| [1] | 1 | |
|---|
| 2 | /* @(#)e_sinh.c 5.1 93/09/24 */ |
|---|
| 3 | /* |
|---|
| 4 | * ==================================================== |
|---|
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
|---|
| 6 | * |
|---|
| 7 | * Developed at SunPro, 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_sinh(x) |
|---|
| 15 | * Method : |
|---|
| 16 | * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 |
|---|
| 17 | * 1. Replace x by |x| (sinh(-x) = -sinh(x)). |
|---|
| 18 | * 2. |
|---|
| 19 | * E + E/(E+1) |
|---|
| 20 | * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) |
|---|
| 21 | * 2 |
|---|
| 22 | * |
|---|
| 23 | * 22 <= x <= lnovft : sinh(x) := exp(x)/2 |
|---|
| 24 | * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) |
|---|
| 25 | * ln2ovft < x : sinh(x) := x*shuge (overflow) |
|---|
| 26 | * |
|---|
| 27 | * Special cases: |
|---|
| 28 | * sinh(x) is |x| if x is +INF, -INF, or NaN. |
|---|
| 29 | * only sinh(0)=0 is exact for finite x. |
|---|
| 30 | */ |
|---|
| 31 | |
|---|
| 32 | #include <libm/fdlibm.h> |
|---|
| 33 | |
|---|
| 34 | #ifdef __STDC__ |
|---|
| 35 | static const double one = 1.0, shuge = 1.0e307; |
|---|
| 36 | #else |
|---|
| 37 | static double one = 1.0, shuge = 1.0e307; |
|---|
| 38 | #endif |
|---|
| 39 | |
|---|
| 40 | #ifdef __STDC__ |
|---|
| 41 | double __ieee754_sinh(double x) |
|---|
| 42 | #else |
|---|
| 43 | double __ieee754_sinh(x) |
|---|
| 44 | double x; |
|---|
| 45 | #endif |
|---|
| 46 | { |
|---|
| 47 | double t,w,h; |
|---|
| 48 | int ix,jx; |
|---|
| 49 | unsigned lx; |
|---|
| 50 | |
|---|
| 51 | /* High word of |x|. */ |
|---|
| 52 | jx = *( (((*(int*)&one)>>29)^1) + (int*)&x); |
|---|
| 53 | ix = jx&0x7fffffff; |
|---|
| 54 | |
|---|
| 55 | /* x is INF or NaN */ |
|---|
| 56 | if(ix>=0x7ff00000) return x+x; |
|---|
| 57 | |
|---|
| 58 | h = 0.5; |
|---|
| 59 | if (jx<0) h = -h; |
|---|
| 60 | /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ |
|---|
| 61 | if (ix < 0x40360000) { /* |x|<22 */ |
|---|
| 62 | if (ix<0x3e300000) /* |x|<2**-28 */ |
|---|
| 63 | if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ |
|---|
| 64 | t = expm1(fabs(x)); |
|---|
| 65 | if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); |
|---|
| 66 | return h*(t+t/(t+one)); |
|---|
| 67 | } |
|---|
| 68 | |
|---|
| 69 | /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
|---|
| 70 | if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); |
|---|
| 71 | |
|---|
| 72 | /* |x| in [log(maxdouble), overflowthresold] */ |
|---|
| 73 | lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); |
|---|
| 74 | if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) { |
|---|
| 75 | w = __ieee754_exp(0.5*fabs(x)); |
|---|
| 76 | t = h*w; |
|---|
| 77 | return t*w; |
|---|
| 78 | } |
|---|
| 79 | |
|---|
| 80 | /* |x| > overflowthresold, sinh(x) overflow */ |
|---|
| 81 | return x*shuge; |
|---|
| 82 | } |
|---|
