| 1 | |
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| 2 | /* @(#)e_cosh.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | */ |
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| 13 | |
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| 14 | /* __ieee754_cosh(x) |
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| 15 | * Method : |
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| 16 | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
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| 17 | * 1. Replace x by |x| (cosh(x) = cosh(-x)). |
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| 18 | * 2. |
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| 19 | * [ exp(x) - 1 ]^2 |
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| 20 | * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
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| 21 | * 2*exp(x) |
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| 22 | * |
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| 23 | * exp(x) + 1/exp(x) |
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| 24 | * ln2/2 <= x <= 22 : cosh(x) := ------------------- |
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| 25 | * 2 |
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| 26 | * 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
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| 27 | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
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| 28 | * ln2ovft < x : cosh(x) := huge*huge (overflow) |
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| 29 | * |
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| 30 | * Special cases: |
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| 31 | * cosh(x) is |x| if x is +INF, -INF, or NaN. |
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| 32 | * only cosh(0)=1 is exact for finite x. |
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| 33 | */ |
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| 34 | |
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| 35 | #include <libm/fdlibm.h> |
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| 36 | |
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| 37 | #ifdef __STDC__ |
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| 38 | static const double one = 1.0, half=0.5, huge = 1.0e300; |
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| 39 | #else |
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| 40 | static double one = 1.0, half=0.5, huge = 1.0e300; |
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| 41 | #endif |
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| 42 | |
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| 43 | #ifdef __STDC__ |
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| 44 | double __ieee754_cosh(double x) |
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| 45 | #else |
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| 46 | double __ieee754_cosh(x) |
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| 47 | double x; |
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| 48 | #endif |
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| 49 | { |
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| 50 | double t,w; |
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| 51 | int ix; |
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| 52 | unsigned lx; |
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| 53 | |
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| 54 | /* High word of |x|. */ |
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| 55 | ix = *( (((*(int*)&one)>>29)^1) + (int*)&x); |
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| 56 | ix &= 0x7fffffff; |
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| 57 | |
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| 58 | /* x is INF or NaN */ |
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| 59 | if(ix>=0x7ff00000) return x*x; |
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| 60 | |
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| 61 | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
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| 62 | if(ix<0x3fd62e43) { |
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| 63 | t = expm1(fabs(x)); |
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| 64 | w = one+t; |
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| 65 | if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ |
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| 66 | return one+(t*t)/(w+w); |
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| 67 | } |
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| 68 | |
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| 69 | /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
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| 70 | if (ix < 0x40360000) { |
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| 71 | t = __ieee754_exp(fabs(x)); |
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| 72 | return half*t+half/t; |
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| 73 | } |
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| 74 | |
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| 75 | /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
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| 76 | if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); |
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| 77 | |
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| 78 | /* |x| in [log(maxdouble), overflowthresold] */ |
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| 79 | lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); |
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| 80 | if (((ix<0x408633CE) || |
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| 81 | (ix==0x408633ce))&&(lx<=(unsigned)0x8fb9f87d)) { |
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| 82 | w = __ieee754_exp(half*fabs(x)); |
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| 83 | t = half*w; |
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| 84 | return t*w; |
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| 85 | } |
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| 86 | |
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| 87 | /* |x| > overflowthresold, cosh(x) overflow */ |
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| 88 | return huge*huge; |
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| 89 | } |
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