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 13 #ifndef lint 14 static char rcsid[] = "$FreeBSD$"; 15 #endif 16 17 /* __ieee754_cosh(x) 18 * Method : 19 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 20 * 1. Replace x by |x| (cosh(x) = cosh(-x)). 21 * 2. 22 * [ exp(x) - 1 ]^2 23 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 24 * 2*exp(x) 25 * 26 * exp(x) + 1/exp(x) 27 * ln2/2 <= x <= 22 : cosh(x) := ------------------- 28 * 2 29 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 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 41 #ifdef __STDC__ 42 static const double one = 1.0, half=0.5, huge = 1.0e300; 43 #else 44 static double one = 1.0, half=0.5, huge = 1.0e300; 45 #endif 46 47 #ifdef __STDC__ 48 double __ieee754_cosh(double x) 49 #else 50 double __ieee754_cosh(x) 51 double x; 52 #endif 53 { 54 double t,w; 55 int32_t ix; 56 u_int32_t lx; 57 58 /* High word of |x|. */ 59 GET_HIGH_WORD(ix,x); 60 ix &= 0x7fffffff; 61 62 /* x is INF or NaN */ 63 if(ix>=0x7ff00000) return x*x; 64 65 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 66 if(ix<0x3fd62e43) { 67 t = expm1(fabs(x)); 68 w = one+t; 69 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 70 return one+(t*t)/(w+w); 71 } 72 73 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 74 if (ix < 0x40360000) { 75 t = __ieee754_exp(fabs(x)); 76 return half*t+half/t; 77 } 78 79 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 80 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); 81 82 /* |x| in [log(maxdouble), overflowthresold] */ 83 GET_LOW_WORD(lx,x); 84 if (ix<0x408633CE || 85 ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { 86 w = __ieee754_exp(half*fabs(x)); 87 t = half*w; 88 return t*w; 89 } 90 91 /* |x| > overflowthresold, cosh(x) overflow */ 92 return huge*huge; 93 } 94