/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include <vector>
/* Given:
* Resultant[a*t^3 + b*t^2 + c*t + d - x, e*t^3 + f*t^2 + g*t + h - y, t]
*/
const char result1[] =
"-d^3 e^3 + c d^2 e^2 f - b d^2 e f^2 + a d^2 f^3 - c^2 d e^2 g + "
" 2 b d^2 e^2 g + b c d e f g - 3 a d^2 e f g - a c d f^2 g - "
" b^2 d e g^2 + 2 a c d e g^2 + a b d f g^2 - a^2 d g^3 + c^3 e^2 h - "
" 3 b c d e^2 h + 3 a d^2 e^2 h - b c^2 e f h + 2 b^2 d e f h + "
" a c d e f h + a c^2 f^2 h - 2 a b d f^2 h + b^2 c e g h - "
" 2 a c^2 e g h - a b d e g h - a b c f g h + 3 a^2 d f g h + "
" a^2 c g^2 h - b^3 e h^2 + 3 a b c e h^2 - 3 a^2 d e h^2 + "
" a b^2 f h^2 - 2 a^2 c f h^2 - a^2 b g h^2 + a^3 h^3 + 3 d^2 e^3 x - "
" 2 c d e^2 f x + 2 b d e f^2 x - 2 a d f^3 x + c^2 e^2 g x - "
" 4 b d e^2 g x - b c e f g x + 6 a d e f g x + a c f^2 g x + "
" b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x + "
" 3 b c e^2 h x - 6 a d e^2 h x - 2 b^2 e f h x - a c e f h x + "
" 2 a b f^2 h x + a b e g h x - 3 a^2 f g h x + 3 a^2 e h^2 x - "
" 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 + "
" 2 b e^2 g x^2 - 3 a e f g x^2 + 3 a e^2 h x^2 + e^3 x^3 - "
" c^3 e^2 y + 3 b c d e^2 y - 3 a d^2 e^2 y + b c^2 e f y - "
" 2 b^2 d e f y - a c d e f y - a c^2 f^2 y + 2 a b d f^2 y - "
" b^2 c e g y + 2 a c^2 e g y + a b d e g y + a b c f g y - "
" 3 a^2 d f g y - a^2 c g^2 y + 2 b^3 e h y - 6 a b c e h y + "
" 6 a^2 d e h y - 2 a b^2 f h y + 4 a^2 c f h y + 2 a^2 b g h y - "
" 3 a^3 h^2 y - 3 b c e^2 x y + 6 a d e^2 x y + 2 b^2 e f x y + "
" a c e f x y - 2 a b f^2 x y - a b e g x y + 3 a^2 f g x y - "
" 6 a^2 e h x y - 3 a e^2 x^2 y - b^3 e y^2 + 3 a b c e y^2 - "
" 3 a^2 d e y^2 + a b^2 f y^2 - 2 a^2 c f y^2 - a^2 b g y^2 + "
" 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3";
const size_t len1 = sizeof(result1) - 1;
/* Given:
* Expand[
* Det[{{a, b, c, (d - x), 0, 0},
* {0, a, b, c, (d - x), 0},
* {0, 0, a, b, c, (d - x)},
* {e, f, g, (h - y), 0, 0},
* {0, e, f, g, (h - y), 0},
* {0, 0, e, f, g, (h - y)}}]]
*/
// result1 and result2 are the same. 102 factors:
const char result2[] =
"-d^3 e^3 + c d^2 e^2 f - b d^2 e f^2 + a d^2 f^3 - c^2 d e^2 g + "
" 2 b d^2 e^2 g + b c d e f g - 3 a d^2 e f g - a c d f^2 g - "
" b^2 d e g^2 + 2 a c d e g^2 + a b d f g^2 - a^2 d g^3 + c^3 e^2 h - "
" 3 b c d e^2 h + 3 a d^2 e^2 h - b c^2 e f h + 2 b^2 d e f h + "
" a c d e f h + a c^2 f^2 h - 2 a b d f^2 h + b^2 c e g h - "
" 2 a c^2 e g h - a b d e g h - a b c f g h + 3 a^2 d f g h + "
" a^2 c g^2 h - b^3 e h^2 + 3 a b c e h^2 - 3 a^2 d e h^2 + "
" a b^2 f h^2 - 2 a^2 c f h^2 - a^2 b g h^2 + a^3 h^3 + 3 d^2 e^3 x - "
