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 #define TinyBound 0x39800000 /* 0x1p-12, below which atanhf(x) rounds to x. */ 19 20 #define C(i) __log1pf_data.coeffs[i] 21 22 static inline float 23 eval_poly (float m) 24 { 25 /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */ 26 float p_12 = fmaf (m, C (1), C (0)); 27 float p_34 = fmaf (m, C (3), C (2)); 28 float p_56 = fmaf (m, C (5), C (4)); 29 float p_78 = fmaf (m, C (7), C (6)); 30 31 float m2 = m * m; 32 float p_02 = fmaf (m2, p_12, m); 33 float p_36 = fmaf (m2, p_56, p_34); 34 float p_79 = fmaf (m2, C (8), p_78); 35 36 float m4 = m2 * m2; 37 float p_06 = fmaf (m4, p_36, p_02); 38 39 return fmaf (m4 * p_79, m4, p_06); 40 } 41 42 static inline float 43 log1pf_inline (float x) 44 { 45 /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no 46 special-case handling. See that file for details of the algorithm. */ 47 float m = x + 1.0f; 48 int k = (asuint (m) - 0x3f400000) & 0xff800000; 49 float s = asfloat (Four - k); 50 float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f); 51 float p = eval_poly (m_scale); 52 float scale_back = (float) k * 0x1.0p-23f; 53 return fmaf (scale_back, Ln2, p); 54 } 55 56 /* Approximation for single-precision inverse tanh(x), using a simplified 57 version of log1p. Maximum error is 3.08 ULP: 58 atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5 59 want 0x1.ffb76ep-5. */ 60 float 61 atanhf (float x) 62 { 63 uint32_t ix = asuint (x); 64 uint32_t iax = ix & AbsMask; 65 uint32_t sign = ix & ~AbsMask; 66 67 if (unlikely (iax < TinyBound)) 68 return x; 69 70 if (iax == One) 71 return __math_divzero (sign); 72 73 if (unlikely (iax > One)) 74 return __math_invalidf (x); 75 76 float halfsign = asfloat (Half | sign); 77 float ax = asfloat (iax); 78 return halfsign * log1pf_inline ((2 * ax) / (1 - ax)); 79 } 80 81 PL_SIG (S, F, 1, atanh, -1.0, 1.0) 82 PL_TEST_ULP (atanhf, 2.59) 83 PL_TEST_INTERVAL (atanhf, 0, 0x1p-12, 500) 84 PL_TEST_INTERVAL (atanhf, 0x1p-12, 1, 200000) 85 PL_TEST_INTERVAL (atanhf, 1, inf, 1000) 86 PL_TEST_INTERVAL (atanhf, -0, -0x1p-12, 500) 87 PL_TEST_INTERVAL (atanhf, -0x1p-12, -1, 200000) 88 PL_TEST_INTERVAL (atanhf, -1, -inf, 1000) 89