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#include <algorithm>
#include <assert.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
int64_t r(int64_t min, int64_t max) {
int64_t n1 = rand();
int64_t n2 = rand();
int64_t n3 = rand();
n1 = n1 ^ (n2 << 16) ^ (n3 << 16);
n1 = n1 % (max - min);
n1 = n1 + min;
return n1;
}
int64_t sdiv(int64_t a, int64_t b) {
return (a - ((a % b) + b) % b) / b;
}
int64_t srzdiv(int64_t a, int64_t b) {
return a / b;
}
bool u_method_0(int den, int sh_post, int bits) {
uint64_t max = (1L << bits) - 1;
for (int64_t num = 0; num <= max; num++) {
uint64_t result = num;
result >>= sh_post;
if (num / den != result) return false;
}
return true;
}
bool u_method_1(int den, int64_t mul, int sh_post, int bits) {
uint64_t max = (1L << bits) - 1;
if (mul > max) return false;
for (uint64_t num = 0; num <= max; num++) {
uint64_t result = num;
result *= mul;
result >>= bits;
if (result > max) return false;
result >>= sh_post;
if (num / den != result) return false;
}
return true;
}
bool u_method_2(int den, int64_t mul, int sh_post, int bits) {
uint64_t max = (1UL << bits) - 1;
if (mul > max) return false;
for (uint64_t num = 0; num <= max; num++) {
uint64_t result = num;
result *= mul;
result >>= bits;
if (result > max) return false;
result = (result + num) >> 1;
if (result > max) return false;
result >>= sh_post;
if (num / den != result) return false;
}
return true;
}
bool u_method_3(int den, int64_t mul, int sh_post, int bits) {
uint64_t max = (1UL << bits) - 1;
if (mul > max) return false;
for (uint64_t num = 0; num <= max; num++) {
uint64_t result = num;
result *= mul;
result >>= bits;
if (result > max) return false;
result = (result + num + 1) >> 1;
if (result > max) return false;
result >>= sh_post;
if (num / den != result) return false;
}
return true;
}
bool s_method_0(int den, int sh_post, int bits) {
int64_t min = -(1L << (bits - 1)), max = (1L << (bits - 1)) - 1;
for (int64_t num = min; num <= max; num++) {
int64_t result = num;
result >>= sh_post;
if (sdiv(num, den) != result) return false;
}
return true;
}
bool s_method_1(int den, int64_t mul, int sh_post, int bits) {
int64_t min = -(1 << (bits - 1)), max = (1 << (bits - 1)) - 1;
for (int64_t num = min; num <= max; num++) {
int64_t result = num;
uint64_t xsign = result >> (bits - 1);
uint64_t q0 = (mul * (xsign ^ result)) >> bits;
result = xsign ^ (q0 >> sh_post);
if (sdiv(num, den) != result) return false;
}
return true;
}
bool srz_method_0(int den, int sh_post, int bits) {
int64_t min = -(1L << (bits - 1)), max = (1L << (bits - 1)) - 1;
for (int64_t num = min; num <= max; num++) {
int64_t result = num;
result += (result >> (bits - 1)) & (den - 1);
result >>= sh_post;
if (srzdiv(num, den) != result) return false;
}
return true;
}
bool srz_method_1(int den, int64_t mul, int sh_post, int bits) {
int64_t min = -(1 << (bits - 1)), max = (1 << (bits - 1)) - 1;
for (int64_t num = min; num <= max; num++) {
int64_t result = num;
uint64_t xsign = result >> (bits - 1);
uint64_t q0 = (mul * result) >> bits;
result = (q0 >> sh_post);
uint64_t mask = (1ULL << bits) - 1;
result -= (xsign & mask);
// Fix-up the sign bits
result <<= (64 - bits);
result >>= (64 - bits);
if (srzdiv(num, den) != result) {
printf("Fail\n");
return false;
}
}
return true;
}
int main(int argc, char **argv) {
/* This program computes a table to help us do cheap integer
division by a constant. It is based on the paper "Division by
Invariant Integers using Multiplication" by Granlund and
Montgomery.
