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Diffstat (limited to 'contrib/kann/kautodiff.c')
| -rw-r--r-- | contrib/kann/kautodiff.c | 2460 |
1 files changed, 2460 insertions, 0 deletions
diff --git a/contrib/kann/kautodiff.c b/contrib/kann/kautodiff.c new file mode 100644 index 0000000..d05cc00 --- /dev/null +++ b/contrib/kann/kautodiff.c @@ -0,0 +1,2460 @@ +#include "config.h" + +#include <stdlib.h> +#include <assert.h> +#include <stdarg.h> +#include <string.h> +#include <float.h> +#include <math.h> +#include "kautodiff.h" +#include "blas-config.h" + +typedef struct { + uint64_t s[2]; + double n_gset; + int n_iset; + volatile int lock; +} kad_rng_t; + +/********************** + * Graph construction * + **********************/ + +static inline kad_node_t *kad_new_core(int n_d, int op, int n_child) +{ + kad_node_t *s; + if (n_d >= KAD_MAX_DIM) return 0; + s = (kad_node_t*)calloc(1, sizeof(kad_node_t)); + s->n_d = n_d, s->op = op, s->n_child = n_child; + if (s->n_child) s->child = (kad_node_t**)calloc(s->n_child, sizeof(kad_node_t*)); + return s; +} + +static inline kad_node_t *kad_vleaf(uint8_t flag, float *x, float *g, int n_d, va_list ap) +{ + int i; + kad_node_t *p; + if (n_d > KAD_MAX_DIM) return 0; + p = (kad_node_t*)calloc(1, sizeof(kad_node_t)); + p->n_d = n_d; + for (i = 0; i < n_d; ++i) + p->d[i] = va_arg(ap, int32_t); + p->x = x, p->g = g, p->flag = flag; + return p; +} + +kad_node_t *kad_const(float *x, int n_d, ...) +{ + kad_node_t *p; + va_list ap; + va_start(ap, n_d); p = kad_vleaf(KAD_CONST, x, 0, n_d, ap); va_end(ap); + return p; +} + +kad_node_t *kad_feed(int n_d, ...) +{ + kad_node_t *p; + va_list ap; + va_start(ap, n_d); p = kad_vleaf(0, 0, 0, n_d, ap); va_end(ap); + return p; +} + +kad_node_t *kad_var(float *x, float *g, int n_d, ...) +{ + kad_node_t *p; + va_list ap; + va_start(ap, n_d); p = kad_vleaf(KAD_VAR, x, g, n_d, ap); va_end(ap); + return p; +} + +static inline kad_node_t *kad_finalize_node(kad_node_t *s) /* a helper function */ +{ + int i; + if (kad_op_list[s->op](s, KAD_SYNC_DIM) < 0) { /* check dimension */ + if (s->ptr) free(s->ptr); + free(s->child); free(s); + return 0; + } + for (i = 0; i < s->n_child; ++i) + if (kad_is_back(s->child[i])) + break; + if (i < s->n_child) s->flag |= KAD_VAR; + return s; +} + +/********** Simple arithmetic **********/ + +static inline kad_node_t *kad_op2_core(int op, kad_node_t *x, kad_node_t *y) +{ + kad_node_t *s; + s = kad_new_core(0, op, 2); + s->child[0] = x, s->child[1] = y; + return kad_finalize_node(s); +} + +static inline kad_node_t *kad_op1_core(int op, kad_node_t *x) +{ + kad_node_t *s; + s = kad_new_core(0, op, 1); + s->child[0] = x; + return kad_finalize_node(s); +} + +#define KAD_FUNC_OP2(fname, op) kad_node_t *fname(kad_node_t *x, kad_node_t *y) { return kad_op2_core((op), x, y); } + +KAD_FUNC_OP2(kad_add, 1) +KAD_FUNC_OP2(kad_sub, 23) +KAD_FUNC_OP2(kad_mul, 2) +KAD_FUNC_OP2(kad_cmul, 3) +KAD_FUNC_OP2(kad_matmul, 9) +KAD_FUNC_OP2(kad_ce_multi, 13) +KAD_FUNC_OP2(kad_ce_bin, 22) +KAD_FUNC_OP2(kad_ce_bin_neg, 4) +KAD_FUNC_OP2(kad_mse, 29) + +#define KAD_FUNC_OP1(fname, op) kad_node_t *fname(kad_node_t *x) { return kad_op1_core((op), x); } + +KAD_FUNC_OP1(kad_log, 27) +KAD_FUNC_OP1(kad_exp, 33) +KAD_FUNC_OP1(kad_sin, 34) +KAD_FUNC_OP1(kad_square, 5) +KAD_FUNC_OP1(kad_sigm, 6) +KAD_FUNC_OP1(kad_tanh, 7) +KAD_FUNC_OP1(kad_relu, 8) +KAD_FUNC_OP1(kad_1minus, 11) +KAD_FUNC_OP1(kad_softmax, 14) +KAD_FUNC_OP1(kad_stdnorm, 32) + +kad_node_t *kad_ce_multi_weighted(kad_node_t *pred, kad_node_t *truth, kad_node_t *weight) +{ + kad_node_t *s; + s = kad_new_core(0, 13, 3); + s->child[0] = pred, s->child[1] = truth, s->child[2] = weight; + return kad_finalize_node(s); +} + +/********** Convolution **********/ + +/* compute output dimension and padding sizes on both sides */ +static inline int conv_find_par(int in_size, int kernel_size, int stride, int pad0, int *new_pad0, int *new_pad1) +{ + int out_size, pad_both; + /* key equation: out_size = (in_size - kernel_size + pad_both) / stride + 1 */ + if (pad0 == KAD_PAD_SAME && stride == 1) out_size = in_size; + else out_size = (in_size - kernel_size + (pad0 > 0? pad0 : 0) + stride - 1) / stride + 1; + pad_both = (out_size - 1) * stride + kernel_size - in_size; + *new_pad0 = pad_both / 2; + *new_pad1 = pad_both - *new_pad0; + return out_size; +} + +typedef struct { + int kernel_size, stride, pad[2]; +} conv_conf_t; + +static inline conv_conf_t *conv2d_gen_aux(int in_row, int in_col, int kernel_r, int kernel_c, int stride_r, int stride_c, int top_pad, int left_pad) +{ + conv_conf_t *cnn; + cnn = (conv_conf_t*)calloc(2, sizeof(conv_conf_t)); + cnn[0].kernel_size = kernel_r, cnn[0].stride = stride_r; + cnn[1].kernel_size = kernel_c, cnn[1].stride = stride_c; + conv_find_par(in_row, kernel_r, stride_r, top_pad, &cnn[0].pad[0], &cnn[0].pad[1]); + conv_find_par(in_col, kernel_c, stride_c, left_pad, &cnn[1].pad[0], &cnn[1].pad[1]); + return cnn; +} + +kad_node_t *kad_conv2d(kad_node_t *x, kad_node_t *w, int stride_r, int stride_c, int top_pad, int left_pad) +{ + kad_node_t *s; + if (x->n_d != 4 || w->n_d != 4) return 0; + s = kad_new_core(0, 16, 2); + s->child[0] = x, s->child[1] = w; + s->ptr = conv2d_gen_aux(x->d[2], x->d[3], w->d[2], w->d[3], stride_r, stride_c, top_pad, left_pad); + s->ptr_size = sizeof(conv_conf_t) * 2; + return kad_finalize_node(s); +} + +kad_node_t *kad_max2d(kad_node_t *x, int kernel_r, int kernel_c, int stride_r, int stride_c, int top_pad, int left_pad) +{ + kad_node_t *s; + if (x->n_d != 4) return 0; + s = kad_new_core(0, 17, 1); + s->child[0] = x; + s->ptr = conv2d_gen_aux(x->d[2], x->d[3], kernel_r, kernel_c, stride_r, stride_c, top_pad, left_pad); + s->ptr_size = sizeof(conv_conf_t) * 2; + return kad_finalize_node(s); +} + +static inline conv_conf_t *conv1d_gen_aux(int in_col, int kernel_c, int stride_c, int left_pad) +{ + conv_conf_t *cnn; + cnn = (conv_conf_t*)calloc(1, sizeof(conv_conf_t)); + cnn->kernel_size = kernel_c, cnn->stride = stride_c; + conv_find_par(in_col, kernel_c, stride_c, left_pad, &cnn->pad[0], &cnn->pad[1]); + return cnn; +} + +kad_node_t *kad_conv1d(kad_node_t *x, kad_node_t *w, int stride, int left_pad) +{ + kad_node_t *s; + if (x->n_d != 3 || w->n_d != 3) return 0; + s = kad_new_core(0, 18, 2); + s->child[0] = x, s->child[1] = w; + s->ptr = conv1d_gen_aux(x->d[2], w->d[2], stride, left_pad); + s->ptr_size = sizeof(conv_conf_t); + return kad_finalize_node(s); +} + +kad_node_t *kad_max1d(kad_node_t *x, int kernel_size, int stride, int left_pad) +{ + kad_node_t *s; + if (x->n_d != 3) return 0; + s = kad_new_core(0, 19, 1); + s->child[0] = x; + s->ptr = conv1d_gen_aux(x->d[2], kernel_size, stride, left_pad); + s->ptr_size = sizeof(conv_conf_t); + return kad_finalize_node(s); +} + +kad_node_t *kad_avg1d(kad_node_t *x, int kernel_size, int stride, int left_pad) +{ + kad_node_t *s; + if (x->n_d != 3) return 0; + s = kad_new_core(0, 28, 1); + s->child[0] = x; + s->ptr = conv1d_gen_aux(x->d[2], kernel_size, stride, left_pad); + s->ptr_size = sizeof(conv_conf_t); + return kad_finalize_node(s); +} + +/********** Multi-node pooling **********/ + +static kad_node_t *kad_pooling_general(int op, int n, kad_node_t **x) +{ + int i; + kad_node_t *s; + s = kad_new_core(0, op, n); + s->flag |= KAD_POOL; + for (i = 0; i < n; ++i) + s->child[i] = x[i]; + return kad_finalize_node(s); +} + +kad_node_t *kad_avg(int n, kad_node_t **x) { return kad_pooling_general(10, n, x); } +kad_node_t *kad_max(int n, kad_node_t **x) { return kad_pooling_general(21, n, x); } +kad_node_t *kad_stack(int n, kad_node_t **x) { return kad_pooling_general(35, n, x); } + +kad_node_t *kad_select(int n, kad_node_t **x, int which) +{ + kad_node_t *s; + int32_t i, *aux; + aux = (int32_t*)calloc(1, 4); + *aux = which; + s = kad_new_core(0, 12, n); + for (i = 0; i < n; ++i) s->child[i] = x[i]; + s->flag |= KAD_POOL, s->ptr = aux, s->ptr_size = 4; + return kad_finalize_node(s); +} + +/********** Dimension reduction **********/ + +static kad_node_t *kad_reduce_general(int op, kad_node_t *x, int axis) +{ + kad_node_t *s; + int32_t *aux; + aux = (int32_t*)malloc(4); + aux[0] = axis; + s = kad_new_core(0, op, 1); + s->child[0] = x; + s->ptr = aux, s->ptr_size = 4; + return kad_finalize_node(s); +} + +kad_node_t *kad_reduce_sum(kad_node_t *x, int axis) { return kad_reduce_general(25, x, axis); } +kad_node_t *kad_reduce_mean(kad_node_t *x, int axis) { return kad_reduce_general(26, x, axis); } + +/********** Sampling related **********/ + +kad_node_t *kad_dropout(kad_node_t *x, kad_node_t *y) +{ + kad_node_t *z; + z = kad_op2_core(15, x, y); + z->ptr = kad_rng(), z->ptr_size = sizeof(kad_rng_t); + return z; +} + +kad_node_t *kad_sample_normal(kad_node_t *x) +{ + kad_node_t *z; + z = kad_op1_core(24, x); + z->ptr = kad_rng(), z->ptr_size = sizeof(kad_rng_t); + return z; +} + +/********** Miscellaneous **********/ + +kad_node_t *kad_slice(kad_node_t *x, int axis, int start, int end) +{ + kad_node_t *s; + int32_t *aux; + if (end < start || start < 0) return 0; + aux = (int32_t*)malloc(3 * 4); + aux[0] = axis, aux[1] = start, aux[2] = end; + s = kad_new_core(0, 20, 1); + s->child[0] = x; + s->ptr = aux, s->ptr_size = 3 * 