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/*
* Single-precision vector log10 function.
*
* Copyright (c) 2020-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "poly_advsimd_f32.h"
#include "pl_sig.h"
#include "pl_test.h"
static const struct data
{
uint32x4_t min_norm;
uint16x8_t special_bound;
float32x4_t poly[8];
float32x4_t inv_ln10, ln2;
uint32x4_t off, mantissa_mask;
} data = {
/* Use order 9 for log10(1+x), i.e. order 8 for log10(1+x)/x, with x in
[-1/3, 1/3] (offset=2/3). Max. relative error: 0x1.068ee468p-25. */
.poly = { V4 (-0x1.bcb79cp-3f), V4 (0x1.2879c8p-3f), V4 (-0x1.bcd472p-4f),
V4 (0x1.6408f8p-4f), V4 (-0x1.246f8p-4f), V4 (0x1.f0e514p-5f),
V4 (-0x1.0fc92cp-4f), V4 (0x1.f5f76ap-5f) },
.ln2 = V4 (0x1.62e43p-1f),
.inv_ln10 = V4 (0x1.bcb7b2p-2f),
.min_norm = V4 (0x00800000),
.special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
.off = V4 (0x3f2aaaab), /* 0.666667. */
.mantissa_mask = V4 (0x007fffff),
};
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, float32x4_t p, float32x4_t r2,
uint16x4_t cmp)
{
/* Fall back to scalar code. */
return v_call_f32 (log10f, x, vfmaq_f32 (y, p, r2), vmovl_u16 (cmp));
}
/* Fast implementation of AdvSIMD log10f,
uses a similar approach as AdvSIMD logf with the same offset (i.e., 2/3) and
an order 9 polynomial.
Maximum error: 3.305ulps (nearest rounding.)
_ZGVnN4v_log10f(0x1.555c16p+0) got 0x1.ffe2fap-4
want 0x1.ffe2f4p-4. */
float32x4_t VPCS_ATTR V_NAME_F1 (log10) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
uint32x4_t u = vreinterpretq_u32_f32 (x);
uint16x4_t special = vcge_u16 (vsubhn_u32 (u, d->min_norm),
vget_low_u16 (d->special_bound));
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
u = vsubq_u32 (u, d->off);
float32x4_t n = vcvtq_f32_s32 (
vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
u = vaddq_u32 (vandq_u32 (u, d->mantissa_mask), d->off);
float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
/* y = log10(1+r) + n * log10(2). */
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t poly = v_pw_horner_7_f32 (r, r2, d->poly);
/* y = Log10(2) * n + poly * InvLn(10). */
float32x4_t y = vfmaq_f32 (r, d->ln2, n);
y = vmulq_f32 (y, d->inv_ln10);
if (unlikely (v_any_u16h (special)))
return special_case (x, y, poly, r2, special);
return vfmaq_f32 (y, poly, r2);
}
PL_SIG (V, F, 1, log10, 0.01, 11.1)
PL_TEST_ULP (V_NAME_F1 (log10), 2.81)
PL_TEST_EXPECT_FENV_ALWAYS (V_NAME_F1 (log10))
PL_TEST_INTERVAL (V_NAME_F1 (log10), -0.0, -inf, 100)
PL_TEST_INTERVAL (V_NAME_F1 (log10), 0, 0x1p-126, 100)
PL_TEST_INTERVAL (V_NAME_F1 (log10), 0x1p-126, 0x1p-23, 50000)
PL_TEST_INTERVAL (V_NAME_F1 (log10), 0x1p-23, 1.0, 50000)
PL_TEST_INTERVAL (V_NAME_F1 (log10), 1.0, 100, 50000)
PL_TEST_INTERVAL (V_NAME_F1 (log10), 100, inf, 50000)
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