" 2 c d e^2 f x + 2 b d e f^2 x - 2 a d f^3 x + c^2 e^2 g x - "
" 4 b d e^2 g x - b c e f g x + 6 a d e f g x + a c f^2 g x + "
" b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x + "
" 3 b c e^2 h x - 6 a d e^2 h x - 2 b^2 e f h x - a c e f h x + "
" 2 a b f^2 h x + a b e g h x - 3 a^2 f g h x + 3 a^2 e h^2 x - "
" 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 + "
" 2 b e^2 g x^2 - 3 a e f g x^2 + 3 a e^2 h x^2 + e^3 x^3 - "
" c^3 e^2 y + 3 b c d e^2 y - 3 a d^2 e^2 y + b c^2 e f y - "
" 2 b^2 d e f y - a c d e f y - a c^2 f^2 y + 2 a b d f^2 y - "
" b^2 c e g y + 2 a c^2 e g y + a b d e g y + a b c f g y - "
" 3 a^2 d f g y - a^2 c g^2 y + 2 b^3 e h y - 6 a b c e h y + "
" 6 a^2 d e h y - 2 a b^2 f h y + 4 a^2 c f h y + 2 a^2 b g h y - "
" 3 a^3 h^2 y - 3 b c e^2 x y + 6 a d e^2 x y + 2 b^2 e f x y + "
" a c e f x y - 2 a b f^2 x y - a b e g x y + 3 a^2 f g x y - "
" 6 a^2 e h x y - 3 a e^2 x^2 y - b^3 e y^2 + 3 a b c e y^2 - "
" 3 a^2 d e y^2 + a b^2 f y^2 - 2 a^2 c f y^2 - a^2 b g y^2 + "
" 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3";
const size_t len2 = sizeof(result2) - 1;
/* Given: r1 = Resultant[
* a*(1 - t)^3 + 3*b*(1 - t)^2*t + 3*c*(1 - t)*t^2 + d*t^3 - x,
* e*(1 - t)^3 + 3*f*(1 - t)^2*t + 3*g*(1 - t)*t^2 + h*t^3 - y, t]
* Collect[r1, {x, y}, Simplify]
* CForm[%]
* then use regex to replace Power\(([a-h]),3\) with \1*\1*\1
* and Power\(([a-h]),2\) with \1*\1
* yields:
d*d*d*e*e*e - 3*d*d*(3*c*e*e*f + 3*b*e*(-3*f*f + 2*e*g) + a*(9*f*f*f - 9*e*f*g + e*e*h)) -
h*(27*c*c*c*e*e - 27*c*c*(3*b*e*f - 3*a*f*f + 2*a*e*g) +
h*(-27*b*b*b*e + 27*a*b*b*f - 9*a*a*b*g + a*a*a*h) +
9*c*(9*b*b*e*g + a*b*(-9*f*g + 3*e*h) + a*a*(3*g*g - 2*f*h))) +
3*d*(9*c*c*e*e*g + 9*b*b*e*(3*g*g - 2*f*h) + 3*a*b*(-9*f*g*g + 6*f*f*h + e*g*h) +
a*a*(9*g*g*g - 9*f*g*h + e*h*h) + 3*c*(3*b*e*(-3*f*g + e*h) + a*(9*f*f*g - 6*e*g*g - e*f*h)))
- Power(e - 3*f + 3*g - h,3)*Power(x,3)
+ 3*(6*b*d*d*e*e - d*d*d*e*e + 18*b*b*d*e*f - 18*b*d*d*e*f -
9*b*d*d*f*f - 54*b*b*d*e*g + 12*b*d*d*e*g - 27*b*b*d*g*g - 18*b*b*b*e*h + 18*b*b*d*e*h +
18*b*b*d*f*h + a*a*a*h*h - 9*b*b*b*h*h + 9*c*c*c*e*(e + 2*h) +
a*a*(-3*b*h*(2*g + h) + d*(-27*g*g + 9*g*h - h*(2*e + h) + 9*f*(g + h))) +
a*(9*b*b*h*(2*f + h) - 3*b*d*(6*f*f - 6*f*(3*g - 2*h) + g*(-9*g + h) + e*(g + h)) +
d*d*(e*e + 9*f*(3*f - g) + e*(-9*f - 9*g + 2*h))) -
9*c*c*(d*e*(e + 2*g) + 3*b*(f*h + e*(f + h)) + a*(-3*f*f - 6*f*h + 2*(g*h + e*(g + h)))) +
3*c*(d*d*e*(e + 2*f) + a*a*(3*g*g + 6*g*h - 2*h*(2*f + h)) + 9*b*b*(g*h + e*(g + h)) +
a*d*(-9*f*f - 18*f*g + 6*g*g + f*h + e*(f + 12*g + h)) +
b*(d*(-3*e*e + 9*f*g + e*(9*f + 9*g - 6*h)) + 3*a*(h*(2*e - 3*g + h) - 3*f*(g + h)))))*y