4; + return kad_finalize_node(s); +} + +kad_node_t *kad_concat_array(int axis, int n, kad_node_t **p) +{ + kad_node_t *s; + int32_t i, *aux; + aux = (int32_t*)malloc(4); + aux[0] = axis; + s = kad_new_core(0, 31, n); + for (i = 0; i < n; ++i) + s->child[i] = p[i]; + s->ptr = aux, s->ptr_size = 4; + return kad_finalize_node(s); +} + +kad_node_t *kad_concat(int axis, int n, ...) +{ + int i; + kad_node_t **p, *s; + va_list ap; + p = (kad_node_t**)malloc(n * sizeof(kad_node_t*)); + va_start(ap, n); + for (i = 0; i < n; ++i) p[i] = va_arg(ap, kad_node_p); + va_end(ap); + s = kad_concat_array(axis, n, p); + free(p); + return s; +} + +kad_node_t *kad_reshape(kad_node_t *x, int n_d, int *d) +{ + kad_node_t *s; + int32_t i, *aux = 0; + if (n_d > 0) { + aux = (int32_t*)malloc(n_d * 4); + for (i = 0; i < n_d; ++i) aux[i] = d? d[i] : -1; + } + s = kad_new_core(0, 30, 1); + s->child[0] = x, s->ptr = aux, s->ptr_size = n_d * 4; + return kad_finalize_node(s); +} + +kad_node_t *kad_reverse(kad_node_t *x, int axis) +{ + kad_node_t *s; + int32_t *aux; + aux = (int32_t*)malloc(4); + *aux = axis; + s = kad_new_core(0, 36, 1); + s->child[0] = x, s->ptr = aux, s->ptr_size = 4; + return kad_finalize_node(s); +} + +kad_node_t *kad_switch(int n, kad_node_t **p) +{ + kad_node_t *s; + int32_t i, *aux; + aux = (int32_t*)calloc(1, 4); + s = kad_new_core(0, 12, n); + for (i = 0; i < n; ++i) + s->child[i] = p[i]; + s->ptr = aux, s->ptr_size = 4; + return kad_finalize_node(s); +} + +/*********************** + * Graph linearization * + ***********************/ + +static void kad_mark_back(int n, kad_node_t **v) +{ + int i, j; + for (i = 0; i < n; ++i) { + if (v[i]->n_child == 0) continue; + for (j = 0; j < v[i]->n_child; ++j) + if (kad_is_back(v[i]->child[j])) + break; + if (j < v[i]->n_child) v[i]->flag |= KAD_VAR; + else v[i]->flag &= ~KAD_VAR; + } +} + +static void kad_allocate_internal(int n, kad_node_t **v) +{ + int i; + kad_mark_back(n, v); + for (i = 0; i < n; ++i) { + kad_node_t *p = v[i]; + if (p->n_child == 0) continue; + p->x = (float*)realloc(p->x, kad_len(p) * sizeof(float)); + if (kad_is_back(p)) { + p->g = (float*)realloc(p->g, kad_len(p) * sizeof(float)); + kad_op_list[p->op](p, KAD_ALLOC); + } + } +} + +int kad_sync_dim(int n, kad_node_t **v, int batch_size) +{ + int i, req_alloc = 0, req_sync = 0, old_size = 0; + for (i = 0; i < n; ++i) { + if (kad_is_feed(v[i])) { + old_size = v[i]->d[0]; /* TODO: check if all feeds have the same batch size */ + if (batch_size > 0 && v[i]->d[0] != batch_size) + v[i]->d[0] = batch_size, req_sync = 1; + } else if (v[i]->n_child > 0 && req_sync) + kad_op_list[v[i]->op](v[i], KAD_SYNC_DIM); + } + if (old_size < batch_size) req_alloc = 1; + for (i = 0; i < n; ++i) + if (v[i]->n_child > 0 && v[i]->x == 0) req_alloc = 1; + if (req_alloc) kad_allocate_internal(n, v); + return batch_size > 0? batch_size : old_size; +} + +#define kvec_t(type) struct { size_t n, m; type *a; } + +#define kv_pop(v) ((v).a[--(v).n]) + +#define kv_push(type, v, x) do { \ + if ((v).n == (v).m) { \ + (v).m = (v).m? (v).m<<1 : 2; \ + (v).a = (type*)realloc((v).a, sizeof(type) * (v).m); \ + } \ + (v).a[(v).n++] = (x); \ + } while (0) + +/* IMPORTANT: kad_node_t::tmp MUST BE set to zero before calling this function */ +kad_node_t **kad_compile_array(int *n_node, int n_roots, kad_node_t **roots) +{ + int i; + kvec_t(kad_node_p) stack = {0,0,0}, a = {0,0,0}; + + /* generate kad_node_t::tmp, the count of the parent nodes; shifted by 1; lowest bit to detect fake roots */ + for (i = 0; i < n_roots; ++i) { + roots[i]->tmp = 1; /* mark the root */ + kv_push(kad_node_p, stack, roots[i]); + } + while (stack.n) { + kad_node_t *p = kv_pop(stack); + for (i = 0; i < p->n_child; ++i) { + kad_node_t *q = p->child[i]; + if (q->tmp == 0) kv_push(kad_node_p, stack, q); + q->tmp += 1<<1; + } + } + + /* topological sorting (Kahn's algorithm) */ + for (i = 0; i < n_roots; ++i) + if (roots[i]->tmp>>1 == 0) /* if roots[i]->tmp>>1 != 0, it is not a real root */ + kv_push(kad_node_p, stack, roots[i]); + while (stack.n) { + kad_node_t *p = kv_pop(stack); + kv_push(kad_node_p, a, p); + for (i = 0; i < p->n_child; ++i) { + p->child[i]->tmp -= 1<<1; + if (p->child[i]->tmp>>1 == 0) + kv_push(kad_node_p, stack, p->child[i]); + } + } + free(stack.a); + for (i = 0; i < (int)a.n; ++i) { /* check cycles; no cycles if constructed with kad_add() etc */ + assert(a.a[i]->tmp>>1 == 0); + a.a[i]->tmp = 0; + } + + /* reverse */ + for (i = 0; i < (int)a.n>>1; ++i) { /* reverse a.a[] */ + kad_node_p t; + t = a.a[i], a.a[i] = a.a[a.n-1-i], a.a[a.n-1-i] = t; + } + kad_allocate_internal(a.n, a.a); + + *n_node = a.n; + return a.a; +} + +kad_node_t **kad_compile(int *n_node, int n_roots, ...) +{ + int i; + kad_node_t **roots, **ret; + va_list ap; + + roots = (kad_node_t**)malloc(n_roots * sizeof(kad_node_t*)); + va_start(ap, n_roots); + for (i = 0; i < n_roots; ++i) roots[i] = va_arg(ap, kad_node_p); + va_end(ap); + ret = kad_compile_array(n_node, n_roots, roots); + free(roots); + return ret; +} + +/************************************ + * Miscellaneous on compiled graphs * + ************************************/ + +void kad_delete(int n, kad_node_t **a) +{ + int i; + for (i = 0; i < n; ++i) { + kad_node_t *p = a[i]; + if (p->n_child) { + free(p->x); free(p->g); + } + free(p->child); free(p->ptr); free(p->gtmp); free(p); + } + free(a); +} + +int kad_size_var(int n, kad_node_t *const* v) +{ + int c, i; + for (i = c = 0; i < n; ++i) + if (kad_is_var(v[i])) + c += kad_len(v[i]); + return c; +} + +int kad_size_const(int n, kad_node_t *const* v) +{ + int c, i; + for (i = c = 0; i < n; ++i) + if (kad_is_const(v[i])) + c += kad_len(v[i]); + return c; +} + +/********************************** + * Computate values and gradients * + **********************************/ + +static void kad_propagate_marks(int n, kad_node_t **a) +{ + int i, j; + for (i = n - 1; i >= 0; --i) { + kad_node_t *p = a[i]; + if (p->tmp > 0) { + if (kad_is_switch(p)) { + int32_t *aux = (int32_t*)p->ptr; + if (p->child[*aux]->tmp == 0) + p->child[*aux]->tmp = 1; + } else { + for (j = 0; j < p->n_child; ++j) + if (p->child[j]->tmp == 0) + p->child[j]->tmp = 1; + } + } + } +} + +void kad_eval_marked(int n, kad_node_t **a) +{ + int i; + kad_propagate_marks(n, a); + for (i = 0; i < n; ++i) + if (a[i]->n_child && a[i]->tmp > 0) + kad_op_list[a[i]->op](a[i], KAD_FORWARD); + for (i = 0; i < n; ++i) a[i]->tmp = 0; +} + +const float *kad_eval_at(int n, kad_node_t **a, int from) +{ + int i; + if (from < 0 || from >= n) from = n - 1; + for (i = 0; i < n; ++i) a[i]->tmp = (i == from); + kad_eval_marked(n, a); + return a[from]->x; +} + +void kad_grad(int n, kad_node_t **a, int from) +{ + int i; + if (from < 0 || from >= n) from = n - 1; + assert(a[from]->n_d == 0); + for (i = 0; i < n; ++i) a[i]->tmp = (i == from); + kad_propagate_marks(n, a); + for (i = 0; i <= from; ++i) /* set all grandients to zero */ + if (a[i]->g && a[i]->tmp > 0) + memset(a[i]->g, 0, kad_len(a[i]) * sizeof(float)); + for (i = from, a[i]->g[0] = 1.0f; i >= 0; --i) /* backprop */ + if (a[i]->n_child && a[i]->tmp > 0) + kad_op_list[a[i]->op](a[i], KAD_BACKWARD); + for (i = 0; i <= from; ++i) a[i]->tmp = 0; +} + +/*********************** + * Load and save graph * + ***********************/ + +static void kad_save1(FILE *fp, const kad_node_t *p) +{ + fwrite(&p->ext_label, 4, 1, fp); + fwrite(&p->ext_flag, 4, 1, fp); + fwrite(&p->flag, 1, 1, fp); + fwrite(&p->n_child, 4, 1, fp); + if (p->n_child) { + int32_t j, pre = p->pre? p->pre->tmp : -1; + fwrite(&p->op, 2, 1, fp); + for (j = 0; j < p->n_child; ++j) + fwrite(&p->child[j]->tmp, 4, 1, fp); + fwrite(&pre, 4, 1, fp); + fwrite(&p->ptr_size, 4, 1, fp); + if (p->ptr_size > 0 && p->ptr) + fwrite(p->ptr, p->ptr_size, 1, fp); + } else { + fwrite(&p->n_d, 1, 1, fp); + if (p->n_d) fwrite(p->d, 4, p->n_d, fp); + } +} + +static kad_node_t *kad_load1(FILE *fp, kad_node_t **node) +{ + kad_node_t *p; + p = (kad_node_t*)calloc(1, sizeof(kad_node_t)); + (void) !fread(&p->ext_label, 4, 1, fp); + (void) !fread(&p->ext_flag, 4, 1, fp); + (void) !fread(&p->flag, 1, 1, fp); + (void) !fread(&p->n_child, 4, 1, fp); + if (p->n_child) { + int32_t j, k; + p->child = (kad_node_t**)calloc(p->n_child, sizeof(kad_node_t*)); + (void) !fread(&p->op, 2, 1, fp); + for (j = 0; j < p->n_child; ++j) { + (void) !fread(&k, 4, 1, fp); + p->child[j] = node? node[k] : 0; + } + (void) !fread(&k, 4, 1, fp); + if (k >= 0) p->pre = node[k]; + (void) !fread(&p->ptr_size, 4, 1, fp); + if (p->ptr_size > 0) { + p->ptr = malloc(p->ptr_size); + (void) !fread(p->ptr, p->ptr_size, 1, fp); + } + } else { + (void) !fread(&p->n_d, 1, 1, fp); + if (p->n_d) (void) !fread(p->d, 4, p->n_d, fp); + } + return p; +} + +int kad_save(FILE *fp, int n_node, kad_node_t **node) +{ + int32_t i, k = n_node; + fwrite(&k, 4, 1, fp); + for (i = 0; i < n_node; ++i) node[i]->tmp = i; + for (i = 0; i < n_node; ++i) kad_save1(fp, node[i]); + for (i = 0; i < n_node; ++i) node[i]->tmp = 0; + return 0; +} + +kad_node_t **kad_load(FILE *fp, int *_n_node) +{ + int32_t i, n_node; + kad_node_t **node; + (void) !fread(&n_node, 4, 1, fp); + node = (kad_node_t**)malloc(n_node * sizeof(kad_node_t*)); + for (i = 0; i < n_node; ++i) { + kad_node_t *p; + p = node[i] = kad_load1(fp, node); + if (p->n_child) { + kad_op_list[p->op](p, KAD_ALLOC); + kad_op_list[p->op](p, KAD_SYNC_DIM); + } + } + *_n_node = n_node; + kad_mark_back(n_node, node); + return node; +} + +/*************** + * Graph clone * + ***************/ + +static inline kad_node_t *kad_dup1(const kad_node_t *p) +{ + kad_node_t *q; + q = (kad_node_t*)malloc(sizeof(kad_node_t)); + memcpy(q, p, sizeof(kad_node_t)); + q->pre = 0, q->tmp = 0, q->gtmp = 0; + if (p->ptr && p->ptr_size > 0) { + if (kad_use_rng(p) && !