135 lines
3.9 KiB
Rust
135 lines
3.9 KiB
Rust
/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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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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const O_THRESHOLD: f32 = 8.8721679688e+01; /* 0x42b17180 */
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const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
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const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
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const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
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/*
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* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
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* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
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* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
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*/
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const Q1: f32 = -3.3333212137e-2; /* -0x888868.0p-28 */
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const Q2: f32 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
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/// Exponential, base *e*, of x-1 (f32)
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///
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/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
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/// to the power `x` minus 1 (where *e* is the base of the natural
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/// system of logarithms, approximately 2.71828).
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/// The result is accurate even for small values of `x`,
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/// where using `exp(x)-1` would lose many significant digits.
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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
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pub fn expm1f(mut x: f32) -> f32 {
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let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
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let mut hx = x.to_bits();
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let sign = (hx >> 31) != 0;
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hx &= 0x7fffffff;
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/* filter out huge and non-finite argument */
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if hx >= 0x4195b844 {
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/* if |x|>=27*ln2 */
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if hx > 0x7f800000 {
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/* NaN */
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return x;
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}
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if sign {
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return -1.;
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}
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if x > O_THRESHOLD {
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x *= x1p127;
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return x;
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}
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}
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let k: i32;
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let hi: f32;
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let lo: f32;
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let mut c = 0f32;
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/* argument reduction */
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if hx > 0x3eb17218 {
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/* if |x| > 0.5 ln2 */
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if hx < 0x3F851592 {
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/* and |x| < 1.5 ln2 */
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if !sign {
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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 = (INV_LN2 * x + (if sign { -0.5 } else { 0.5 })) as i32;
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let t = k as f32;
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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 < 0x33000000 {
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/* when |x|<2**-25, return x */
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if hx < 0x00800000 {
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force_eval!(x * x);
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}
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return x;
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} else {
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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. + hxs * (Q1 + hxs * Q2);
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let t = 3. - r1 * hfx;
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let mut e = hxs * ((r1 - t) / (6. - 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. * (e - (x + 0.5));
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}
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return 1. + 2. * (x - e);
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}
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let twopk = f32::from_bits(((0x7f + k) << 23) as u32); /* 2^k */
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if !(0..=56).contains(&k) {
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/* suffice to return exp(x)-1 */
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let mut y = x - e + 1.;
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if k == 128 {
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y = y * 2. * x1p127;
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} else {
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y = y * twopk;
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}
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return y - 1.;
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}
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let uf = f32::from_bits(((0x7f - k) << 23) as u32); /* 2^-k */
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if k < 23 {
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(x - e + (1. - uf)) * twopk
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} else {
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(x - (e + uf) + 1.) * twopk
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}
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}
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