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 /* coshl(x) 14 * Method : 15 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 16 * 1. Replace x by |x| (coshl(x) = coshl(-x)). 17 * 2. 18 * [ exp(x) - 1 ]^2 19 * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- 20 * 2*exp(x) 21 * 22 * exp(x) + 1/exp(x) 23 * ln2/2 <= x <= 22 : coshl(x) := ------------------- 24 * 2 25 * 22 <= x <= lnovft : coshl(x) := expl(x)/2 26 * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) 27 * ln2ovft < x : coshl(x) := huge*huge (overflow) 28 * 29 * Special cases: 30 * coshl(x) is |x| if x is +INF, -INF, or NaN. 31 * only coshl(0)=1 is exact for finite x. 32 */ 33 34 #include "math.h" 35 #include "math_private.h" 36 37 static const long double one = 1.0, half=0.5, huge = 1.0e4900L; 38 39 long double 40 coshl(long double x) 41 { 42 long double t,w; 43 int32_t ex; 44 u_int32_t mx,lx; 45 46 /* High word of |x|. */ 47 GET_LDOUBLE_WORDS(ex,mx,lx,x); 48 ex &= 0x7fff; 49 50 /* x is INF or NaN */ 51 if(ex==0x7fff) return x*x; 52 53 /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ 54 if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { 55 t = expm1l(fabsl(x)); 56 w = one+t; 57 if (ex<0x3fbc) 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 (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { 63 t = expl(fabsl(x)); 64 return half*t+half/t; 65 } 66 67 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ 68 if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) 69 return half*expl(fabsl(x)); 70 71 /* |x| in [log(maxdouble), log(2*maxdouble)) */ 72 if (ex == 0x400c && (mx < 0xb174ddc0u 73 || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) 74 { 75 w = expl(half*fabsl(x)); 76 t = half*w; 77 return t*w; 78 } 79 80 /* |x| >= log(2*maxdouble), cosh(x) overflow */ 81 return huge*huge; 82 } 83 DEF_STD(coshl); 84