1 /* 2 * Single-precision vector atanh(x) function. 3 * 4 * Copyright (c) 2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #include "sv_log1pf_inline.h" 14 15 #define One (0x3f800000) 16 #define Half (0x3f000000) 17 18 static svfloat32_t NOINLINE 19 special_case (svfloat32_t x, svfloat32_t y, svbool_t special) 20 { 21 return sv_call_f32 (atanhf, x, y, special); 22 } 23 24 /* Approximation for vector single-precision atanh(x) using modified log1p. 25 The maximum error is 2.28 ULP: 26 _ZGVsMxv_atanhf(0x1.ff1194p-5) got 0x1.ffbbbcp-5 27 want 0x1.ffbbb6p-5. */ 28 svfloat32_t SV_NAME_F1 (atanh) (svfloat32_t x, const svbool_t pg) 29 { 30 svfloat32_t ax = svabs_x (pg, x); 31 svuint32_t iax = svreinterpret_u32 (ax); 32 svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax); 33 svfloat32_t halfsign = svreinterpret_f32 (svorr_x (pg, sign, Half)); 34 svbool_t special = svcmpge (pg, iax, One); 35 36 /* Computation is performed based on the following sequence of equality: 37 * (1+x)/(1-x) = 1 + 2x/(1-x). */ 38 svfloat32_t y = svadd_x (pg, ax, ax); 39 y = svdiv_x (pg, y, svsub_x (pg, sv_f32 (1), ax)); 40 /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */ 41 y = sv_log1pf_inline (y, pg); 42 43 if (unlikely (svptest_any (pg, special))) 44 return special_case (x, svmul_x (pg, halfsign, y), special); 45 46 return svmul_x (pg, halfsign, y); 47 } 48 49 PL_SIG (SV, F, 1, atanh, -1.0, 1.0) 50 PL_TEST_ULP (SV_NAME_F1 (atanh), 2.59) 51 /* atanh is asymptotic at 1, which is the default control value - have to set 52 -c 0 specially to ensure fp exceptions are triggered correctly (choice of 53 control lane is irrelevant if fp exceptions are disabled). */ 54 PL_TEST_SYM_INTERVAL_C (SV_NAME_F1 (atanh), 0, 0x1p-12, 1000, 0) 55 PL_TEST_SYM_INTERVAL_C (SV_NAME_F1 (atanh), 0x1p-12, 1, 20000, 0) 56 PL_TEST_SYM_INTERVAL_C (SV_NAME_F1 (atanh), 1, inf, 1000, 0) 57