- 3*(18*c*c*c*e - 18*c*c*d*e + 6*c*d*d*e - d*d*d*e + 3*c*d*d*f - 9*c*c*d*g + a*a*a*h + 9*c*c*c*h -
9*b*b*b*(e + 2*h) - a*a*(d*(e - 9*f + 18*g - 7*h) + 3*c*(2*f - 6*g + h)) +
a*(-9*c*c*(2*e - 6*f + 2*g - h) + d*d*(-7*e + 18*f - 9*g + h) + 3*c*d*(7*e - 17*f + 3*g + h)) +
9*b*b*(3*c*(e + g + h) + a*(f + 2*h) - d*(e - 2*(f - 3*g + h))) -
3*b*(-(d*d*(e - 6*f + 2*g)) - 3*c*d*(e + 3*f + 3*g - h) + 9*c*c*(e + f + h) + a*a*(g + 2*h) +
a*(c*(-3*e + 9*f + 9*g + 3*h) + d*(e + 3*f - 17*g + 7*h))))*Power(y,2)
+ Power(a - 3*b + 3*c - d,3)*Power(y,3)
+ Power(x,2)*(-3*(-9*b*e*f*f + 9*a*f*f*f + 6*b*e*e*g - 9*a*e*f*g + 27*b*e*f*g - 27*a*f*f*g + 18*a*e*g*g - 54*b*e*g*g +
27*a*f*g*g + 27*b*f*g*g - 18*a*g*g*g + a*e*e*h - 9*b*e*e*h + 3*a*e*f*h + 9*b*e*f*h + 9*a*f*f*h -
18*b*f*f*h - 21*a*e*g*h + 51*b*e*g*h - 9*a*f*g*h - 27*b*f*g*h + 18*a*g*g*h + 7*a*e*h*h - 18*b*e*h*h - 3*a*f*h*h +
18*b*f*h*h - 6*a*g*h*h - 3*b*g*h*h + a*h*h*h +
3*c*(-9*f*f*(g - 2*h) + 3*g*g*h - f*h*(9*g + 2*h) + e*e*(f - 6*g + 6*h) +
e*(9*f*g + 6*g*g - 17*f*h - 3*g*h + 3*h*h)) -
d*(e*e*e + e*e*(-6*f - 3*g + 7*h) - 9*(2*f - g)*(f*f + g*g - f*(g + h)) +
e*(18*f*f + 9*g*g + 3*g*h + h*h - 3*f*(3*g + 7*h)))) )
+ Power(x,2)*(3*(a - 3*b + 3*c - d)*Power(e - 3*f + 3*g - h,2)*y)
+ x*(-3*(27*b*b*e*g*g - 27*a*b*f*g*g + 9*a*a*g*g*g - 18*b*b*e*f*h + 18*a*b*f*f*h + 3*a*b*e*g*h -
27*b*b*e*g*h - 9*a*a*f*g*h + 27*a*b*f*g*h - 9*a*a*g*g*h + a*a*e*h*h - 9*a*b*e*h*h +
27*b*b*e*h*h + 6*a*a*f*h*h - 18*a*b*f*h*h - 9*b*b*f*h*h + 3*a*a*g*h*h +
6*a*b*g*h*h - a*a*h*h*h + 9*c*c*(e*e*(g - 3*h) - 3*f*f*h + e*(3*f + 2*g)*h) +
d*d*(e*e*e - 9*f*f*f + 9*e*f*(f + g) - e*e*(3*f + 6*g + h)) +
d*(-3*c*(-9*f*f*g + e*e*(2*f - 6*g - 3*h) + e*(9*f*g + 6*g*g + f*h)) +
a*(-18*f*f*f - 18*e*g*g + 18*g*g*g - 2*e*e*h + 3*e*g*h + 2*e*h*h + 9*f*f*(3*g + 2*h) +
3*f*(6*e*g - 9*g*g - e*h - 6*g*h)) - 3*b*(9*f*g*g + e*e*(4*g - 3*h) - 6*f*f*h -
e*(6*f*f + g*(18*g + h) - 3*f*(3*g + 4*h)))) +
3*c*(3*b*(e*e*h + 3*f*g*h - e*(3*f*g - 6*f*h + 6*g*h + h*h)) +
a*(9*f*f*(g - 2*h) + f*h*(-e + 9*g + 4*h) - 3*(2*g*g*h + e*(2*g*g - 4*g*h + h*h))))) )
+ x*3*(-2*a*d*e*e - 7*d*d*e*e + 15*a*d*e*f + 21*d*d*e*f - 9*a*d*f*f - 18*d*d*f*f - 15*a*d*e*g -
3*d*d*e*g - 9*a*a*f*g + 9*d*d*f*g + 18*a*a*g*g + 9*a*d*g*g + 2*a*a*e*h - 2*d*d*e*h +
3*a*a*f*h + 15*a*d*f*h - 21*a*a*g*h - 15*a*d*g*h + 7*a*a*h*h + 2*a*d*h*h -
9*c*c*(2*e*e + 3*f*f + 3*f*h - 2*g*h + e*(-3*f - 4*g + h)) +
9*b*b*(3*g*g - 3*g*h + 2*h*(-2*f + h) + e*(-2*f + 3*g + h)) +
3*b*(3*c*(e*e + 3*e*(f - 3*g) + (9*f - 3*g - h)*h) + a*(6*f*f + e*g - 9*f*g - 9*g*g - 5*e*h + 9*f*h + 14*g*h - 7*h*h) +
d*(-e*e + 12*f*f - 27*f*g + e*(-9*f + 20*g - 5*h) + g*(9*g + h))) +
