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loops_exponent_log.dispatch.c.src
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loops_exponent_log.dispatch.c.src
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/*@targets
** $maxopt baseline
** (avx2 fma3) avx512f avx512_skx
**/
#define _UMATHMODULE
#define _MULTIARRAYMODULE
#define NPY_NO_DEPRECATED_API NPY_API_VERSION
#include <float.h>
#include "numpy/npy_math.h"
#include "simd/simd.h"
#include "loops_utils.h"
#include "loops.h"
#include "lowlevel_strided_loops.h"
// Provides the various *_LOOP macros
#include "fast_loop_macros.h"
#include "npy_simd_data.h"
// TODO: tweak & replace raw SIMD with NPYV
/********************************************************************************
** bunch of helper functions used in ISA_exp/log_FLOAT
********************************************************************************/
#if !defined(_MSC_VER) && defined(NPY_HAVE_AVX512F)
/**
* For somehow MSVC commit aggressive optimization lead
* to raises 'RuntimeWarning: RuntimeWarning: overflow encountered in exp'
*
* the issue mainly caused by '_mm512_maskz_loadu_ps', we need to
* investigate about it while moving to NPYV.
*/
#define SIMD_AVX512F
#elif defined(NPY_HAVE_AVX2) && defined(NPY_HAVE_FMA3)
#define SIMD_AVX2_FMA3
#endif
#if !defined(_MSC_VER) && defined(NPY_HAVE_AVX512_SKX)
#define SIMD_AVX512_SKX
#endif
#if defined(SIMD_AVX512F) && !(defined(__clang__) && (__clang_major__ < 10 || \
(__clang_major__ == 10 && __clang_minor__ < 1)))
#define SIMD_AVX512F_NOCLANG_BUG
#endif
#ifdef SIMD_AVX2_FMA3
static NPY_INLINE __m256
fma_get_full_load_mask_ps(void)
{
return _mm256_set1_ps(-1.0);
}
static NPY_INLINE __m256i
fma_get_full_load_mask_pd(void)
{
return _mm256_castpd_si256(_mm256_set1_pd(-1.0));
}
static NPY_INLINE __m256
fma_get_partial_load_mask_ps(const npy_int num_elem, const npy_int num_lanes)
{
float maskint[16] = {-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,
1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0};
float* addr = maskint + num_lanes - num_elem;
return _mm256_loadu_ps(addr);
}
static NPY_INLINE __m256i
fma_get_partial_load_mask_pd(const npy_int num_elem, const npy_int num_lanes)
{
npy_int maskint[16] = {-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1};
npy_int* addr = maskint + 2*num_lanes - 2*num_elem;
return _mm256_loadu_si256((__m256i*) addr);
}
static NPY_INLINE __m256
fma_masked_gather_ps(__m256 src,
npy_float* addr,
__m256i vindex,
__m256 mask)
{
return _mm256_mask_i32gather_ps(src, addr, vindex, mask, 4);
}
static NPY_INLINE __m256d
fma_masked_gather_pd(__m256d src,
npy_double* addr,
__m128i vindex,
__m256d mask)
{
return _mm256_mask_i32gather_pd(src, addr, vindex, mask, 8);
}
static NPY_INLINE __m256
fma_masked_load_ps(__m256 mask, npy_float* addr)
{
return _mm256_maskload_ps(addr, _mm256_cvtps_epi32(mask));
}
static NPY_INLINE __m256d
fma_masked_load_pd(__m256i mask, npy_double* addr)
{
return _mm256_maskload_pd(addr, mask);
}
static NPY_INLINE __m256
fma_set_masked_lanes_ps(__m256 x, __m256 val, __m256 mask)
{
return _mm256_blendv_ps(x, val, mask);
}
static NPY_INLINE __m256d
fma_set_masked_lanes_pd(__m256d x, __m256d val, __m256d mask)
{
return _mm256_blendv_pd(x, val, mask);
}
static NPY_INLINE __m256
fma_blend(__m256 x, __m256 y, __m256 ymask)
{
return _mm256_blendv_ps(x, y, ymask);
}
static NPY_INLINE __m256
fma_invert_mask_ps(__m256 ymask)
{
return _mm256_andnot_ps(ymask, _mm256_set1_ps(-1.0));
}
static NPY_INLINE __m256i
fma_invert_mask_pd(__m256i ymask)
{
return _mm256_andnot_si256(ymask, _mm256_set1_epi32(0xFFFFFFFF));
}
static NPY_INLINE __m256
fma_get_exponent(__m256 x)
{
/*
* Special handling of denormals:
* 1) Multiply denormal elements with 2**100 (0x71800000)
* 2) Get the 8 bits of unbiased exponent
* 3) Subtract 100 from exponent of denormals
*/
