kautodiff.h

/*
  The MIT License

  Copyright (c) 2016, 2017  Broad Institute

  Permission is hereby granted, free of charge, to any person obtaining
  a copy of this software and associated documentation files (the
  "Software"), to deal in the Software without restriction, including
  without limitation the rights to use, copy, modify, merge, publish,
  distribute, sublicense, and/or sell copies of the Software, and to
  permit persons to whom the Software is furnished to do so, subject to
  the following conditions:

  The above copyright notice and this permission notice shall be
  included in all copies or substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/

#ifndef KANN_AUTODIFF_H
#define KANN_AUTODIFF_H

#define KAD_VERSION "r393"

#include <stdio.h>
#include <stdint.h>

#define KAD_MAX_DIM 4     // max dimension
#define KAD_MAX_OP  64    // max number of operators

struct kad_node_t;
typedef struct kad_node_t kad_node_t;

/* A computational graph is an acyclic directed graph. In the graph, an
 * external node represents a variable, a constant or a feed; an internal node
 * represents an operator; an edge from node v to w indicates v is an operand
 * of w.
 */

// an edge between two nodes in the computational graph
typedef struct {
	kad_node_t *p;  // child node, not allocated
	void *t;        // temporary data needed for backprop; allocated on heap if not NULL
} kad_edge_t;

#define KAD_F_WITH_PD  0x1 // PD = partial derivative
#define KAD_F_CONSTANT 0x2
#define KAD_F_POOLING  0x4
#define KAD_F_INST_FOR 0x8

#define kad_is_back(p)  ((p)->flag & KAD_F_WITH_PD)
#define kad_is_ext(p)   ((p)->n_child == 0)
#define kad_is_var(p)   (kad_is_ext(p) && kad_is_back(p))
#define kad_is_const(p) (kad_is_ext(p) && ((p)->flag & KAD_F_CONSTANT))
#define kad_is_feed(p)  (kad_is_ext(p) && !kad_is_back(p) && !((p)->flag & KAD_F_CONSTANT))
#define kad_is_pivot(p) ((p)->n_child == 1 && ((p)->flag & KAD_F_POOLING))

#define kad_eval_enable(p) ((p)->tmp = 1)
#define kad_eval_disable(p) ((p)->tmp = -1)

// a node in the computational graph
struct kad_node_t {
	uint8_t     n_d;            // number of dimensions; no larger than KAD_MAX_DIM
	uint8_t     flag;           // type of the node; see KAD_F_* for valid flags
	uint16_t    op;             // operator; kad_op_list[op] is the actual function
	int32_t     n_child;        // number of operands/child nodes
	int32_t     tmp;            // temporary field; MUST BE zero before calling kad_compile()
	int32_t     ptr_size;       // size of ptr below
	int32_t     d[KAD_MAX_DIM]; // dimensions
	int32_t     ext_label;      // labels for external uses (not modified by the kad_* APIs)
	uint32_t    ext_flag;       // flags for external uses (not modified by the kad_* APIs)
	float      *x;              // value; allocated for internal nodes
	float      *g;              // gradient; allocated for internal nodes
	kad_edge_t *child;          // operands/child nodes
	kad_node_t *pre;            // usually NULL; only used for RNN
	void       *ptr;            // for special operators that need additional parameters (e.g. conv2d)
};

#ifdef __cplusplus
extern "C" {
#endif

/**
 * Compile/linearize a computational graph
 *
 * @param n_node   number of nodes (out)
 * @param n_roots  number of nodes without predecessors
 * @param roots    list of nodes without predecessors
 *
 * @return list of nodes, of size *n_node
 */
kad_node_t **kad_compile_array(int *n_node, int n_roots, kad_node_t **roots);

kad_node_t **kad_compile(int *n_node, int n_roots, ...); // an alternative API to above
void kad_delete(int n, kad_node_t **a); // deallocate a compiled/linearized graph

void kad_delete1(kad_node_t *root);

