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# Solve cubic equations

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 Submitted on: 7/27/2000 8:43:30 PM By: Bob Stout (republished under Open Content License) Level: Intermediate User Rating: Unrated Compatibility: C, C++ (general), Microsoft Visual C++, Borland C++, UNIX C++ Views: 4973

CUBIC.C - Solve a cubic polynomial

### INCLUDE files:

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 ```//************************************** //INCLUDE files for :Solve cubic equations //************************************** /* +++Date last modified: 05-Jul-1997 */ /* ** SNIPMATH.H - Header file for SNIPPETS math functions and macros */ #ifndef SNIPMATH__H #define SNIPMATH__H #include #include "sniptype.h" #include "round.h" /* ** Callable library functions begin here */ voidSetBCDLen(int n); /* Bcdl.C */ longBCDtoLong(char *BCDNum); /* Bcdl.C */ voidLongtoBCD(long num, char BCDNum[]);/* Bcdl.C */ double bcd_to_double(void *buf, size_t len, /* Bcdd.C */ int digits); int double_to_bcd(double arg, char *buf, /* Bcdd.C */ size_t length, size_t digits ); DWORDncomb1 (int n, int m);/* Combin.C*/ DWORDncomb2 (int n, int m);/* Combin.C*/ voidSolveCubic(double a, double b, double c, /* Cubic.C*/ double d, int *solutions, double *x); DWORDdbl2ulong(double t); /* Dbl2Long.C */ longdbl2long(double t);/* Dbl2Long.C */ double dround(double x); /* Dblround.C */ /* Use #defines for Permutations and Combinations -- Factoryl.C */ #define log10P(n,r) (log10factorial(n)-log10factorial((n)-(r))) #define log10C(n,r) (log10P((n),(r))-log10factorial(r)) double log10factorial(double N); /* Factoryl.C */ double fibo(unsigned short term);/* Fibo.C */ double frandom(int n);/* Frand.C*/ double ipow(double x, int n);/* Ipow.C */ int ispow2(int x);/* Ispow2.C*/ longdouble ldfloor(long double a);/* Ldfloor.C */ int initlogscale(long dmax, long rmax);/* Logscale.C */ longlogscale(long d); /* Logscale.C */ floatMSBINToIEEE(float f); /* Msb2Ieee.C */ floatIEEEToMSBIN(float f); /* Msb2Ieee.C */ int perm_index (char pit[], int size);/* Perm_Idx.C */ int round_div(int n, int d); /* Rnd_Div.C */ longround_ldiv(long n, long d);/* Rnd_Div.C */ double rad2deg(double rad); /* Rad2Deg.C */ double deg2rad(double deg); /* Rad2Deg.C */ #include "pi.h" #ifndef PHI #define PHI ((1.0+sqrt(5.0))/2.0) /* the golden number*/ #define INV_PHI (1.0/PHI) /* the golden ratio */ #endif /* ** File: ISQRT.C */ struct int_sqrt { unsigned sqrt, frac; }; void usqrt(unsigned long x, struct int_sqrt *q); #endif /* SNIPMATH__H */ ```
code:
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 Terms of Agreement:    By using this code, you agree to the following terms...    You may use this code in your own programs (and may compile it into a program and distribute it in compiled format for languages that allow it) freely and with no charge. You MAY NOT redistribute this code (for example to a web site) without written permission from the original author. Failure to do so is a violation of copyright laws.    You may link to this code from another website, but ONLY if it is not wrapped in a frame.  You will abide by any additional copyright restrictions which the author may have placed in the code or code's description. ``` //************************************** // Name: Solve cubic equations // Description:CUBIC.C - Solve a cubic polynomial // By: Bob Stout (republished under Open Content License) // //This code is copyrighted and has// limited warranties.Please see http://www.Planet-Source-Code.com/vb/scripts/ShowCode.asp?txtCodeId=627&lngWId=3//for details.//************************************** /* +++Date last modified: 05-Jul-1997 */ /* ** CUBIC.C - Solve a cubic polynomial ** public domain by Ross Cottrell */ #include #include #include "snipmath.h" void SolveCubic(double a, double b, double c, double d, int*solutions, double *x) { long doublea1 = b/a, a2 = c/a, a3 = d/a; long doubleQ = (a1*a1 - 3.0*a2)/9.0; long double R = (2.0*a1*a1*a1 - 9.0*a1*a2 + 27.0*a3)/54.0; doubleR2_Q3 = R*R - Q*Q*Q; doubletheta; if (R2_Q3 <= 0) { *solutions = 3; theta = acos(R/sqrt(Q*Q*Q)); x[0] = -2.0*sqrt(Q)*cos(theta/3.0) - a1/3.0; x[1] = -2.0*sqrt(Q)*cos((theta+2.0*PI)/3.0) - a1/3.0; x[2] = -2.0*sqrt(Q)*cos((theta+4.0*PI)/3.0) - a1/3.0; } else { *solutions = 1; x[0] = pow(sqrt(R2_Q3)+fabs(R), 1/3.0); x[0] += Q/x[0]; x[0] *= (R < 0.0) ? 1 : -1; x[0] -= a1/3.0; } } #ifdef TEST int main(void) { double a1 = 1.0, b1 = -10.5, c1 = 32.0, d1 = -30.0; double a2 = 1.0, b2 = -4.5, c2 = 17.0, d2 = -30.0; double x[3]; int solutions; SolveCubic(a1, b1, c1, d1, &solutions, x); /* should get 3 solutions: 2, 6 & 2.5*/ SolveCubic(a2, b2, c2, d2, &solutions, x); /* should get 1 solution: 2.5*/ return 0; } #endif /* TEST */ ```

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there is an error in file snipmath.h :
near the middle in the line :

longdouble ldfloor(long double a);/* Ldfloor.C */

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5/1/2002 11:16:26 PMMitch Foral

I dont believe this solves for imaginary roots.....correct me if i'm wrong plz.
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