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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 | /* 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. * ==================================================== */ #include "libm.h" static const float o_threshold = 8.8721679688e+01, /* 0x42b17180 */ ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ invln2 = 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): */ Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ float expm1f(float x) { float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk; union {float f; uint32_t i;} u = {x}; uint32_t hx = u.i & 0x7fffffff; int k, sign = u.i >> 31; /* 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 *= 0x1p127f; return x; } } /* 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 = invln2*x + (sign ? -0.5f : 0.5f); t = k; 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 */ hfx = 0.5f*x; hxs = x*hfx; r1 = 1.0f+hxs*(Q1+hxs*Q2); t = 3.0f - r1*hfx; e = hxs*((r1-t)/(6.0f - 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 0.5f*(x-e) - 0.5f; if (k == 1) { if (x < -0.25f) return -2.0f*(e-(x+0.5f)); return 1.0f + 2.0f*(x-e); } u.i = (0x7f+k)<<23; /* 2^k */ twopk = u.f; if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ y = x - e + 1.0f; if (k == 128) y = y*2.0f*0x1p127f; else y = y*twopk; return y - 1.0f; } u.i = (0x7f-k)<<23; /* 2^-k */ if (k < 23) y = (x-e+(1-u.f))*twopk; else y = (x-(e+u.f)+1)*twopk; return y; } |