| 1 |
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| 2 | /* @(#)e_sinh.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_sinh.c,v 1.9 2005/02/04 18:26:06 das Exp $";
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| 16 | #endif
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| 17 |
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| 18 | /* __ieee754_sinh(x)
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| 19 | * Method :
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| 20 | * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
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| 21 | * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
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| 22 | * 2.
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| 23 | * E + E/(E+1)
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| 24 | * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
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| 25 | * 2
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| 26 | *
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| 27 | * 22 <= x <= lnovft : sinh(x) := exp(x)/2
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| 28 | * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
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| 29 | * ln2ovft < x : sinh(x) := x*shuge (overflow)
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| 30 | *
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| 31 | * Special cases:
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| 32 | * sinh(x) is |x| if x is +INF, -INF, or NaN.
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| 33 | * only sinh(0)=0 is exact for finite x.
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| 34 | */
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| 35 |
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| 36 | #include "math.h"
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| 37 | #include "math_private.h"
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| 38 |
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| 39 | static const double one = 1.0, shuge = 1.0e307;
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| 40 |
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| 41 | double
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| 42 | __ieee754_sinh(double x)
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| 43 | {
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| 44 | double t,w,h;
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| 45 | int32_t ix,jx;
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| 46 | u_int32_t lx;
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| 47 |
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| 48 | /* High word of |x|. */
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| 49 | GET_HIGH_WORD(jx,x);
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| 50 | ix = jx&0x7fffffff;
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| 51 |
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| 52 | /* x is INF or NaN */
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| 53 | if(ix>=0x7ff00000) return x+x;
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| 54 |
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| 55 | h = 0.5;
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| 56 | if (jx<0) h = -h;
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| 57 | /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
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| 58 | if (ix < 0x40360000) { /* |x|<22 */
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| 59 | if (ix<0x3e300000) /* |x|<2**-28 */
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| 60 | if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
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| 61 | t = expm1(fabs(x));
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| 62 | if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
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| 63 | return h*(t+t/(t+one));
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| 64 | }
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| 65 |
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| 66 | /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
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| 67 | if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
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| 68 |
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| 69 | /* |x| in [log(maxdouble), overflowthresold] */
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| 70 | GET_LOW_WORD(lx,x);
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| 71 | if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
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| 72 | w = __ieee754_exp(0.5*fabs(x));
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| 73 | t = h*w;
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| 74 | return t*w;
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| 75 | }
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| 76 |
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| 77 | /* |x| > overflowthresold, sinh(x) overflow */
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| 78 | return x*shuge;
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| 79 | }
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