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path: root/src/math/cosh.c
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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 ``` ``````/* origin: FreeBSD /usr/src/lib/msun/src/e_cosh.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* cosh(x) * Method : * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 * 1. Replace x by |x| (cosh(x) = cosh(-x)). * 2. * [ exp(x) - 1 ]^2 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- * 2*exp(x) * * exp(x) + 1/exp(x) * ln2/2 <= x <= 22 : cosh(x) := ------------------- * 2 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : cosh(x) := inf (overflow) * * Special cases: * cosh(x) is |x| if x is +INF, -INF, or NaN. * only cosh(0)=1 is exact for finite x. */ #include "libm.h" double cosh(double x) { union {double f; uint64_t i;} u = {.f = x}; uint32_t ix; double t; /* |x| */ u.i &= (uint64_t)-1/2; x = u.f; ix = u.i >> 32; /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if (ix < 0x3fd62e43) { t = expm1(x); if (ix < 0x3c800000) return 1; return 1 + t*t/(2*(1+t)); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */ if (ix < 0x40360000) { t = exp(x); return 0.5*t + 0.5/t; } /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x40862e42) return 0.5*exp(x); /* |x| in [log(maxdouble), overflowthresold] */ if (ix <= 0x408633ce) return __expo2(x); /* overflow (or nan) */ x *= 0x1p1023; return x; } ``````