/**
 * Compute the value at a node
 * 
 * @param n       number of nodes
 * @param a       list of nodes
 * @param from    compute the value at this node, 0<=from<n
 *
 * @return a pointer to the value (pointing to kad_node_t::x, so don't call
 *         free() on it!)
 */
const float *kad_eval_at(int n, kad_node_t **a, int from);

void kad_eval_marked(int n, kad_node_t **a);

/**
 * Compute gradient
 *
 * @param n       number of nodes
 * @param a       list of nodes
 * @param from    the function node; must be a scalar (compute \nabla a[from])
 */
void kad_grad(int n, kad_node_t **a, int from);

void kad_grad1(kad_node_t *root);

/**
 * Test if a computational graph can be unrolled
 *
 * A graph is unrollable if and only if: 1) it has a recurrent node (i.e.
 * kad_node_t::pre is not NULL) and 2) it has a pooling node (i.e.
 * kad_node_t::op is either kad_avg or kad_max) with exactly one child.
 *
 * @param n       number of nodes
 * @param v       list of nodes
 *
 * @return 1 if the graph can be unrolled or 0 otherwise
 */
int kad_unrollable(int n, kad_node_t *const* v);

/**
 * Unroll a recurrent computation graph
 *
 * @param n_v     number of nodes
 * @param v       list of nodes
 * @param len     how many times to unroll
 * @param new_n   number of nodes in the unrolled graph (out)
 *
 * @return list of nodes in the unrolled graph
 */
kad_node_t **kad_unroll(int n_v, kad_node_t **v, int len, int *new_n);

// define a variable, a constant or a feed (placeholder in TensorFlow)
kad_node_t *kad_var(float *x, float *g, int n_d, ...); // a variable; gradients to be computed; not unrolled
kad_node_t *kad_const(float *x, int n_d, ...);         // a constant; no gradients computed; not unrolled
kad_node_t *kad_feed(int n_d, ...);                    // an input/output; no gradients computed; unrolled

kad_node_t *kad_var_inst(float *x, float *g, int n_d, ...);
kad_node_t *kad_const_inst(float *x, int n_d, ...);

// operators taking two operands
kad_node_t *kad_add(kad_node_t *x, kad_node_t *y); // f(x,y) = x + y (generalized element-wise addition; f[i*n+j]=x[i*n+j]+y[j], n=kad_len(y), 0<j<n, 0<i<kad_len(x)/n)
kad_node_t *kad_sub(kad_node_t *x, kad_node_t *y); // f(x,y) = x - y (generalized element-wise subtraction)
kad_node_t *kad_mul(kad_node_t *x, kad_node_t *y); // f(x,y) = x * y (generalized element-wise product)

kad_node_t *kad_matmul(kad_node_t *x, kad_node_t *y);     // f(x,y) = x * y   (general matrix product)
kad_node_t *kad_cmul(kad_node_t *x, kad_node_t *y);       // f(x,y) = x * y^T (column-wise matrix product; i.e. y is transposed)

kad_node_t *kad_mse(kad_node_t *x, kad_node_t *y);        // mean square error
kad_node_t *kad_ce_multi(kad_node_t *x, kad_node_t *y);   // multi-class cross-entropy; output is a scalar; x is the preidction and y is the truth
kad_node_t *kad_ce_bin(kad_node_t *x, kad_node_t *y);     // binary cross-entropy for (0,1)
kad_node_t *kad_ce_bin_neg(kad_node_t *x, kad_node_t *y); // binary cross-entropy for (-1,1)

#define KAD_PAD_NONE  0      // use the smallest zero-padding
#define KAD_PAD_SAME  (-2)   // output to have the same dimension as input

kad_node_t *kad_conv2d(kad_node_t *x, kad_node_t *w, int r_stride, int c_stride, int r_pad, int c_pad);             // 2D convolution with weight matrix flipped
kad_node_t *kad_max2d(kad_node_t *x, int kernel_h, int kernel_w, int r_stride, int c_stride, int r_pad, int c_pad); // 2D max pooling
kad_node_t *kad_conv1d(kad_node_t *x, kad_node_t *w, int stride, int pad);  // 1D convolution with weight flipped
kad_node_t *kad_max1d(kad_node_t *x, int kernel_size, int stride, int pad); // 1D max pooling
kad_node_t *kad_avg1d(kad_node_t *x, int kernel_size, int stride, int pad); // 1D average pooling

kad_node_t *kad_dropout(kad_node_t *x, kad_node_t *r);  // dropout at rate r
kad_node_t *kad_sample_normal(kad_node_t *x);           // f(x) = x * r, where r is drawn from a standard normal distribution

