| 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_acosh(x) |
| 13 | * Method : |
| 14 | * Based on |
| 15 | * acosh(x) = log [ x + sqrt(x*x-1) ] |
| 16 | * we have |
| 17 | * acosh(x) := log(x)+ln2, if x is large; else |
| 18 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
| 19 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
| 20 | * |
| 21 | * Special cases: |
| 22 | * acosh(x) is NaN with signal if x<1. |
| 23 | * acosh(NaN) is NaN without signal. |
| 24 | */ |
| 25 | |
| 26 | #include "math.h" |
| 27 | #include "math_private.h" |
| 28 | |
| 29 | static const double |
| 30 | one = 1.0, |
| 31 | ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
| 32 | |
| 33 | double attribute_hidden __ieee754_acosh(double x) |
| 34 | { |
| 35 | double t; |
| 36 | int32_t hx; |
| 37 | u_int32_t lx; |
| 38 | EXTRACT_WORDS(hx,lx,x); |
| 39 | if(hx<0x3ff00000) { /* x < 1 */ |
| 40 | return (x-x)/(x-x); |
| 41 | } else if(hx >=0x41b00000) { /* x > 2**28 */ |
| 42 | if(hx >=0x7ff00000) { /* x is inf of NaN */ |
| 43 | return x+x; |
| 44 | } else |
| 45 | return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ |
| 46 | } else if(((hx-0x3ff00000)|lx)==0) { |
| 47 | return 0.0; /* acosh(1) = 0 */ |
| 48 | } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
| 49 | t=x*x; |
| 50 | return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); |
| 51 | } else { /* 1<x<2 */ |
| 52 | t = x-one; |
| 53 | return log1p(t+sqrt(2.0*t+t*t)); |
| 54 | } |
| 55 | } |
| 56 | |
| 57 | /* |
| 58 | * wrapper acosh(x) |
| 59 | */ |
| 60 | #ifndef _IEEE_LIBM |
| 61 | double acosh(double x) |
| 62 | { |
| 63 | double z = __ieee754_acosh(x); |
| 64 | if (_LIB_VERSION == _IEEE_ || isnan(x)) |
| 65 | return z; |
| 66 | if (x < 1.0) |
| 67 | return __kernel_standard(x, x, 29); /* acosh(x<1) */ |
| 68 | return z; |
| 69 | } |
| 70 | #else |
| 71 | strong_alias(__ieee754_acosh, acosh) |
| 72 | #endif |
| 73 | libm_hidden_def(acosh) |