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/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.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.
* ====================================================
*/
const O_THRESHOLD: f32 = 8.8721679688e+01; /* 0x42b17180 */
const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
*/
const Q1: f32 = -3.3333212137e-2; /* -0x888868.0p-28 */
const Q2: f32 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
/// Exponential, base *e*, of x-1 (f32)
///
/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
/// to the power `x` minus 1 (where *e* is the base of the natural
/// system of logarithms, approximately 2.71828).
/// The result is accurate even for small values of `x`,
/// where using `exp(x)-1` would lose many significant digits.
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn expm1f(mut x: f32) -> f32 {
let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
let mut hx = x.to_bits();
let sign = (hx >> 31) != 0;
hx &= 0x7fffffff;
/* filter out huge and non-finite argument */
if hx >= 0x4195b844 {
/* if |x|>=27*ln2 */
if hx > 0x7f800000 {
/* NaN */
return x;
}
if sign {
return -1.;
}
if x > O_THRESHOLD {
x *= x1p127;
return x;
}
}
let k: i32;
let hi: f32;
let lo: f32;
let mut c = 0f32;
/* argument reduction */
if hx > 0x3eb17218 {
/* if |x| > 0.5 ln2 */
if hx < 0x3F851592 {
/* and |x| < 1.5 ln2 */
if !sign {
hi = x - LN2_HI;
lo = LN2_LO;
k = 1;
} else {
hi = x + LN2_HI;
lo = -LN2_LO;
k = -1;
}
} else {
k = (INV_LN2 * x + (if sign { -0.5 } else { 0.5 })) as i32;
let t = k as f32;
hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
lo = t * LN2_LO;
}
x = hi - lo;
c = (hi - x) - lo;
} else if hx < 0x33000000 {
/* when |x|<2**-25, return x */
if hx < 0x00800000 {
force_eval!(x * x);
}
return x;
} else {
k = 0;
}
/* x is now in primary range */
let hfx = 0.5 * x;
let hxs = x * hfx;
let r1 = 1. + hxs * (Q1 + hxs * Q2);
let t = 3. - r1 * hfx;
let mut e = hxs * ((r1 - t) / (6. - x * t));
if k == 0 {
/* c is 0 */
return x - (x * e - hxs);
}
e = x * (e - c) - c;
e -= hxs;
/* exp(x) ~ 2^k (x_reduced - e + 1) */
if k == -1 {
return 0.5 * (x - e) - 0.5;
}
if k == 1 {
if x < -0.25 {
return -2. * (e - (x + 0.5));
}
return 1. + 2. * (x - e);
}
let twopk = f32::from_bits(((0x7f + k) << 23) as u32); /* 2^k */
if (k < 0) || (k > 56) {
/* suffice to return exp(x)-1 */
let mut y = x - e + 1.;
if k == 128 {
y = y * 2. * x1p127;
} else {
y = y * twopk;
}
return y - 1.;
}
let uf = f32::from_bits(((0x7f - k) << 23) as u32); /* 2^-k */
if k < 23 {
(x - e + (1. - uf)) * twopk
} else {
(x - (e + uf) + 1.) * twopk
}
}