__m256 two_power_100 = _mm256_castsi256_ps(_mm256_set1_epi32(0x71800000));
__m256 denormal_mask = _mm256_cmp_ps(x, _mm256_set1_ps(FLT_MIN), _CMP_LT_OQ);
__m256 normal_mask = _mm256_cmp_ps(x, _mm256_set1_ps(FLT_MIN), _CMP_GE_OQ);
/*
* The volatile is probably unnecessary now since we compile clang with
* `-ftrapping-math`: https://github.com/numpy/numpy/issues/18005
*/
volatile __m256 temp1 = _mm256_blendv_ps(x, _mm256_set1_ps(0.0f), normal_mask);
__m256 temp = _mm256_mul_ps(temp1, two_power_100);
x = _mm256_blendv_ps(x, temp, denormal_mask);
__m256 exp = _mm256_cvtepi32_ps(
_mm256_sub_epi32(
_mm256_srli_epi32(
_mm256_castps_si256(x), 23),_mm256_set1_epi32(0x7E)));
__m256 denorm_exp = _mm256_sub_ps(exp, _mm256_set1_ps(100.0f));
return _mm256_blendv_ps(exp, denorm_exp, denormal_mask);
}
static NPY_INLINE __m256
fma_get_mantissa(__m256 x)
{
/*
* Special handling of denormals:
* 1) Multiply denormal elements with 2**100 (0x71800000)
* 2) Get the 23 bits of mantissa
* 3) Mantissa for denormals is not affected by the multiplication
*/
__m256 two_power_100 = _mm256_castsi256_ps(_mm256_set1_epi32(0x71800000));
__m256 denormal_mask = _mm256_cmp_ps(x, _mm256_set1_ps(FLT_MIN), _CMP_LT_OQ);
__m256 normal_mask = _mm256_cmp_ps(x, _mm256_set1_ps(FLT_MIN), _CMP_GE_OQ);
/*
* The volatile is probably unnecessary now since we compile clang with
* `-ftrapping-math`: https://github.com/numpy/numpy/issues/18005
*/
volatile __m256 temp1 = _mm256_blendv_ps(x, _mm256_set1_ps(0.0f), normal_mask);
__m256 temp = _mm256_mul_ps(temp1, two_power_100);
x = _mm256_blendv_ps(x, temp, denormal_mask);
__m256i mantissa_bits = _mm256_set1_epi32(0x7fffff);
__m256i exp_126_bits = _mm256_set1_epi32(126 << 23);
return _mm256_castsi256_ps(
_mm256_or_si256(
_mm256_and_si256(
_mm256_castps_si256(x), mantissa_bits), exp_126_bits));
}
static NPY_INLINE __m256
fma_scalef_ps(__m256 poly, __m256 quadrant)
{
/*
* Handle denormals (which occur when quadrant <= -125):
* 1) This function computes poly*(2^quad) by adding the exponent of
poly to quad
* 2) When quad <= -125, the output is a denormal and the above logic
breaks down
* 3) To handle such cases, we split quadrant: -125 + (quadrant + 125)
* 4) poly*(2^-125) is computed the usual way
* 5) 2^(quad-125) can be computed by: 2 << abs(quad-125)
* 6) The final div operation generates the denormal
*/
__m256 minquadrant = _mm256_set1_ps(-125.0f);
__m256 denormal_mask = _mm256_cmp_ps(quadrant, minquadrant, _CMP_LE_OQ);
if (_mm256_movemask_ps(denormal_mask) != 0x0000) {
__m256 quad_diff = _mm256_sub_ps(quadrant, minquadrant);
quad_diff = _mm256_sub_ps(_mm256_setzero_ps(), quad_diff);
quad_diff = _mm256_blendv_ps(_mm256_setzero_ps(), quad_diff, denormal_mask);
__m256i two_power_diff = _mm256_sllv_epi32(
_mm256_set1_epi32(1), _mm256_cvtps_epi32(quad_diff));
quadrant = _mm256_max_ps(quadrant, minquadrant); //keep quadrant >= -126
__m256i exponent = _mm256_slli_epi32(_mm256_cvtps_epi32(quadrant), 23);
poly = _mm256_castsi256_ps(
_mm256_add_epi32(
_mm256_castps_si256(poly), exponent));
__m256 denorm_poly = _mm256_div_ps(poly, _mm256_cvtepi32_ps(two_power_diff));
return _mm256_blendv_ps(poly, denorm_poly, denormal_mask);
}
else {
__m256i exponent = _mm256_slli_epi32(_mm256_cvtps_epi32(quadrant), 23);
poly = _mm256_castsi256_ps(
_mm256_add_epi32(
_mm256_castps_si256(poly), exponent));
return poly;
}
}
#endif // SIMD_AVX2_FMA3
#ifdef SIMD_AVX512F
static NPY_INLINE NPY_GCC_OPT_3 NPY_GCC_TARGET_AVX512F __mmask16
avx512_get_full_load_mask_ps(void)
{
return 0xFFFF;
}
static NPY_INLINE __mmask8
avx512_get_full_load_mask_pd(void)
{
return 0xFF;
}
static NPY_INLINE __mmask16
avx512_get_partial_load_mask_ps(const npy_int num_elem, const npy_int total_elem)
{
return (0x0001 << num_elem) - 0x0001;
}
static NPY_INLINE __mmask8
avx512_get_partial_load_mask_pd(const npy_int num_elem, const npy_int total_elem)
{
return (0x01 << num_elem) - 0x01;
}
static NPY_INLINE __m512
avx512_masked_gather_ps(__m512 src,
npy_float* addr,
__m512i vindex,
__mmask16 kmask)
{
