1 /* Copyright (C) 2011-2022 Free Software Foundation, Inc. 2 This file is part of the GNU C Library. 3 4 The GNU C Library is free software; you can redistribute it and/or 5 modify it under the terms of the GNU Lesser General Public 6 License as published by the Free Software Foundation; either 7 version 2.1 of the License, or (at your option) any later version. 8 9 The GNU C Library is distributed in the hope that it will be useful, 10 but WITHOUT ANY WARRANTY; without even the implied warranty of 11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 12 Lesser General Public License for more details. 13 14 You should have received a copy of the GNU Lesser General Public 15 License along with the GNU C Library; if not, see 16 <https://www.gnu.org/licenses/>. */ 17 18 19 /* __ieee754_atanh(x) 20 Method : 21 1.Reduced x to positive by atanh(-x) = -atanh(x) 22 2.For x>=0.5 23 1 2x x 24 atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 25 2 1 - x 1 - x 26 27 For x<0.5 28 atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) 29 30 Special cases: 31 atanh(x) is NaN if |x| > 1 with signal; 32 atanh(NaN) is that NaN with no signal; 33 atanh(+-1) is +-INF with signal. 34 35 */ 36 37 #include <float.h> 38 #include <inttypes.h> 39 #include <math.h> 40 #include <math-barriers.h> 41 #include <math_private.h> 42 #include <math-underflow.h> 43 #include <libm-alias-finite.h> 44 45 static const float huge = 1e30; 46 47 float __ieee754_atanhf(float x)48__ieee754_atanhf (float x) 49 { 50 float xa = fabsf (x); 51 float t; 52 if (isless (xa, 0.5f)) 53 { 54 if (__glibc_unlikely (xa < 0x1.0p-28f)) 55 { 56 math_force_eval (huge + x); 57 math_check_force_underflow (x); 58 return x; 59 } 60 61 t = xa + xa; 62 t = 0.5f * __log1pf (t + t * xa / (1.0f - xa)); 63 } 64 else if (__glibc_likely (isless (xa, 1.0f))) 65 t = 0.5f * __log1pf ((xa + xa) / (1.0f - xa)); 66 else 67 { 68 if (isgreater (xa, 1.0f)) 69 return (x - x) / (x - x); 70 71 return x / 0.0f; 72 } 73 74 return copysignf (t, x); 75 } 76 libm_alias_finite (__ieee754_atanhf, __atanhf) 77