/src/moddable/xs/tools/fdlibm/e_acosh.c
Line | Count | Source |
1 | | |
2 | | /* |
3 | | * ==================================================== |
4 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | | * |
6 | | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
7 | | * Permission to use, copy, modify, and distribute this |
8 | | * software is freely granted, provided that this notice |
9 | | * is preserved. |
10 | | * ==================================================== |
11 | | * |
12 | | */ |
13 | | |
14 | | /* acosh(x) |
15 | | * Method : |
16 | | * Based on |
17 | | * acosh(x) = log [ x + sqrt(x*x-1) ] |
18 | | * we have |
19 | | * acosh(x) := log(x)+ln2, if x is large; else |
20 | | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
21 | | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
22 | | * |
23 | | * Special cases: |
24 | | * acosh(x) is NaN with signal if x<1. |
25 | | * acosh(NaN) is NaN without signal. |
26 | | */ |
27 | | |
28 | | #include "math_private.h" |
29 | | |
30 | | static const double |
31 | | one = 1.0, |
32 | | ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
33 | | |
34 | | double |
35 | | __ieee754_acosh(double x) |
36 | 267k | { |
37 | 267k | double t; |
38 | 267k | int32_t hx; |
39 | 267k | u_int32_t lx; |
40 | 267k | EXTRACT_WORDS(hx,lx,x); |
41 | 267k | if(hx<0x3ff00000) { /* x < 1 */ |
42 | 20.9k | return (x-x)/(x-x); |
43 | 246k | } else if(hx >=0x41b00000) { /* x > 2**28 */ |
44 | 6.01k | if(hx >=0x7ff00000) { /* x is inf of NaN */ |
45 | 4.11k | return x+x; |
46 | 4.11k | } else |
47 | 1.89k | return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ |
48 | 240k | } else if(((hx-0x3ff00000)|lx)==0) { |
49 | 21.1k | return 0.0; /* acosh(1) = 0 */ |
50 | 219k | } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
51 | 195k | t=x*x; |
52 | 195k | return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); |
53 | 195k | } else { /* 1<x<2 */ |
54 | 23.6k | t = x-one; |
55 | 23.6k | return s_log1p(t+sqrt(2.0*t+t*t)); |
56 | 23.6k | } |
57 | 267k | } |