*/
FILE *c_out = fopen("IntegerDivisionTable.cpp", "w");
FILE *h_out = fopen("IntegerDivisionTable.h", "w");
fprintf(h_out, "%s",
"#ifndef HALIDE_INTEGER_DIVISION_TABLE_H\n"
"#define HALIDE_INTEGER_DIVISION_TABLE_H\n"
"\n"
"#include <cstdint>\n"
"\n"
"/** \\file\n"
" * Tables telling us how to do integer division via fixed-point\n"
" * multiplication for various small constants. This file is \n"
" * automatically generated by find_inverse.cpp.\n"
" */\n"
"namespace Halide {\n"
"namespace Internal {\n"
"namespace IntegerDivision {\n");
fprintf(c_out, "%s",
"/** \\file\n"
" * Tables telling us how to do integer division\n"
" * via fixed-point multiplication for various small\n"
" * constants. This file is automatically generated\n"
" * by find_inverse.cpp. There are two sets of tables.\n"
" * The first set is for compile-time-constant divisors\n"
" * from 2 to 256. The second is for runtime divisors\n"
" * from 1 to 255. The second set always uses the most\n"
" * expensive method, while the compile-time set uses\n"
" * the cheapest method for the given divisor.\n"
" */\n"
"\n"
"#include \"IntegerDivisionTable.h\"\n"
"\n"
"namespace Halide {\n"
"namespace Internal {\n"
"namespace IntegerDivision {\n\n");
for (int runtime = 0; runtime < 2; runtime++) {
for (int bits = 8; bits <= 32; bits *= 2) {
printf("Generating table%s_u%d...\n", runtime ? "_runtime" : "", bits);
if (runtime) {
fprintf(h_out, "extern const int64_t table_runtime_u%d[256][4];\n", bits);
fprintf(c_out, "const int64_t table_runtime_u%d[256][4] = {\n", bits);
} else {
fprintf(h_out, "extern const int64_t table_u%d[256][4];\n", bits);
fprintf(c_out, "const int64_t table_u%d[256][4] = {\n", bits);
}
for (int d = 0; d < 256; d++) {
if (runtime && d < 2) {
fprintf(c_out, " {0, 0, 0, 0}, // unused\n");
continue;
}
int den = d;
if (den == 0) den = 256;
if (!runtime) {
for (int shift = 0; shift < 16; shift++) {
if (u_method_0(den, shift, bits)) {
fprintf(c_out, " {%d, 0, 0, %d},\n", den, shift);
goto next_unsigned;
}
}
for (int shift = 0; shift < 8; shift++) {
int64_t mul = (1L << (bits + shift)) / den + 1;
if (u_method_1(den, mul, shift, bits)) {
fprintf(c_out, " {%d, 1, %lldULL, %d},\n", den, (long long)mul, shift);
goto next_unsigned;
}
}
for (int shift = 0; shift < 8; shift++) {
int64_t mul = (1L << (bits + shift + 1)) / den - (1L << bits);
mul &= (1L << bits) - 1;
if (u_method_3(den, mul, shift, bits)) {
fprintf(c_out, " {%d, 3, %lldULL, %d},\n", den, (long long)mul, shift);
goto next_unsigned;
}
}
} else if (d == 1) {
// Runtime division by one is handled by a select
fprintf(c_out, " {1, 0, 0ULL, 0},\n");
goto next_unsigned;
}
{
int shift = 31 - __builtin_clz(den - 1);
int64_t mul = (1L << (bits + shift + 1)) / den - (1L << bits) + 1;
mul &= (1L << bits) - 1;
if (u_method_2(den, mul, shift, bits)) {
fprintf(c_out, " {%d, 2, %lldULL, %d},\n", den, (long long)mul, shift);
goto next_unsigned;
}
}
fprintf(c_out, "ERROR! No solution found for unsigned %d\n", den);
next_unsigned:;
}
fprintf(c_out, "};\n");
printf("Generating table%s_s%d...\n", runtime ? "_runtime" : "", bits);
if (runtime) {
fprintf(h_out, "extern const int64_t table_runtime_s%d[256][4];\n", bits);
fprintf(c_out, "const int64_t table_runtime_s%d[256][4] = {\n", bits);
} else {
fprintf(h_out, "extern const int64_t table_s%d[256][4];\n", bits);
fprintf(c_out, "const int64_t table_s%d[256][4] = {\n", bits);
}
for (int d = 0; d < 256; d++) {
if (runtime && d < 2) {
fprintf(c_out, " {0, 0, 0, 0}, // unused\n");
continue;
}
int den = d;
if (den == 0) den = 256;
if (!runtime) {
for (int shift = 0; shift < 8; shift++) {
if (s_method_0(den, shift, bits)) {
fprintf(c_out, " {%d, 0, 0, %d},\n", den, shift);
goto next_signed;
}
}
}
{
int shift = 31 - __builtin_clz(den - 1);
int64_t mul = (1L << (shift + bits)) / den + 1;
if (s_method_1(den, mul, shift, bits)) {
fprintf(c_out, " {%d, 1, %lldLL, %d},\n", den, (long long)mul, shift);
goto next_signed;
}
}
fprintf(c_out, "ERROR! No solution found for signed %d\n", den);
next_signed:;
}
fprintf(c_out, "};\n");
printf("Generating table%s_srz%d...\n", runtime ? "_runtime" : "", bits);
if (runtime) {
fprintf(h_out, "extern const int64_t table_runtime_srz%d[256][4];\n", bits);
fprintf(c_out, "const int64_t table_runtime_srz%d[256][4] = {\n", bits);
} else {
fprintf(h_out, "extern const int64_t table_srz%d[256][4];\n", bits);
fprintf(c_out, "const int64_t table_srz%d[256][4] = {\n", bits);
}
for (int d = 0; d < 256; d++) {
if (runtime && d < 2) {
fprintf(c_out, " {0, 0, 0, 0}, // unused\n");
continue;
}
int den = d;
if (den == 0) den = 256;
if (!runtime) {
for (int shift = 0; shift < 8; shift++) {
if (srz_method_0(den, shift, bits)) {
fprintf(c_out, " {%d, 0, 0, %d},\n", den, shift);
goto next_signedrz;
}
}
}
{
int shift = 31 - __builtin_clz(den - 1);
int64_t mul = (1L << (shift + bits)) / den + 1;
if (srz_method_1(den, mul, shift, bits)) {
fprintf(c_out, " {%d, 1, %lldLL, %d},\n", den, (long long)mul, shift);
goto next_signedrz;
}
}
fprintf(c_out, "ERROR! No solution found for signed %d\n", den);
next_signedrz:;
}
fprintf(c_out, "};\n");
}
}
fprintf(h_out, "}\n}\n}\n\n#endif\n");
fprintf(c_out, "}\n}\n}\n");
fclose(h_out);
fclose(c_out);
return 0;
}
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