1 2 /* @(#)e_cosh.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 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 <float.h> 39 40 #include "math.h" 41 #include "math_private.h" 42 43 static const double one = 1.0, half=0.5, huge = 1.0e300; 44 45 double __ieee754_cosh(double x)46 __ieee754_cosh(double x) 47 { 48 double t,w; 49 int32_t ix; 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 = __ieee754_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*__ieee754_exp(fabs(x)); 74 75 /* |x| in [log(maxdouble), overflowthresold] */ 76 if (ix<=0x408633CE) 77 return __ldexp_exp(fabs(x), -1); 78 79 /* |x| > overflowthresold, cosh(x) overflow */ 80 return huge*huge; 81 } 82 83 #if (LDBL_MANT_DIG == 53) 84 __weak_reference(cosh, coshl); 85 #endif 86