libm/math/
log1p.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12/* double log1p(double x)
13 * Return the natural logarithm of 1+x.
14 *
15 * Method :
16 *   1. Argument Reduction: find k and f such that
17 *                      1+x = 2^k * (1+f),
18 *         where  sqrt(2)/2 < 1+f < sqrt(2) .
19 *
20 *      Note. If k=0, then f=x is exact. However, if k!=0, then f
21 *      may not be representable exactly. In that case, a correction
22 *      term is need. Let u=1+x rounded. Let c = (1+x)-u, then
23 *      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
24 *      and add back the correction term c/u.
25 *      (Note: when x > 2**53, one can simply return log(x))
26 *
27 *   2. Approximation of log(1+f): See log.c
28 *
29 *   3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
30 *
31 * Special cases:
32 *      log1p(x) is NaN with signal if x < -1 (including -INF) ;
33 *      log1p(+INF) is +INF; log1p(-1) is -INF with signal;
34 *      log1p(NaN) is that NaN with no signal.
35 *
36 * Accuracy:
37 *      according to an error analysis, the error is always less than
38 *      1 ulp (unit in the last place).
39 *
40 * Constants:
41 * The hexadecimal values are the intended ones for the following
42 * constants. The decimal values may be used, provided that the
43 * compiler will convert from decimal to binary accurately enough
44 * to produce the hexadecimal values shown.
45 *
46 * Note: Assuming log() return accurate answer, the following
47 *       algorithm can be used to compute log1p(x) to within a few ULP:
48 *
49 *              u = 1+x;
50 *              if(u==1.0) return x ; else
51 *                         return log(u)*(x/(u-1.0));
52 *
53 *       See HP-15C Advanced Functions Handbook, p.193.
54 */
55
56const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
57const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
58const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
59const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
60const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
61const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
62const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
63const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
64const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
65
66/// The natural logarithm of 1+`x` (f64).
67#[cfg_attr(assert_no_panic, no_panic::no_panic)]
68pub fn log1p(x: f64) -> f64 {
69    let mut ui: u64 = x.to_bits();
70    let hfsq: f64;
71    let mut f: f64 = 0.;
72    let mut c: f64 = 0.;
73    let s: f64;
74    let z: f64;
75    let r: f64;
76    let w: f64;
77    let t1: f64;
78    let t2: f64;
79    let dk: f64;
80    let hx: u32;
81    let mut hu: u32;
82    let mut k: i32;
83
84    hx = (ui >> 32) as u32;
85    k = 1;
86    if hx < 0x3fda827a || (hx >> 31) > 0 {
87        /* 1+x < sqrt(2)+ */
88        if hx >= 0xbff00000 {
89            /* x <= -1.0 */
90            if x == -1. {
91                return x / 0.0; /* log1p(-1) = -inf */
92            }
93            return (x - x) / 0.0; /* log1p(x<-1) = NaN */
94        }
95        if hx << 1 < 0x3ca00000 << 1 {
96            /* |x| < 2**-53 */
97            /* underflow if subnormal */
98            if (hx & 0x7ff00000) == 0 {
99                unsafe { ::core::ptr::read_volatile(&(x as f32)) };force_eval!(x as f32);
100            }
101            return x;
102        }
103        if hx <= 0xbfd2bec4 {
104            /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
105            k = 0;
106            c = 0.;
107            f = x;
108        }
109    } else if hx >= 0x7ff00000 {
110        return x;
111    }
112    if k > 0 {
113        ui = (1. + x).to_bits();
114        hu = (ui >> 32) as u32;
115        hu += 0x3ff00000 - 0x3fe6a09e;
116        k = (hu >> 20) as i32 - 0x3ff;
117        /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
118        if k < 54 {
119            c = if k >= 2 {
120                1. - (f64::from_bits(ui) - x)
121            } else {
122                x - (f64::from_bits(ui) - 1.)
123            };
124            c /= f64::from_bits(ui);
125        } else {
126            c = 0.;
127        }
128        /* reduce u into [sqrt(2)/2, sqrt(2)] */
129        hu = (hu & 0x000fffff) + 0x3fe6a09e;
130        ui = ((hu as u64) << 32) | (ui & 0xffffffff);
131        f = f64::from_bits(ui) - 1.;
132    }
133    hfsq = 0.5 * f * f;
134    s = f / (2.0 + f);
135    z = s * s;
136    w = z * z;
137    t1 = w * (LG2 + w * (LG4 + w * LG6));
138    t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
139    r = t2 + t1;
140    dk = k as f64;
141    s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
142}
libm/math/log1p.rs

libm/math/
log1p.rs
