c682590538
git-svn-id: http://skia.googlecode.com/svn/trunk@3141 2bbb7eff-a529-9590-31e7-b0007b416f81
400 lines
16 KiB
C++
400 lines
16 KiB
C++
#include <vector>
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/* Given:
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* Resultant[a*t^3 + b*t^2 + c*t + d - x, e*t^3 + f*t^2 + g*t + h - y, t]
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*/
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const char result1[] =
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"-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 + "
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" 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 - "
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" 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 - "
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" 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 + "
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" 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 - "
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" 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 + "
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" 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 + "
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" 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 - "
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" 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 - "
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" 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 + "
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" b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x + "
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" 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 + "
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" 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 - "
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" 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 + "
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" 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 - "
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" 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 - "
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" 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 - "
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" 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 - "
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" 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 + "
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" 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 - "
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" 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 + "
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" 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 - "
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" 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 - "
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" 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 + "
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" 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3";
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const size_t len1 = sizeof(result1) - 1;
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/* Given:
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* Expand[
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* Det[{{a, b, c, (d - x), 0, 0},
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* {0, a, b, c, (d - x), 0},
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* {0, 0, a, b, c, (d - x)},
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* {e, f, g, (h - y), 0, 0},
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* {0, e, f, g, (h - y), 0},
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* {0, 0, e, f, g, (h - y)}}]]
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*/
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// result1 and result2 are the same. 102 factors:
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const char result2[] =
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"-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 + "
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" 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 - "
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" 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 - "
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" 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 + "
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" 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 - "
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" 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 + "
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" 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 + "
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" 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 - "
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" 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 - "
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" 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 + "
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" b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x + "
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" 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 + "
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" 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 - "
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" 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 + "
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" 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 - "
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" 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 - "
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" 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 - "
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" 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 - "
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" 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 + "
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" 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 - "
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" 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 + "
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" 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 - "
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" 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 - "
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" 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 + "
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" 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3";
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const size_t len2 = sizeof(result2) - 1;
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/* Given: r1 = Resultant[
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* a*(1 - t)^3 + 3*b*(1 - t)^2*t + 3*c*(1 - t)*t^2 + d*t^3 - x,
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* e*(1 - t)^3 + 3*f*(1 - t)^2*t + 3*g*(1 - t)*t^2 + h*t^3 - y, t]
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* Collect[r1, {x, y}, Simplify]
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* CForm[%]
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* then use regex to replace Power\(([a-h]),3\) with \1*\1*\1
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* and Power\(([a-h]),2\) with \1*\1
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* yields:
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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)) -
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h*(27*c*c*c*e*e - 27*c*c*(3*b*e*f - 3*a*f*f + 2*a*e*g) +
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h*(-27*b*b*b*e + 27*a*b*b*f - 9*a*a*b*g + a*a*a*h) +
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9*c*(9*b*b*e*g + a*b*(-9*f*g + 3*e*h) + a*a*(3*g*g - 2*f*h))) +
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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) +
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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)))
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- Power(e - 3*f + 3*g - h,3)*Power(x,3)
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+ 3*(6*b*d*d*e*e - d*d*d*e*e + 18*b*b*d*e*f - 18*b*d*d*e*f -
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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 +
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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) +
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a*a*(-3*b*h*(2*g + h) + d*(-27*g*g + 9*g*h - h*(2*e + h) + 9*f*(g + h))) +
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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)) +
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d*d*(e*e + 9*f*(3*f - g) + e*(-9*f - 9*g + 2*h))) -
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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)))) +
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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)) +
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a*d*(-9*f*f - 18*f*g + 6*g*g + f*h + e*(f + 12*g + h)) +
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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
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- 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 -
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9*b*b*b*(e + 2*h) - a*a*(d*(e - 9*f + 18*g - 7*h) + 3*c*(2*f - 6*g + h)) +
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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)) +
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9*b*b*(3*c*(e + g + h) + a*(f + 2*h) - d*(e - 2*(f - 3*g + h))) -
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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) +
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a*(c*(-3*e + 9*f + 9*g + 3*h) + d*(e + 3*f - 17*g + 7*h))))*Power(y,2)
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+ Power(a - 3*b + 3*c - d,3)*Power(y,3)
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+ 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 +
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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 -
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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 +
