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#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 result[] =
"-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 len = sizeof(result) - 1;
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(size_t& index) {
do {
++index;
} while (result[index] == ' ');
return result[index];
}
static char backSkipSpace(size_t& end) {
while (result[end - 1] == ' ') {
--end;
}
return result[end - 1];
}
static void match(coeffs& co, const char pattern[]) {
size_t patternLen = strlen(pattern);
size_t index = 0;
while (index < len) {
char ch = result[index];
if (ch != '-' && ch != '+') {
printf("missing sign\n");
}
size_t end = index + 1;
while (result[end] != '+' && result[end] != '-' && ++end < len) {
;
}
backSkipSpace(end);
size_t idx = index;
index = end;
skipSpace(index);
if (!strncmp(&result[end - patternLen], pattern, patternLen) == 0) {
continue;
}
size_t endCoeff = end - patternLen;
char last = backSkipSpace(endCoeff);
if (last == '2' || last == '3') {
last = result[endCoeff - 3]; // skip ^2
}
if (last == 'x' || last == 'y') {
continue;
}
coeff c;
c.s = result[idx] == '-' ? -1 : 1;
bzero(c.n, sizeof(c.n));
ch = skipSpace(idx);
if (ch >= '2' && ch <= '6') {
c.s *= ch - '0';
ch = skipSpace(idx);
}
while (idx < endCoeff) {
char x = result[idx];
if (x < 'a' || x > 'a' + factors) {
printf("expected factor\n");
}
idx++;
int pow = 1;
if (result[idx] == '^') {
idx++;
char exp = result[idx];
if (exp < '2' || exp > '3') {
printf("expected exponent\n");
}
pow = exp - '0';
}
skipSpace(idx);
c.n[x - 'a'] = pow;
}
co.push_back(c);
}
}
void cubecode_test();
void cubecode_test() {
n_coeffs c(coeff_count);
match(c[xxx_coeff], "x^3"); // 1 factor
match(c[xxy_coeff], "x^2 y"); // 1 factor
match(c[xyy_coeff], "x y^2"); // 1 factor
match(c[yyy_coeff], "y^3"); // 1 factor
match(c[xx_coeff], "x^2"); // 7 factors
match(c[xy_coeff], "x y"); // 8 factors
match(c[yy_coeff], "y^2"); // 7 factors
match(c[x_coeff], "x"); // 21 factors
match(c[y_coeff], "y"); // 21 factors
match(c[c_coeff], ""); // 34 factors
#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
*/
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