projects / thirdparty / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| 0ac5ae23 | 1 | /* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ |
| f7eac6eb RM |
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 | |
| 0ac5ae23 | 8 | * software is freely granted, provided that this notice |
| f7eac6eb RM |
9 | * is preserved. |
| 10 | * ==================================================== | |
| 11 | */ | |
| 12 | ||
| 13 | #if defined(LIBM_SCCS) && !defined(lint) | |
| 14 | static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; | |
| 15 | #endif | |
| 16 | ||
| 17 | /* __ieee754_cosh(x) | |
| 0ac5ae23 | 18 | * Method : |
| f7eac6eb | 19 | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
| 0ac5ae23 UD |
20 | * 1. Replace x by |x| (cosh(x) = cosh(-x)). |
| 21 | * 2. | |
| 22 | * [ exp(x) - 1 ]^2 | |
| f7eac6eb | 23 | * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
| 0ac5ae23 | 24 | * 2*exp(x) |
| f7eac6eb | 25 | * |
| 0ac5ae23 | 26 | * exp(x) + 1/exp(x) |
| f7eac6eb | 27 | * ln2/2 <= x <= 22 : cosh(x) := ------------------- |
| 0ac5ae23 UD |
28 | * 2 |
| 29 | * 22 <= x <= lnovft : cosh(x) := exp(x)/2 | |
| f7eac6eb RM |
30 | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
| 31 | * ln2ovft < x : cosh(x) := huge*huge (overflow) | |
| 32 | * | |
| 33 | * Special cases: | |
| 34 | * cosh(x) is |x| if x is +INF, -INF, or NaN. | |
| 35 | * only cosh(0)=1 is exact for finite x. | |
| 36 | */ | |
| 37 | ||
| 38 | #include "math.h" | |
| 39 | #include "math_private.h" | |
| 40 | ||
| f7eac6eb | 41 | static const double one = 1.0, half=0.5, huge = 1.0e300; |
| f7eac6eb | 42 | |
| 0ac5ae23 UD |
43 | double |
| 44 | __ieee754_cosh (double x) | |
| 45 | { | |
| f7eac6eb RM |
46 | double t,w; |
| 47 | int32_t ix; | |
| 48 | u_int32_t lx; | |
| 49 | ||
| 50 | /* High word of |x|. */ | |
| 51 | GET_HIGH_WORD(ix,x); | |
| 52 | ix &= 0x7fffffff; | |
| 53 | ||
| 0ac5ae23 | 54 | /* |x| in [0,22] */ |
| f7eac6eb | 55 | if (ix < 0x40360000) { |
| 0ac5ae23 UD |
56 | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
| 57 | if(ix<0x3fd62e43) { | |
| 58 | t = __expm1(fabs(x)); | |
| 59 | w = one+t; | |
| 60 | if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ | |
| 61 | return one+(t*t)/(w+w); | |
| 62 | } | |
| 63 | ||
| 64 | /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ | |
| f7eac6eb RM |
65 | t = __ieee754_exp(fabs(x)); |
| 66 | return half*t+half/t; | |
| 67 | } | |
| 68 | ||
| 69 | /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ | |
| 6796bc80 | 70 | if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x)); |
| f7eac6eb RM |
71 | |
| 72 | /* |x| in [log(maxdouble), overflowthresold] */ | |
| 73 | GET_LOW_WORD(lx,x); | |
| 6796bc80 | 74 | if (ix<0x408633ce || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { |
| f7eac6eb RM |
75 | w = __ieee754_exp(half*fabs(x)); |
| 76 | t = half*w; | |
| 77 | return t*w; | |
| 78 | } | |
| 79 | ||
| 0ac5ae23 UD |
80 | /* x is INF or NaN */ |
| 81 | if(ix>=0x7ff00000) return x*x; | |
| 82 | ||
| f7eac6eb RM |
83 | /* |x| > overflowthresold, cosh(x) overflow */ |
| 84 | return huge*huge; | |
| 85 | } | |
| 0ac5ae23 | 86 | strong_alias (__ieee754_cosh, __cosh_finite) |