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 <float.h> 35 #include <math.h> 36 37 #include "math_private.h" 38 39 static const double one = 1.0, half=0.5, huge = 1.0e300; 40 41 double 42 cosh(double x) 43 { 44 double t,w; 45 int32_t ix; 46 u_int32_t lx; 47 48 /* High word of |x|. */ 49 GET_HIGH_WORD(ix,x); 50 ix &= 0x7fffffff; 51 52 /* x is INF or NaN */ 53 if(ix>=0x7ff00000) return x*x; 54 55 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 56 if(ix<0x3fd62e43) { 57 t = expm1(fabs(x)); 58 w = one+t; 59 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 60 return one+(t*t)/(w+w); 61 } 62 63 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 64 if (ix < 0x40360000) { 65 t = exp(fabs(x)); 66 return half*t+half/t; 67 } 68 69 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 70 if (ix < 0x40862E42) return half*exp(fabs(x)); 71 72 /* |x| in [log(maxdouble), overflowthresold] */ 73 GET_LOW_WORD(lx,x); 74 if (ix<0x408633CE || 75 ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { 76 w = exp(half*fabs(x)); 77 t = half*w; 78 return t*w; 79 } 80 81 /* |x| > overflowthresold, cosh(x) overflow */ 82 return huge*huge; 83 } 84 85 #if LDBL_MANT_DIG == DBL_MANT_DIG 86 __strong_alias(coshl, cosh); 87 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 88