(p->flag & KAD_SHARE_RNG) && p->ptr_size == sizeof(kad_rng_t)) { + q->ptr = kad_rng(); /* each time step uses a different RNG */ + } else { + q->ptr = malloc(p->ptr_size); + memcpy(q->ptr, p->ptr, p->ptr_size); + } + } + if (q->n_child) { + q->x = q->g = 0; + q->child = (kad_node_t**)calloc(q->n_child, sizeof(kad_node_t*)); + } + return q; +} + +kad_node_t **kad_clone(int n, kad_node_t **v, int batch_size) +{ + int i, j; + kad_node_t **u; + u = (kad_node_t**)calloc(n, sizeof(kad_node_t*)); + for (i = 0; i < n; ++i) v[i]->tmp = i; + for (i = 0; i < n; ++i) { + kad_node_t *p = v[i], *q; + q = u[i] = kad_dup1(p); + if (p->pre) q->pre = u[p->pre->tmp]; + if (p->n_child) { + for (j = 0; j < p->n_child; ++j) + q->child[j] = u[p->child[j]->tmp]; + } else if (!kad_is_feed(p)) { + q->x = (float*)malloc(kad_len(p) * sizeof(float)); + memcpy(q->x, p->x, kad_len(p) * sizeof(float)); + q->g = 0; + } + } + for (i = 0; i < n; ++i) v[i]->tmp = 0; + kad_sync_dim(n, u, batch_size); /* this will allocate x[] and g[] at internal nodes */ + return u; +} + +/************** + * Unroll RNN * + **************/ + +typedef struct { + int32_t n, m; + kad_node_t **v; +} nodes_t; + +static inline void push_nodes(nodes_t *w, kad_node_t *p) +{ + if (w->n == w->m) { + w->m = w->m? w->m<<1 : 16; + w->v = (kad_node_t**)realloc(w->v, w->m * sizeof(kad_node_t*)); + } + w->v[w->n++] = p; +} + +static void kad_unroll_helper(int n_v, kad_node_t **v, int i_pivot, kad_node_t **t, int len, nodes_t *w) +{ + int i, j, l; + uint8_t *flag; + kad_node_t **aux; + + assert(kad_is_pivot(v[i_pivot]) && t[i_pivot] == 0); + t[i_pivot] = kad_dup1(v[i_pivot]); + t[i_pivot]->n_child = len; + t[i_pivot]->child = (kad_node_t**)realloc(t[i_pivot]->child, len * sizeof(kad_node_t*)); + + flag = (uint8_t*)calloc(n_v, 1); + for (i = i_pivot, flag[i] = 16; i >= 0; --i) { + if (i < i_pivot && kad_is_pivot(v[i])) continue; /* don't trespass other pivots */ + if (flag[i]&16) /* flag 16: nodes to unroll */ + for (j = 0; j < v[i]->n_child; ++j) + flag[v[i]->child[j]->tmp] = 16; + } + for (i = 0; i < i_pivot; ++i) { + if (!(flag[i]&16)) continue; + if (kad_is_var(v[i]) || kad_is_const(v[i]) || kad_is_pivot(v[i])) flag[i] |= 1; /* external nodes that should not be duplicated */ + if (v[i]->pre) flag[v[i]->pre->tmp] |= 2; + } + flag[v[i_pivot]->child[0]->tmp] |= 4; + aux = (kad_node_t**)calloc(n_v, sizeof(kad_node_t*)); + for (l = 0; l < len; ++l) { + for (i = 0; i < i_pivot; ++i) { + if (!(flag[i]&16) || ((flag[i]&3) && t[i])) continue; + t[i] = kad_dup1(v[i]); + if (v[i]->n_child) + for (j = 0; j < v[i]->n_child; ++j) + t[i]->child[j] = t[v[i]->child[j]->tmp]; + if (flag[i]&4) t[i_pivot]->child[l] = t[i]; + if (l == 0 && (flag[i]&2)) aux[i] = t[i]; + if (v[i]->pre) { + t[v[i]->pre->tmp] = t[i]; + if (l == len - 1) t[i]->pre = aux[v[i]->pre->tmp]; /* this forms a cycle! */ + } + push_nodes(w, t[i]); + } + } + push_nodes(w, t[i_pivot]); + free(aux); free(flag); +} + +int kad_n_pivots(int n_v, kad_node_t **v) +{ + int i, n_pivots = 0; + for (i = 0; i < n_v; ++i) + if (kad_is_pivot(v[i])) ++n_pivots; + return n_pivots; +} + +kad_node_t **kad_unroll(int n_v, kad_node_t **v, int *new_n, int *len) +{ + int i, j, n_pivots = 0; + kad_node_t **t; + nodes_t w = {0,0,0}; + + t = (kad_node_t**)calloc(n_v, sizeof(kad_node_t*)); + n_pivots = kad_n_pivots(n_v, v); + for (i = 0; i < n_v; ++i) v[i]->tmp = i; + if (n_pivots) { + int k, *i_pivots; + i_pivots = (int*)calloc(n_pivots, sizeof(int)); + for (i = k = 0; i < n_v; ++i) /* collect pivots */ + if (kad_is_pivot(v[i])) i_pivots[k++] = i; + for (i = 0; i < n_pivots; ++i) /* unroll each pivot, from the lowest to the highest */ + kad_unroll_helper(n_v, v, i_pivots[i], t, len[i], &w); + free(i_pivots); + } + for (i = 0; i < n_v; ++i) { /* copy over the rest of nodes */ + if (t[i]) continue; + t[i] = kad_dup1(v[i]); + if (v[i]->n_child) + for (j = 0; j < v[i]->n_child; ++j) + t[i]->child[j] = t[v[i]->child[j]->tmp]; + push_nodes(&w, t[i]); + } + free(t); + for (i = 0; i < n_v; ++i) v[i]->tmp = 0; + for (i = 0; i < w.n; ++i) /* stack may change the output dimension */ + if (w.v[i]->n_child > 0) + kad_op_list[w.v[i]->op](w.v[i], KAD_SYNC_DIM); + kad_allocate_internal(w.n, w.v); + *new_n = w.n; + return w.v; +} + +/******************************** + * Vector and matrix operations * + ********************************/ + +#ifdef __SSE__ +#include <xmmintrin.h> + +static inline float kad_sdot(int n, const float *x, const float *y) /* BLAS sdot using SSE */ +{ + int i, n8 = n>>3<<3; + __m128 vs1, vs2; + float s, t[4]; + vs1 = _mm_setzero_ps(); + vs2 = _mm_setzero_ps(); + for (i = 0; i < n8; i += 8) { + __m128 vx1, vx2, vy1, vy2; + vx1 = _mm_loadu_ps(&x[i]); + vx2 = _mm_loadu_ps(&x[i+4]); + vy1 = _mm_loadu_ps(&y[i]); + vy2 = _mm_loadu_ps(&y[i+4]); + vs1 = _mm_add_ps(vs1, _mm_mul_ps(vx1, vy1)); + vs2 = _mm_add_ps(vs2, _mm_mul_ps(vx2, vy2)); + } + for (s = 0.; i < n; ++i) s += x[i] * y[i]; + _mm_storeu_ps(t, vs1); + s += t[0] + t[1] + t[2] + t[3]; + _mm_storeu_ps(t, vs2); + s += t[0] + t[1] + t[2] + t[3]; + return s; +} +static inline void kad_saxpy_inlined(int n, float a, const float *x, float *y) /* BLAS saxpy using SSE */ +{ + int i, n8 = n>>3<<3; + __m128 va; + va = _mm_set1_ps(a); + for (i = 0; i < n8; i += 8) { + __m128 vx1, vx2, vy1, vy2, vt1, vt2; + vx1 = _mm_loadu_ps(&x[i]); + vx2 = _mm_loadu_ps(&x[i+4]); + vy1 = _mm_loadu_ps(&y[i]); + vy2 = _mm_loadu_ps(&y[i+4]); + vt1 = _mm_add_ps(_mm_mul_ps(va, vx1), vy1); + vt2 = _mm_add_ps(_mm_mul_ps(va, vx2), vy2); + _mm_storeu_ps(&y[i], vt1); + _mm_storeu_ps(&y[i+4], vt2); + } + for (; i < n; ++i) y[i] += a * x[i]; +} +#else +static inline float kad_sdot(int n, const float *x, const float *y) /* BLAS sdot */ +{ + int i; + float s = 0.; + for (i = 0; i < n; ++i) s += x[i] * y[i]; + return s; +} +static inline void kad_saxpy_inlined(int n, float a, const float *x, float *y) // BLAS saxpy +{ + int i; + for (i = 0; i < n; ++i) y[i] += a * x[i]; +} +#endif + +void kad_vec_mul_sum(int n, float *a, const float *b, const float *c) +{ + int i; + for (i = 0; i < n; ++i) a[i] += b[i] * c[i]; +} + +/* This is actually lapack not cblas, but this definition is used */ +#ifdef HAVE_CBLAS +#ifndef __APPLE__ +/* As gfortran mangles names */ +#define ssyev ssyev_ +#endif +extern void ssyev(const char* jobz, const char* uplo, int* n, float* a, int* lda, float* w, float* work, int* lwork, int* info); +#endif + +#ifdef HAVE_CBLAS_SGEMM + +#ifdef HAVE_CBLAS_H +#include "cblas.h" +#else +/* Poor man approach, thanks for that Apple */ +enum CBLAS_ORDER {CblasRowMajor=101, CblasColMajor=102 }; +enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112 }; +extern void cblas_sgemm(const enum CBLAS_ORDER Order, + const enum CBLAS_TRANSPOSE TA, + const enum CBLAS_TRANSPOSE TB, + const int M, const int N, const int K, + const float alpha, const float *A, const int lda, + const float *B, const int ldb, const float beta, + float *C, const int ldc); +#endif + +void kad_sgemm_simple(int trans_A, int trans_B, int M, int N, int K, const float *A, const float *B, float *C) +{ + cblas_sgemm(CblasRowMajor, trans_A? CblasTrans : CblasNoTrans, trans_B? CblasTrans : CblasNoTrans, M, N, K, 1.0f, A, trans_A? M : K, B, trans_B? K : N, 1.0f, C, N); +} +#else +void kad_sgemm_simple(int trans_A, int trans_B, int M, int N, int K, const float *A, const float *B, float *C) /* simplified BLAS sgemm */ +{ + static const int x = 16; + int i, j, k; + if (!trans_A && trans_B) { + for (i = 0; i < M; i += x) + for (j = 0; j < N; j += x) { + int ii, ie = M < i + x? M : i + x; + int jj, je = N < j + x? N : j + x; + for (ii = i; ii < ie; ++ii) { /* loop tiling */ + const float *aii = A + ii * K, *bjj; + float *cii = C + ii * N; + for (jj = j, bjj = B + j * K; jj < je; ++jj, bjj += K) + cii[jj] += kad_sdot(K, aii, bjj); + } + } + } else if (!trans_A && !trans_B) { + for (i = 0; i < M; ++i) + for (k = 0; k < K; ++k) + kad_saxpy_inlined(N, A[i*K+k], &B[k*N], &C[i*N]); + } else if (trans_A && !trans_B) { + for (k = 0; k < K; ++k) + for (i = 0; i < M; ++i) + kad_saxpy_inlined(N, A[k*M+i], &B[k*N], &C[i*N]); + } else abort(); /* not implemented for (trans_A && trans_B) */ +} +#endif + +#ifdef HAVE_CBLAS_SAXPY +#ifndef HAVE_CBLAS_H +extern void cblas_saxpy(const int __N, + const float __alpha, const float *__X, const int __incX, float *__Y, const int __incY); +#endif + +void kad_saxpy(int n, float a, const float *x, float *y) { cblas_saxpy(n, a, x, 1, y, 1); } +#else +void kad_saxpy(int n, float a, const float *x, float *y) { kad_saxpy_inlined(n, a, x, y); } +#endif + +bool kad_ssyev_simple(int N, float *A, float *eigenvals) +{ +#ifndef