3*c*(a*(-(e*f) - 9*f*f + 27*f*g - 12*g*g + 5*e*h - 20*f*h + 9*g*h + h*h) +
d*(7*e*e + 9*f*f + 9*f*g - 6*g*g - f*h + e*(-14*f - 9*g + 5*h))))*y
- x*3*Power(a - 3*b + 3*c - d,2)*(e - 3*f + 3*g - h)*Power(y,2)
*/
const int factors = 8;
struct coeff {
int s; // constant and coefficient sign
int n[factors]; // 0 or power of a (1, 2, or 3) for a through h
};
enum {
xxx_coeff,
xxy_coeff,
xyy_coeff,
yyy_coeff,
xx_coeff,
xy_coeff,
yy_coeff,
x_coeff,
y_coeff,
c_coeff,
coeff_count
};
typedef std::vector<coeff> coeffs;
typedef std::vector<coeffs> n_coeffs;
static char skipSpace(const char* str, size_t& index) {
do {
++index;
} while (str[index] == ' ');
return str[index];
}
static char backSkipSpace(const char* str, size_t& end) {
while (str[end - 1] == ' ') {
--end;
}
return str[end - 1];
}
static void match(const char* str, size_t len, coeffs& co, const char pattern[]) {
size_t patternLen = strlen(pattern);
size_t index = 0;
while (index < len) {
char ch = str[index];
if (ch != '-' && ch != '+') {
printf("missing sign\n");
}
size_t end = index + 1;
while (str[end] != '+' && str[end] != '-' && ++end < len) {
;
}
backSkipSpace(str, end);
size_t idx = index;
index = end;
skipSpace(str, index);
if (!strncmp(&str[end - patternLen], pattern, patternLen) == 0) {
continue;
}
size_t endCoeff = end - patternLen;
char last = backSkipSpace(str, endCoeff);
if (last == '2' || last == '3') {
last = str[endCoeff - 3]; // skip ^2
}
if (last == 'x' || last == 'y') {
continue;
}
coeff c;
c.s = str[idx] == '-' ? -1 : 1;
bzero(c.n, sizeof(c.n));
ch = skipSpace(str, idx);
if (ch >= '2' && ch <= '6') {
c.s *= ch - '0';
ch = skipSpace(str, idx);
}
while (idx < endCoeff) {
char x = str[idx];
if (x < 'a' || x > 'a' + factors) {
printf("expected factor\n");
}
idx++;
int pow = 1;
if (str[idx] == '^') {
idx++;
char exp = str[idx];
if (exp < '2' || exp > '3') {
printf("expected exponent\n");
}
pow = exp - '0';
}
skipSpace(str, idx);
c.n[x - 'a'] = pow;
}
co.push_back(c);
}
}
void cubecode_test(int test);
void cubecode_test(int test) {
const char* str = test ? result2 : result1;
size_t len = strlen(str);
n_coeffs c(coeff_count);
match(str, len, c[xxx_coeff], "x^3"); // 1 factor
match(str, len, c[xxy_coeff], "x^2 y"); // 1 factor
match(str, len, c[xyy_coeff], "x y^2"); // 1 factor
match(str, len, c[yyy_coeff], "y^3"); // 1 factor
match(str, len, c[xx_coeff], "x^2"); // 7 factors
match(str, len, c[xy_coeff], "x y"); // 8 factors
match(str, len, c[yy_coeff], "y^2"); // 7 factors
match(str, len, c[x_coeff], "x"); // 21 factors
match(str, len, c[y_coeff], "y"); // 21 factors
match(str, len, c[c_coeff], ""); // 34 factors : total 102
#define COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS 0