return _mm512_mask_i32gather_ps(src, kmask, vindex, addr, 4);
}
static NPY_INLINE __m512d
avx512_masked_gather_pd(__m512d src,
npy_double* addr,
__m256i vindex,
__mmask8 kmask)
{
return _mm512_mask_i32gather_pd(src, kmask, vindex, addr, 8);
}
static NPY_INLINE __m512
avx512_masked_load_ps(__mmask16 mask, npy_float* addr)
{
return _mm512_maskz_loadu_ps(mask, (__m512 *)addr);
}
static NPY_INLINE __m512d
avx512_masked_load_pd(__mmask8 mask, npy_double* addr)
{
return _mm512_maskz_loadu_pd(mask, (__m512d *)addr);
}
static NPY_INLINE __m512
avx512_set_masked_lanes_ps(__m512 x, __m512 val, __mmask16 mask)
{
return _mm512_mask_blend_ps(mask, x, val);
}
static NPY_INLINE __m512d
avx512_set_masked_lanes_pd(__m512d x, __m512d val, __mmask8 mask)
{
return _mm512_mask_blend_pd(mask, x, val);
}
static NPY_INLINE __m512
avx512_blend(__m512 x, __m512 y, __mmask16 ymask)
{
return _mm512_mask_mov_ps(x, ymask, y);
}
static NPY_INLINE __mmask16
avx512_invert_mask_ps(__mmask16 ymask)
{
return _mm512_knot(ymask);
}
static NPY_INLINE __mmask8
avx512_invert_mask_pd(__mmask8 ymask)
{
return _mm512_knot(ymask);
}
static NPY_INLINE __m512
avx512_get_exponent(__m512 x)
{
return _mm512_add_ps(_mm512_getexp_ps(x), _mm512_set1_ps(1.0f));
}
static NPY_INLINE __m512
avx512_get_mantissa(__m512 x)
{
return _mm512_getmant_ps(x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
}
static NPY_INLINE __m512
avx512_scalef_ps(__m512 poly, __m512 quadrant)
{
return _mm512_scalef_ps(poly, quadrant);
}
static NPY_INLINE __m512d
avx512_permute_x4var_pd(__m512d t0,
__m512d t1,
__m512d t2,
__m512d t3,
__m512i index)
{
__mmask8 lut_mask = _mm512_cmp_epi64_mask(
_mm512_and_epi64(_mm512_set1_epi64(0x10ULL), index),
_mm512_set1_epi64(0), _MM_CMPINT_GT);
__m512d res1 = _mm512_permutex2var_pd(t0, index, t1);
__m512d res2 = _mm512_permutex2var_pd(t2, index, t3);
return _mm512_mask_blend_pd(lut_mask, res1, res2);
}
static NPY_INLINE __m512d
avx512_permute_x8var_pd(__m512d t0, __m512d t1, __m512d t2, __m512d t3,
__m512d t4, __m512d t5, __m512d t6, __m512d t7,
__m512i index)
{
__mmask8 lut_mask = _mm512_cmp_epi64_mask(
_mm512_and_epi64(_mm512_set1_epi64(0x20ULL), index),
_mm512_set1_epi64(0), _MM_CMPINT_GT);
__m512d res1 = avx512_permute_x4var_pd(t0, t1, t2, t3, index);
__m512d res2 = avx512_permute_x4var_pd(t4, t5, t6, t7, index);
return _mm512_mask_blend_pd(lut_mask, res1, res2);
}
#endif // SIMD_AVX512F
/********************************************************************************
** Defining the SIMD kernels
********************************************************************************/
/**begin repeat
* #ISA = FMA, AVX512F#
* #isa = fma, avx512#
* #vtype = __m256, __m512#
* #vsize = 256, 512#
* #BYTES = 32, 64#
* #NUM_LANES = 8, 16#
* #mask = __m256, __mmask16#
* #vsub = , _mask#
* #or_masks =_mm256_or_ps, _mm512_kor#
* #and_masks =_mm256_and_ps, _mm512_kand#
* #xor_masks =_mm256_xor_ps, _mm512_kxor#
* #fmadd = _mm256_fmadd_ps, _mm512_fmadd_ps#
* #mask_to_int = _mm256_movemask_ps, #
* #full_mask= 0xFF, 0xFFFF#
* #masked_store = _mm256_maskstore_ps, _mm512_mask_storeu_ps#
* #cvtps_epi32 = _mm256_cvtps_epi32, #
* #CHK = SIMD_AVX2_FMA3, SIMD_AVX512F#
*/
#ifdef @CHK@
/*
* Vectorized Cody-Waite range reduction technique
* Performs the reduction step x* = x - y*C in three steps:
* 1) x* = x - y*c1
* 2) x* = x - y*c2
* 3) x* = x - y*c3
* c1, c2 are exact floating points, c3 = C - c1 - c2 simulates higher precision
*/
static NPY_INLINE @vtype@
simd_range_reduction(@vtype@ x, @vtype@ y, @vtype@ c1, @vtype@ c2, @vtype@ c3)
{
@vtype@ reduced_x = @fmadd@(y, c1, x);
reduced_x = @fmadd@(y, c2, reduced_x);
reduced_x = @fmadd@(y, c3, reduced_x);
return reduced_x;
}
/*
* Vectorized implementation of exp using AVX2 and AVX512:
* 1) if x >= xmax; return INF (overflow)
* 2) if x <= xmin; return 0.0f (underflow)
* 3) Range reduction (using Coyd-Waite):
* a) y = x - k*ln(2); k = rint(x/ln(2)); y \in [0, ln(2)]