HAVE_CBLAS + return false; +#else + int n = N, lda = N, info, lwork; + float wkopt; + float *work; + + /* Query and allocate the optimal workspace */ + lwork = -1; + ssyev ("Vectors", "Upper", &n, A, &lda, eigenvals, &wkopt, &lwork, &info); + lwork = wkopt; + work = (float*) g_malloc(lwork * sizeof(double)); + ssyev ("Vectors", "Upper", &n, A, &lda, eigenvals, work, &lwork, &info); + /* Check for convergence */ + if (info > 0) { + g_free (work); + + return false; + } + + g_free (work); + + return true; +#endif +} + +/*************************** + * Random number generator * + ***************************/ + +static kad_rng_t kad_rng_dat = { {0x50f5647d2380309dULL, 0x91ffa96fc4c62cceULL}, 0.0, 0, 0 }; + +static inline uint64_t kad_splitmix64(uint64_t x) +{ + uint64_t z = (x += 0x9E3779B97F4A7C15ULL); + z = (z ^ (z >> 30)) * 0xBF58476D1CE4E5B9ULL; + z = (z ^ (z >> 27)) * 0x94D049BB133111EBULL; + return z ^ (z >> 31); +} + +static inline uint64_t kad_xoroshiro128plus_next(kad_rng_t *r) +{ + const uint64_t s0 = r->s[0]; + uint64_t s1 = r->s[1]; + const uint64_t result = s0 + s1; + s1 ^= s0; + r->s[0] = (s0 << 55 | s0 >> 9) ^ s1 ^ (s1 << 14); + r->s[1] = s0 << 36 | s0 >> 28; + return result; +} + +static inline void kad_xoroshiro128plus_jump(kad_rng_t *r) +{ + static const uint64_t JUMP[] = { 0xbeac0467eba5facbULL, 0xd86b048b86aa9922ULL }; + uint64_t s0 = 0, s1 = 0; + int i, b; + for (i = 0; i < 2; ++i) + for (b = 0; b < 64; b++) { + if (JUMP[i] & 1ULL << b) + s0 ^= r->s[0], s1 ^= r->s[1]; + kad_xoroshiro128plus_next(r); + } + r->s[0] = s0, r->s[1] = s1; +} + +void kad_srand(void *d, uint64_t seed) +{ + kad_rng_t *r = d? (kad_rng_t*)d : &kad_rng_dat; + r->n_gset = 0.0, r->n_iset = 0; + r->s[0] = kad_splitmix64(seed); + r->s[1] = kad_splitmix64(r->s[0]); +} + +void *kad_rng(void) +{ + kad_rng_t *r; + r = (kad_rng_t*)calloc(1, sizeof(kad_rng_t)); + kad_xoroshiro128plus_jump(&kad_rng_dat); + r->s[0] = kad_rng_dat.s[0], r->s[1] = kad_rng_dat.s[1]; + return r; +} + +uint64_t kad_rand(void *d) { return kad_xoroshiro128plus_next(d? (kad_rng_t*)d : &kad_rng_dat); } + +double kad_drand(void *d) +{ + union { uint64_t i; double d; } u; + u.i = 0x3FFULL << 52 | kad_xoroshiro128plus_next(d? (kad_rng_t*)d : &kad_rng_dat) >> 12; + return u.d - 1.0; +} + +double kad_drand_normal(void *d) +{ + kad_rng_t *r = d? (kad_rng_t*)d : &kad_rng_dat; + if (r->n_iset == 0) { + double fac, rsq, v1, v2; + do { + v1 = 2.0 * kad_drand(d) - 1.0; + v2 = 2.0 * kad_drand(d) - 1.0; + rsq = v1 * v1 + v2 * v2; + } while (rsq >= 1.0 || rsq == 0.0); + fac = sqrt(-2.0 * log(rsq) / rsq); + r->n_gset = v1 * fac; + r->n_iset = 1; + return v2 * fac; + } else { + r->n_iset = 0; + return r->n_gset; + } +} + +/************* + * Operators * + *************/ + +static inline void kad_copy_dim1(kad_node_t *dst, const kad_node_t *src) /* set the dimension/shape of dst to src */ +{ + dst->n_d = src->n_d; + if (src->n_d) memcpy(dst->d, src->d, src->n_d * sizeof(int)); +} + +/********** Arithmetic operations **********/ + +int kad_op_add(kad_node_t *p, int action) +{ + int i, n0, n1; + kad_node_t *q[2]; + + q[0] = p->child[0], n0 = kad_len(q[0]); + q[1] = p->child[1], n1 = kad_len(q[1]); + if (action == KAD_SYNC_DIM) { + if (n0 % n1 != 0) return -1; + kad_copy_dim1(p, q[0]); + } else if (action == KAD_FORWARD) { + assert(n0 >= n1); + memcpy(p->x, q[0]->x, n0 * sizeof(float)); + for (i = 0; i < n0; i += n1) + kad_saxpy(n1, 1.0f, q[1]->x, p->x + i); + } else if (action == KAD_BACKWARD) { + if (kad_is_back(q[0])) kad_saxpy(n0, 1.0f, p->g, q[0]->g); + if (kad_is_back(q[1])) + for (i = 0; i < n0; i += n1) + kad_saxpy(n1, 1.0f, p->g + i, q[1]->g); + } + return 0; +} + +int kad_op_sub(kad_node_t *p, int action) +{ + int i, n0, n1; + kad_node_t *q[2]; + + q[0] = p->child[0], n0 = kad_len(q[0]); + q[1] = p->child[1], n1 = kad_len(q[1]); + if (action == KAD_SYNC_DIM) { + if (n0 % n1 != 0) return -1; + kad_copy_dim1(p, q[0]); + } else if (action == KAD_FORWARD) { + assert(n0 >= n1); + memcpy(p->x, q[0]->x, n0 * sizeof(float)); + for (i = 0; i < n0; i += n1) + kad_saxpy(n1, -1.0f, q[1]->x, p->x + i); + } else if (action == KAD_BACKWARD) { + if (kad_is_back(q[0])) kad_saxpy(n0, 1.0f, p->g, q[0]->g); + if (kad_is_back(q[1])) + for (i = 0; i < n0; i += n1) + kad_saxpy(n1, -1.0f, p->g + i, q[1]->g); + } + return 0; +} + +int kad_op_mul(kad_node_t *p, int action) +{ + int i, n0, n1; + kad_node_t *q[2]; + + q[0] = p->child[0], n0 = kad_len(q[0]); + q[1] = p->child[1], n1 = kad_len(q[1]); + if (action == KAD_SYNC_DIM) { + if (n0 % n1 != 0) return -1; + kad_copy_dim1(p, q[0]); + } else if (action == KAD_FORWARD) { + assert(n0 >= n1); + memset(p->x, 0, n0 * sizeof(float)); + if (q[0]->x != 0 && q[1]->x != 0) + for (i = 0; i < n0; i += n1) /* TODO: optimize when n1==1 */ + kad_vec_mul_sum(n1, p->x + i, q[0]->x + i, q[1]->x); + } else if (action == KAD_BACKWARD) { + if (kad_is_back(q[0]) && q[1]->x) + for (i = 0; i < n0; i += n1) + kad_vec_mul_sum(n1, q[0]->g + i, p->g + i, q[1]->x); + if (kad_is_back(q[1]) && q[0]->x) + for (i = 0; i < n0; i += n1) + kad_vec_mul_sum(n1, q[1]->g, p->g + i, q[0]->x + i); + } + return 0; +} + +int kad_op_cmul(kad_node_t *p, int action) +{ + int i, n_a_row, n_b_row, n_col, n_a_col = 1, n_b_col = 1; + kad_node_t *q[2]; + + q[0] = p->child[0], q[1] = p->child[1]; + n_col = q[0]->d[q[0]->n_d - 1] > q[1]->d[q[1]->n_d - 1]? q[0]->d[q[0]->n_d - 1] : q[1]->d[q[1]->n_d - 1]; + for (i = q[0]->n_d - 1; i >= 0; --i) if (n_a_col < n_col) n_a_col *= q[0]->d[i]; + for (i = q[1]->n_d - 1; i >= 0; --i) if (n_b_col < n_col) n_b_col *= q[1]->d[i]; + n_a_row = kad_len(q[0]) / n_a_col, n_b_row = kad_len(q[1]) / n_b_col; + if (action == KAD_SYNC_DIM) { + if (n_a_col != n_b_col) return -1; + p->n_d = 2, p->d[0] = n_a_row, p->d[1] = n_b_row; + } else if (action == KAD_FORWARD) { + memset(p->x, 0, n_a_row * n_b_row * sizeof(float)); + if (q[0]->x && q[1]->x) + kad_sgemm_simple(0, 1, n_a_row, n_b_row, n_col, q[0]->x, q[1]->x, p->x); /* Y = X * trans(W) */ + } else if (action == KAD_BACKWARD) { + if (kad_is_back(q[0]) && q[1]->x) + kad_sgemm_simple(0, 0, n_a_row, n_col, n_b_row, p->g, q[1]->x, q[0]->g); /* G_x <- G_y * W */ + if (kad_is_back(q[1]) && q[0]->x) + kad_sgemm_simple(1, 0, n_b_row, n_col, n_a_row, p->g, q[0]->x, q[1]->g); /* G_w <- trans(G_y) * X */ + } + return 0; +} + +int kad_op_matmul(kad_node_t *p, int action) /* TODO: matmul and cmul have different broadcasting rules */ +{ + int n_a_row, n_b_row, n_a_col, n_b_col; + kad_node_t *q[2]; + + q[0] = p->child[0]; + q[1] = p->child[1]; + n_a_row = q[0]->n_d == 1? 1 : q[0]->d[0]; + n_b_row = q[1]->n_d == 1? 1 : q[1]->d[0]; + n_a_col = kad_len(q[0]) / n_a_row; + n_b_col = kad_len(q[1]) / n_b_row; + if (action == KAD_SYNC_DIM) { + if (n_a_col != n_b_row) return -1; + p->n_d = 2, p->d[0] = n_a_row, p->d[1] = n_b_col; + } else if (action == KAD_FORWARD) { + memset(p->x, 0, n_a_row * n_b_col * sizeof(float)); + if (q[0]->x && q[1]->x) + kad_sgemm_simple(0, 0, n_a_row, n_b_col, n_a_col, q[0]->x, q[1]->x, p->x); /* Y = X * W */ + } else if (action == KAD_BACKWARD) { + if (kad_is_back(q[0]) && q[1]->x) + kad_sgemm_simple(0, 1, n_a_row, n_a_col, n_b_col, p->g, q[1]->x, q[0]->g); /* G_x <- G_y * trans(W) */ + if (kad_is_back(q[1]) && q[0]->x) + kad_sgemm_simple(1, 0, n_b_row, n_b_col, n_a_row, q[0]->x, p->g, q[1]->g); /* G_y <- trans(A) * G_y */ + } + return 0; +} + +int kad_op_square(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) + p->x[i] = q->x[i] * q->x[i]; + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] * (q->x[i] + q->x[i]); + } + return 0; +} + +int kad_op_1minus(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) p->x[i] = 1.0f - q->x[i]; + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + kad_saxpy(n, -1.0f, p->g, q->g); + } + return 0; +} + +int kad_op_exp(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) p->x[i] = expf(q->x[i]); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] * p->x[i]; + } + return 0; +} + +int kad_op_log(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) p->x[i] = logf(q->x[i]); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] / q->x[i]; + } + return 0; +} + +int kad_op_reduce_sum(kad_node_t *p, int action) +{ + kad_node_t *q = p->child[0]; + int i, j, k, axis, d0, d1; + + assert(p->ptr); + axis = *(int32_t*)p->ptr; + if (axis < 0 || axis >= q->n_d) return -1; + for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i]; + for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i]; + if (action == KAD_SYNC_DIM) { + p->n_d = q->n_d - 1; + for (i = j = 0; i < q->n_d; ++i) + if (i != axis) p->d[j++] = q->d[i]; + } else if (action == KAD_FORWARD) { + memset(p->x, 0, kad_len(p) * sizeof(float)); + for (i = 0; i < d0; ++i) + for (j = 0; j < q->d[axis]; ++j) + for (k = 0; k < d1; ++k) + p->x[i * d1 + k] += q->x[(i * q->d[axis] + j) * d1 + k]; + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < d0; ++i) + for (j = 0; j < q->d[axis]; ++j) + for (k = 0; k < d1; ++k) + q->g[(i * q->d[axis] + j) * d1 + k] += p->g[i * d1 + k]; + } + return 0; +} + +int kad_op_reduce_mean(kad_node_t *p, int action) +{ + kad_node_t *q = p->child[0]; + int i, j, k, axis, d0, d1; + + assert(p->ptr); + axis = *(int32_t*)p->ptr; + if (axis < 0 || axis >= q->n_d) return -1; + for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i]; + for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i]; + if (action == KAD_SYNC_DIM) { + p->n_d = q->n_d - 1; + for (i = j = 0; i < q->n_d; ++i) + if (i != axis) p->d[j++] = q->d[i]; + } else if (action == KAD_FORWARD) { + float t = 1.0f / q->d[axis]; + memset(p->x, 0, kad_len(p) * sizeof(float)); + for (i = 0; i < d0; ++i) + for (j = 0; j < q->d[axis]; ++j) + for (k = 0; k < d1; ++k) + p->x[i * d1 + k] += t * q->x[(i * q->d[axis] + j) * d1 + k]; + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + float t = 1.0f / q->d[axis]; + for (i = 0; i < d0; ++i) + for (j = 0; j < q->d[axis]; ++j) + for (k = 0; k < d1; ++k) + q->g[(i * q->d[axis] + j) * d1 + k] += t * p->g[i * d1 + k]; + } + return 0; +} + +/********** Miscellaneous **********/ + +int kad_op_dropout(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + assert(p->child[1]->n_d == 0); + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_ALLOC) { + if (kad_is_back(p->child[0])) + p->gtmp = realloc(p->gtmp, n); + } else if (action == KAD_FORWARD) { + float r = kad_is_const(q) || kad_is_var(q)? 