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#ifndef _NPY_UMATH_LOOPS_UTILS_H_
#define _NPY_UMATH_LOOPS_UTILS_H_
#include "numpy/npy_common.h" // NPY_FINLINE
#include "numpy/halffloat.h" // npy_half_to_float
/**
* Old versions of MSVC causes ambiguous link errors when we deal with large SIMD kernels
* which lead to break the build, probably related to the following bug:
* https://developercommunity.visualstudio.com/content/problem/415095/internal-compiler-error-with-perfectly-forwarded-r.html
*/
#if defined(_MSC_VER) && _MSC_VER < 1916
#define SIMD_MSVC_NOINLINE __declspec(noinline)
#else
#define SIMD_MSVC_NOINLINE
#endif
/*
* nomemoverlap - returns false if two strided arrays have an overlapping
* region in memory. ip_size/op_size = size of the arrays which can be negative
* indicating negative steps.
*/
NPY_FINLINE npy_bool
nomemoverlap(char *ip, npy_intp ip_size, char *op, npy_intp op_size)
{
char *ip_start, *ip_end, *op_start, *op_end;
if (ip_size < 0) {
ip_start = ip + ip_size;
ip_end = ip;
}
else {
ip_start = ip;
ip_end = ip + ip_size;
}
if (op_size < 0) {
op_start = op + op_size;
op_end = op;
}
else {
op_start = op;
op_end = op + op_size;
}
return (ip_start == op_start && op_end == ip_end) ||
(ip_start > op_end) || (op_start > ip_end);
}
// returns true if two strided arrays have an overlapping region in memory
// same as `nomemoverlap()` but requires array length and step sizes
NPY_FINLINE npy_bool
is_mem_overlap(const void *src, npy_intp src_step, const void *dst, npy_intp dst_step, npy_intp len)
{
return !(nomemoverlap((char*)src, src_step*len, (char*)dst, dst_step*len));
}
/*
* cutoff blocksize for pairwise summation
* decreasing it decreases errors slightly as more pairs are summed but
* also lowers performance, as the inner loop is unrolled eight times it is
* effectively 16
*/
#define PW_BLOCKSIZE 128
/**begin repeat
* Float types
* #type = npy_float, npy_double, npy_longdouble, npy_float#
* #dtype = npy_float, npy_double, npy_longdouble, npy_half#
* #TYPE = FLOAT, DOUBLE, LONGDOUBLE, HALF#
* #c = f, , l, #
* #C = F, , L, #
* #trf = , , , npy_half_to_float#
*/
/*
* Pairwise summation, rounding error O(lg n) instead of O(n).
* The recursion depth is O(lg n) as well.
* when updating also update similar complex floats summation
*/
static inline @type@
@TYPE@_pairwise_sum(char *a, npy_intp n, npy_intp stride)
{
if (n < 8) {
npy_intp i;
/*
* Start with -0 to preserve -0 values. The reason is that summing
* only -0 should return -0, but `0 + -0 == 0` while `-0 + -0 == -0`.
*/
@type@ res = -0.0;
for (i = 0; i < n; i++) {
res += @trf@(*((@dtype@*)(a + i * stride)));
}
return res;
}
else if (n <= PW_BLOCKSIZE) {
npy_intp i;
@type@ r[8], res;
/*
* sum a block with 8 accumulators
* 8 times unroll reduces blocksize to 16 and allows vectorization with
* avx without changing summation ordering
*/
r[0] = @trf@(*((@dtype@ *)(a + 0 * stride)));
r[1] = @trf@(*((@dtype@ *)(a + 1 * stride)));
r[2] = @trf@(*((@dtype@ *)(a + 2 * stride)));
r[3] = @trf@(*((@dtype@ *)(a + 3 * stride)));
r[4] = @trf@(*((@dtype@ *)(a + 4 * stride)));
r[5] = @trf@(*((@dtype@ *)(a + 5 * stride)));
r[6] = @trf@(*((@dtype@ *)(a + 6 * stride)));
r[7] = @trf@(*((@dtype@ *)(a + 7 * stride)));
for (i = 8; i < n - (n % 8); i += 8) {
/* small blocksizes seems to mess with hardware prefetch */
NPY_PREFETCH(a + (i + 512/(npy_intp)sizeof(@dtype@))*stride, 0, 3);