* 4) Compute exp(y) = P/Q, ratio of 2 polynomials P and Q
* b) P = 5th order and Q = 2nd order polynomials obtained from Remez's
* algorithm (mini-max polynomial approximation)
* 5) Compute exp(x) = exp(y) * 2^k
* 6) Max ULP error measured across all 32-bit FP's = 2.52 (x = 0xc2781e37)
* 7) Max relative error measured across all 32-bit FP's= 2.1264E-07 (for the
* same x = 0xc2781e37)
*/
static void
simd_exp_FLOAT(npy_float * op,
npy_float * ip,
const npy_intp array_size,
const npy_intp steps)
{
const npy_intp stride = steps/(npy_intp)sizeof(npy_float);
const npy_int num_lanes = @BYTES@/(npy_intp)sizeof(npy_float);
npy_float xmax = 88.72283935546875f;
npy_float xmin = -103.97208404541015625f;
/*
* Note: while generally indices are npy_intp, we ensure that our maximum index
* will fit in an int32 as a precondition for this function via
* IS_OUTPUT_BLOCKABLE_UNARY
*/
npy_int32 indexarr[16];
for (npy_int32 ii = 0; ii < 16; ii++) {
indexarr[ii] = ii*stride;
}
/* Load up frequently used constants */
@vtype@ codyw_c1 = _mm@vsize@_set1_ps(NPY_CODY_WAITE_LOGE_2_HIGHf);
@vtype@ codyw_c2 = _mm@vsize@_set1_ps(NPY_CODY_WAITE_LOGE_2_LOWf);
@vtype@ exp_p0 = _mm@vsize@_set1_ps(NPY_COEFF_P0_EXPf);
@vtype@ exp_p1 = _mm@vsize@_set1_ps(NPY_COEFF_P1_EXPf);
@vtype@ exp_p2 = _mm@vsize@_set1_ps(NPY_COEFF_P2_EXPf);
@vtype@ exp_p3 = _mm@vsize@_set1_ps(NPY_COEFF_P3_EXPf);
@vtype@ exp_p4 = _mm@vsize@_set1_ps(NPY_COEFF_P4_EXPf);
@vtype@ exp_p5 = _mm@vsize@_set1_ps(NPY_COEFF_P5_EXPf);
@vtype@ exp_q0 = _mm@vsize@_set1_ps(NPY_COEFF_Q0_EXPf);
@vtype@ exp_q1 = _mm@vsize@_set1_ps(NPY_COEFF_Q1_EXPf);
@vtype@ exp_q2 = _mm@vsize@_set1_ps(NPY_COEFF_Q2_EXPf);
@vtype@ cvt_magic = _mm@vsize@_set1_ps(NPY_RINT_CVT_MAGICf);
@vtype@ log2e = _mm@vsize@_set1_ps(NPY_LOG2Ef);
@vtype@ inf = _mm@vsize@_set1_ps(NPY_INFINITYF);
@vtype@ zeros_f = _mm@vsize@_set1_ps(0.0f);
@vtype@ poly, num_poly, denom_poly, quadrant;
@vtype@i vindex = _mm@vsize@_loadu_si@vsize@((@vtype@i*)&indexarr[0]);
@mask@ xmax_mask, xmin_mask, nan_mask, inf_mask;
@mask@ overflow_mask = @isa@_get_partial_load_mask_ps(0, num_lanes);
@mask@ underflow_mask = @isa@_get_partial_load_mask_ps(0, num_lanes);
@mask@ load_mask = @isa@_get_full_load_mask_ps();
npy_intp num_remaining_elements = array_size;
while (num_remaining_elements > 0) {
if (num_remaining_elements < num_lanes) {
load_mask = @isa@_get_partial_load_mask_ps(num_remaining_elements,
num_lanes);
}
@vtype@ x;
if (stride == 1) {
x = @isa@_masked_load_ps(load_mask, ip);
}
else {
x = @isa@_masked_gather_ps(zeros_f, ip, vindex, load_mask);
}
nan_mask = _mm@vsize@_cmp_ps@vsub@(x, x, _CMP_NEQ_UQ);
x = @isa@_set_masked_lanes_ps(x, zeros_f, nan_mask);
xmax_mask = _mm@vsize@_cmp_ps@vsub@(x, _mm@vsize@_set1_ps(xmax), _CMP_GE_OQ);
xmin_mask = _mm@vsize@_cmp_ps@vsub@(x, _mm@vsize@_set1_ps(xmin), _CMP_LE_OQ);
inf_mask = _mm@vsize@_cmp_ps@vsub@(x, inf, _CMP_EQ_OQ);
overflow_mask = @or_masks@(overflow_mask,
@xor_masks@(xmax_mask, inf_mask));
underflow_mask = @or_masks@(underflow_mask, xmin_mask);
x = @isa@_set_masked_lanes_ps(x, zeros_f, @or_masks@(
@or_masks@(nan_mask, xmin_mask), xmax_mask));
quadrant = _mm@vsize@_mul_ps(x, log2e);
/* round to nearest */
quadrant = _mm@vsize@_add_ps(quadrant, cvt_magic);
quadrant = _mm@vsize@_sub_ps(quadrant, cvt_magic);
/* Cody-Waite's range reduction algorithm */
x = simd_range_reduction(x, quadrant, codyw_c1, codyw_c2, zeros_f);
num_poly = @fmadd@(exp_p5, x, exp_p4);
num_poly = @fmadd@(num_poly, x, exp_p3);
num_poly = @fmadd@(num_poly, x, exp_p2);
num_poly = @fmadd@(num_poly, x, exp_p1);
num_poly = @fmadd@(num_poly, x, exp_p0);
denom_poly = @fmadd@(exp_q2, x, exp_q1);
denom_poly = @fmadd@(denom_poly, x, exp_q0);
poly = _mm@vsize@_div_ps(num_poly, denom_poly);
/*
* compute val = poly * 2^quadrant; which is same as adding the
* exponent of quadrant to the exponent of poly. quadrant is an int,
* so extracting exponent is simply extracting 8 bits.