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18*b*f*h*h - 6*a*g*h*h - 3*b*g*h*h + a*h*h*h +
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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) +
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e*(9*f*g + 6*g*g - 17*f*h - 3*g*h + 3*h*h)) -
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d*(e*e*e + e*e*(-6*f - 3*g + 7*h) - 9*(2*f - g)*(f*f + g*g - f*(g + h)) +
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e*(18*f*f + 9*g*g + 3*g*h + h*h - 3*f*(3*g + 7*h)))) )
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+ Power(x,2)*(3*(a - 3*b + 3*c - d)*Power(e - 3*f + 3*g - h,2)*y)
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+ 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 -
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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 +
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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 +
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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) +
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d*d*(e*e*e - 9*f*f*f + 9*e*f*(f + g) - e*e*(3*f + 6*g + h)) +
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d*(-3*c*(-9*f*f*g + e*e*(2*f - 6*g - 3*h) + e*(9*f*g + 6*g*g + f*h)) +
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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) +
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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 -
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e*(6*f*f + g*(18*g + h) - 3*f*(3*g + 4*h)))) +
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3*c*(3*b*(e*e*h + 3*f*g*h - e*(3*f*g - 6*f*h + 6*g*h + h*h)) +
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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))))) )
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+ 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 -
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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 +
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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 -
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9*c*c*(2*e*e + 3*f*f + 3*f*h - 2*g*h + e*(-3*f - 4*g + h)) +
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9*b*b*(3*g*g - 3*g*h + 2*h*(-2*f + h) + e*(-2*f + 3*g + h)) +
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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) +
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d*(-e*e + 12*f*f - 27*f*g + e*(-9*f + 20*g - 5*h) + g*(9*g + h))) +
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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) +
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d*(7*e*e + 9*f*f + 9*f*g - 6*g*g - f*h + e*(-14*f - 9*g + 5*h))))*y
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- x*3*Power(a - 3*b + 3*c - d,2)*(e - 3*f + 3*g - h)*Power(y,2)
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*/
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const int factors = 8;
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struct coeff {
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int s; // constant and coefficient sign
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int n[factors]; // 0 or power of a (1, 2, or 3) for a through h
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};
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enum {
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xxx_coeff,
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xxy_coeff,
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xyy_coeff,
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yyy_coeff,
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xx_coeff,
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xy_coeff,
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yy_coeff,
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x_coeff,
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y_coeff,
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c_coeff,
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coeff_count
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};
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typedef std::vector<coeff> coeffs;
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typedef std::vector<coeffs> n_coeffs;
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static char skipSpace(const char* str, size_t& index) {
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do {
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++index;
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} while (str[index] == ' ');
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return str[index];
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}
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static char backSkipSpace(const char* str, size_t& end) {
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while (str[end - 1] == ' ') {
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--end;
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}
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return str[end - 1];
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}
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static void match(const char* str, size_t len, coeffs& co, const char pattern[]) {
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size_t patternLen = strlen(pattern);
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size_t index = 0;
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while (index < len) {
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char ch = str[index];
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if (ch != '-' && ch != '+') {
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printf("missing sign\n");
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}
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size_t end = index + 1;
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while (str[end] != '+' && str[end] != '-' && ++end < len) {
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;
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}
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backSkipSpace(str, end);
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size_t idx = index;
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index = end;
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skipSpace(str, index);
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if (!strncmp(&str[end - patternLen], pattern, patternLen) == 0) {
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continue;
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}
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size_t endCoeff = end - patternLen;
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char last = backSkipSpace(str, endCoeff);
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if (last == '2' || last == '3') {
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last = str[endCoeff - 3]; // skip ^2
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}
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if (last == 'x' || last == 'y') {
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continue;
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}
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coeff c;
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c.s = str[idx] == '-' ? -1 : 1;
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bzero(c.n, sizeof(c.n));
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ch = skipSpace(str, idx);
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if (ch >= '2' && ch <= '6') {
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c.s *= ch - '0';
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ch = skipSpace(str, idx);
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}
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while (idx < endCoeff) {
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char x = str[idx];
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if (x < 'a' || x > 'a' + factors) {
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printf("expected factor\n");
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}
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idx++;
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int pow = 1;
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if (str[idx] == '^') {
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idx++;
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char exp = str[idx];
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if (exp < '2' || exp > '3') {
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printf("expected exponent\n");
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}
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pow = exp - '0';
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}
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skipSpace(str, idx);
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c.n[x - 'a'] = pow;
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}
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co.push_back(c);
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}
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}
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void cubecode_test(int test);
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void cubecode_test(int test) {
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const char* str = test ? result2 : result1;
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size_t len = strlen(str);
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n_coeffs c(coeff_count);
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match(str, len, c[xxx_coeff], "x^3"); // 1 factor
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match(str, len, c[xxy_coeff], "x^2 y"); // 1 factor
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match(str, len, c[xyy_coeff], "x y^2"); // 1 factor
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match(str, len, c[yyy_coeff], "y^3"); // 1 factor
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match(str, len, c[xx_coeff], "x^2"); // 7 factors
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match(str, len, c[xy_coeff], "x y"); // 8 factors
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match(str, len, c[yy_coeff], "y^2"); // 7 factors
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match(str, len, c[x_coeff], "x"); // 21 factors
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match(str, len, c[y_coeff], "y"); // 21 factors
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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
|
|
*/
|