e_cosh.cpp (2205B)
1 /* @(#)e_cosh.c 1.3 95/01/18 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 //#include <sys/cdefs.h> 14 //__FBSDID("$FreeBSD$"); 15 16 /* __ieee754_cosh(x) 17 * Method : 18 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 19 * 1. Replace x by |x| (cosh(x) = cosh(-x)). 20 * 2. 21 * [ exp(x) - 1 ]^2 22 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 23 * 2*exp(x) 24 * 25 * exp(x) + 1/exp(x) 26 * ln2/2 <= x <= 22 : cosh(x) := ------------------- 27 * 2 28 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 29 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) 30 * ln2ovft < x : cosh(x) := huge*huge (overflow) 31 * 32 * Special cases: 33 * cosh(x) is |x| if x is +INF, -INF, or NaN. 34 * only cosh(0)=1 is exact for finite x. 35 */ 36 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 __ieee754_cosh(double x) 46 { 47 double t,w; 48 int32_t ix; 49 50 /* High word of |x|. */ 51 GET_HIGH_WORD(ix,x); 52 ix &= 0x7fffffff; 53 54 /* x is INF or NaN */ 55 if(ix>=0x7ff00000) return x*x; 56 57 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 58 if(ix<0x3fd62e43) { 59 t = expm1(fabs(x)); 60 w = one+t; 61 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 62 return one+(t*t)/(w+w); 63 } 64 65 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 66 if (ix < 0x40360000) { 67 t = __ieee754_exp(fabs(x)); 68 return half*t+half/t; 69 } 70 71 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 72 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); 73 74 /* |x| in [log(maxdouble), overflowthresold] */ 75 if (ix<=0x408633CE) 76 return __ldexp_exp(fabs(x), -1); 77 78 /* |x| > overflowthresold, cosh(x) overflow */ 79 return huge*huge; 80 }