| The Android Open Source Project | b07e1d9 | 2009-03-03 19:29:30 -0800 | [diff] [blame] | 1 | |
| 2 | /* @(#)e_cosh.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| 14 | /* __ieee754_cosh(x) |
| 15 | * Method : |
| 16 | * mathematically ieee_cosh(x) if defined to be (ieee_exp(x)+ieee_exp(-x))/2 |
| 17 | * 1. Replace x by |x| (ieee_cosh(x) = ieee_cosh(-x)). |
| 18 | * 2. |
| 19 | * [ ieee_exp(x) - 1 ]^2 |
| 20 | * 0 <= x <= ln2/2 : ieee_cosh(x) := 1 + ------------------- |
| 21 | * 2*ieee_exp(x) |
| 22 | * |
| 23 | * ieee_exp(x) + 1/ieee_exp(x) |
| 24 | * ln2/2 <= x <= 22 : ieee_cosh(x) := ------------------- |
| 25 | * 2 |
| 26 | * 22 <= x <= lnovft : ieee_cosh(x) := ieee_exp(x)/2 |
| 27 | * lnovft <= x <= ln2ovft: ieee_cosh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2) |
| 28 | * ln2ovft < x : ieee_cosh(x) := huge*huge (overflow) |
| 29 | * |
| 30 | * Special cases: |
| 31 | * cosh(x) is |x| if x is +INF, -INF, or NaN. |
| 32 | * only ieee_cosh(0)=1 is exact for finite x. |
| 33 | */ |
| 34 | |
| 35 | #include "fdlibm.h" |
| 36 | |
| 37 | #ifdef __STDC__ |
| 38 | static const double one = 1.0, half=0.5, huge = 1.0e300; |
| 39 | #else |
| 40 | static double one = 1.0, half=0.5, huge = 1.0e300; |
| 41 | #endif |
| 42 | |
| 43 | #ifdef __STDC__ |
| 44 | double __ieee754_cosh(double x) |
| 45 | #else |
| 46 | double __ieee754_cosh(x) |
| 47 | double x; |
| 48 | #endif |
| 49 | { |
| 50 | double t,w; |
| 51 | int ix; |
| 52 | unsigned lx; |
| 53 | |
| 54 | /* High word of |x|. */ |
| 55 | ix = __HI(x); |
| 56 | ix &= 0x7fffffff; |
| 57 | |
| 58 | /* x is INF or NaN */ |
| 59 | if(ix>=0x7ff00000) return x*x; |
| 60 | |
| 61 | /* |x| in [0,0.5*ln2], return 1+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */ |
| 62 | if(ix<0x3fd62e43) { |
| 63 | t = ieee_expm1(ieee_fabs(x)); |
| 64 | w = one+t; |
| 65 | if (ix<0x3c800000) return w; /* ieee_cosh(tiny) = 1 */ |
| 66 | return one+(t*t)/(w+w); |
| 67 | } |
| 68 | |
| 69 | /* |x| in [0.5*ln2,22], return (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */ |
| 70 | if (ix < 0x40360000) { |
| 71 | t = __ieee754_exp(ieee_fabs(x)); |
| 72 | return half*t+half/t; |
| 73 | } |
| 74 | |
| 75 | /* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */ |
| 76 | if (ix < 0x40862E42) return half*__ieee754_exp(ieee_fabs(x)); |
| 77 | |
| 78 | /* |x| in [log(maxdouble), overflowthresold] */ |
| 79 | lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); |
| 80 | if (ix<0x408633CE || |
| 81 | (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { |
| 82 | w = __ieee754_exp(half*ieee_fabs(x)); |
| 83 | t = half*w; |
| 84 | return t*w; |
| 85 | } |
| 86 | |
| 87 | /* |x| > overflowthresold, ieee_cosh(x) overflow */ |
| 88 | return huge*huge; |
| 89 | } |