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 /* LINTLIBRARY */ 14 15 /* cosh(x) 16 * Method : 17 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 18 * 1. Replace x by |x| (cosh(x) = cosh(-x)). 19 * 2. 20 * [ exp(x) - 1 ]^2 21 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 22 * 2*exp(x) 23 * 24 * exp(x) + 1/exp(x) 25 * ln2/2 <= x <= 22 : cosh(x) := ------------------- 26 * 2 27 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 28 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) 29 * ln2ovft < x : cosh(x) := huge*huge (overflow) 30 * 31 * Special cases: 32 * cosh(x) is |x| if x is +INF, -INF, or NaN. 33 * only cosh(0)=1 is exact for finite x. 34 */ 35 36 #include <sys/cdefs.h> 37 #include <float.h> 38 #include <math.h> 39 40 #include "math_private.h" 41 42 static const double one = 1.0, half=0.5, huge = 1.0e300; 43 44 double 45 cosh(double x) 46 { 47 double t,w; 48 int32_t ix; 49 u_int32_t lx; 50 51 /* High word of |x|. */ 52 GET_HIGH_WORD(ix,x); 53 ix &= 0x7fffffff; 54 55 /* x is INF or NaN */ 56 if(ix>=0x7ff00000) return x*x; 57 58 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 59 if(ix<0x3fd62e43) { 60 t = expm1(fabs(x)); 61 w = one+t; 62 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 63 return one+(t*t)/(w+w); 64 } 65 66 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 67 if (ix < 0x40360000) { 68 t = exp(fabs(x)); 69 return half*t+half/t; 70 } 71 72 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 73 if (ix < 0x40862E42) return half*exp(fabs(x)); 74 75 /* |x| in [log(maxdouble), overflowthresold] */ 76 GET_LOW_WORD(lx,x); 77 if (ix<0x408633CE || 78 ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { 79 w = exp(half*fabs(x)); 80 t = half*w; 81 return t*w; 82 } 83 84 /* |x| > overflowthresold, cosh(x) overflow */ 85 return huge*huge; 86 } 87 88 #if LDBL_MANT_DIG == 53 89 #ifdef lint 90 /* PROTOLIB1 */ 91 long double coshl(long double); 92 #else /* lint */ 93 __weak_alias(coshl, cosh); 94 #endif /* lint */ 95 #endif /* LDBL_MANT_DIG == 53 */ 96