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