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/* @(#)e_sinh.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
 
/* __ieee754_sinh(x)
 * Method :
 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
 *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
 *      2.
 *                                                  E + E/(E+1)
 *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
 *                                                      2
 *
 *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
 *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
 *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
 *
 * Special cases:
 *      sinh(x) is |x| if x is +INF, -INF, or NaN.
 *      only sinh(0)=0 is exact for finite x.
 */
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double one = 1.0, shuge = 1.0e307;
#else
static double one = 1.0, shuge = 1.0e307;
#endif
 
#ifdef __STDC__
        double __ieee754_sinh(double x)
#else
        double __ieee754_sinh(x)
        double x;
#endif
{
        double t,w,h;
        __int32_t ix,jx;
        __uint32_t lx;
 
    /* High word of |x|. */
        GET_HIGH_WORD(jx,x);
        ix = jx&0x7fffffff;
 
    /* x is INF or NaN */
        if(ix>=0x7ff00000) return x+x;
 
        h = 0.5;
        if (jx<0) h = -h;
    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
        if (ix < 0x40360000) {          /* |x|<22 */
            if (ix<0x3e300000)          /* |x|<2**-28 */
                if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
            t = expm1(fabs(x));
            if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
            return h*(t+t/(t+one));
        }
 
    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
        if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
 
    /* |x| in [log(maxdouble), overflowthresold] */
        GET_LOW_WORD(lx,x);
        if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(__uint32_t)0x8fb9f87d)) {
            w = __ieee754_exp(0.5*fabs(x));
            t = h*w;
            return t*w;
        }
 
    /* |x| > overflowthresold, sinh(x) overflow */
        return x*shuge;
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */

Line No.	Rev	Author	Line
1	39	lampret
2			`/* @(#)e_sinh.c 5.1 93/09/24 */`
3			`/*`
4			`* ====================================================`
5			`* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
6			`*`
7			`* Developed at SunPro, 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			`/* __ieee754_sinh(x)`
15			`* Method :`
16			`* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2`
17			`* 1. Replace x by \|x\| (sinh(-x) = -sinh(x)).`
18			`* 2.`
19			`* E + E/(E+1)`
20			`* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)`
21			`* 2`
22			`*`
23			`* 22 <= x <= lnovft : sinh(x) := exp(x)/2`
24			`* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)`
25			`* ln2ovft < x : sinh(x) := x*shuge (overflow)`
26			`*`
27			`* Special cases:`
28			`* sinh(x) is \|x\| if x is +INF, -INF, or NaN.`
29			`* only sinh(0)=0 is exact for finite x.`
30			`*/`
31
32			`#include "fdlibm.h"`
33
34			`#ifndef _DOUBLE_IS_32BITS`
35
36			`#ifdef __STDC__`
37			`static const double one = 1.0, shuge = 1.0e307;`
38			`#else`
39			`static double one = 1.0, shuge = 1.0e307;`
40			`#endif`
41
42			`#ifdef __STDC__`
43			`double __ieee754_sinh(double x)`
44			`#else`
45			`double __ieee754_sinh(x)`
46			`double x;`
47			`#endif`
48			`{`
49			`double t,w,h;`
50			`__int32_t ix,jx;`
51			`__uint32_t lx;`
52
53			`/* High word of \|x\|. */`
54			`GET_HIGH_WORD(jx,x);`
55			`ix = jx&0x7fffffff;`
56
57			`/* x is INF or NaN */`
58			`if(ix>=0x7ff00000) return x+x;`
59
60			`h = 0.5;`
61			`if (jx<0) h = -h;`
62			`/* \|x\| in [0,22], return sign(x)0.5(E+E/(E+1))) */`
63			`if (ix < 0x40360000) { /* \|x\|<22 */`
64			`if (ix<0x3e300000) /* \|x\|<2*-28 /`
65			`if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */`
66			`t = expm1(fabs(x));`
67			`if(ix<0x3ff00000) return h(2.0t-t*t/(t+one));`
68			`return h*(t+t/(t+one));`
69			`}`
70
71			`/* \|x\| in [22, log(maxdouble)] return 0.5exp(\|x\|) /`
72			`if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));`
73
74			`/* \|x\| in [log(maxdouble), overflowthresold] */`
75			`GET_LOW_WORD(lx,x);`
76			`if (ix<0x408633CE \|\| (ix==0x408633ce)&&(lx<=(__uint32_t)0x8fb9f87d)) {`
77			`w = __ieee754_exp(0.5*fabs(x));`
78			`t = h*w;`
79			`return t*w;`
80			`}`
81
82			`/* \|x\| > overflowthresold, sinh(x) overflow */`
83			`return x*shuge;`
84			`}`
85
86			`#endif /* defined(_DOUBLE_IS_32BITS) */`

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[/] [or1k/] [trunk/] [newlib/] [newlib/] [libm/] [math/] [e_sinh.c] - Blame information for rev 1774