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| 1906 | serge | 1 | |
| 2 | /* |
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| 3 | * ==================================================== |
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 5 | * |
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 7 | * Permission to use, copy, modify, and distribute this |
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| 8 | * software is freely granted, provided that this notice |
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| 9 | * is preserved. |
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| 10 | * ==================================================== |
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| 11 | */ |
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| 12 | |||
| 13 | |||
| 14 | * Method : |
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| 15 | * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 |
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| 16 | * 1. Replace x by |x| (sinh(-x) = -sinh(x)). |
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| 17 | * 2. |
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| 18 | * E + E/(E+1) |
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| 19 | * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) |
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| 20 | * 2 |
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| 21 | * |
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| 22 | * 22 <= x <= lnovft : sinh(x) := exp(x)/2 |
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| 23 | * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) |
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| 24 | * ln2ovft < x : sinh(x) := x*shuge (overflow) |
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| 25 | * |
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| 26 | * Special cases: |
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| 27 | * sinh(x) is |x| if x is +INF, -INF, or NaN. |
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| 28 | * only sinh(0)=0 is exact for finite x. |
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| 29 | */ |
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| 30 | |||
| 31 | |||
| 32 | |||
| 33 | |||
| 34 | static const double one = 1.0, shuge = 1.0e307; |
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| 35 | #else |
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| 36 | static double one = 1.0, shuge = 1.0e307; |
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| 37 | #endif |
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| 38 | |||
| 39 | |||
| 40 | double sinh(double x) |
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| 41 | #else |
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| 42 | double sinh(x) |
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| 43 | double x; |
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| 44 | #endif |
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| 45 | { |
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| 46 | double t,w,h; |
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| 47 | __int32_t ix,jx; |
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| 48 | __uint32_t lx; |
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| 49 | |||
| 50 | |||
| 51 | GET_HIGH_WORD(jx,x); |
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| 52 | ix = jx&0x7fffffff; |
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| 53 | |||
| 54 | |||
| 55 | if(ix>=0x7ff00000) return x+x; |
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| 56 | |||
| 57 | |||
| 58 | if (jx<0) h = -h; |
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| 59 | /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ |
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| 60 | if (ix < 0x40360000) { /* |x|<22 */ |
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| 61 | if (ix<0x3e300000) /* |x|<2**-28 */ |
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| 62 | if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ |
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| 63 | t = expm1(fabs(x)); |
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| 64 | if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); |
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| 65 | return h*(t+t/(t+one)); |
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| 66 | } |
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| 67 | |||
| 68 | |||
| 69 | if (ix < 0x40862E42) return h * exp(fabs(x)); |
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| 70 | |||
| 71 | |||
| 72 | GET_LOW_WORD(lx,x); |
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| 73 | if (ix<0x408633CE || (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) { |
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| 74 | w = exp(0.5*fabs(x)); |
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| 75 | t = h*w; |
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| 76 | return t*w; |
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| 77 | } |
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| 78 | |||
| 79 | |||
| 80 | return x*shuge; |
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| 81 | } |
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| 82 |