projects / thirdparty / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| f964490f RM |
1 | /* @(#)e_cosh.c 5.1 93/09/24 */ |
| 2 | /* | |
| 3 | * ==================================================== | |
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
| 5 | * | |
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
| 7 | * Permission to use, copy, modify, and distribute this | |
| 8 | * software is freely granted, provided that this notice | |
| 9 | * is preserved. | |
| 10 | * ==================================================== | |
| 11 | */ | |
| 12 | ||
| f964490f RM |
13 | /* __ieee754_cosh(x) |
| 14 | * Method : | |
| 15 | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 | |
| 16 | * 1. Replace x by |x| (cosh(x) = cosh(-x)). | |
| 17 | * 2. | |
| 0ac5ae23 | 18 | * [ exp(x) - 1 ]^2 |
| f964490f | 19 | * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
| 0ac5ae23 | 20 | * 2*exp(x) |
| f964490f | 21 | * |
| 0ac5ae23 | 22 | * exp(x) + 1/exp(x) |
| bbb78d03 | 23 | * ln2/2 <= x <= 40 : cosh(x) := ------------------- |
| 0ac5ae23 | 24 | * 2 |
| bbb78d03 | 25 | * 40 <= x <= lnovft : cosh(x) := exp(x)/2 |
| f964490f RM |
26 | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
| 27 | * ln2ovft < x : cosh(x) := huge*huge (overflow) | |
| 28 | * | |
| 29 | * Special cases: | |
| 30 | * cosh(x) is |x| if x is +INF, -INF, or NaN. | |
| 31 | * only cosh(0)=1 is exact for finite x. | |
| 32 | */ | |
| 33 | ||
| 1ed0291c RH |
34 | #include <math.h> |
| 35 | #include <math_private.h> | |
| f964490f | 36 | |
| f964490f | 37 | static const long double one = 1.0L, half=0.5L, huge = 1.0e300L; |
| f964490f | 38 | |
| 0ac5ae23 UD |
39 | long double |
| 40 | __ieee754_coshl (long double x) | |
| f964490f RM |
41 | { |
| 42 | long double t,w; | |
| 43 | int64_t ix; | |
| 4ebd120c | 44 | double xhi; |
| f964490f RM |
45 | |
| 46 | /* High word of |x|. */ | |
| 4ebd120c AM |
47 | xhi = ldbl_high (x); |
| 48 | EXTRACT_WORDS64 (ix, xhi); | |
| f964490f RM |
49 | ix &= 0x7fffffffffffffffLL; |
| 50 | ||
| 51 | /* x is INF or NaN */ | |
| 52 | if(ix>=0x7ff0000000000000LL) return x*x; | |
| 53 | ||
| 54 | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ | |
| 55 | if(ix<0x3fd62e42fefa39efLL) { | |
| 56 | t = __expm1l(fabsl(x)); | |
| 57 | w = one+t; | |
| 58 | if (ix<0x3c80000000000000LL) return w; /* cosh(tiny) = 1 */ | |
| 59 | return one+(t*t)/(w+w); | |
| 60 | } | |
| 61 | ||
| bbb78d03 AS |
62 | /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ |
| 63 | if (ix < 0x4044000000000000LL) { | |
| f964490f RM |
64 | t = __ieee754_expl(fabsl(x)); |
| 65 | return half*t+half/t; | |
| 66 | } | |
| 67 | ||
| bbb78d03 | 68 | /* |x| in [40, log(maxdouble)] return half*exp(|x|) */ |
| f964490f RM |
69 | if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x)); |
| 70 | ||
| 71 | /* |x| in [log(maxdouble), overflowthresold] */ | |
| 0ac5ae23 | 72 | if (ix < 0x408633ce8fb9f87dLL) { |
| f964490f RM |
73 | w = __ieee754_expl(half*fabsl(x)); |
| 74 | t = half*w; | |
| 75 | return t*w; | |
| 76 | } | |
| 77 | ||
| 78 | /* |x| > overflowthresold, cosh(x) overflow */ | |
| 79 | return huge*huge; | |
| 80 | } | |
| 0ac5ae23 | 81 | strong_alias (__ieee754_coshl, __coshl_finite) |