[352] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
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| 2 | /*
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| 3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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| 4 | */
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| 5 | /*
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| 6 | * ====================================================
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 8 | *
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 10 | * Permission to use, copy, modify, and distribute this
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| 11 | * software is freely granted, provided that this notice
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| 12 | * is preserved.
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| 13 | * ====================================================
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| 14 | */
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| 15 |
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| 16 | #include "libm.h"
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| 17 |
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| 18 | static const float
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| 19 | o_threshold = 8.8721679688e+01, /* 0x42b17180 */
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| 20 | ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
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| 21 | ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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| 22 | invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
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| 23 | /*
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| 24 | * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
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| 25 | * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
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| 26 | * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
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| 27 | */
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| 28 | Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
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| 29 | Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
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| 30 |
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| 31 | float expm1f(float x)
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| 32 | {
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| 33 | float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
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| 34 | union {float f; uint32_t i;} u = {x};
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| 35 | uint32_t hx = u.i & 0x7fffffff;
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| 36 | int k, sign = u.i >> 31;
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| 37 |
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| 38 | /* filter out huge and non-finite argument */
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| 39 | if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
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| 40 | if (hx > 0x7f800000) /* NaN */
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| 41 | return x;
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| 42 | if (sign)
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| 43 | return -1;
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| 44 | if (x > o_threshold) {
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| 45 | x *= 0x1p127f;
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| 46 | return x;
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| 47 | }
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| 48 | }
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| 49 |
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| 50 | /* argument reduction */
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| 51 | if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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| 52 | if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
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| 53 | if (!sign) {
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| 54 | hi = x - ln2_hi;
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| 55 | lo = ln2_lo;
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| 56 | k = 1;
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| 57 | } else {
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| 58 | hi = x + ln2_hi;
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| 59 | lo = -ln2_lo;
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| 60 | k = -1;
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| 61 | }
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| 62 | } else {
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| 63 | k = invln2*x + (sign ? -0.5f : 0.5f);
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| 64 | t = k;
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| 65 | hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
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| 66 | lo = t*ln2_lo;
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| 67 | }
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| 68 | x = hi-lo;
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| 69 | c = (hi-x)-lo;
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| 70 | } else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
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| 71 | if (hx < 0x00800000)
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| 72 | FORCE_EVAL(x*x);
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| 73 | return x;
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| 74 | } else
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| 75 | k = 0;
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| 76 |
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| 77 | /* x is now in primary range */
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| 78 | hfx = 0.5f*x;
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| 79 | hxs = x*hfx;
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| 80 | r1 = 1.0f+hxs*(Q1+hxs*Q2);
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| 81 | t = 3.0f - r1*hfx;
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| 82 | e = hxs*((r1-t)/(6.0f - x*t));
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| 83 | if (k == 0) /* c is 0 */
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| 84 | return x - (x*e-hxs);
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| 85 | e = x*(e-c) - c;
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| 86 | e -= hxs;
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| 87 | /* exp(x) ~ 2^k (x_reduced - e + 1) */
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| 88 | if (k == -1)
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| 89 | return 0.5f*(x-e) - 0.5f;
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| 90 | if (k == 1) {
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| 91 | if (x < -0.25f)
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| 92 | return -2.0f*(e-(x+0.5f));
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| 93 | return 1.0f + 2.0f*(x-e);
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| 94 | }
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| 95 | u.i = (0x7f+k)<<23; /* 2^k */
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| 96 | twopk = u.f;
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| 97 | if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
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| 98 | y = x - e + 1.0f;
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| 99 | if (k == 128)
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| 100 | y = y*2.0f*0x1p127f;
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| 101 | else
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| 102 | y = y*twopk;
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| 103 | return y - 1.0f;
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| 104 | }
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| 105 | u.i = (0x7f-k)<<23; /* 2^-k */
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| 106 | if (k < 23)
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| 107 | y = (x-e+(1-u.f))*twopk;
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| 108 | else
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| 109 | y = (x-(e+u.f)+1)*twopk;
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| 110 | return y;
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| 111 | }
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