1 /* 2 * Double-precision SVE acosh(x) function. 3 * Copyright (c) 2023, Arm Limited. 4 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 */ 6 7 #include "sv_math.h" 8 #include "pl_sig.h" 9 #include "pl_test.h" 10 11 #define WANT_SV_LOG1P_K0_SHORTCUT 1 12 #include "sv_log1p_inline.h" 13 14 #define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */ 15 #define OneTop 0x3ff 16 17 static NOINLINE svfloat64_t 18 special_case (svfloat64_t x, svfloat64_t y, svbool_t special) 19 { 20 return sv_call_f64 (acosh, x, y, special); 21 } 22 23 /* SVE approximation for double-precision acosh, based on log1p. 24 The largest observed error is 3.19 ULP in the region where the 25 argument to log1p falls in the k=0 interval, i.e. x close to 1: 26 SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2 27 want 0x1.ed23399f51373p-2. */ 28 svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg) 29 { 30 svuint64_t itop = svlsr_x (pg, svreinterpret_u64 (x), 52); 31 /* (itop - OneTop) >= (BigBoundTop - OneTop). */ 32 svbool_t special = svcmpge (pg, svsub_x (pg, itop, OneTop), sv_u64 (0x1ff)); 33 34 svfloat64_t xm1 = svsub_x (pg, x, 1); 35 svfloat64_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1)); 36 svfloat64_t y = sv_log1p_inline (svadd_x (pg, xm1, svsqrt_x (pg, u)), pg); 37 38 /* Fall back to scalar routine for special lanes. */ 39 if (unlikely (svptest_any (pg, special))) 40 return special_case (x, y, special); 41 42 return y; 43 } 44 45 PL_SIG (SV, D, 1, acosh, 1.0, 10.0) 46 PL_TEST_ULP (SV_NAME_D1 (acosh), 2.69) 47 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 1, 0x1p511, 90000) 48 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 0x1p511, inf, 10000) 49 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 0, 1, 1000) 50 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), -0, -inf, 10000) 51