1/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16#include "libm.h"
17
18static const float
19ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
20ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
21invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
22/*
23 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
24 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
25 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
26 */
27Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
28Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
29
30float expm1f(float x)
31{
32 float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
33 union {float f; uint32_t i;} u = {x};
34 uint32_t hx = u.i & 0x7fffffff;
35 int k, sign = u.i >> 31;
36
37 /* filter out huge and non-finite argument */
38 if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
39 if (hx > 0x7f800000) /* NaN */
40 return x;
41 if (sign)
42 return -1;
43 if (hx > 0x42b17217) { /* x > log(FLT_MAX) */
44 x *= 0x1p127f;
45 return x;
46 }
47 }
48
49 /* argument reduction */
50 if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
51 if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
52 if (!sign) {
53 hi = x - ln2_hi;
54 lo = ln2_lo;
55 k = 1;
56 } else {
57 hi = x + ln2_hi;
58 lo = -ln2_lo;
59 k = -1;
60 }
61 } else {
62 k = invln2*x + (sign ? -0.5f : 0.5f);
63 t = k;
64 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
65 lo = t*ln2_lo;
66 }
67 x = hi-lo;
68 c = (hi-x)-lo;
69 } else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
70 if (hx < 0x00800000)
71 FORCE_EVAL(x*x);
72 return x;
73 } else
74 k = 0;
75
76 /* x is now in primary range */
77 hfx = 0.5f*x;
78 hxs = x*hfx;
79 r1 = 1.0f+hxs*(Q1+hxs*Q2);
80 t = 3.0f - r1*hfx;
81 e = hxs*((r1-t)/(6.0f - x*t));
82 if (k == 0) /* c is 0 */
83 return x - (x*e-hxs);
84 e = x*(e-c) - c;
85 e -= hxs;
86 /* exp(x) ~ 2^k (x_reduced - e + 1) */
87 if (k == -1)
88 return 0.5f*(x-e) - 0.5f;
89 if (k == 1) {
90 if (x < -0.25f)
91 return -2.0f*(e-(x+0.5f));
92 return 1.0f + 2.0f*(x-e);
93 }
94 u.i = (0x7f+k)<<23; /* 2^k */
95 twopk = u.f;
96 if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
97 y = x - e + 1.0f;
98 if (k == 128)
99 y = y*2.0f*0x1p127f;
100 else
101 y = y*twopk;
102 return y - 1.0f;
103 }
104 u.i = (0x7f-k)<<23; /* 2^-k */
105 if (k < 23)
106 y = (x-e+(1-u.f))*twopk;
107 else
108 y = (x-(e+u.f)+1)*twopk;
109 return y;
110}