1 /* 2 * Double-precision SVE 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 "pl_sig.h" 10 #include "pl_test.h" 11 12 #define WANT_SV_LOG1P_K0_SHORTCUT 0 13 #include "sv_log1p_inline.h" 14 15 #define One (0x3ff0000000000000) 16 #define Half (0x3fe0000000000000) 17 18 static svfloat64_t NOINLINE 19 special_case (svfloat64_t x, svfloat64_t y, svbool_t special) 20 { 21 return sv_call_f64 (atanh, x, y, special); 22 } 23 24 /* SVE approximation for double-precision atanh, based on log1p. 25 The greatest observed error is 2.81 ULP: 26 _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6 27 want 0x1.ffd8ff31b501cp-6. */ 28 svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg) 29 { 30 31 svfloat64_t ax = svabs_x (pg, x); 32 svuint64_t iax = svreinterpret_u64 (ax); 33 svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax); 34 svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half)); 35 36 /* It is special if iax >= 1. */ 37 // svbool_t special = svcmpge (pg, iax, One); 38 svbool_t special = svacge (pg, x, 1.0); 39 40 /* Computation is performed based on the following sequence of equality: 41 (1+x)/(1-x) = 1 + 2x/(1-x). */ 42 svfloat64_t y; 43 y = svadd_x (pg, ax, ax); 44 y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax)); 45 /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */ 46 y = sv_log1p_inline (y, pg); 47 48 if (unlikely (svptest_any (pg, special))) 49 return special_case (x, svmul_x (pg, halfsign, y), special); 50 return svmul_x (pg, halfsign, y); 51 } 52 53 PL_SIG (SV, D, 1, atanh, -1.0, 1.0) 54 PL_TEST_ULP (SV_NAME_D1 (atanh), 3.32) 55 /* atanh is asymptotic at 1, which is the default control value - have to set 56 -c 0 specially to ensure fp exceptions are triggered correctly (choice of 57 control lane is irrelevant if fp exceptions are disabled). */ 58 PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 0, 0x1p-23, 10000, 0) 59 PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 0x1p-23, 1, 90000, 0) 60 PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 1, inf, 100, 0) 61