1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135

/* 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.
#[inline]
#[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
    }
}