| 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_cosh(x) |
| 13 | * Method : |
| 14 | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
| 15 | * 1. Replace x by |x| (cosh(x) = cosh(-x)). |
| 16 | * 2. |
| 17 | * [ exp(x) - 1 ]^2 |
| 18 | * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
| 19 | * 2*exp(x) |
| 20 | * |
| 21 | * exp(x) + 1/exp(x) |
| 22 | * ln2/2 <= x <= 22 : cosh(x) := ------------------- |
| 23 | * 2 |
| 24 | * 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
| 25 | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
| 26 | * ln2ovft < x : cosh(x) := huge*huge (overflow) |
| 27 | * |
| 28 | * Special cases: |
| 29 | * cosh(x) is |x| if x is +INF, -INF, or NaN. |
| 30 | * only cosh(0)=1 is exact for finite x. |
| 31 | */ |
| 32 | |
| 33 | #include "math.h" |
| 34 | #include "math_private.h" |
| 35 | |
| 36 | static const double one = 1.0, half=0.5, huge = 1.0e300; |
| 37 | |
| 38 | double attribute_hidden __ieee754_cosh(double x) |
| 39 | { |
| 40 | double t,w; |
| 41 | int32_t ix; |
| 42 | u_int32_t lx; |
| 43 | |
| 44 | /* High word of |x|. */ |
| 45 | GET_HIGH_WORD(ix,x); |
| 46 | ix &= 0x7fffffff; |
| 47 | |
| 48 | /* x is INF or NaN */ |
| 49 | if(ix>=0x7ff00000) return x*x; |
| 50 | |
| 51 | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
| 52 | if(ix<0x3fd62e43) { |
| 53 | t = expm1(fabs(x)); |
| 54 | w = one+t; |
| 55 | if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ |
| 56 | return one+(t*t)/(w+w); |
| 57 | } |
| 58 | |
| 59 | /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
| 60 | if (ix < 0x40360000) { |
| 61 | t = __ieee754_exp(fabs(x)); |
| 62 | return half*t+half/t; |
| 63 | } |
| 64 | |
| 65 | /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
| 66 | if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); |
| 67 | |
| 68 | /* |x| in [log(maxdouble), overflowthresold] */ |
| 69 | GET_LOW_WORD(lx,x); |
| 70 | if (ix<0x408633CE || |
| 71 | ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { |
| 72 | w = __ieee754_exp(half*fabs(x)); |
| 73 | t = half*w; |
| 74 | return t*w; |
| 75 | } |
| 76 | |
| 77 | /* |x| > overflowthresold, cosh(x) overflow */ |
| 78 | return huge*huge; |
| 79 | } |
| 80 | |
| 81 | /* |
| 82 | * wrapper cosh(x) |
| 83 | */ |
| 84 | #ifndef _IEEE_LIBM |
| 85 | double cosh(double x) |
| 86 | { |
| 87 | double z = __ieee754_cosh(x); |
| 88 | if (_LIB_VERSION == _IEEE_ || isnan(x)) |
| 89 | return z; |
| 90 | if (fabs(x) > 7.10475860073943863426e+02) |
| 91 | return __kernel_standard(x, x, 5); /* cosh overflow */ |
| 92 | return z; |
| 93 | } |
| 94 | #else |
| 95 | strong_alias(__ieee754_cosh, cosh) |
| 96 | #endif |
| 97 | libm_hidden_def(cosh) |