0.0f : *p->child[1]->x, z = 1.0f / (1.0f - r); + uint8_t *flag = (uint8_t*)p->gtmp; + for (i = 0; i < n; ++i) { + int kept = (kad_drand(p->ptr) >= r); + p->x[i] = kept? q->x[i] * z : 0.0f; + if (flag) flag[i] = kept; + } + } else if (action == KAD_BACKWARD && kad_is_back(p->child[0])) { + float r = kad_is_const(q) || kad_is_var(q)? 0.0f : *p->child[1]->x, z = 1.0f / (1.0f - r); + uint8_t *flag = (uint8_t*)p->gtmp; + for (i = 0; i < n; ++i) + if (flag[i]) q->g[i] += z * p->g[i]; + } + return 0; +} + +int kad_op_sample_normal(kad_node_t *p, int action) /* not tested */ +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_ALLOC) { + if (kad_is_back(p->child[0])) + p->gtmp = realloc(p->gtmp, n * sizeof(float)); + } else if (action == KAD_FORWARD) { + float *r = (float*)p->gtmp; + for (i = 0; i < n; ++i) { + float z; + z = (float)kad_drand_normal(p->ptr); + p->x[i] = q->x[i] * z; + if (r) r[i] = z; + } + } else if (action == KAD_BACKWARD && kad_is_back(p->child[0])) { + float *r = (float*)p->gtmp; + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] * r[i]; + } + return 0; +} + +int kad_op_slice(kad_node_t *p, int action) +{ + kad_node_t *q = p->child[0]; + int32_t *aux, *range; + int i, axis, d0, d1; + + assert(p->ptr); + aux = (int32_t*)p->ptr, axis = aux[0], range = aux + 1; + if (axis < 0 || axis >= q->n_d) return -1; + for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i]; + for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i]; + if (action == KAD_SYNC_DIM) { + if (range[0] >= range[1] || range[0] < 0 || range[1] > q->d[axis]) return -1; + kad_copy_dim1(p, q); + p->d[axis] = range[1] - range[0]; + } else if (action == KAD_FORWARD) { + for (i = 0; i < d0; ++i) + memcpy(&p->x[i * p->d[axis] * d1], &q->x[(i * q->d[axis] + range[0]) * d1], (range[1] - range[0]) * d1 * sizeof(float)); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < d0; ++i) + kad_saxpy((range[1] - range[0]) * d1, 1.0f, &p->g[i * p->d[axis] * d1], &q->g[(i * q->d[axis] + range[0]) * d1]); + } + return 0; +} + +int kad_op_concat(kad_node_t *p, int action) +{ + kad_node_t *q = p->child[0]; + int32_t *aux; + int i, j, k, axis, d0, d1; + + assert(p->ptr); + aux = (int32_t*)p->ptr, axis = aux[0]; + for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i]; + for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i]; + if (action == KAD_SYNC_DIM) { + for (i = 1; i < p->n_child; ++i) { + if (p->child[i]->n_d != q->n_d) return -1; + for (j = 0; j < q->n_d; ++j) + if (j != axis && q->d[j] != p->child[i]->d[j]) return -1; + } + kad_copy_dim1(p, q); + for (i = 1; i < p->n_child; ++i) + p->d[axis] += p->child[i]->d[axis]; + } else if (action == KAD_FORWARD) { + for (i = 0; i < d0; ++i) + for (j = k = 0; j < p->n_child; ++j) { + q = p->child[j]; + memcpy(&p->x[(i * p->d[axis] + k) * d1], &q->x[i * q->d[axis] * d1], q->d[axis] * d1 * sizeof(float)); + k += q->d[axis]; + } + } else if (action == KAD_BACKWARD) { + for (i = 0; i < d0; ++i) + for (j = k = 0; j < p->n_child; ++j) { + q = p->child[j]; + if (!kad_is_back(q)) continue; + kad_saxpy(q->d[axis] * d1, 1.0f, &p->g[(i * p->d[axis] + k) * d1], &q->g[i * q->d[axis] * d1]); + k += q->d[axis]; + } + } + return 0; +} + +int kad_op_reshape(kad_node_t *p, int action) +{ + kad_node_t *q = p->child[0]; + + if (action == KAD_SYNC_DIM) { + if (p->ptr) { + int32_t *aux = (int32_t*)p->ptr; + int i, len = 1, n_missing = 0; + p->n_d = p->ptr_size / 4; + for (i = 0; i < p->n_d; ++i) p->d[i] = aux[i]; + for (i = 0; i < p->n_d; ++i) + if (p->d[i] <= 0) ++n_missing; + else len *= p->d[i]; + if (n_missing == 0 && len != kad_len(q)) return -1; + if (n_missing > 1) { /* attempt to infer missing dimensions except the last one */ + for (i = 0; i < p->n_d; ++i) + if (p->d[i] <= 0 && i < q->n_d) { + p->d[i] = q->d[i], len *= p->d[i]; + if (--n_missing == 1) break; + } + if (n_missing > 1) return -1; + } + if (n_missing == 1) { /* infer the last missing dimension */ + if (kad_len(q) % len != 0) return -1; + for (i = 0; i < p->n_d; ++i) + if (p->d[i] <= 0) p->d[i] = kad_len(q) / len; + } + } else kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + memcpy(p->x, q->x, kad_len(p) * sizeof(float)); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + kad_saxpy(kad_len(p), 1.0f, p->g, q->g); + } + return 0; +} + +int kad_op_reverse(kad_node_t *p, int action) +{ + kad_node_t *q = p->child[0]; + int axis, i, j, n, d0, d1; + + axis = p->ptr? *(int32_t*)p->ptr : 0; + if (axis < 0) axis += q->n_d; + assert(axis >= 0 && axis < q->n_d); + for (i = 0, d0 = 1; i < axis; ++i) d0 *= q->d[i]; + n = q->d[axis]; + for (i = axis + 1, d1 = 1; i < q->n_d; ++i) d1 *= q->d[i]; + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < d0; ++i) + for (j = 0; j < n; ++j) + memcpy(&p->x[(i * n + n - 1 - j) * d1], &q->x[(i * n + j) * d1], d1 * sizeof(float)); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < d0; ++i) + for (j = 0; j < n; ++j) + kad_saxpy(d1, 1.0f, &p->g[(i * n + n - 1 - j) * d1], &q->g[(i * n + j) * d1]); + } + return 0; +} + +/********** Cost functions **********/ + +int kad_op_mse(kad_node_t *p, int action) +{ + kad_node_t *y1 = p->child[0]; /* test */ + kad_node_t *y0 = p->child[1]; /* truth */ + int i, n; + + n = kad_len(y0); + if (action == KAD_SYNC_DIM) { + if (n != kad_len(y1)) return -1; + p->n_d = 0; + } else if (action == KAD_FORWARD) { + double cost = 0.0; + for (i = 0; i < n; ++i) + cost += (y1->x[i] - y0->x[i]) * (y1->x[i] - y0->x[i]); + p->x[0] = (float)(cost / n); + } else if (action == KAD_BACKWARD && kad_is_back(y1)) { + float t = 2.0f * p->g[0] / n; + for (i = 0; i < n; ++i) + y1->g[i] += t * (y1->x[i] - y0->x[i]); + } + return 0; +} + +int kad_op_ce_bin(kad_node_t *p, int action) +{ + static const float tiny = 1e-9f; + kad_node_t *y1 = p->child[0]; /* test */ + kad_node_t *y0 = p->child[1]; /* truth */ + int i, n; + + n = kad_len(y0); + if (action == KAD_SYNC_DIM) { + if (n != kad_len(y1)) return -1; + p->n_d = 0; + } else if (action == KAD_FORWARD) { + double cost = 0.0; + for (i = 0; i < n; ++i) { + if (y0->x[i] > 0.0f) + cost += y0->x[i] * log(y0->x[i] / (y1->x[i] > tiny? y1->x[i] : tiny)); + if (1.0f - y0->x[i] > 0.0f) + cost += (1.0f - y0->x[i]) * log((1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny)); + } + p->x[0] = (float)(cost / n); + } else if (action == KAD_BACKWARD && kad_is_back(y1)) { + float t = p->g[0] / n; + for (i = 0; i < n; ++i) { + if (y0->x[i] > 0.0f) + y1->g[i] -= t * y0->x[i] / (y1->x[i] > tiny? y1->x[i] : tiny); + if (1.0f - y0->x[i] > 0.0f) + y1->g[i] += t * (1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny); + } + } + return 0; +} + +int kad_op_ce_bin_neg(kad_node_t *p, int action) +{ + static const float tiny = 1e-9f; + kad_node_t *y1 = p->child[0]; /* test */ + kad_node_t *y0 = p->child[1]; /* truth */ + int i, n; + + n = kad_len(y0); + if (action == KAD_SYNC_DIM) { + if (n != kad_len(y1)) return -1; + p->n_d = 0; + } else if (action == KAD_FORWARD) { + double cost = 0.0; + for (i = 0; i < n; ++i) { + if (1.0f + y0->x[i] > 0.0f) + cost += .5f * (1.0f + y0->x[i]) * log((1.0f + y0->x[i]) / (1.0f + y1->x[i] > tiny? 1.0f + y1->x[i] : tiny)); + if (1.0f - y0->x[i] > 0.0f) + cost += .5f * (1.0f - y0->x[i]) * log((1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny)); + } + p->x[0] = (float)(cost / n); + } else if (action == KAD_BACKWARD && kad_is_back(y1)) { + float t = p->g[0] / n; + for (i = 0; i < n; ++i) { + if (1.0f + y0->x[i] > 0.0f) + y1->g[i] -= .5f * t * (1.0f + y0->x[i]) / (1.0f + y1->x[i] > tiny? 1.0f + y1->x[i] : tiny); + if (1.0f - y0->x[i] > 0.0f) + y1->g[i] += .5f * t * (1.0f - y0->x[i]) / (1.0f - y1->x[i] > tiny? 1.0f - y1->x[i] : tiny); + } + } + return 0; +} + +int kad_op_ce_multi(kad_node_t *p, int action) +{ + static const float tiny = 1e-9f; + kad_node_t *y1 = p->child[0]; /* test */ + kad_node_t *y0 = p->child[1]; /* truth */ + kad_node_t *c = 0; + int i, j, n1, d0; + + n1 = y0->d[y0->n_d - 1]; + d0 = kad_len(y0) / n1; + if (p->n_child == 3) { + c = p->child[2]; + assert(c->n_d == 1 && c->d[0] == n1); + } + if (action == KAD_SYNC_DIM) { + if (kad_len(y0) != kad_len(y1) || y0->d[y0->n_d - 1] != y1->d[y1->n_d - 1]) return -1; + p->n_d = 0; + } else if (action == KAD_FORWARD) { + double cost = 0.0; + if (c == 0) { + for (j = 0; j < d0; ++j) { + float *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1]; + for (i = 0; i < n1; ++i) + if (x0[i] > 0.0f) + cost += x0[i] * log(x0[i] / (x1[i] > tiny? x1[i] : tiny)); + } + } else { + for (j = 0; j < d0; ++j) { + float *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1]; + for (i = 0; i < n1; ++i) + if (x0[i] > 0.0f) + cost += c->x[i] * x0[i] * log(x0[i] / (x1[i] > tiny? x1[i] : tiny)); + } + } + p->x[0] = (float)(cost / d0); + } else if (action == KAD_BACKWARD && kad_is_back(y1)) { + float t = p->g[0] / d0; + if (c == 0) { + for (j = 0; j < d0; ++j) { + float *g = &y1->g[j * n1], *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1]; + for (i = 0; i < n1; ++i) + g[i] -= t * x0[i] / (x1[i] > tiny? x1[i] : tiny); + } + } else { + for (j = 0; j < d0; ++j) { + float *g = &y1->g[j * n1], *x1 = &y1->x[j * n1], *x0 = &y0->x[j * n1]; + for (i = 0; i < n1; ++i) + g[i] -= t * c->x[i] * x0[i] / (x1[i] > tiny? x1[i] : tiny); + } + } + } + return 0; +} + +/********** Normalization **********/ + +int kad_op_stdnorm(kad_node_t *p, int action) +{ + int i, j, n, m; + kad_node_t *q = p->child[0]; + assert(q->n_d > 0); + n = q->d[q->n_d - 1]; + m = kad_len(q) / n; + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_ALLOC) { + p->gtmp = realloc(p->gtmp, m * sizeof(float)); + } else if (action == KAD_FORWARD) { + float *si = (float*)p->gtmp; + for (j = 0; j < m; ++j) { + float *px = &p->x[j * n], *qx = &q->x[j * n]; + float avg, std_inv; + double s; + for (i = 0, s = 0.0; i < n; ++i) s += qx[i]; + avg = (float)(s / n); + for (i = 0; i < n; ++i) px[i] = qx[i] - avg; + for (i = 0, s = 0.0; i < n; ++i) s += px[i] * px[i]; + std_inv = s == 0.0? 1.0f : (float)(1.0 / sqrt(s / n)); + for (i = 0; i < n; ++i) px[i] *= std_inv; + si[j] = std_inv; + } + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + float *si = (float*)p->gtmp; + for (j = 0; j < m; ++j) { + float *pg = &p->g[j * n], *qg = &q->g[j * n], *px = &p->x[j * n], std_inv = si[j]; + double s, t; + for (i = 0, s = t = 0.0; i < n; ++i) + s += pg[i], t += px[i] * pg[i]; + s /= n, t /= n; + for (i = 0; i < n; ++i) + qg[i] += std_inv * (pg[i] - s - px[i] * t); + } + } + return 0; +} + +/********** Activation functions **********/ + +int kad_op_sigm(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) + p->x[i] = 1.0f / (1.0f + expf(-q->x[i])); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] * (p->x[i] * (1.0f - p->x[i])); + } + return 0; +} + +int kad_op_tanh(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) { + if (q->x[i] < -20.0f) p->x[i] = -1.0f; + else { + float y; + y = expf(-2.0f * q->x[i]); + p->x[i] = (1.0f - y) / (1.0f + y); + } + } + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] * (1.0f - p->x[i] * p->x[i]); + } + return 0; +} + +int kad_op_relu(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) + p->x[i] = q->x[i] > 0.0f? q->x[i] : 0.0f; + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + if (q->x[i] > 0.0f) + q->g[i] += p->g[i]; + } + return 0; +} + +int kad_op_sin(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (i = 0; i < n; ++i) p->x[i] = sinf(q->x[i]); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (i = 0; i < n; ++i) + q->g[i] += p->g[i] * cosf(q->x[i]); + } + return 0; +} + +int kad_op_softmax(kad_node_t *p, int action) +{ + int i, j, n1, d0; + kad_node_t *q = p->child[0]; + + n1 = q->d[q->n_d - 1]; + d0 = kad_len(q) / n1; + if (action == KAD_SYNC_DIM) { + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + for (j = 0; j < d0; ++j) { + float s, max, *x = &q->x[j * n1], *y = &p->x[j * n1]; + for (i = 0, max = -FLT_MAX; i < n1; ++i) + max = max > x[i]? max : x[i]; + for (i = 0, s = 0.0f; i < n1; ++i) { + y[i] = expf(x[i] - max); + s += y[i]; + } + for (i = 0, s = 1.0f / s; i < n1; ++i) y[i] *= s; + } + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + for (j = 0; j < d0; ++j) { + float s, *g = &p->g[j * n1], *y = &p->x[j * n1], *h = &q->g[j * n1]; + for (i = 0, s = 0.0f; i < n1; ++i) + s += g[i] * y[i]; + for (i = 0; i < n1; ++i) + h[i] += y[i] * (g[i] - s); + } + } + return 0; +} + +/********** Multi-node pooling **********/ + +int kad_op_avg(kad_node_t *p, int action) +{ + int i, n; + float tmp; + kad_node_t *q; + + assert(p->n_child > 0); + tmp = 1.0f / p->n_child; + q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + for (i = 1; i < p->n_child; ++i) + if (kad_len(p->child[i]) != n) return -1; + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + memcpy(p->x, q->x, n * sizeof(float)); + for (i = 1; i < p->n_child; ++i) + kad_saxpy(n, 1.0f, p->child[i]->x, p->x); + for (i = 0; i < n; ++i) p->x[i] *= tmp; + } else if (action == KAD_BACKWARD) { + for (i = 0; i < p->n_child; ++i) + if (kad_is_back(p->child[i])) + kad_saxpy(n, tmp, p->g, p->child[i]->g); + } + return 0; +} + +int kad_op_max(kad_node_t *p, int action) +{ + int i, n; + kad_node_t *q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + int *max_j; + for (i = 1; i < p->n_child; ++i) + if (kad_len(p->child[i]) != n) return -1; + kad_copy_dim1(p, q); + max_j = (int*)calloc(n, sizeof(int)); + p->gtmp = max_j; + } else if (action == KAD_FORWARD) { + int j, *max_j = (int*)p->gtmp; + memset(max_j, 0, n * sizeof(int)); + memcpy(p->x, q->x, n * sizeof(float)); + for (j = 1; j < p->n_child; ++j) + for (i = 0, q = p->child[j]; i < n; ++i) + if (q->x[i] > p->x[i]) p->x[i] = q->x[i], max_j[i] = j; + } else if (action == KAD_BACKWARD) { + int *max_j = (int*)p->gtmp; + for (i = 0; i < n; ++i) + p->child[max_j[i]]->g[i] += p->g[i]; + } + return 0; +} + +int kad_op_stack(kad_node_t *p, int action) /* TODO: allow axis, as in TensorFlow */ +{ + int i, n, axis = 0; + kad_node_t *q; + + assert(p->n_child > 0); + q = p->child[0]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + for (i = 1; i < p->n_child; ++i) + if (kad_len(p->child[i]) != n) return -1; + p->n_d = q->n_d + 1; + for (i = 0; i < axis; ++i) p->d[i] = q->d[i]; + p->d[axis] = p->n_child; + for (; i < q->n_d; ++i) p->d[i+1] = q->d[i]; + } else if (action == KAD_FORWARD) { /* TODO: doesn't work when axis != 0 */ + for (i = 0; i < p->n_child; ++i) + memcpy(&p->x[i * n], p->child[i]->x, n * sizeof(float)); + } else if (action == KAD_BACKWARD) { + for (i = 0; i < p->n_child; ++i) + if (kad_is_back(p->child[i])) + kad_saxpy(n, 1.0f, &p->g[i * n], p->child[i]->g); + } + return 0; +} + +int kad_op_select(kad_node_t *p, int action) +{ + kad_node_t *q; + int i, n, which; + + which = *(int32_t*)p->ptr; + if (which < 0) which += p->n_child; + assert(which >= 0 && which < p->n_child); + q = p->child[which]; + n = kad_len(q); + if (action == KAD_SYNC_DIM) { + for (i = 0; i < p->n_child; ++i) + if (p->child[i]->n_d != q->n_d || kad_len(p->child[i]) != n) + break; + if (i < p->n_child) return -1; + kad_copy_dim1(p, q); + } else if (action == KAD_FORWARD) { + memcpy(p->x, q->x, n * sizeof(float)); + } else if (action == KAD_BACKWARD && kad_is_back(q)) { + kad_saxpy(n, 1.0f, p->g, q->g); + } + return 0; +} + +/********** 2D convolution **********/ + +static void conv_rot180(int d0, int d1, float *x) /* rotate/reverse a weight martix */ +{ + int i, j; + for (i = 0; i < d0; ++i) { + float tmp, *xi = &x[i * d1]; + for (j = 0; j < d1>>1; ++j) + tmp = xi[j], xi[j] = xi[d1-1-j], xi[d1-1-j] = tmp; + } +} + +static void conv2d_move_1to3(int d[4], const float *x, float *y) /* convert the NCHW shape to the NHWC shape */ +{ + int i, j, k, l; + for (i = 0; i < d[0]; ++i) + for (j = 0; j < d[1]; ++j) + for (k = 0; k < d[2]; ++k) { + int ik = (i * d[2] + k) * d[3], ijk = ((i * d[1] + j) * d[2] + k) * d[3]; + for (l = 0; l < d[3]; ++l) + y[(ik + l) * d[1] + j] = x[ijk + l]; + } +} + +static void conv2d_add_3to1(int d[4], const float *y, float *x) /* convert the NHWC shape back to NCHW and add to another NCHW-shaped array */ +{ + int i, j, k, l; + for (i = 0; i < d[0]; ++i) + for (j = 0; j < d[1]; ++j) + for (k = 0; k < d[2]; ++k) { + int ik = (i * d[2] + k) * d[3], ijk = ((i * d[1] + j) * d[2] + k) * d[3]; + for (l = 0; l < d[3]; ++l) + x[ijk + l] += y[(ik + l) * d[1] + j]; + } +} + +#define conv_out_size(in_size, aux) (((in_size) - (aux)->kernel_size + (aux)->pad[0] + (aux)->pad[1]) / (aux)->stride + 1) + +#define process_row_for(_xx, _ww, _yy, _wn, _pn, _stride, _pad, _t) do { \ + int j, l; \ + if (_stride > 1) { \ + for (l = 0; l < _wn; ++l) { \ + const float *xl = &_xx[l - _pad]; \ + for (j = 0; j < _pn; ++j, xl += _stride) _t[j] = *xl; \ + kad_saxpy(_pn, _ww[l], _t, _yy); \ + } \ + } else for (l = 0; l < _wn; ++l) kad_saxpy(_pn, _ww[l], &_xx[l - _pad], _yy); \ +} while (0) + +#define process_row_back_x(_xx, _ww, _yy, _wn, _pn, _stride, _pad, _t) do { \ + int j, l; \ + if (_stride > 1) { \ + for (l = 0; l < _wn; ++l) { \ + float *xl = &_xx[l - _pad]; \ + memset(_t, 0, _pn * sizeof(float)); \ + kad_saxpy(_pn, _ww[l], _yy, _t); \ + for (j = 0; j < _pn; ++j, xl += _stride) *xl += _t[j]; \ + } \ + } else for (l = 0; l < _wn; ++l) kad_saxpy(_pn, _ww[l], _yy, &_xx[l - _pad]); \ +} while (0) + +#define process_row_back_w(_xx, _ww, _yy, _wn, _pn, _stride, _pad, _t) do { \ + int j, l; \ + if (_stride > 1) { \ + for (l = 0; l < _wn; ++l) { \ + const float *xl = &_xx[l - _pad]; \ + for (j = 0; j < _pn; ++j, xl += _stride) _t[j] = *xl; \ + _ww[l] += kad_sdot(_pn, _yy, _t); \ + } \ + } else for (l = 0; l < _wn; ++l) _ww[l] += kad_sdot(_pn, _yy, &_xx[l - _pad]); \ +} while (0) + +/* Forward and backward passes are implemented with two different algorithms. + * The first is faster for small kernels with few input channels; otherwise the + * second algorithm is faster. Both algorithms should produce identical + * results, up to the precision of "float". + */ +int kad_op_conv2d(kad_node_t *p, int action) /* in the number-channel-height-width (NCHW) shape */ +{ +#define conv2d_loop1(_x, _w, _y, _tmp, _row_func) do { /* for the NCHW shape */ \ + int n, c1, c0, i, k, ii; \ + for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \ + for (c1 = 0; c1 < w->d[0]; ++c1) /* output channel */ \ + for (c0 = 0; c0 < w->d[1]; ++c0) /* input channel */ \ + for (k = 0; k < w->d[2]; ++k) { /* kernel row */ \ + float *_ww = &(_w)[((c1 * w->d[1] + c0) * w->d[2] + k) * w->d[3]]; \ + for (i = 0, ii = k - aux[0].pad[0]; i < p->d[2] && ii >= 0 && ii < q->d[2]; ++i, ii += aux[0].stride) { /* output row */ \ + float *_xx = &(_x)[((n * q->d[1] + c0) * q->d[2] + ii) * q->d[3]]; \ + float *_yy = &(_y)[((n * p->d[1] + c1) * p->d[2] + i) * p->d[3]]; \ + if (x_padded) { \ + memcpy(x_padded + aux[1].pad[0], _xx, q->d[3] * sizeof(float)); \ + _xx = x_padded + aux[1].pad[0]; \ + } \ + _row_func(_xx, _ww, _yy, w->d[3], p->d[3], aux[1].stride, aux[1].pad[0], (_tmp)); \ + } /* ~i */ \ + } /* ~k, c0, c1, n */ \ + } while (0) + +#define conv2d_loop2(_x, _w, _y, _code) do { /* for the NHWC shape */ \ + int n, c1, i, j, k, ii, j_skip = aux[1].stride * q->d[1], m = w->d[3] * w->d[1]; \ + for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \ + for (c1 = 0; c1 < w->d[0]; ++c1) /* output channel */ \ + for (k = 0; k < w->d[2]; ++k) { /* kernel row */ \ + float *_ww = &(_w)[(c1 * w->d[2] + k) * m]; \ + for (i = 0, ii = k - aux[0].pad[0]; i < p->d[2] && ii >= 0 && ii < q->d[2]; ++i, ii += aux[0].stride) { /* output and input row */ \ + float *_xx = &(_x)[(n * q->d[2] + ii) * q->d[3] * q->d[1]]; \ + float *_yy = &(_y)[((n * p->d[1] + c1) * p->d[2] + i) * p->d[3]]; \ + if (x_padded) { \ + memcpy(x_padded + aux[1].pad[0] * q->d[1], _xx, q->d[3] * q->d[1] * sizeof(float)); \ + _xx = x_padded; \ + } \ + for (j = 0; j < p->d[3]; ++j, _xx += j_skip, ++_yy) _code; /* output and input column */ \ + } /* ~i */ \ + } /* ~k, c1, n */ \ + } while (0) + + conv_conf_t *aux = (conv_conf_t*)p->ptr; + kad_node_t *q = p->child[0], *w = p->child[1]; + float *t = 0, *q1 = 0, *w1 = 0, *x_padded = 0; + int algo_switch = 0; + + if (action == KAD_FORWARD || action == KAD_BACKWARD) { /* allocate working space */ + if (w->d[3] * w->d[1] < 16) { + t = (float*)malloc(p->d[3] * sizeof(float)); + x_padded = aux[1].pad[0] + aux[1].pad[1] > 0? (float*)calloc(q->d[3] + aux[1].pad[0] + aux[1].pad[1], sizeof(float)) : 0; + } else { + q1 = (float*)malloc(kad_len(q) * sizeof(float)); + w1 = (float*)malloc(kad_len(w) * sizeof(float)); + x_padded = aux[1].pad[0] + aux[1].pad[1] > 0? (float*)calloc((q->d[3] + aux[1].pad[0] + aux[1].pad[1]) * q->d[1], sizeof(float)) : 0; + algo_switch = 1; + } + } + if (action == KAD_SYNC_DIM) { + if (q->n_d != 4 || w->n_d != 4) return -1; + if (q->d[1] != w->d[1]) return -1; /* unmatched input channels */ + p->n_d = 4; + p->d[0] = q->d[0], p->d[1] = w->d[0], p->d[2] = conv_out_size(q->d[2], &aux[0]), p->d[3] = conv_out_size(q->d[3], &aux[1]); + } else if (action == KAD_FORWARD) { + conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x); + memset(p->x, 0, kad_len(p) * sizeof(float)); + if (!algo_switch) { /* this is the first algorithm */ + conv2d_loop1(q->x, w->x, p->x, t, process_row_for); + } else { /* this is the second algorithm */ + conv2d_move_1to3(q->d, q->x, q1); + conv2d_move_1to3(w->d, w->x, w1); + conv2d_loop2(q1, w1, p->x, (*_yy += kad_sdot(m, _ww, _xx))); + } + conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x); + } else if (action == KAD_BACKWARD) { + if (kad_is_back(p->child[0])) { /* backprop to the input array */ + conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x); + if (!algo_switch) { + conv2d_loop1(q->g, w->x, p->g, t, process_row_back_x); + } else { + memset(q1, 0, kad_len(q) * sizeof(float)); + conv2d_move_1to3(w->d, w->x, w1); + conv2d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _ww, _xx)); + conv2d_add_3to1(q->d, q1, q->g); + } + conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->x); + } + if (kad_is_back(p->child[1])) { /* backprop to the weight matrix */ + conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->g); + if (!algo_switch) { + conv2d_loop1(q->x, w->g, p->g, t, process_row_back_w); + } else { + conv2d_move_1to3(q->d, q->x, q1); + memset(w1, 0, kad_len(w) * sizeof(float)); + conv2d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _xx, _ww)); + conv2d_add_3to1(w->d, w1, w->g); + } + conv_rot180(w->d[0] * w->d[1], w->d[2] * w->d[3], w->g); + } + } + free(t); free(q1); free(w1); free(x_padded); + return 0; +} + +int kad_op_max2d(kad_node_t *p, int action) +{ + conv_conf_t *aux = (conv_conf_t*)p->ptr; + kad_node_t *q = p->child[0]; + if (action == KAD_SYNC_DIM) { + if (q->n_d != 4) return -1; + p->n_d = 4; + p->d[0] = q->d[0], p->d[1] = q->d[1], p->d[2] = conv_out_size(q->d[2], &aux[0]), p->d[3] = conv_out_size(q->d[3], &aux[1]); + } else if (action == KAD_ALLOC) { + p->gtmp = realloc(p->gtmp, kad_len(p) * sizeof(int)); + } else if (action == KAD_FORWARD) { + int rest = 1, len, t, i; + int *f = (int*)p->gtmp; + len = kad_len(p); + for (i = 0; i < len; ++i) p->x[i] = -FLT_MAX; + for (i = 0; i < p->n_d - 2; ++i) rest *= p->d[i]; + for (t = 0; t < rest; ++t) { + int i, j, k, l, p_row = p->d[p->n_d - 2], p_col = p->d[p->n_d - 1]; + for (i = 0; i < p_row; ++i) { + int u = (t * p_row + i) * p_col; + for (k = 0; k < aux[0].kernel_size; ++k) { + int v, v0, v_end, ii = i * aux[0].stride + k - aux[0].pad[0]; + if (ii < 0 || ii >= q->d[p->n_d - 2]) continue; + v0 = (t * q->d[p->n_d - 2] + ii) * q->d[p->n_d - 1]; + v_end = v0 + q->d[p->n_d - 1]; + for (l = 0; l < aux[1].kernel_size; ++l) + for (j = 0, v = v0 + (l > aux[1].pad[0]? l - aux[1].pad[0] : 0); j < p_col && v < v_end; ++j, v += aux[1].stride) + if (p->x[u + j] < q->x[v]) + p->x[u + j] = q->x[v], f[u + j] = v; + } /* ~k */ + } /* ~i */ + } + } else if (action == KAD_BACKWARD) { + int i, len, *f = (int*)p->gtmp; + len = kad_len(p); + for (i = 0; i < len; ++i) q->g[f[i]] += p->g[i]; + } + return 0; +} + +/********** 1D convolution **********/ + +static void conv1d_move_1to2(int d[3], const float *x, float *y) +{ + int i, j, k; + for (k = 0; k < d[0]; ++k) + for (j = 0; j < d[1]; ++j) + for (i = 0; i < d[2]; ++i) + y[(k * d[2] + i) * d[1] + j] = x[(k * d[1] + j) * d[2] + i]; +} + +static void conv1d_add_2to1(int d[3], const float *y, float *x) +{ + int i, j, k; + for (k = 0; k < d[0]; ++k) + for (j = 0; j < d[1]; ++j) + for (i = 0; i < d[2]; ++i) + x[(k * d[1] + j) * d[2] + i] += y[(k * d[2] + i) * d[1] + j]; +} + +int kad_op_conv1d(kad_node_t *p, int action) /* in the number-channel-width (NCW) shape */ +{ +#define conv1d_loop1(_x, _w, _y, _tmp, _row_func) do { /* for the NCW shape */ \ + int n, c1, c0; \ + for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \ + for (c1 = 0; c1 < w->d[0]; ++c1) /* output channel */ \ + for (c0 = 0; c0 < w->d[1]; ++c0) { /* input channel */ \ + float *_ww = &(_w)[(c1 * w->d[1] + c0) * w->d[2]]; \ + float *_xx = &(_x)[(n * q->d[1] + c0) * q->d[2]]; \ + float *_yy = &(_y)[(n * p->d[1] + c1) * p->d[2]]; \ + if (x_padded) { \ + memcpy(x_padded + aux->pad[0], _xx, q->d[2] * sizeof(float)); \ + _xx = x_padded + aux->pad[0]; \ + } \ + _row_func(_xx, _ww, _yy, w->d[2], p->d[2], aux->stride, aux->pad[0], (_tmp)); \ + } /* ~c0, c1, n */ \ + } while (0) + +#define conv1d_loop2(_x, _w, _y, _code) do { /* for the NWC shape */ \ + int n, c1, j, j_skip = aux->stride * q->d[1], m = w->d[2] * w->d[1]; \ + for (n = 0; n < q->d[0]; ++n) /* mini-batch */ \ + for (c1 = 0; c1 < w->d[0]; ++c1) { /* output channel */ \ + float *_ww = &(_w)[c1 * m]; \ + float *_xx = &(_x)[n * q->d[1] * q->d[2]]; \ + float *_yy = &(_y)[(n * p->d[1] + c1) * p->d[2]]; \ + if (x_padded) { \ + memcpy(x_padded + aux->pad[0] * q->d[1], _xx, q->d[2] * q->d[1] * sizeof(float)); \ + _xx = x_padded; \ + } \ + for (j = 0; j < p->d[2]; ++j, _xx += j_skip, ++_yy) _code; \ + } /* ~c1, n */ \ + } while (0) + + conv_conf_t *aux = (conv_conf_t*)p->ptr; + kad_node_t *q = p->child[0], *w = p->child[1]; + float *t = 0, *q1 = 0, *w1 = 0, *x_padded = 0; + int algo_switch = 0; + + if (action == KAD_FORWARD || action == KAD_BACKWARD) { /* allocate working space */ + if (w->d[2] * w->d[1] < 32) { + t = (float*)malloc(p->d[2] * sizeof(float)); + x_padded = aux->pad[0] + aux->pad[1] > 0? (float*)calloc(q->d[2] + aux->pad[0] + aux->pad[1], sizeof(float)) : 0; + } else { + q1 = (float*)malloc(kad_len(q) * sizeof(float)); + w1 = (float*)malloc(kad_len(w) * sizeof(float)); + x_padded = aux->pad[0] + aux->pad[1] > 0? (float*)calloc((q->d[2] + aux->pad[0] + aux->pad[1]) * q->d[1], sizeof(float)) : 0; + algo_switch = 1; + } + } + if (action == KAD_SYNC_DIM) { + if (q->n_d != 3 || w->n_d != 3) return -1; + if (q->d[1] != w->d[1]) return -1; /* unmatched input channels */ + p->n_d = 3; + p->d[0] = q->d[0], p->d[1] = w->d[0], p->d[2] = conv_out_size(q->d[2], aux); + } else if (action == KAD_FORWARD) { + conv_rot180(w->d[0] * w->d[1], w->d[2], w->x); + memset(p->x, 0, kad_len(p) * sizeof(float)); + if (!algo_switch) { /* this is the first algorithm */ + conv1d_loop1(q->x, w->x, p->x, t, process_row_for); + } else { /* this is the second algorithm */ + conv1d_move_1to2(q->d, q->x, q1); + conv1d_move_1to2(w->d, w->x, w1); + conv1d_loop2(q1, w1, p->x, (*_yy += kad_sdot(m, _ww, _xx))); + } + conv_rot180(w->d[0] * w->d[1], w->d[2], w->x); + } else if (action == KAD_BACKWARD) { + if (kad_is_back(p->child[0])) { /* backprop to the input array */ + conv_rot180(w->d[0] * w->d[1], w->d[2], w->x); + if (!algo_switch) { + conv1d_loop1(q->g, w->x, p->g, t, process_row_back_x); + } else { + memset(q1, 0, kad_len(q) * sizeof(float)); + conv1d_move_1to2(w->d, w->x, w1); + conv1d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _ww, _xx)); + conv1d_add_2to1(q->d, q1, q->g); + } + conv_rot180(w->d[0] * w->d[1], w->d[2], w->x); + } + if (kad_is_back(p->child[1])) { /* backprop to the weight matrix */ + conv_rot180(w->d[0] * w->d[1], w->d[2], w->g); + if (!algo_switch) { + conv1d_loop1(q->x, w->g, p->g, t, process_row_back_w); + } else { + conv1d_move_1to2(q->d, q->x, q1); + memset(w1, 0, kad_len(w) * sizeof(float)); + conv1d_loop2(q1, w1, p->g, kad_saxpy(m, *_yy, _xx, _ww)); + conv1d_add_2to1(w->d, w1, w->g); + } + conv_rot180(w->d[0] * w->d[1], w->d[2], w->g); + } + } + free(t); free(q1); free(w1); free(x_padded); + return 0; +} + +int kad_op_max1d(kad_node_t *p, int action) +{ + conv_conf_t *aux = (conv_conf_t*)p->ptr; + kad_node_t *q = p->child[0]; + if (action == KAD_SYNC_DIM) { + if (q->n_d != 3) return -1; + p->n_d = 3; + p->d[0] = q->d[0], p->d[1] = q->d[1], p->d[2] = conv_out_size(q->d[2], aux); + } else if (action == KAD_ALLOC) { + p->gtmp = realloc(p->gtmp, kad_len(p) * sizeof(int)); + } else if (action == KAD_FORWARD) { + int rest = 1, len, t, i; + int *f = (int*)p->gtmp; + len = kad_len(p); + for (i = 0; i < len; ++i) p->x[i] = -FLT_MAX; + for (i = 0; i < p->n_d - 1; ++i) rest *= p->d[i]; + for (t = 0; t < rest; ++t) { + int j, l, p_width = p->d[p->n_d - 1]; + int u = t * p_width, v, v0 = t * q->d[p->n_d - 1], v_end = v0 + q->d[p->n_d - 1]; + for (l = 0; l < aux->kernel_size; ++l) + for (j = 0, v = v0 + (l > aux->pad[0]? l - aux->pad[0] : 0); j < p_width && v < v_end; ++j, v += aux->stride) + if (p->x[u + j] < q->x[v]) + p->x[u + j] = q->x[v], f[u + j] = v; + } + } else if (action == KAD_BACKWARD) { + int i, len, *f = (int*)p->gtmp; + len = kad_len(p); + for (i = 0; i < len; ++i) q->g[f[i]] += p->g[i]; + } + return 0; +} + +int kad_op_avg1d(kad_node_t *p, int action) +{ + conv_conf_t *aux = (conv_conf_t*)p->ptr; + kad_node_t *q = p->child[0]; + if (action == KAD_SYNC_DIM) { + if (q->n_d != 3) return -1; + p->n_d = 3; + p->d[0] = q->d[0], p->d[1] = q->d[1], p->d[2] = conv_out_size(q->d[2], aux); + } else if (action == KAD_ALLOC) { + p->gtmp = realloc(p->gtmp, kad_len(p) * sizeof(int)); + } else if (action == KAD_FORWARD) { + int rest = 1, len, t, i; + int *f = (int*)p->gtmp; + len = kad_len(p); + for (i = 0; i < len; ++i) p->x[i] = 0.0f, f[i] = 0; + for (i = 0; i < p->n_d - 1; ++i) rest *= p->d[i]; + for (t = 0; t < rest; ++t) { + int j, l, p_width = p->d[p->n_d - 1]; + int u = t * p_width, v, v0 = t * q->d[p->n_d - 1], v_end = v0 + q->d[p->n_d - 1]; + for (l = 0; l < aux->kernel_size; ++l) + for (j = 0, v = v0 + (l > aux->pad[0]? l - aux->pad[0] : 0); j < p_width && v < v_end; ++j, v += aux->stride) + p->x[u + j] += q->x[v], ++f[u + j]; + } + for (i = 0; i < len; ++i) p->x[i] /= f[i]; + } else if (action == KAD_BACKWARD) { + int rest = 1, t, i; + int *f = (int*)p->gtmp; + for (i = 0; i < p->n_d - 1; ++i) rest *= p->d[i]; + for (t = 0; t < rest; ++t) { + int j, l, p_width = p->d[p->n_d - 1]; + int u = t * p_width, v, v0 = t * q->d[p->n_d - 1], v_end = v0 + q->d[p->n_d - 1]; + for (l = 0; l < aux->kernel_size; ++l) + for (j = 0, v = v0 + (l > aux->pad[0]? l - aux->pad[0] : 0); j < p_width && v < v_end; ++j, v += aux->stride) + q->g[v] += p->g[u + j] / f[u + j]; + } + } + return 0; +} + +/********** List of operators **********/ + +kad_op_f kad_op_list[KAD_MAX_OP] = { + 0, + kad_op_add, /* 1: element-wise addition */ + kad_op_mul, /* 2: element-wise multiplication */ + kad_op_cmul, /* 3: column multiplication */ + kad_op_ce_bin_neg, /* 4: binary cross-entropy for (-1,1) */ + kad_op_square, /* 5: square */ + kad_op_sigm, /* 6: sigmoid */ + kad_op_tanh, /* 7: tanh */ + kad_op_relu, /* 8: ReLU */ + kad_op_matmul, /* 9: matrix multiplication */ + kad_op_avg, /* 10: general average pooling (not for ConvNet) */ + kad_op_1minus, /* 11: 1-x */ + kad_op_select, /* 12: choose between one of the children */ + kad_op_ce_multi, /* 13: multi-class cross-entropy */ + kad_op_softmax, /* 14: softmax */ + kad_op_dropout, /* 15: dropout */ + kad_op_conv2d, /* 16: 2D convolution */ + kad_op_max2d, /* 17: 2D max pooling (for 2D ConvNet) */ + kad_op_conv1d, /* 18: 1D convolution */ + kad_op_max1d, /* 19: 1D max pooling (for 1D ConvNet) */ + kad_op_slice, /* 20: slice data at a dimension */ + kad_op_max, /* 21: general max pooling */ + kad_op_ce_bin, /* 22: binary cross-entropy for (0,1) */ + kad_op_sub, /* 23: element-wise subtraction */ + kad_op_sample_normal, /* 24: sample from a normal distribution */ + kad_op_reduce_sum, /* 25 */ + kad_op_reduce_mean, /* 26 */ + kad_op_log, /* 27: log() */ + kad_op_avg1d, /* 28: 1D average pooling (for 1D ConvNet) */ + kad_op_mse, /* 29: mean square error */ + kad_op_reshape, /* 30 */ + kad_op_concat, /* 31 */ + kad_op_stdnorm, /* 32: layer normalization */ + kad_op_exp, /* 33: exp() */ + kad_op_sin, /* 34: sin() */ + kad_op_stack, /* 35: tf.stack, but on the first axis only */ + kad_op_reverse /* 36: tf.reverse, but on one axis only */ +}; + +char *kad_op_name[KAD_MAX_OP] = { + 0, "add", "mul", "cmul", "ce_bin_neg", "square", "sigm", "tanh", "relu", "matmul", "avg", "1minus", "select", "ce_multi", "softmax", + "dropout", "conv2d", "max2d", "conv1d", "max1d", "slice", "max", "ce_bin", "sub", "sample_normal", "reduce_sum", "reduce_mean", "log", + "avg1d", "mse", "reshape", "concat", "stdnorm", "exp", "sin", "stack", "reverse" +}; + +/************************** + *** Debugging routines *** + **************************/ + +void kad_trap_fe(void) +{ +#ifdef __SSE__ + _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~(_MM_MASK_INVALID | _MM_MASK_DIV_ZERO)); +#endif +} + +void kad_print_graph(FILE *fp, int n, kad_node_t **v) +{ + int i, j; + for (i = 0; i < n; ++i) v[i]->tmp = i; + for (i = 0; i < n; ++i) { + kad_node_t *p = v[i]; + fprintf(fp, "%d\t%x:%x\t%d\t", i, p->flag, p->ext_flag, p->ext_label); + if (p->pre) fprintf(fp, "%d\t", p->pre->tmp); + else fprintf(fp, ".\t"); + fputs("[", fp); + for (j = 0; j < p->n_d; ++j) { + if (j) fputc(',', fp); + fprintf(fp, "%d", p->d[j]); + } + fprintf(fp, "]\t"); + if (p->n_child) { + fprintf(fp, "%s(", kad_op_name[p->op]); + for (j = 0; j < p->n_child; ++j) { + if (j) fputc(',', fp); + fprintf(fp, "$%d", p->child[j]->tmp); + } + fprintf(fp, ")"); + } else fprintf(fp, "%s", kad_is_feed(p)? "feed" : kad_is_var(p)? "var" : kad_is_const(p)? "const" : "N/A"); + fputc('\n', fp); + } + for (i = 0; i < n; ++i) v[i]->tmp = 0; +} + +static void kad_add_delta(int n, kad_node_t **a, float c, float *delta) +{ + int i, k; + for (i = k = 0; i < n; ++i) + if (kad_is_var(a[i])) { + kad_saxpy(kad_len(a[i]), c, &delta[k], a[i]->x); + k += kad_len(a[i]); + } +} + +void kad_check_grad(int n, kad_node_t **a, int from) +{ + const float eps = 1e-5f, rel = 1e-7f / eps; + int i, k, n_var; + float *g0, *delta, f0, f_minus, f_plus, s0, s1, rel_err, p_m_err; + n_var = kad_size_var(n, a); + g0 = (float*)calloc(n_var, sizeof(float)); + f0 = *kad_eval_at(n, a, from); + kad_grad(n, a, from); + for (i = k = 0; i < n; ++i) + if (kad_is_var(a[i])) { + memcpy(&g0[k], a[i]->g, kad_len(a[i]) * sizeof(float)); + k += kad_len(a[i]); + } + delta = (float*)calloc(n_var, sizeof(float)); + for (k = 0; k < n_var; ++k) delta[k] = (float)kad_drand(0) * eps; + kad_add_delta(n, a, 1.0f, delta); + f_plus = *kad_eval_at(n, a, from); + kad_add_delta(n, a, -2.0f, delta); + f_minus = *kad_eval_at(n, a, from); + kad_add_delta(n, a, 1.0f, delta); + s0 = kad_sdot(n_var, g0, delta); + s1 = .5f * (f_plus - f_minus); + fprintf(stderr, "Gradient check -- %g <=> %g @ %g -- ", s0/eps, s1/eps, f0); + if (fabs(s1) >= rel * eps) { + rel_err = fabsf(fabsf(s0) - fabsf(s1)) / (fabsf(s0) + fabsf(s1)); + p_m_err = fabsf(f_plus + f_minus - 2.0f * f0) / fabsf(f_plus - f_minus); + fprintf(stderr, "rel_err:%g p_m_err:%g -- ", rel_err, p_m_err); + if (rel_err >= rel && rel_err > p_m_err) fprintf(stderr, "failed\n"); + else fprintf(stderr, "passed\n"); + } else fprintf(stderr, "skipped\n"); + free(delta); free(g0); +} |