| yuezonghe | 824eb0c | 2024-06-27 02:32:26 -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_atanh(x) |
| 13 | * Method : |
| 14 | * 1.Reduced x to positive by atanh(-x) = -atanh(x) |
| 15 | * 2.For x>=0.5 |
| 16 | * 1 2x x |
| 17 | * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) |
| 18 | * 2 1 - x 1 - x |
| 19 | * |
| 20 | * For x<0.5 |
| 21 | * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) |
| 22 | * |
| 23 | * Special cases: |
| 24 | * atanh(x) is NaN if |x| > 1 with signal; |
| 25 | * atanh(NaN) is that NaN with no signal; |
| 26 | * atanh(+-1) is +-INF with signal. |
| 27 | * |
| 28 | */ |
| 29 | |
| 30 | #include "math.h" |
| 31 | #include "math_private.h" |
| 32 | |
| 33 | static const double one = 1.0, huge = 1e300; |
| 34 | |
| 35 | static const double zero = 0.0; |
| 36 | |
| 37 | double attribute_hidden __ieee754_atanh(double x) |
| 38 | { |
| 39 | double t; |
| 40 | int32_t hx,ix; |
| 41 | u_int32_t lx; |
| 42 | EXTRACT_WORDS(hx,lx,x); |
| 43 | ix = hx&0x7fffffff; |
| 44 | if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ |
| 45 | return (x-x)/(x-x); |
| 46 | if(ix==0x3ff00000) |
| 47 | return x/zero; |
| 48 | if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ |
| 49 | SET_HIGH_WORD(x,ix); |
| 50 | if(ix<0x3fe00000) { /* x < 0.5 */ |
| 51 | t = x+x; |
| 52 | t = 0.5*log1p(t+t*x/(one-x)); |
| 53 | } else |
| 54 | t = 0.5*log1p((x+x)/(one-x)); |
| 55 | if(hx>=0) return t; else return -t; |
| 56 | } |
| 57 | |
| 58 | /* |
| 59 | * wrapper atanh(x) |
| 60 | */ |
| 61 | #ifndef _IEEE_LIBM |
| 62 | double atanh(double x) |
| 63 | { |
| 64 | double z, y; |
| 65 | z = __ieee754_atanh(x); |
| 66 | if (_LIB_VERSION == _IEEE_ || isnan(x)) |
| 67 | return z; |
| 68 | y = fabs(x); |
| 69 | if (y >= 1.0) { |
| 70 | if (y > 1.0) |
| 71 | return __kernel_standard(x, x, 30); /* atanh(|x|>1) */ |
| 72 | return __kernel_standard(x, x, 31); /* atanh(|x|==1) */ |
| 73 | } |
| 74 | return z; |
| 75 | } |
| 76 | #else |
| 77 | strong_alias(__ieee754_atanh, atanh) |
| 78 | #endif |
| 79 | libm_hidden_def(atanh) |