*/
poly = @isa@_scalef_ps(poly, quadrant);
/*
* elem > xmax; return inf
* elem < xmin; return 0.0f
* elem = +/- nan, return nan
*/
poly = @isa@_set_masked_lanes_ps(poly, _mm@vsize@_set1_ps(NPY_NANF), nan_mask);
poly = @isa@_set_masked_lanes_ps(poly, inf, xmax_mask);
poly = @isa@_set_masked_lanes_ps(poly, zeros_f, xmin_mask);
@masked_store@(op, @cvtps_epi32@(load_mask), poly);
ip += num_lanes*stride;
op += num_lanes;
num_remaining_elements -= num_lanes;
}
if (@mask_to_int@(overflow_mask)) {
npy_set_floatstatus_overflow();
}
if (@mask_to_int@(underflow_mask)) {
npy_set_floatstatus_underflow();
}
}
/*
* Vectorized implementation of log using AVX2 and AVX512
* 1) if x < 0.0f; return -NAN (invalid input)
* 2) Range reduction: y = x/2^k;
* a) y = normalized mantissa, k is the exponent (0.5 <= y < 1)
* 3) Compute log(y) = P/Q, ratio of 2 polynomials P and Q
* b) P = 5th order and Q = 5th order polynomials obtained from Remez's
* algorithm (mini-max polynomial approximation)
* 5) Compute log(x) = log(y) + k*ln(2)
* 6) Max ULP error measured across all 32-bit FP's = 3.83 (x = 0x3f486945)
* 7) Max relative error measured across all 32-bit FP's = 2.359E-07 (for same
* x = 0x3f486945)
*/
static void
simd_log_FLOAT(npy_float * op,
npy_float * ip,
const npy_intp array_size,
const npy_intp steps)
{
const npy_intp stride = steps/(npy_intp)sizeof(npy_float);
const npy_int num_lanes = @BYTES@/(npy_intp)sizeof(npy_float);
/*
* Note: while generally indices are npy_intp, we ensure that our maximum index
* will fit in an int32 as a precondition for this function via
* IS_OUTPUT_BLOCKABLE_UNARY
*/
npy_int32 indexarr[16];
for (npy_int32 ii = 0; ii < 16; ii++) {
indexarr[ii] = ii*stride;
}
/* Load up frequently used constants */
@vtype@ log_p0 = _mm@vsize@_set1_ps(NPY_COEFF_P0_LOGf);
@vtype@ log_p1 = _mm@vsize@_set1_ps(NPY_COEFF_P1_LOGf);
@vtype@ log_p2 = _mm@vsize@_set1_ps(NPY_COEFF_P2_LOGf);
@vtype@ log_p3 = _mm@vsize@_set1_ps(NPY_COEFF_P3_LOGf);
@vtype@ log_p4 = _mm@vsize@_set1_ps(NPY_COEFF_P4_LOGf);
@vtype@ log_p5 = _mm@vsize@_set1_ps(NPY_COEFF_P5_LOGf);
@vtype@ log_q0 = _mm@vsize@_set1_ps(NPY_COEFF_Q0_LOGf);
@vtype@ log_q1 = _mm@vsize@_set1_ps(NPY_COEFF_Q1_LOGf);
@vtype@ log_q2 = _mm@vsize@_set1_ps(NPY_COEFF_Q2_LOGf);
@vtype@ log_q3 = _mm@vsize@_set1_ps(NPY_COEFF_Q3_LOGf);
@vtype@ log_q4 = _mm@vsize@_set1_ps(NPY_COEFF_Q4_LOGf);
@vtype@ log_q5 = _mm@vsize@_set1_ps(NPY_COEFF_Q5_LOGf);
@vtype@ loge2 = _mm@vsize@_set1_ps(NPY_LOGE2f);
@vtype@ nan = _mm@vsize@_set1_ps(NPY_NANF);
@vtype@ neg_nan = _mm@vsize@_set1_ps(-NPY_NANF);
@vtype@ neg_inf = _mm@vsize@_set1_ps(-NPY_INFINITYF);
@vtype@ inf = _mm@vsize@_set1_ps(NPY_INFINITYF);
@vtype@ zeros_f = _mm@vsize@_set1_ps(0.0f);
@vtype@ ones_f = _mm@vsize@_set1_ps(1.0f);
@vtype@i vindex = _mm@vsize@_loadu_si@vsize@((@vtype@i*)indexarr);
@vtype@ poly, num_poly, denom_poly, exponent;
@mask@ inf_mask, nan_mask, sqrt2_mask, zero_mask, negx_mask;
@mask@ invalid_mask = @isa@_get_partial_load_mask_ps(0, num_lanes);
@mask@ divide_by_zero_mask = invalid_mask;
@mask@ load_mask = @isa@_get_full_load_mask_ps();
npy_intp num_remaining_elements = array_size;
while (num_remaining_elements > 0) {
if (num_remaining_elements < num_lanes) {
load_mask = @isa@_get_partial_load_mask_ps(num_remaining_elements,
num_lanes);
}
@vtype@ x_in;
if (stride == 1) {
x_in = @isa@_masked_load_ps(load_mask, ip);
}
else {
x_in = @isa@_masked_gather_ps(zeros_f, ip, vindex, load_mask);
}
negx_mask = _mm@vsize@_cmp_ps@vsub@(x_in, zeros_f, _CMP_LT_OQ);
zero_mask = _mm@vsize@_cmp_ps@vsub@(x_in, zeros_f, _CMP_EQ_OQ);
inf_mask = _mm@vsize@_cmp_ps@vsub@(x_in, inf, _CMP_EQ_OQ);
nan_mask = _mm@vsize@_cmp_ps@vsub@(x_in, x_in, _CMP_NEQ_UQ);
divide_by_zero_mask = @or_masks@(divide_by_zero_mask,
@and_masks@(zero_mask, load_mask));
invalid_mask = @or_masks@(invalid_mask, negx_mask);
@vtype@ x = @isa@_set_masked_lanes_ps(x_in, zeros_f, negx_mask);
/* set x = normalized mantissa */
exponent = @isa@_get_exponent(x);
x = @isa@_get_mantissa(x);
/* if x < sqrt(2) {exp = exp-1; x = 2*x} */
sqrt2_mask = _mm@vsize@_cmp_ps@vsub@(x, _mm@vsize@_set1_ps(NPY_SQRT1_2f), _CMP_LE_OQ);
x = @isa@_blend(x, _mm@vsize@_add_ps(x,x), sqrt2_mask);
exponent = @isa@_blend(exponent,
_mm@vsize@_sub_ps(exponent,ones_f), sqrt2_mask);
/* x = x - 1 */
x = _mm@vsize@_sub_ps(x, ones_f);
/* Polynomial approximation for log(1+x) */
num_poly = @fmadd@(log_p5, x, log_p4);
num_poly = @fmadd@(num_poly, x, log_p3);
num_poly = @fmadd@(num_poly, x, log_p2);
num_poly = @fmadd@(num_poly, x, log_p1);
num_poly = @fmadd@(num_poly, x, log_p0);
denom_poly = @fmadd@(log_q5, x, log_q4);
denom_poly = @fmadd@(denom_poly, x, log_q3);
denom_poly = @fmadd@(denom_poly, x, log_q2);
denom_poly = @fmadd@(denom_poly, x, log_q1);
denom_poly = @fmadd@(denom_poly, x, log_q0);
poly = _mm@vsize@_div_ps(num_poly, denom_poly);
poly = @fmadd@(exponent, loge2, poly);
/*
* x < 0.0f; return -NAN
* x = +/- NAN; return NAN
* x = 0.0f; return -INF
*/
poly = @isa@_set_masked_lanes_ps(poly, nan, nan_mask);
poly = @isa@_set_masked_lanes_ps(poly, neg_nan, negx_mask);
poly = @isa@_set_masked_lanes_ps(poly, neg_inf, zero_mask);
poly = @isa@_set_masked_lanes_ps(poly, inf, inf_mask);
@masked_store@(op, @cvtps_epi32@(load_mask), poly);
ip += num_lanes*stride;
op += num_lanes;
num_remaining_elements -= num_lanes;
}
if (@mask_to_int@(invalid_mask)) {
npy_set_floatstatus_invalid();
}
if (@mask_to_int@(divide_by_zero_mask)) {
npy_set_floatstatus_divbyzero();
}
}
#endif // @CHK@
/**end repeat**/
#ifdef SIMD_AVX512F_NOCLANG_BUG
/*
* Vectorized implementation of exp double using AVX512
* Reference: Tang, P.T.P., "Table-driven implementation of the
* exponential function in IEEE floating-point
* arithmetic," ACM Transactions on Mathematical
* Software, vol. 15, pp. 144-157, 1989.
