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// Start of copy.h
// Cache-oblivious map-transpose function.
#define GEN_MAP_TRANSPOSE(NAME, ELEM_TYPE) \
static void map_transpose_##NAME \
(ELEM_TYPE* dst, ELEM_TYPE* src, \
int64_t k, int64_t m, int64_t n, \
int64_t cb, int64_t ce, int64_t rb, int64_t re) \
{ \
int32_t r = re - rb; \
int32_t c = ce - cb; \
if (k == 1) { \
if (r <= 64 && c <= 64) { \
for (int64_t j = 0; j < c; j++) { \
for (int64_t i = 0; i < r; i++) { \
dst[(j + cb) * n + (i + rb)] = src[(i + rb) * m + (j + cb)]; \
} \
} \
} else if (c <= r) { \
map_transpose_##NAME(dst, src, k, m, n, cb, ce, rb, rb + r/2); \
map_transpose_##NAME(dst, src, k, m, n, cb, ce, rb + r/2, re); \
} else { \
map_transpose_##NAME(dst, src, k, m, n, cb, cb + c/2, rb, re); \
map_transpose_##NAME(dst, src, k, m, n, cb + c/2, ce, rb, re); \
} \
} else { \
for (int64_t i = 0; i < k; i++) { \
map_transpose_##NAME(dst + i * m * n, src + i * m * n, 1, m, n, cb, ce, rb, re); \
}\
} \
}
// Straightforward LMAD copy function.
#define GEN_LMAD_COPY_ELEMENTS(NAME, ELEM_TYPE) \
static void lmad_copy_elements_##NAME(int r, \
ELEM_TYPE* dst, int64_t dst_strides[r], \
ELEM_TYPE *src, int64_t src_strides[r], \
int64_t shape[r]) { \
if (r == 1) { \
for (int i = 0; i < shape[0]; i++) { \
dst[i*dst_strides[0]] = src[i*src_strides[0]]; \
} \
} else if (r > 1) { \
for (int i = 0; i < shape[0]; i++) { \
lmad_copy_elements_##NAME(r-1, \
dst+i*dst_strides[0], dst_strides+1, \
src+i*src_strides[0], src_strides+1, \
shape+1); \
} \
} \
} \
// Check whether this LMAD can be seen as a transposed 2D array. This
// is done by checking every possible splitting point.
static bool lmad_is_tr(int64_t *n_out, int64_t *m_out,
int r,
const int64_t strides[r],
const int64_t shape[r]) {
for (int i = 1; i < r; i++) {
int n = 1, m = 1;
bool ok = true;
int64_t expected = 1;
// Check strides before 'i'.
for (int j = i-1; j >= 0; j--) {
ok = ok && strides[j] == expected;
expected *= shape[j];
n *= shape[j];
}
// Check strides after 'i'.
for (int j = r-1; j >= i; j--) {
ok = ok && strides[j] == expected;
expected *= shape[j];
m *= shape[j];
}
if (ok) {
*n_out = n;
*m_out = m;
return true;
}
}
return false;
}
// This function determines whether the a 'dst' LMAD is row-major and
// 'src' LMAD is column-major. Both LMADs are for arrays of the same
// shape. Both LMADs are allowed to have additional dimensions "on
// top". Essentially, this function determines whether a copy from
// 'src' to 'dst' is a "map(transpose)" that we know how to implement
// efficiently. The LMADs can have arbitrary rank, and the main
// challenge here is checking whether the src LMAD actually
// corresponds to a 2D column-major layout by morally collapsing
// dimensions. There is a lot of looping here, but the actual trip
// count is going to be very low in practice.
//
// Returns true if this is indeed a map(transpose), and writes the
// number of arrays, and moral array size to appropriate output
// parameters.
static bool lmad_map_tr(int64_t *num_arrays_out, int64_t *n_out, int64_t *m_out,
int r,
const int64_t dst_strides[r],
const int64_t src_strides[r],
const int64_t shape[r]) {
int64_t rowmajor_strides[r];
rowmajor_strides[r-1] = 1;
for (int i = r-2; i >= 0; i--) {
rowmajor_strides[i] = rowmajor_strides[i+1] * shape[i+1];
}
// map_r will be the number of mapped dimensions on top.
int map_r = 0;
int64_t num_arrays = 1;
for (int i = 0; i < r; i++) {
if (dst_strides[i] != rowmajor_strides[i] ||
src_strides[i] != rowmajor_strides[i]) {
break;
} else {
num_arrays *= shape[i];
map_r++;
}
}
*num_arrays_out = num_arrays;
if (r==map_r) {
return false;
}
if (memcmp(&rowmajor_strides[map_r],
&dst_strides[map_r],
sizeof(int64_t)*(r-map_r)) == 0) {
return lmad_is_tr(n_out, m_out, r-map_r, src_strides+map_r, shape+map_r);
} else if (memcmp(&rowmajor_strides[map_r],
&src_strides[map_r],
sizeof(int64_t)*(r-map_r)) == 0) {
return lmad_is_tr(m_out, n_out, r-map_r, dst_strides+map_r, shape+map_r);
}
return false;
}
// Check if the strides correspond to row-major strides of *any*
// permutation of the shape. This is done by recursive search with
// backtracking. This is worst-case exponential, but hopefully the
// arrays we encounter do not have that many dimensions.
