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 } 90
