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/*
* Single-precision vector/SVE log2 function.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.h"
static const struct data
{
float poly_02468[5];
float poly_1357[4];
} data = {
.poly_1357 = {
/* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs
1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane
variant of MLA intrinsic. */
-0x1.715458p-1f, -0x1.7171a4p-2f, -0x1.e5143ep-3f, -0x1.c675bp-3f
},
.poly_02468 = { 0x1.715476p0f, 0x1.ec701cp-2f, 0x1.27a0b8p-2f,
0x1.9d8ecap-3f, 0x1.9e495p-3f },
};
#define Min (0x00800000)
#define Max (0x7f800000)
#define Thres (0x7f000000) /* Max - Min. */
#define MantissaMask (0x007fffff)
#define Off (0x3f2aaaab) /* 0.666667. */
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
{
return sv_call_f32 (log2f, x, y, cmp);
}
/* Optimised implementation of SVE log2f, using the same algorithm
and polynomial as AdvSIMD log2f.
Maximum error is 2.48 ULPs:
SV_NAME_F1 (log2)(0x1.558174p+0) got 0x1.a9be84p-2
want 0x1.a9be8p-2. */
svfloat32_t SV_NAME_F1 (log2) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svuint32_t u = svreinterpret_u32 (x);
svbool_t special = svcmpge (pg, svsub_x (pg, u, Min), Thres);
/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
u = svsub_x (pg, u, Off);
svfloat32_t n = svcvt_f32_x (
pg, svasr_x (pg, svreinterpret_s32 (u), 23)); /* Sign-extend. */
u = svand_x (pg, u, MantissaMask);
u = svadd_x (pg, u, Off);
svfloat32_t r = svsub_x (pg, svreinterpret_f32 (u), 1.0f);
/* y = log2(1+r) + n. */
svfloat32_t r2 = svmul_x (pg, r, r);
/* Evaluate polynomial using pairwise Horner scheme. */
svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]);
svfloat32_t q_01 = svmla_lane (sv_f32 (d->poly_02468[0]), r, p_1357, 0);
svfloat32_t q_23 = svmla_lane (sv_f32 (d->poly_02468[1]), r, p_1357, 1);
svfloat32_t q_45 = svmla_lane (sv_f32 (d->poly_02468[2]), r, p_1357, 2);
svfloat32_t q_67 = svmla_lane (sv_f32 (d->poly_02468[3]), r, p_1357, 3);
svfloat32_t y = svmla_x (pg, q_67, r2, sv_f32 (d->poly_02468[4]));
y = svmla_x (pg, q_45, r2, y);
y = svmla_x (pg, q_23, r2, y);
y = svmla_x (pg, q_01, r2, y);
if (unlikely (svptest_any (pg, special)))
return special_case (x, svmla_x (svnot_z (pg, special), n, r, y), special);
return svmla_x (pg, n, r, y);
}
PL_SIG (SV, F, 1, log2, 0.01, 11.1)
PL_TEST_ULP (SV_NAME_F1 (log2), 1.99)
PL_TEST_EXPECT_FENV_ALWAYS (SV_NAME_F1 (log2))
PL_TEST_INTERVAL (SV_NAME_F1 (log2), -0.0, -0x1p126, 4000)
PL_TEST_INTERVAL (SV_NAME_F1 (log2), 0.0, 0x1p-126, 4000)
PL_TEST_INTERVAL (SV_NAME_F1 (log2), 0x1p-126, 0x1p-23, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (log2), 0x1p-23, 1.0, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (log2), 1.0, 100, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (log2), 100, inf, 50000)
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