* 1) if x > mTH_max or x is INF; return INF (overflow)
* 2) if x < mTH_min; return 0.0f (underflow)
* 3) if abs(x) < mTH_nearzero; return 1.0f + x
* 4) if x is Nan; return Nan
* 5) Range reduction:
* x = (32m + j)ln2 / 32 + r; r in [-ln2/64, ln2/64]
* 6) exp(r) - 1 is approximated by a polynomial function p(r)
* exp(x) = 2^m(2^(j/32) + 2^(j/32)p(r));
*/
static void
AVX512F_exp_DOUBLE(npy_double * op,
npy_double * ip,
const npy_intp array_size,
const npy_intp steps)
{
npy_intp num_remaining_elements = array_size;
const npy_intp stride = steps / (npy_intp)sizeof(npy_double);
const npy_int num_lanes = 64 / (npy_intp)sizeof(npy_double);
npy_int32 indexarr[8];
for (npy_int32 ii = 0; ii < 8; ii++) {
indexarr[ii] = ii*stride;
}
__m512d InvLn2N = _mm512_set1_pd(NPY_INV_LN2_MUL_32);
__m512d mShift = _mm512_set1_pd(NPY_RINT_CVT_MAGIC);
__m512d mNegL1 = _mm512_set1_pd(NPY_TANG_NEG_L1);
__m512d mNegL2 = _mm512_set1_pd(NPY_TANG_NEG_L2);
__m512i mMod = _mm512_set1_epi64(0x1f);
__m512d mA1 = _mm512_set1_pd(NPY_TANG_A1);
__m512d mA2 = _mm512_set1_pd(NPY_TANG_A2);
__m512d mA3 = _mm512_set1_pd(NPY_TANG_A3);
__m512d mA4 = _mm512_set1_pd(NPY_TANG_A4);
__m512d mA5 = _mm512_set1_pd(NPY_TANG_A5);
__m512d mTH_nearzero = _mm512_set1_pd(0x1p-54);
__m512d mTH_max = _mm512_set1_pd(0x1.62e42fefa39efp+9);
__m512d mTH_min = _mm512_set1_pd(-0x1.74910d52d3053p+9);
__m512d mTH_inf = _mm512_set1_pd(NPY_INFINITY);
__m512d zeros_d = _mm512_set1_pd(0.0f);
__m512d ones_d = _mm512_set1_pd(1.0f);
__m256i vindex = _mm256_loadu_si256((__m256i*)&indexarr[0]);
__m512d mTable_top_0 = _mm512_loadu_pd(&(EXP_Table_top[8*0]));
__m512d mTable_top_1 = _mm512_loadu_pd(&(EXP_Table_top[8*1]));
__m512d mTable_top_2 = _mm512_loadu_pd(&(EXP_Table_top[8*2]));
__m512d mTable_top_3 = _mm512_loadu_pd(&(EXP_Table_top[8*3]));
__m512d mTable_tail_0 = _mm512_loadu_pd(&(EXP_Table_tail[8*0]));
__m512d mTable_tail_1 = _mm512_loadu_pd(&(EXP_Table_tail[8*1]));
__m512d mTable_tail_2 = _mm512_loadu_pd(&(EXP_Table_tail[8*2]));
__m512d mTable_tail_3 = _mm512_loadu_pd(&(EXP_Table_tail[8*3]));
__mmask8 overflow_mask = avx512_get_partial_load_mask_pd(0, num_lanes);
__mmask8 underflow_mask = avx512_get_partial_load_mask_pd(0, num_lanes);
__mmask8 load_mask = avx512_get_full_load_mask_pd();
__mmask8 xmin_mask, xmax_mask, inf_mask, nan_mask, nearzero_mask;
while (num_remaining_elements > 0) {
if (num_remaining_elements < num_lanes) {
load_mask = avx512_get_partial_load_mask_pd(num_remaining_elements,
num_lanes);
}
__m512d x;
if (1 == stride) {
x = avx512_masked_load_pd(load_mask, ip);
}
else {
x = avx512_masked_gather_pd(zeros_d, ip, vindex, load_mask);
}
nan_mask = _mm512_cmp_pd_mask(x, x, _CMP_NEQ_UQ);
x = avx512_set_masked_lanes_pd(x, zeros_d, nan_mask);
xmax_mask = _mm512_cmp_pd_mask(x, mTH_max, _CMP_GT_OQ);
xmin_mask = _mm512_cmp_pd_mask(x, mTH_min, _CMP_LT_OQ);
inf_mask = _mm512_cmp_pd_mask(x, mTH_inf, _CMP_EQ_OQ);
__m512i x_abs = _mm512_and_epi64(_mm512_castpd_si512(x),
_mm512_set1_epi64(0x7FFFFFFFFFFFFFFF));
nearzero_mask = _mm512_cmp_pd_mask(_mm512_castsi512_pd(x_abs),
