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4973 | right-hear | 1 | /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
2 | /* @(#)e_sinh.c 5.1 93/09/24 */ |
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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 SunPro, 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 | |||
14 | #if defined(LIBM_SCCS) && !defined(lint) |
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15 | static char rcsid[] = "$Id: e_sinh.c,v 1.5 1994/08/18 23:06:03 jtc Exp $"; |
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16 | #endif |
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17 | |||
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 | |||
36 | #include "math.h" |
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37 | #include "math_private.h" |
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38 | |||
39 | #ifdef __STDC__ |
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40 | static const double one = 1.0, shuge = 1.0e307; |
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41 | #else |
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42 | static double one = 1.0, shuge = 1.0e307; |
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43 | #endif |
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44 | |||
45 | #ifdef __STDC__ |
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46 | double __ieee754_sinh(double x) |
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47 | #else |
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48 | double __ieee754_sinh(x) |
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49 | double x; |
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50 | #endif |
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51 | { |
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52 | double t,w,h; |
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53 | int32_t ix,jx; |
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54 | u_int32_t lx; |
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55 | |||
56 | /* High word of |x|. */ |
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57 | GET_HIGH_WORD(jx,x); |
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58 | ix = jx&0x7fffffff; |
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59 | |||
60 | /* x is INF or NaN */ |
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61 | if(ix>=0x7ff00000) return x+x; |
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62 | |||
63 | h = 0.5; |
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64 | if (jx<0) h = -h; |
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65 | /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ |
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66 | if (ix < 0x40360000) { /* |x|<22 */ |
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67 | if (ix<0x3e300000) /* |x|<2**-28 */ |
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68 | if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ |
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69 | t = expm1(fabs(x)); |
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70 | if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); |
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71 | return h*(t+t/(t+one)); |
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72 | } |
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73 | |||
74 | /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
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75 | if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); |
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76 | |||
77 | /* |x| in [log(maxdouble), overflowthresold] */ |
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78 | GET_LOW_WORD(lx,x); |
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79 | if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) { |
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80 | w = __ieee754_exp(0.5*fabs(x)); |
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81 | t = h*w; |
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82 | return t*w; |
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83 | } |
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84 | |||
85 | /* |x| > overflowthresold, sinh(x) overflow */ |
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86 | return x*shuge; |
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87 | }=(u_int32_t)0x8fb9f87d))>0x408633CE>>0x3ff00000)>2**-28>0x3e300000)>22>>0)>>=>=>=>=>=>=> |