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| 2 | /* @(#)e_acosh.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 | */ |
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| 14 | |
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| 15 | /* __ieee754_acosh(x) |
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| 16 | * Method : |
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| 17 | * Based on |
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| 18 | * acosh(x) = log [ x + sqrt(x*x-1) ] |
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| 19 | * we have |
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| 20 | * acosh(x) := log(x)+ln2, if x is large; else |
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| 21 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
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| 22 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
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| 23 | * |
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| 24 | * Special cases: |
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| 25 | * acosh(x) is NaN with signal if x<1. |
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| 26 | * acosh(NaN) is NaN without signal. |
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| 27 | */ |
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| 28 | |
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| 29 | #include <libm/fdlibm.h> |
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| 30 | |
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| 31 | #ifdef __STDC__ |
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| 32 | static const double |
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| 33 | #else |
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| 34 | static double |
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| 35 | #endif |
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| 36 | one = 1.0, |
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| 37 | ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
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| 38 | |
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| 39 | #ifdef __STDC__ |
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| 40 | double __ieee754_acosh(double x) |
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| 41 | #else |
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| 42 | double __ieee754_acosh(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; |
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| 47 | int n0,hx; |
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| 48 | n0 = ((*(int*)&one)>>29)^1; |
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| 49 | hx = *(n0+(int*)&x); |
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| 50 | if(hx<0x3ff00000) { /* x < 1 */ |
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| 51 | return (x-x)/(x-x); |
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| 52 | } else if(hx >=0x41b00000) { /* x > 2**28 */ |
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| 53 | if(hx >=0x7ff00000) { /* x is inf of NaN */ |
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| 54 | return x+x; |
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| 55 | } else |
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| 56 | return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ |
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| 57 | } else if(((hx-0x3ff00000)|*(1-n0+(int*)&x))==0) { |
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| 58 | return 0.0; /* acosh(1) = 0 */ |
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| 59 | } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
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| 60 | t=x*x; |
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| 61 | return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); |
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| 62 | } else { /* 1<x<2 */ |
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| 63 | t = x-one; |
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| 64 | return log1p(t+sqrt(2.0*t+t*t)); |
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| 65 | } |
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| 66 | } |
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