| lh | 9ed821d | 2023-04-07 01:36:19 -0700 | [diff] [blame] | 1 | /* |
| 2 | * ==================================================== |
| 3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 4 | * |
| 5 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 6 | * Permission to use, copy, modify, and distribute this |
| 7 | * software is freely granted, provided that this notice |
| 8 | * is preserved. |
| 9 | * ==================================================== |
| 10 | */ |
| 11 | |
| 12 | /* __ieee754_sinh(x) |
| 13 | * Method : |
| 14 | * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 |
| 15 | * 1. Replace x by |x| (sinh(-x) = -sinh(x)). |
| 16 | * 2. |
| 17 | * E + E/(E+1) |
| 18 | * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) |
| 19 | * 2 |
| 20 | * |
| 21 | * 22 <= x <= lnovft : sinh(x) := exp(x)/2 |
| 22 | * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) |
| 23 | * ln2ovft < x : sinh(x) := x*shuge (overflow) |
| 24 | * |
| 25 | * Special cases: |
| 26 | * sinh(x) is |x| if x is +INF, -INF, or NaN. |
| 27 | * only sinh(0)=0 is exact for finite x. |
| 28 | */ |
| 29 | |
| 30 | #include "math.h" |
| 31 | #include "math_private.h" |
| 32 | |
| 33 | static const double one = 1.0, shuge = 1.0e307; |
| 34 | |
| 35 | double attribute_hidden __ieee754_sinh(double x) |
| 36 | { |
| 37 | double t,w,h; |
| 38 | int32_t ix,jx; |
| 39 | u_int32_t lx; |
| 40 | |
| 41 | /* High word of |x|. */ |
| 42 | GET_HIGH_WORD(jx,x); |
| 43 | ix = jx&0x7fffffff; |
| 44 | |
| 45 | /* x is INF or NaN */ |
| 46 | if(ix>=0x7ff00000) return x+x; |
| 47 | |
| 48 | h = 0.5; |
| 49 | if (jx<0) h = -h; |
| 50 | /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ |
| 51 | if (ix < 0x40360000) { /* |x|<22 */ |
| 52 | if (ix<0x3e300000) /* |x|<2**-28 */ |
| 53 | if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ |
| 54 | t = expm1(fabs(x)); |
| 55 | if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); |
| 56 | return h*(t+t/(t+one)); |
| 57 | } |
| 58 | |
| 59 | /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
| 60 | if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); |
| 61 | |
| 62 | /* |x| in [log(maxdouble), overflowthresold] */ |
| 63 | GET_LOW_WORD(lx,x); |
| 64 | if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { |
| 65 | w = __ieee754_exp(0.5*fabs(x)); |
| 66 | t = h*w; |
| 67 | return t*w; |
| 68 | } |
| 69 | |
| 70 | /* |x| > overflowthresold, sinh(x) overflow */ |
| 71 | return x*shuge; |
| 72 | } |
| 73 | |
| 74 | /* |
| 75 | * wrapper sinh(x) |
| 76 | */ |
| 77 | #ifndef _IEEE_LIBM |
| 78 | double sinh(double x) |
| 79 | { |
| 80 | double z = __ieee754_sinh(x); |
| 81 | if (_LIB_VERSION == _IEEE_) |
| 82 | return z; |
| 83 | if (!isfinite(z) && isfinite(x)) |
| 84 | return __kernel_standard(x, x, 25); /* sinh overflow */ |
| 85 | return z; |
| 86 | } |
| 87 | #else |
| 88 | strong_alias(__ieee754_sinh, sinh) |
| 89 | #endif |
| 90 | libm_hidden_def(sinh) |