mTH_nearzero, _CMP_LT_OQ);
nearzero_mask = _mm512_kxor(nearzero_mask, nan_mask);
overflow_mask = _mm512_kor(overflow_mask,
_mm512_kxor(xmax_mask, inf_mask));
underflow_mask = _mm512_kor(underflow_mask, xmin_mask);
x = avx512_set_masked_lanes_pd(x, zeros_d,
_mm512_kor(_mm512_kor(nan_mask, xmin_mask),
_mm512_kor(xmax_mask, nearzero_mask)));
/* z = x * 32/ln2 */
__m512d z = _mm512_mul_pd(x, InvLn2N);
/* round to nearest */
__m512d kd = _mm512_add_pd(z, mShift);
__m512i ki = _mm512_castpd_si512(kd);
kd = _mm512_sub_pd(kd, mShift);
/* r = (x + kd*mNegL1) + kd*mNegL2 */
__m512d r1 = _mm512_fmadd_pd(kd, mNegL1, x);
__m512d r2 = _mm512_mul_pd(kd, mNegL2);
__m512d r = _mm512_add_pd(r1,r2);
/* Polynomial approximation for exp(r) - 1 */
__m512d q = _mm512_fmadd_pd(mA5, r, mA4);
q = _mm512_fmadd_pd(q, r, mA3);
q = _mm512_fmadd_pd(q, r, mA2);
q = _mm512_fmadd_pd(q, r, mA1);
q = _mm512_mul_pd(q, r);
__m512d p = _mm512_fmadd_pd(r, q, r2);;
p = _mm512_add_pd(r1, p);
/* Get 2^(j/32) from lookup table */
__m512i j = _mm512_and_epi64(ki, mMod);
__m512d top = avx512_permute_x4var_pd(mTable_top_0, mTable_top_1,
mTable_top_2, mTable_top_3, j);
__m512d tail = avx512_permute_x4var_pd(mTable_tail_0, mTable_tail_1,
mTable_tail_2, mTable_tail_3, j);
/*
* s = top + tail;
* exp(x) = 2^m * (top + (tail + s * p));
*/
__m512d s = _mm512_add_pd(top, tail);
__m512d res = _mm512_fmadd_pd(s, p, tail);
res = _mm512_add_pd(res, top);
res= _mm512_scalef_pd(res, _mm512_div_pd(kd, _mm512_set1_pd(32)));
/* return special cases */
res = avx512_set_masked_lanes_pd(res, _mm512_add_pd(x, ones_d),
nearzero_mask);
res = avx512_set_masked_lanes_pd(res, _mm512_set1_pd(NPY_NAN),
nan_mask);
res = avx512_set_masked_lanes_pd(res, mTH_inf, xmax_mask);
res = avx512_set_masked_lanes_pd(res, zeros_d, xmin_mask);
_mm512_mask_storeu_pd(op, load_mask, res);
ip += num_lanes * stride;
op += num_lanes;
num_remaining_elements -= num_lanes;
}
if (overflow_mask) {
npy_set_floatstatus_overflow();
}
if (underflow_mask) {
npy_set_floatstatus_underflow();
}
}
/*
* Vectorized implementation of log double using AVX512
* Reference:
* [1] Tang, Ping Tak Peter. Table-lookup algorithms for elementary functions
* and their error analysis. No. CONF-9106103-1. Argonne National Lab.,
* IL (USA), 1991.
* [2] Tang, Ping-Tak Peter. "Table-driven implementation of the logarithm
* function in IEEE floating-point arithmetic." ACM Transactions on
* Mathematical Software (TOMS) 16.4 (1990): 378-400.
* [3] Muller, Jean-Michel. "Elementary functions: algorithms and
* implementation." (2016).
* 1) if x = 0; return -INF
* 2) if x < 0; return NAN
* 3) if x is INF; return INF
* 4) if x is NAN; return NAN
* 5) if x on (1.0 - 0x1p-4, 1.0 + 0x1.09p-4), calling npy_log()
* 6) Range reduction:
* log(x) = log(2^m * z)
* = mln2 + log(z)
* 7) log(z) = log(z / c_k) + log(c_k);
* where c_k = 1 + k/64, k = 0,1,...,64
* s.t. |x - c_k| <= 1/128 when x on[1,2].
* 8) r = 2(x - c_k)/(x + c_k)
* log(x/c_k) = log((1 + r/2) / (1 - r/2))
* = p(r)
* = 2((r/2) + 1/3*(r/2)^3 + 1/5*(r/2)^5 + ...)
