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Diffstat (limited to 'pl/math/sv_log10_2u5.c')
-rw-r--r-- | pl/math/sv_log10_2u5.c | 89 |
1 files changed, 89 insertions, 0 deletions
diff --git a/pl/math/sv_log10_2u5.c b/pl/math/sv_log10_2u5.c new file mode 100644 index 0000000..884e201 --- /dev/null +++ b/pl/math/sv_log10_2u5.c @@ -0,0 +1,89 @@ +/* + * Double-precision SVE log10(x) function. + * + * Copyright (c) 2022-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "math_config.h" +#include "pl_sig.h" +#include "pl_test.h" + +#if SV_SUPPORTED + +#define OFF 0x3fe6900900000000 +#define N (1 << V_LOG10_TABLE_BITS) + +#define A(i) __v_log10_data.poly[i] + +static inline sv_f64_t +specialcase (sv_f64_t x, sv_f64_t y, svbool_t special) +{ + return sv_call_f64 (log10, x, y, special); +} + +/* SVE log10 algorithm. Maximum measured error is 2.46 ulps. + __sv_log10(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6 + want 0x1.fffbdf6eaa667p-6. */ +sv_f64_t +__sv_log10_x (sv_f64_t x, const svbool_t pg) +{ + sv_u64_t ix = sv_as_u64_f64 (x); + sv_u64_t top = svlsr_n_u64_x (pg, ix, 48); + + svbool_t is_special_case + = svcmpge_n_u64 (pg, svsub_n_u64_x (pg, top, 0x0010), 0x07ff0 - 0x0010); + + /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. + The range is split into N subintervals. + The ith subinterval contains z and c is near its center. */ + sv_u64_t tmp = svsub_n_u64_x (pg, ix, OFF); + sv_u64_t i + = sv_mod_n_u64_x (pg, svlsr_n_u64_x (pg, tmp, 52 - V_LOG10_TABLE_BITS), N); + sv_f64_t k + = sv_to_f64_s64_x (pg, svasr_n_s64_x (pg, sv_as_s64_u64 (tmp), 52)); + sv_f64_t z = sv_as_f64_u64 ( + svsub_u64_x (pg, ix, svand_n_u64_x (pg, tmp, 0xfffULL << 52))); + + /* log(x) = k*log(2) + log(c) + log(z/c). */ + + sv_u64_t idx = svmul_n_u64_x (pg, i, 2); + sv_f64_t invc = sv_lookup_f64_x (pg, &__v_log10_data.tab[0].invc, idx); + sv_f64_t logc = sv_lookup_f64_x (pg, &__v_log10_data.tab[0].log10c, idx); + + /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1): + r = z/c - 1 (we look up precomputed 1/c) + log(z/c) ~= P(r). */ + sv_f64_t r = sv_fma_f64_x (pg, z, invc, sv_f64 (-1.0)); + + /* hi = log(c) + k*log(2). */ + sv_f64_t w = sv_fma_n_f64_x (pg, __v_log10_data.invln10, r, logc); + sv_f64_t hi = sv_fma_n_f64_x (pg, __v_log10_data.log10_2, k, w); + + /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ + sv_f64_t r2 = svmul_f64_x (pg, r, r); + sv_f64_t y = sv_fma_n_f64_x (pg, A (3), r, sv_f64 (A (2))); + sv_f64_t p = sv_fma_n_f64_x (pg, A (1), r, sv_f64 (A (0))); + y = sv_fma_n_f64_x (pg, A (4), r2, y); + y = sv_fma_f64_x (pg, y, r2, p); + y = sv_fma_f64_x (pg, y, r2, hi); + + if (unlikely (svptest_any (pg, is_special_case))) + { + return specialcase (x, y, is_special_case); + } + return y; +} + +PL_ALIAS (__sv_log10_x, _ZGVsMxv_log10) + +PL_SIG (SV, D, 1, log10, 0.01, 11.1) +PL_TEST_ULP (__sv_log10, 1.97) +PL_TEST_INTERVAL (__sv_log10, -0.0, -0x1p126, 100) +PL_TEST_INTERVAL (__sv_log10, 0x1p-149, 0x1p-126, 4000) +PL_TEST_INTERVAL (__sv_log10, 0x1p-126, 0x1p-23, 50000) +PL_TEST_INTERVAL (__sv_log10, 0x1p-23, 1.0, 50000) +PL_TEST_INTERVAL (__sv_log10, 1.0, 100, 50000) +PL_TEST_INTERVAL (__sv_log10, 100, inf, 50000) +#endif |