r[0] += @trf@(*((@dtype@ *)(a + (i + 0) * stride)));
r[1] += @trf@(*((@dtype@ *)(a + (i + 1) * stride)));
r[2] += @trf@(*((@dtype@ *)(a + (i + 2) * stride)));
r[3] += @trf@(*((@dtype@ *)(a + (i + 3) * stride)));
r[4] += @trf@(*((@dtype@ *)(a + (i + 4) * stride)));
r[5] += @trf@(*((@dtype@ *)(a + (i + 5) * stride)));
r[6] += @trf@(*((@dtype@ *)(a + (i + 6) * stride)));
r[7] += @trf@(*((@dtype@ *)(a + (i + 7) * stride)));
}
/* accumulate now to avoid stack spills for single peel loop */
res = ((r[0] + r[1]) + (r[2] + r[3])) +
((r[4] + r[5]) + (r[6] + r[7]));
/* do non multiple of 8 rest */
for (; i < n; i++) {
res += @trf@(*((@dtype@ *)(a + i * stride)));
}
return res;
}
else {
/* divide by two but avoid non-multiples of unroll factor */
npy_intp n2 = n / 2;
n2 -= n2 % 8;
return @TYPE@_pairwise_sum(a, n2, stride) +
@TYPE@_pairwise_sum(a + n2 * stride, n - n2, stride);
}
}
/**end repeat**/
/**begin repeat
* complex types
* #TYPE = CFLOAT, CDOUBLE, CLONGDOUBLE#
* #ftype = npy_float, npy_double, npy_longdouble#
* #c = f, , l#
* #C = F, , L#
* #SIMD = 1, 1, 0#
*/
/* similar to pairwise sum of real floats */
static inline void
@TYPE@_pairwise_sum(@ftype@ *rr, @ftype@ * ri, char * a, npy_intp n,
npy_intp stride)
{
assert(n % 2 == 0);
if (n < 8) {
npy_intp i;
*rr = -0.0;
*ri = -0.0;
for (i = 0; i < n; i += 2) {
*rr += *((@ftype@ *)(a + i * stride + 0));
*ri += *((@ftype@ *)(a + i * stride + sizeof(@ftype@)));
}
return;
}
else if (n <= PW_BLOCKSIZE) {
npy_intp i;
@ftype@ r[8];
/*
* sum a block with 8 accumulators
* 8 times unroll reduces blocksize to 16 and allows vectorization with
* avx without changing summation ordering
*/
r[0] = *((@ftype@ *)(a + 0 * stride));
r[1] = *((@ftype@ *)(a + 0 * stride + sizeof(@ftype@)));
r[2] = *((@ftype@ *)(a + 2 * stride));
r[3] = *((@ftype@ *)(a + 2 * stride + sizeof(@ftype@)));
r[4] = *((@ftype@ *)(a + 4 * stride));
r[5] = *((@ftype@ *)(a + 4 * stride + sizeof(@ftype@)));
r[6] = *((@ftype@ *)(a + 6 * stride));
r[7] = *((@ftype@ *)(a + 6 * stride + sizeof(@ftype@)));
for (i = 8; i < n - (n % 8); i += 8) {
/* small blocksizes seems to mess with hardware prefetch */
NPY_PREFETCH(a + (i + 512/(npy_intp)sizeof(@ftype@))*stride, 0, 3);
r[0] += *((@ftype@ *)(a + (i + 0) * stride));
r[1] += *((@ftype@ *)(a + (i + 0) * stride + sizeof(@ftype@)));
r[2] += *((@ftype@ *)(a + (i + 2) * stride));
r[3] += *((@ftype@ *)(a + (i + 2) * stride + sizeof(@ftype@)));
r[4] += *((@ftype@ *)(a + (i + 4) * stride));
r[5] += *((@ftype@ *)(a + (i + 4) * stride + sizeof(@ftype@)));
r[6] += *((@ftype@ *)(a + (i + 6) * stride));
r[7] += *((@ftype@ *)(a + (i + 6) * stride + sizeof(@ftype@)));
}
/* accumulate now to avoid stack spills for single peel loop */
*rr = ((r[0] + r[2]) + (r[4] + r[6]));
*ri = ((r[1] + r[3]) + (r[5] + r[7]));
/* do non multiple of 8 rest */
for (; i < n; i+=2) {
*rr += *((@ftype@ *)(a + i * stride + 0));
*ri += *((@ftype@ *)(a + i * stride + sizeof(@ftype@)));
}
return;
}
else {
/* divide by two but avoid non-multiples of unroll factor */
@ftype@ rr1, ri1, rr2, ri2;
npy_intp n2 = n / 2;
n2 -= n2 % 8;
@TYPE@_pairwise_sum(&rr1, &ri1, a, n2, stride);
@TYPE@_pairwise_sum(&rr2, &ri2, a + n2 * stride, n - n2, stride);
*rr = rr1 + rr2;
*ri = ri1 + ri2;
return;
}
}
/**end repeat**/
#endif // _NPY_UMATH_LOOPS_UTILS_H_
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