1 /* 2 * Single-precision atanh(x) function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "math_config.h" 9 #include "mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #define AbsMask 0x7fffffff 14 #define Half 0x3f000000 15 #define One 0x3f800000 16 #define Four 0x40800000 17 #define Ln2 0x1.62e43p-1f 18 /* asuint(0x1p-12), below which atanhf(x) rounds to x. */ 19 #define TinyBound 0x39800000 20 21 #define C(i) __log1pf_data.coeffs[i] 22 23 static inline float 24 eval_poly (float m) 25 { 26 /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */ 27 float p_12 = fmaf (m, C (1), C (0)); 28 float p_34 = fmaf (m, C (3), C (2)); 29 float p_56 = fmaf (m, C (5), C (4)); 30 float p_78 = fmaf (m, C (7), C (6)); 31 32 float m2 = m * m; 33 float p_02 = fmaf (m2, p_12, m); 34 float p_36 = fmaf (m2, p_56, p_34); 35 float p_79 = fmaf (m2, C (8), p_78); 36 37 float m4 = m2 * m2; 38 float p_06 = fmaf (m4, p_36, p_02); 39 40 return fmaf (m4 * p_79, m4, p_06); 41 } 42 43 static inline float 44 log1pf_inline (float x) 45 { 46 /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no 47 special-case handling. See that file for details of the algorithm. */ 48 float m = x + 1.0f; 49 int k = (asuint (m) - 0x3f400000) & 0xff800000; 50 float s = asfloat (Four - k); 51 float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f); 52 float p = eval_poly (m_scale); 53 float scale_back = (float) k * 0x1.0p-23f; 54 return fmaf (scale_back, Ln2, p); 55 } 56 57 /* Approximation for single-precision inverse tanh(x), using a simplified 58 version of log1p. Maximum error is 3.08 ULP: 59 atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5 60 want 0x1.ffb76ep-5. */ 61 float 62 atanhf (float x) 63 { 64 uint32_t ix = asuint (x); 65 uint32_t iax = ix & AbsMask; 66 uint32_t sign = ix & ~AbsMask; 67 68 if (unlikely (iax < TinyBound)) 69 return x; 70 71 if (iax == One) 72 return __math_divzero (sign); 73 74 if (unlikely (iax > One)) 75 return __math_invalidf (x); 76 77 float halfsign = asfloat (Half | sign); 78 float ax = asfloat (iax); 79 return halfsign * log1pf_inline ((2 * ax) / (1 - ax)); 80 } 81 82 PL_SIG (S, F, 1, atanh, -1.0, 1.0) 83 PL_TEST_ULP (atanhf, 2.59) 84 PL_TEST_SYM_INTERVAL (atanhf, 0, 0x1p-12, 500) 85 PL_TEST_SYM_INTERVAL (atanhf, 0x1p-12, 1, 200000) 86 PL_TEST_SYM_INTERVAL (atanhf, 1, inf, 1000) 87