// operators taking one operand
kad_node_t *kad_square(kad_node_t *x); // f(x) = x^2                         (element-wise square)
kad_node_t *kad_sigm(kad_node_t *x);   // f(x) = 1/(1+exp(-x))               (element-wise sigmoid)
kad_node_t *kad_tanh(kad_node_t *x);   // f(x) = (1-exp(-2x)) / (1+exp(-2x)) (element-wise tanh)
kad_node_t *kad_relu(kad_node_t *x);   // f(x) = max{0,x}                    (element-wise rectifier, aka ReLU)
kad_node_t *kad_softmax(kad_node_t *x);// f_i(x_1,...,x_n) = exp(x_i) / \sum_j exp(x_j) (softmax)
kad_node_t *kad_1minus(kad_node_t *x); // f(x) = 1 - x
kad_node_t *kad_log(kad_node_t *x);    // f(x) = log(x)

kad_node_t *kad_layernorm(kad_node_t *x); // layer normalization

// operators taking an indefinite number of operands (e.g. pooling)
kad_node_t *kad_avg(int n, kad_node_t **x); // f(x_1,...,x_n) = \sum_i x_i/n      (mean pooling)
kad_node_t *kad_max(int n, kad_node_t **x); // f(x_1,...,x_n) = max{x_1,...,x_n}  (max pooling)

// dimension reduction
kad_node_t *kad_reduce_sum(kad_node_t *x, int dim);   // reduce dimension by 1 at dimension _dim_ (similar to TensorFlow's reduce_sum())
kad_node_t *kad_reduce_mean(kad_node_t *x, int dim);

// special operators
kad_node_t *kad_slice(kad_node_t *x, int dim, int start, int end); // take a slice on the dim-th dimension
kad_node_t *kad_concat(int dim, int n, ...);                       // concatenate on the dim-th dimension
kad_node_t *kad_concat_array(int dim, int n, kad_node_t **p);      // the array version of concat
kad_node_t *kad_reshape(kad_node_t *x, int n_d, int *d);           // reshape; similar behavior to TensorFlow's reshape()
kad_node_t *kad_switch(int n, kad_node_t **p);                     // manually (as a hyperparameter) choose one input, default to 0

// miscellaneous operations on a compiled graph
int kad_size_var(int n, kad_node_t *const* v);   // total size of all variables
int kad_size_const(int n, kad_node_t *const* v); // total size of all constants

// graph I/O
int kad_save(FILE *fp, int n_node, kad_node_t **node);
kad_node_t **kad_load(FILE *fp, int *_n_node);

// random number generator
void *kad_rng(void);
void kad_srand(void *d, uint64_t seed);
uint64_t kad_rand(void *d);
double kad_drand(void *d);
double kad_drand_normal(void *d);

// debugging routines
void kad_trap_fe(void); // abort on divide-by-zero and NaN
void kad_print_graph(FILE *fp, int n, kad_node_t **v);
void kad_check_grad(int n, kad_node_t **a, int from);

#ifdef __cplusplus
}
#endif

#define KAD_ALLOC      1
#define KAD_FORWARD    2
#define KAD_BACKWARD   3
#define KAD_SYNC_DIM   4

typedef int (*kad_op_f)(kad_node_t*, int);
extern kad_op_f kad_op_list[KAD_MAX_OP];

static inline int kad_len(const kad_node_t *p) // calculate the size of p->x
{
	int n = 1, i;
	for (i = 0; i < p->n_d; ++i) n *= p->d[i];
	return n;
}

#endif