| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 1 | /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */ |
| 2 | |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 14 | /* |
| 15 | * See s_asinh.c for complete comments. |
| 16 | * |
| 17 | * Converted to long double by David Schultz <das@FreeBSD.ORG> and |
| 18 | * Bruce D. Evans. |
| 19 | */ |
| 20 | |
| 21 | #include <float.h> |
| 22 | #ifdef __i386__ |
| 23 | #include <ieeefp.h> |
| 24 | #endif |
| 25 | |
| 26 | #include "fpmath.h" |
| 27 | #include "math.h" |
| 28 | #include "math_private.h" |
| 29 | |
| 30 | /* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */ |
| 31 | /* EXP_TINY is the threshold below which we use asinh(x) ~= x. */ |
| 32 | #if LDBL_MANT_DIG == 64 |
| 33 | #define EXP_LARGE 34 |
| 34 | #define EXP_TINY -34 |
| 35 | #elif LDBL_MANT_DIG == 113 |
| 36 | #define EXP_LARGE 58 |
| 37 | #define EXP_TINY -58 |
| 38 | #else |
| 39 | #error "Unsupported long double format" |
| 40 | #endif |
| 41 | |
| 42 | #if LDBL_MAX_EXP != 0x4000 |
| 43 | /* We also require the usual expsign encoding. */ |
| 44 | #error "Unsupported long double format" |
| 45 | #endif |
| 46 | |
| 47 | #define BIAS (LDBL_MAX_EXP - 1) |
| 48 | |
| 49 | static const double |
| 50 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| 51 | huge= 1.00000000000000000000e+300; |
| 52 | |
| 53 | #if LDBL_MANT_DIG == 64 |
| 54 | static const union IEEEl2bits |
| 55 | u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); |
| 56 | #define ln2 u_ln2.e |
| 57 | #elif LDBL_MANT_DIG == 113 |
| 58 | static const long double |
| 59 | ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ |
| 60 | #else |
| 61 | #error "Unsupported long double format" |
| 62 | #endif |
| 63 | |
| 64 | long double |
| 65 | asinhl(long double x) |
| 66 | { |
| 67 | long double t, w; |
| 68 | uint16_t hx, ix; |
| 69 | |
| 70 | ENTERI(); |
| 71 | GET_LDBL_EXPSIGN(hx, x); |
| 72 | ix = hx & 0x7fff; |
| 73 | if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */ |
| 74 | if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */ |
| 75 | if (huge + x > one) RETURNI(x); /* return x inexact except 0 */ |
| 76 | } |
| 77 | if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */ |
| 78 | w = logl(fabsl(x))+ln2; |
| 79 | } else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */ |
| 80 | t = fabsl(x); |
| 81 | w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); |
| 82 | } else { /* 2.0 > |x| >= TINY, or misnormal */ |
| 83 | t = x*x; |
| 84 | w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); |
| 85 | } |
| 86 | RETURNI((hx & 0x8000) == 0 ? w : -w); |
| 87 | } |