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Diffstat (limited to 'pl/math/v_log10_2u5.c')
-rw-r--r-- | pl/math/v_log10_2u5.c | 110 |
1 files changed, 110 insertions, 0 deletions
diff --git a/pl/math/v_log10_2u5.c b/pl/math/v_log10_2u5.c new file mode 100644 index 0000000..86d398c --- /dev/null +++ b/pl/math/v_log10_2u5.c @@ -0,0 +1,110 @@ +/* + * Double-precision vector log10(x) function. + * + * Copyright (c) 2022-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "v_math.h" +#include "include/mathlib.h" +#include "pl_sig.h" +#include "pl_test.h" + +#if V_SUPPORTED + +#define A(i) v_f64 (__v_log10_data.poly[i]) +#define T(s, i) __v_log10_data.tab[i].s +#define Ln2 v_f64 (0x1.62e42fefa39efp-1) +#define N (1 << V_LOG10_TABLE_BITS) +#define OFF v_u64 (0x3fe6900900000000) + +struct entry +{ + v_f64_t invc; + v_f64_t log10c; +}; + +static inline struct entry +lookup (v_u64_t i) +{ + struct entry e; +#ifdef SCALAR + e.invc = T (invc, i); + e.log10c = T (log10c, i); +#else + e.invc[0] = T (invc, i[0]); + e.log10c[0] = T (log10c, i[0]); + e.invc[1] = T (invc, i[1]); + e.log10c[1] = T (log10c, i[1]); +#endif + return e; +} + +VPCS_ATTR +inline static v_f64_t +specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp) +{ + return v_call_f64 (log10, x, y, cmp); +} + +/* Our implementation of v_log10 is a slight modification of v_log (1.660ulps). + Max ULP error: < 2.5 ulp (nearest rounding.) + Maximum measured at 2.46 ulp for x in [0.96, 0.97] + __v_log10(0x1.13192407fcb46p+0) got 0x1.fff6be3cae4bbp-6 + want 0x1.fff6be3cae4b9p-6 + -0.459999 ulp err 1.96. */ +VPCS_ATTR +v_f64_t V_NAME (log10) (v_f64_t x) +{ + v_f64_t z, r, r2, p, y, kd, hi; + v_u64_t ix, iz, tmp, top, i, cmp; + v_s64_t k; + struct entry e; + + ix = v_as_u64_f64 (x); + top = ix >> 48; + cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 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. */ + tmp = ix - OFF; + i = (tmp >> (52 - V_LOG10_TABLE_BITS)) % N; + k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift. */ + iz = ix - (tmp & v_u64 (0xfffULL << 52)); + z = v_as_f64_u64 (iz); + e = lookup (i); + + /* log10(x) = log1p(z/c-1)/log(10) + log10(c) + k*log10(2). */ + r = v_fma_f64 (z, e.invc, v_f64 (-1.0)); + kd = v_to_f64_s64 (k); + + /* hi = r / log(10) + log10(c) + k*log10(2). + Constants in `v_log10_data.c` are computed (in extended precision) as + e.log10c := e.logc * ivln10. */ + v_f64_t w = v_fma_f64 (r, v_f64 (__v_log10_data.invln10), e.log10c); + + /* y = log10(1+r) + n * log10(2). */ + hi = v_fma_f64 (kd, v_f64 (__v_log10_data.log10_2), w); + + /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ + r2 = r * r; + y = v_fma_f64 (A (3), r, A (2)); + p = v_fma_f64 (A (1), r, A (0)); + y = v_fma_f64 (A (4), r2, y); + y = v_fma_f64 (y, r2, p); + y = v_fma_f64 (y, r2, hi); + + if (unlikely (v_any_u64 (cmp))) + return specialcase (x, y, cmp); + return y; +} +VPCS_ALIAS + +PL_SIG (V, D, 1, log10, 0.01, 11.1) +PL_TEST_ULP (V_NAME (log10), 1.97) +PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log10)) +PL_TEST_INTERVAL (V_NAME (log10), 0, 0xffff000000000000, 10000) +PL_TEST_INTERVAL (V_NAME (log10), 0x1p-4, 0x1p4, 400000) +PL_TEST_INTERVAL (V_NAME (log10), 0, inf, 400000) +#endif |