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/*
* Double-precision vector log2 function.
*
* Copyright (c) 2022, 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 2.59 ULP:
__v_log2(0x1.0b555054a9bd1p+0) got 0x1.fff6977bdced3p-5
want 0x1.fff6977bdced6p-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), 2.10)
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
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