static bool lmad_contiguous_search(int checked, int64_t expected,
int r,
int64_t strides[r], int64_t shape[r], bool used[r]) {
for (int i = 0; i < r; i++) {
for (int j = 0; j < r; j++) {
if (!used[j] && strides[j] == expected && strides[j] >= 0) {
used[j] = true;
if (checked+1 == r ||
lmad_contiguous_search(checked+1, expected * shape[j], r, strides, shape, used)) {
return true;
}
used[j] = false;
}
}
}
return false;
}
// Does this LMAD correspond to an array with positive strides and no
// holes?
static bool lmad_contiguous(int r, int64_t strides[r], int64_t shape[r]) {
bool used[r];
for (int i = 0; i < r; i++) {
used[i] = false;
}
return lmad_contiguous_search(0, 1, r, strides, shape, used);
}
// Does this copy correspond to something that could be done with a
// memcpy()-like operation? I.e. do the LMADs actually represent the
// same in-memory layout and are they contiguous?
static bool lmad_memcpyable(int r,
int64_t dst_strides[r], int64_t src_strides[r], int64_t shape[r]) {
if (!lmad_contiguous(r, dst_strides, shape)) {
return false;
}
for (int i = 0; i < r; i++) {
if (dst_strides[i] != src_strides[i] && shape[i] != 1) {
return false;
}
}
return true;
}
static void log_copy(struct futhark_context* ctx,
const char *kind, const char *provenance,
int r,
int64_t dst_offset, int64_t dst_strides[r],
int64_t src_offset, int64_t src_strides[r],
int64_t shape[r]) {
if (ctx->logging) {
fprintf(ctx->log, "\n# Copy %s\n", kind);
if (provenance) { fprintf(ctx->log, "At: %s\n", provenance); }
fprintf(ctx->log, "Shape: ");
for (int i = 0; i < r; i++) { fprintf(ctx->log, "[%ld]", (long int)shape[i]); }
fprintf(ctx->log, "\n");
fprintf(ctx->log, "Dst offset: %ld\n", (long int)dst_offset);
fprintf(ctx->log, "Dst strides:");
for (int i = 0; i < r; i++) { fprintf(ctx->log, " %ld", (long int)dst_strides[i]); }
fprintf(ctx->log, "\n");
fprintf(ctx->log, "Src offset: %ld\n", (long int)src_offset);
fprintf(ctx->log, "Src strides:");
for (int i = 0; i < r; i++) { fprintf(ctx->log, " %ld", (long int)src_strides[i]); }
fprintf(ctx->log, "\n");
}
}
static void log_transpose(struct futhark_context* ctx,
int64_t k, int64_t n, int64_t m) {
if (ctx->logging) {
fprintf(ctx->log, "## Transpose\n");
fprintf(ctx->log, "Arrays : %ld\n", (long int)k);
fprintf(ctx->log, "X elements : %ld\n", (long int)m);
fprintf(ctx->log, "Y elements : %ld\n", (long int)n);
fprintf(ctx->log, "\n");
}
}
#define GEN_LMAD_COPY(NAME, ELEM_TYPE) \
static void lmad_copy_##NAME \
(struct futhark_context *ctx, int r, \
ELEM_TYPE* dst, int64_t dst_offset, int64_t dst_strides[r], \
ELEM_TYPE *src, int64_t src_offset, int64_t src_strides[r], \
int64_t shape[r]) { \
log_copy(ctx, "CPU to CPU", NULL, r, dst_offset, dst_strides, \
src_offset, src_strides, shape); \
int64_t size = 1; \
for (int i = 0; i < r; i++) { size *= shape[i]; } \
if (size == 0) { return; } \
int64_t k, n, m; \
if (lmad_map_tr(&k, &n, &m, \
r, dst_strides, src_strides, shape)) { \
log_transpose(ctx, k, n, m); \
map_transpose_##NAME \
(dst+dst_offset, src+src_offset, k, n, m, 0, n, 0, m); \
} else if (lmad_memcpyable(r, dst_strides, src_strides, shape)) { \
if (ctx->logging) {fprintf(ctx->log, "## Flat copy\n\n");} \
memcpy(dst+dst_offset, src+src_offset, size*sizeof(*dst)); \
} else { \
if (ctx->logging) {fprintf(ctx->log, "## General copy\n\n");} \
lmad_copy_elements_##NAME \
(r, \
dst+dst_offset, dst_strides, \
src+src_offset, src_strides, shape); \
} \
}
GEN_MAP_TRANSPOSE(1b, uint8_t)
GEN_MAP_TRANSPOSE(2b, uint16_t)
GEN_MAP_TRANSPOSE(4b, uint32_t)
GEN_MAP_TRANSPOSE(8b, uint64_t)
GEN_LMAD_COPY_ELEMENTS(1b, uint8_t)
GEN_LMAD_COPY_ELEMENTS(2b, uint16_t)
GEN_LMAD_COPY_ELEMENTS(4b, uint32_t)
GEN_LMAD_COPY_ELEMENTS(8b, uint64_t)
GEN_LMAD_COPY(1b, uint8_t)
GEN_LMAD_COPY(2b, uint16_t)
GEN_LMAD_COPY(4b, uint32_t)
GEN_LMAD_COPY(8b, uint64_t)
// End of copy.h
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