#define WRITE_AS_NONOPTIMIZED_C_CODE 0
#if COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS
int count[factors][factors][factors];
bzero(count, sizeof(count));
#endif
#if WRITE_AS_NONOPTIMIZED_C_CODE
printf("// start of generated code");
#endif
for (n_coeffs::iterator it = c.begin(); it < c.end(); ++it) {
coeffs& co = *it;
#if WRITE_AS_NONOPTIMIZED_C_CODE
printf("\nstatic double calc_%c(double a, double b, double c, double d,"
"\n double e, double f, double g, double h) {"
"\n return"
"\n ", 'A' + (it - c.begin()));
if (co[0].s > 0) {
printf(" ");
}
if (abs(co[0].s) == 1) {
printf(" ");
}
#endif
for (coeffs::iterator ct = co.begin(); ct < co.end(); ++ct) {
const coeff& cf = *ct;
#if WRITE_AS_NONOPTIMIZED_C_CODE
printf(" ");
bool firstFactor = false;
if (ct - co.begin() > 0 || cf.s < 0) {
printf("%c", cf.s < 0 ? '-' : '+');
}
if (ct - co.begin() > 0) {
printf(" ");
}
if (abs(cf.s) > 1) {
printf("%d * ", abs(cf.s));
} else {
if (ct - co.begin() > 0) {
printf(" ");
}
}
#endif
for (int x = 0; x < factors; ++x) {
if (cf.n[x] == 0) {
continue;
}
#if WRITE_AS_NONOPTIMIZED_C_CODE
for (int y = 0 ; y < cf.n[x]; ++y) {
if (y > 0 || firstFactor) {
printf(" * ");
}
printf("%c", 'a' + x);
}
firstFactor = true;
#endif
#if COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS
for (int y = x; y < factors; ++y) {
if (cf.n[y] == 0) {
continue;
}
if (x == y && cf.n[y] == 1) {
continue;
}
for (int z = y; z < factors; ++z) {
if (cf.n[z] == 0) {
continue;
}
if ((x == z || y == z) && cf.n[z] == 1) {
continue;
}
if (x == y && y == z && cf.n[z] == 2) {
continue;
}
count[x][y][z]++;
}
}
#endif
}
#if WRITE_AS_NONOPTIMIZED_C_CODE
if (ct + 1 < co.end()) {
printf("\n");
}
#endif
}
#if WRITE_AS_NONOPTIMIZED_C_CODE
printf(";\n}\n");
#endif
}
#if WRITE_AS_NONOPTIMIZED_C_CODE
printf("// end of generated code\n");
#endif
#if COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS
const int bestCount = 20;
int best[bestCount][4];
bzero(best, sizeof(best));
for (int x = 0; x < factors; ++x) {
for (int y = x; y < factors; ++y) {
for (int z = y; z < factors; ++z) {
if (!count[x][y][z]) {
continue;
}
for (int w = 0; w < bestCount; ++w) {
if (best[w][0] < count[x][y][z]) {
best[w][0] = count[x][y][z];
best[w][1] = x;
best[w][2] = y;
best[w][3] = z;
break;
}
}
}
}
}
for (int w = 0; w < bestCount; ++w) {
printf("%c%c%c=%d\n", 'a' + best[w][1], 'a' + best[w][2],
'a' + best[w][3], best[w][0]);
}
#endif
#if WRITE_AS_NONOPTIMIZED_C_CODE
printf("\n");
#endif
}
/* results: variable triplets used 10 or more times:
aah=14
ade=14
aeh=14
dee=14
bce=13
beg=13
beh=12
bbe=11
bef=11
cee=11
cef=11
def=11
ceh=10
deg=10
*/