diff options
Diffstat (limited to 'pl/math/v_log2_3u.c')
-rw-r--r-- | pl/math/v_log2_3u.c | 100 |
1 files changed, 100 insertions, 0 deletions
diff --git a/pl/math/v_log2_3u.c b/pl/math/v_log2_3u.c new file mode 100644 index 0000000..fac73f6 --- /dev/null +++ b/pl/math/v_log2_3u.c @@ -0,0 +1,100 @@ +/* + * Double-precision vector log2 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 InvLn2 v_f64 (0x1.71547652b82fep0) +#define N (1 << V_LOG2_TABLE_BITS) +#define OFF v_u64 (0x3fe6900900000000) +#define P(i) v_f64 (__v_log2_data.poly[i]) + +struct entry +{ + v_f64_t invc; + v_f64_t log2c; +}; + +static inline struct entry +lookup (v_u64_t i) +{ + struct entry e; +#ifdef SCALAR + e.invc = __v_log2_data.tab[i].invc; + e.log2c = __v_log2_data.tab[i].log2c; +#else + e.invc[0] = __v_log2_data.tab[i[0]].invc; + e.log2c[0] = __v_log2_data.tab[i[0]].log2c; + e.invc[1] = __v_log2_data.tab[i[1]].invc; + e.log2c[1] = __v_log2_data.tab[i[1]].log2c; +#endif + return e; +} + +VPCS_ATTR +NOINLINE static v_f64_t +specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp) +{ + return v_call_f64 (log2, x, y, cmp); +} + +/* Double-precision vector log2 routine. Implements the same algorithm as vector + log10, with coefficients and table entries scaled in extended precision. + The maximum observed error is 2.58 ULP: + __v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5 + want 0x1.fffb34198d9ddp-5. */ +VPCS_ATTR +v_f64_t V_NAME (log2) (v_f64_t x) +{ + v_u64_t ix = v_as_u64_f64 (x); + v_u64_t top = ix >> 48; + v_u64_t special + = 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. */ + v_u64_t tmp = ix - OFF; + v_u64_t i = (tmp >> (52 - V_LOG2_TABLE_BITS)) % N; + v_s64_t k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift. */ + v_u64_t iz = ix - (tmp & v_u64 (0xfffULL << 52)); + v_f64_t z = v_as_f64_u64 (iz); + struct entry e = lookup (i); + + /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */ + + v_f64_t r = v_fma_f64 (z, e.invc, v_f64 (-1.0)); + v_f64_t kd = v_to_f64_s64 (k); + v_f64_t w = v_fma_f64 (r, InvLn2, e.log2c); + + v_f64_t r2 = r * r; + v_f64_t p_23 = v_fma_f64 (P (3), r, P (2)); + v_f64_t p_01 = v_fma_f64 (P (1), r, P (0)); + v_f64_t y = v_fma_f64 (P (4), r2, p_23); + y = v_fma_f64 (r2, y, p_01); + y = v_fma_f64 (r2, y, kd + w); + + if (unlikely (v_any_u64 (special))) + return specialcase (x, y, special); + return y; +} +VPCS_ALIAS + +PL_SIG (V, D, 1, log2, 0.01, 11.1) +PL_TEST_ULP (V_NAME (log2), 2.09) +PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log2)) +PL_TEST_INTERVAL (V_NAME (log2), -0.0, -0x1p126, 100) +PL_TEST_INTERVAL (V_NAME (log2), 0x1p-149, 0x1p-126, 4000) +PL_TEST_INTERVAL (V_NAME (log2), 0x1p-126, 0x1p-23, 50000) +PL_TEST_INTERVAL (V_NAME (log2), 0x1p-23, 1.0, 50000) +PL_TEST_INTERVAL (V_NAME (log2), 1.0, 100, 50000) +PL_TEST_INTERVAL (V_NAME (log2), 100, inf, 50000) +#endif |