Benjamin Schultzer
103 lines
3.0 KiB
Rust
103 lines
3.0 KiB
Rust
/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.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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use super::scalbnf;
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const HALF: [f32; 2] = [0.5, -0.5];
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const LN2_HI: f32 = 6.9314575195e-01; /* 0x3f317200 */
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const LN2_LO: f32 = 1.4286067653e-06; /* 0x35bfbe8e */
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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 ~[-4.278e-9, 4.447e-9]:
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* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
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*/
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const P1: f32 = 1.6666625440e-1; /* 0xaaaa8f.0p-26 */
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const P2: f32 = -2.7667332906e-3; /* -0xb55215.0p-32 */
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/// Exponential, base *e* (f32)
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///
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/// Calculate the exponential of `x`, that is, *e* raised to the power `x`
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/// (where *e* is the base of the natural system of logarithms, approximately 2.71828).
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#[inline]
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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
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pub fn expf(mut x: f32) -> f32 {
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let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
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let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126 /*original 0x1p-149f ??????????? */
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let mut hx = x.to_bits();
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let sign = (hx >> 31) as i32; /* sign bit of x */
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let signb: bool = sign != 0;
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hx &= 0x7fffffff; /* high word of |x| */
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/* special cases */
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if hx >= 0x42aeac50 {
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/* if |x| >= -87.33655f or NaN */
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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 (hx >= 0x42b17218) && (!signb) {
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/* x >= 88.722839f */
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/* overflow */
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x *= x1p127;
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return x;
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}
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if signb {
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/* underflow */
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force_eval!(-x1p_126 / x);
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if hx >= 0x42cff1b5 {
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/* x <= -103.972084f */
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return 0.;
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}
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}
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}
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/* argument reduction */
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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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if hx > 0x3eb17218 {
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/* if |x| > 0.5 ln2 */
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if hx > 0x3f851592 {
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/* if |x| > 1.5 ln2 */
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k = (INV_LN2 * x + HALF[sign as usize]) as i32;
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} else {
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k = 1 - sign - sign;
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}
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let kf = k as f32;
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hi = x - kf * LN2_HI; /* k*ln2hi is exact here */
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lo = kf * LN2_LO;
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x = hi - lo;
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} else if hx > 0x39000000 {
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/* |x| > 2**-14 */
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k = 0;
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hi = x;
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lo = 0.;
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} else {
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/* raise inexact */
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force_eval!(x1p127 + x);
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return 1. + x;
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}
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/* x is now in primary range */
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let xx = x * x;
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let c = x - xx * (P1 + xx * P2);
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let y = 1. + (x * c / (2. - c) - lo + hi);
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if k == 0 {
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y
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} else {
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scalbnf(y, k)
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}
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}
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