
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}
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ui = ((0x3ff - k) as u64) << 52; /* 2^-k */
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let uf = f64::from_bits(ui);
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if k < 20 {
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y = (x - e + (1.0 - uf)) * twopk;
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} else {
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y = (x - (e + uf) + 1.0) * twopk;
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}
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y
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}
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#[cfg(test)]
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mod tests {
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#[test]
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fn sanity_check() {
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assert_eq!(super::expm1(1.1), 2.0041660239464334);
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}
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}
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