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320054e8 DG |
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 | ||
18 | static const float | |
19 | o_threshold = 8.8721679688e+01, /* 0x42b17180 */ | |
20 | ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ | |
21 | ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ | |
22 | invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ | |
23 | /* | |
24 | * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: | |
25 | * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 | |
26 | * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): | |
27 | */ | |
28 | Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ | |
29 | Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ | |
30 | ||
31 | float expm1f(float x) | |
32 | { | |
33 | float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk; | |
34 | union {float f; uint32_t i;} u = {x}; | |
35 | uint32_t hx = u.i & 0x7fffffff; | |
36 | int k, sign = u.i >> 31; | |
37 | ||
38 | /* filter out huge and non-finite argument */ | |
39 | if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */ | |
40 | if (hx > 0x7f800000) /* NaN */ | |
41 | return x; | |
42 | if (sign) | |
43 | return -1; | |
44 | if (x > o_threshold) { | |
45 | x *= 0x1p127f; | |
46 | return x; | |
47 | } | |
48 | } | |
49 | ||
50 | /* argument reduction */ | |
51 | if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ | |
52 | if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ | |
53 | if (!sign) { | |
54 | hi = x - ln2_hi; | |
55 | lo = ln2_lo; | |
56 | k = 1; | |
57 | } else { | |
58 | hi = x + ln2_hi; | |
59 | lo = -ln2_lo; | |
60 | k = -1; | |
61 | } | |
62 | } else { | |
63 | k = invln2*x + (sign ? -0.5f : 0.5f); | |
64 | t = k; | |
65 | hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ | |
66 | lo = t*ln2_lo; | |
67 | } | |
68 | x = hi-lo; | |
69 | c = (hi-x)-lo; | |
70 | } else if (hx < 0x33000000) { /* when |x|<2**-25, return x */ | |
71 | if (hx < 0x00800000) | |
72 | FORCE_EVAL(x*x); | |
73 | return x; | |
74 | } else | |
75 | k = 0; | |
76 | ||
77 | /* x is now in primary range */ | |
78 | hfx = 0.5f*x; | |
79 | hxs = x*hfx; | |
80 | r1 = 1.0f+hxs*(Q1+hxs*Q2); | |
81 | t = 3.0f - r1*hfx; | |
82 | e = hxs*((r1-t)/(6.0f - x*t)); | |
83 | if (k == 0) /* c is 0 */ | |
84 | return x - (x*e-hxs); | |
85 | e = x*(e-c) - c; | |
86 | e -= hxs; | |
87 | /* exp(x) ~ 2^k (x_reduced - e + 1) */ | |
88 | if (k == -1) | |
89 | return 0.5f*(x-e) - 0.5f; | |
90 | if (k == 1) { | |
91 | if (x < -0.25f) | |
92 | return -2.0f*(e-(x+0.5f)); | |
93 | return 1.0f + 2.0f*(x-e); | |
94 | } | |
95 | u.i = (0x7f+k)<<23; /* 2^k */ | |
96 | twopk = u.f; | |
97 | if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ | |
98 | y = x - e + 1.0f; | |
99 | if (k == 128) | |
100 | y = y*2.0f*0x1p127f; | |
101 | else | |
102 | y = y*twopk; | |
103 | return y - 1.0f; | |
104 | } | |
105 | u.i = (0x7f-k)<<23; /* 2^-k */ | |
106 | if (k < 23) | |
107 | y = (x-e+(1-u.f))*twopk; | |
108 | else | |
109 | y = (x-(e+u.f)+1)*twopk; | |
110 | return y; | |
111 | } |