| 1 |
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| 2 | /* @(#)e_cosh.c 1.3 95/01/18 */
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| 3 | /*
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| 4 | * ====================================================
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 6 | *
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| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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| 8 | * Permission to use, copy, modify, and distribute this
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| 9 | * software is freely granted, provided that this notice
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| 10 | * is preserved.
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| 11 | * ====================================================
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| 12 | */
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| 13 |
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| 14 | #ifndef lint
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| 15 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_cosh.c,v 1.8 2005/02/04 18:26:05 das Exp $";
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| 16 | #endif
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| 17 |
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| 18 | /* __ieee754_cosh(x)
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| 19 | * Method :
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| 20 | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
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| 21 | * 1. Replace x by |x| (cosh(x) = cosh(-x)).
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| 22 | * 2.
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| 23 | * [ exp(x) - 1 ]^2
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| 24 | * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
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| 25 | * 2*exp(x)
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| 26 | *
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| 27 | * exp(x) + 1/exp(x)
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| 28 | * ln2/2 <= x <= 22 : cosh(x) := -------------------
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| 29 | * 2
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| 30 | * 22 <= x <= lnovft : cosh(x) := exp(x)/2
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| 31 | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
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| 32 | * ln2ovft < x : cosh(x) := huge*huge (overflow)
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| 33 | *
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| 34 | * Special cases:
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| 35 | * cosh(x) is |x| if x is +INF, -INF, or NaN.
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| 36 | * only cosh(0)=1 is exact for finite x.
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| 37 | */
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| 38 |
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| 39 | #include "math.h"
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| 40 | #include "math_private.h"
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| 41 |
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| 42 | static const double one = 1.0, half=0.5, huge = 1.0e300;
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| 43 |
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| 44 | double
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| 45 | __ieee754_cosh(double x)
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| 46 | {
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| 47 | double t,w;
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| 48 | int32_t ix;
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| 49 | u_int32_t lx;
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| 50 |
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| 51 | /* High word of |x|. */
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| 52 | GET_HIGH_WORD(ix,x);
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| 53 | ix &= 0x7fffffff;
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| 54 |
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| 55 | /* x is INF or NaN */
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| 56 | if(ix>=0x7ff00000) return x*x;
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| 57 |
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| 58 | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
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| 59 | if(ix<0x3fd62e43) {
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| 60 | t = expm1(fabs(x));
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| 61 | w = one+t;
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| 62 | if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
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| 63 | return one+(t*t)/(w+w);
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| 64 | }
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| 65 |
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| 66 | /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
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| 67 | if (ix < 0x40360000) {
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| 68 | t = __ieee754_exp(fabs(x));
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| 69 | return half*t+half/t;
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| 70 | }
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| 71 |
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| 72 | /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
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| 73 | if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
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| 74 |
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| 75 | /* |x| in [log(maxdouble), overflowthresold] */
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| 76 | GET_LOW_WORD(lx,x);
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| 77 | if (ix<0x408633CE ||
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| 78 | ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
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| 79 | w = __ieee754_exp(half*fabs(x));
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| 80 | t = half*w;
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| 81 | return t*w;
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| 82 | }
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| 83 |
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| 84 | /* |x| > overflowthresold, cosh(x) overflow */
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| 85 | return huge*huge;
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| 86 | }
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