diff options
Diffstat (limited to 'pl/math/sv_erf_3u.c')
| -rw-r--r-- | pl/math/sv_erf_3u.c | 103 |
1 files changed, 103 insertions, 0 deletions
diff --git a/pl/math/sv_erf_3u.c b/pl/math/sv_erf_3u.c new file mode 100644 index 0000000..bec7f8a --- /dev/null +++ b/pl/math/sv_erf_3u.c @@ -0,0 +1,103 @@ +/* + * Double-precision SVE erf(x) function. + * + * Copyright (c) 2020-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "pl_sig.h" +#include "pl_test.h" + +#if SV_SUPPORTED + +#define Scale (8.0) +#define AbsMask (0x7fffffffffffffff) + +static NOINLINE sv_f64_t +__sv_erf_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp) +{ + return sv_call_f64 (erf, x, y, cmp); +} + +/* Optimized double precision SVE error function erf. + Maximum observed error is 2.62 ULP: + __sv_erf(0x1.79cab7e3078fap+2) got 0x1.0000000000001p+0 + want 0x1.fffffffffffffp-1. */ +sv_f64_t +__sv_erf_x (sv_f64_t x, const svbool_t pg) +{ + /* Use top 16 bits to test for special cases and small values. */ + sv_u64_t ix = sv_as_u64_f64 (x); + sv_u64_t atop = svand_n_u64_x (pg, svlsr_n_u64_x (pg, ix, 48), 0x7fff); + + /* Handle both inf/nan as well as small values (|x|<2^-28). */ + svbool_t cmp + = svcmpge_n_u64 (pg, svsub_n_u64_x (pg, atop, 0x3e30), 0x7ff0 - 0x3e30); + + /* Get sign and absolute value. */ + sv_f64_t a = sv_as_f64_u64 (svand_n_u64_x (pg, ix, AbsMask)); + sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask); + + /* i = trunc(Scale*x). */ + sv_f64_t a_scale = svmul_n_f64_x (pg, a, Scale); + /* Saturate index of intervals. */ + svbool_t a_lt_6 = svcmplt_n_u64 (pg, atop, 0x4018); + sv_u64_t i = svcvt_u64_f64_m (sv_u64 (V_ERF_NINTS - 1), a_lt_6, a_scale); + + /* Load polynomial coefficients. */ + sv_f64_t P_0 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[0], i); + sv_f64_t P_1 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[1], i); + sv_f64_t P_2 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[2], i); + sv_f64_t P_3 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[3], i); + sv_f64_t P_4 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[4], i); + sv_f64_t P_5 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[5], i); + sv_f64_t P_6 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[6], i); + sv_f64_t P_7 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[7], i); + sv_f64_t P_8 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[8], i); + sv_f64_t P_9 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[9], i); + + /* Get shift and scale. */ + sv_f64_t shift = sv_lookup_f64_x (pg, __v_erf_data.shifts, i); + + /* Transform polynomial variable. + Set z = 0 in the boring domain to avoid overflow. */ + sv_f64_t z = svmla_f64_m (a_lt_6, shift, sv_f64 (Scale), a); + + /* Evaluate polynomial P(z) using level-2 Estrin. */ + sv_f64_t r1 = sv_fma_f64_x (pg, z, P_1, P_0); + sv_f64_t r2 = sv_fma_f64_x (pg, z, P_3, P_2); + sv_f64_t r3 = sv_fma_f64_x (pg, z, P_5, P_4); + sv_f64_t r4 = sv_fma_f64_x (pg, z, P_7, P_6); + sv_f64_t r5 = sv_fma_f64_x (pg, z, P_9, P_8); + + sv_f64_t z2 = svmul_f64_x (pg, z, z); + sv_f64_t z4 = svmul_f64_x (pg, z2, z2); + + sv_f64_t q2 = sv_fma_f64_x (pg, r4, z2, r3); + sv_f64_t q1 = sv_fma_f64_x (pg, r2, z2, r1); + + sv_f64_t y = sv_fma_f64_x (pg, z4, r5, q2); + y = sv_fma_f64_x (pg, z4, y, q1); + + /* y = erf(x) if x > 0, -erf(-x) otherwise. */ + y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign)); + + if (unlikely (svptest_any (pg, cmp))) + return __sv_erf_specialcase (x, y, cmp); + return y; +} + +PL_ALIAS (__sv_erf_x, _ZGVsMxv_erf) + +PL_SIG (SV, D, 1, erf, -4.0, 4.0) +PL_TEST_ULP (__sv_erf, 2.13) +PL_TEST_INTERVAL (__sv_erf, 0, 0x1p-28, 20000) +PL_TEST_INTERVAL (__sv_erf, 0x1p-28, 1, 60000) +PL_TEST_INTERVAL (__sv_erf, 1, 0x1p28, 60000) +PL_TEST_INTERVAL (__sv_erf, 0x1p28, inf, 20000) +PL_TEST_INTERVAL (__sv_erf, -0, -0x1p-28, 20000) +PL_TEST_INTERVAL (__sv_erf, -0x1p-28, -1, 60000) +PL_TEST_INTERVAL (__sv_erf, -1, -0x1p28, 60000) +PL_TEST_INTERVAL (__sv_erf, -0x1p28, -inf, 20000) +#endif |