*/
static void
AVX512F_log_DOUBLE(npy_double * op,
npy_double * ip,
const npy_intp array_size,
const npy_intp steps)
{
npy_intp num_remaining_elements = array_size;
const npy_intp stride = steps / (npy_intp)sizeof(npy_double);
const npy_int num_lanes = 64 / (npy_intp)sizeof(npy_double);
npy_int32 indexarr[8];
for (npy_int32 ii = 0; ii < 8; ii++) {
indexarr[ii] = ii*stride;
}
__m512d zeros_d = _mm512_set1_pd(0.0f);
__m512d ones_d = _mm512_set1_pd(1.0f);
__m512d mInf = _mm512_set1_pd(NPY_INFINITY);
__m512d mInv64 = _mm512_castsi512_pd(_mm512_set1_epi64(0x3f90000000000000));
__m512d mNeg_nan = _mm512_set1_pd(-NPY_NAN);
__m512d mNan = _mm512_set1_pd(NPY_NAN);
__m512d mNeg_inf = _mm512_set1_pd(-NPY_INFINITY);
__m512d mA1 = _mm512_set1_pd(NPY_TANG_LOG_A1);
__m512d mA2 = _mm512_set1_pd(NPY_TANG_LOG_A2);
__m512d mA3 = _mm512_set1_pd(NPY_TANG_LOG_A3);
__m512d mA4 = _mm512_set1_pd(NPY_TANG_LOG_A4);
__m512d mLN2HI = _mm512_set1_pd(NPY_TANG_LOG_LN2HI);
__m512d mLN2LO = _mm512_set1_pd(NPY_TANG_LOG_LN2LO);
__m512d mTo_glibc_min = _mm512_set1_pd(1.0 - 0x1p-4);
__m512d mTo_glibc_max = _mm512_set1_pd(1.0 + 0x1.09p-4);
__m256i vindex = _mm256_loadu_si256((__m256i*)&indexarr[0]);
/* Load lookup table data */
/**begin repeat
* #i = 0, 1, 2, 3, 4, 5, 6, 7#
*/
__m512d mLUT_TOP_@i@ = _mm512_loadu_pd(&(LOG_TABLE_TOP[8*@i@]));
__m512d mLUT_TAIL_@i@ = _mm512_loadu_pd(&(LOG_TABLE_TAIL[8*@i@]));
/**end repeat**/
__mmask8 load_mask = avx512_get_full_load_mask_pd();
__mmask8 invalid_mask = avx512_get_partial_load_mask_pd(0, num_lanes);
__mmask8 divide_by_zero_mask = invalid_mask;
__mmask8 inf_mask, nan_mask, zero_mask, negx_mask, denormal_mask,
glibc_mask;
__m512d x_in;
while (num_remaining_elements > 0) {
if (num_remaining_elements < num_lanes) {
load_mask = avx512_get_partial_load_mask_pd(num_remaining_elements,
num_lanes);
}
if (1 == stride) {
x_in = avx512_masked_load_pd(load_mask, ip);
}
else {
x_in = avx512_masked_gather_pd(zeros_d, ip, vindex, load_mask);
}
/* call glibc when x on [1.0 - 0x1p-4, 1.0 + 0x1.09p-4] */
__mmask8 m1 = _mm512_cmp_pd_mask(x_in, mTo_glibc_max, _CMP_LT_OQ);
__mmask8 m2 = _mm512_cmp_pd_mask(x_in, mTo_glibc_min, _CMP_GT_OQ);
glibc_mask = m1 & m2;
if (glibc_mask != 0xFF) {
zero_mask = _mm512_cmp_pd_mask(x_in, zeros_d, _CMP_EQ_OQ);
inf_mask = _mm512_cmp_pd_mask(x_in, mInf, _CMP_EQ_OQ);
negx_mask = _mm512_cmp_pd_mask(x_in, zeros_d, _CMP_LT_OQ);
nan_mask = _mm512_cmp_pd_mask(x_in, x_in, _CMP_NEQ_UQ);
divide_by_zero_mask = divide_by_zero_mask | (zero_mask & load_mask);
invalid_mask = invalid_mask | negx_mask;
__m512d x = avx512_set_masked_lanes_pd(x_in, zeros_d, negx_mask);
__m512i ix = _mm512_castpd_si512(x);
/* Normalize x when it is denormal */
__m512i top12 = _mm512_and_epi64(ix,
_mm512_set1_epi64(0xfff0000000000000));
denormal_mask = _mm512_cmp_epi64_mask(top12, _mm512_set1_epi64(0),
_CMP_EQ_OQ);
denormal_mask = (~zero_mask) & denormal_mask;
ix = _mm512_castpd_si512(_mm512_mask_mul_pd(x, denormal_mask,
x, _mm512_set1_pd(0x1p52)));
ix = _mm512_mask_sub_epi64(ix, denormal_mask,
ix, _mm512_set1_epi64(52ULL << 52));
/*
* x = 2^k * z; where z in range [1,2]
*/
__m512i tmp = _mm512_sub_epi64(ix,
_mm512_set1_epi64(0x3ff0000000000000));
__m512i i = _mm512_and_epi64(_mm512_srai_epi64(tmp, 52 - 6),
_mm512_set1_epi64(0x3fULL));
__m512i ik = _mm512_srai_epi64(tmp, 52);
__m512d z = _mm512_castsi512_pd(_mm512_sub_epi64(ix, _mm512_and_epi64(tmp,
_mm512_set1_epi64(0xfff0000000000000))));
/* c = i/64 + 1 */
__m256i i_32 = _mm512_cvtepi64_epi32(i);
__m512d c = _mm512_fmadd_pd(_mm512_cvtepi32_pd(i_32), mInv64, ones_d);
/* u = 2 * (z - c) / (z + c) */
__m512d u = _mm512_div_pd(_mm512_sub_pd(z, c), _mm512_add_pd(z, c));
u = _mm512_mul_pd(_mm512_set1_pd(2.0), u);
/* v = u * u */
__m512d v = _mm512_mul_pd(u,u);
/* log(z/c) = u + u*v*(A1 + v*(A2 + v*(A3 + v*A4))) */
__m512d res = _mm512_fmadd_pd(v, mA4, mA3);
res = _mm512_fmadd_pd(v, res, mA2);
res = _mm512_fmadd_pd(v, res, mA1);
res = _mm512_mul_pd(v, res);
res = _mm512_fmadd_pd(u, res, u);
/* Load lookup table data */
__m512d c_hi = avx512_permute_x8var_pd(mLUT_TOP_0, mLUT_TOP_1,
mLUT_TOP_2, mLUT_TOP_3, mLUT_TOP_4, mLUT_TOP_5,
mLUT_TOP_6, mLUT_TOP_7, i);
__m512d c_lo = avx512_permute_x8var_pd(mLUT_TAIL_0, mLUT_TAIL_1,
mLUT_TAIL_2, mLUT_TAIL_3, mLUT_TAIL_4, mLUT_TAIL_5,
mLUT_TAIL_6, mLUT_TAIL_7, i);
/*
* log(x) = k * ln2_hi + c_hi +
* k * ln2_lo + c_lo +