/* TomsFastMath, a fast ISO C bignum library.
  * 
  * This project is meant to fill in where LibTomMath
  * falls short.  That is speed ;-)
  *
  * This project is public domain and free for all purposes.
  * 
  * Tom St Denis, tomstdenis@gmail.com
  */
 #include "bignum_fast.h"
 
 static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
 {
   fp_int  x, y, u, v, A, B, C, D;
   int     res;
 
   /* b cannot be negative */
   if (b->sign == FP_NEG || fp_iszero(b) == 1) {
     return FP_VAL;
   }
 
   /* init temps */
   fp_init(&x);    fp_init(&y);
   fp_init(&u);    fp_init(&v);
   fp_init(&A);    fp_init(&B);
   fp_init(&C);    fp_init(&D);
 
   /* x = a, y = b */
   if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
       return res;
   }
   fp_copy(b, &y);
 
   /* 2. [modified] if x,y are both even then return an error! */
   if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
     return FP_VAL;
   }
 
   /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
   fp_copy (&x, &u);
   fp_copy (&y, &v);
   fp_set (&A, 1);
   fp_set (&D, 1);
 
 top:
   /* 4.  while u is even do */
   while (fp_iseven (&u) == 1) {
     /* 4.1 u = u/2 */
     fp_div_2 (&u, &u);
 
     /* 4.2 if A or B is odd then */
     if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
       /* A = (A+y)/2, B = (B-x)/2 */
       fp_add (&A, &y, &A);
       fp_sub (&B, &x, &B);
     }
     /* A = A/2, B = B/2 */
     fp_div_2 (&A, &A);
     fp_div_2 (&B, &B);
   }
 
   /* 5.  while v is even do */
   while (fp_iseven (&v) == 1) {
     /* 5.1 v = v/2 */
     fp_div_2 (&v, &v);
 
     /* 5.2 if C or D is odd then */
     if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
       /* C = (C+y)/2, D = (D-x)/2 */
       fp_add (&C, &y, &C);
       fp_sub (&D, &x, &D);
     }
     /* C = C/2, D = D/2 */
     fp_div_2 (&C, &C);
     fp_div_2 (&D, &D);
   }
 
   /* 6.  if u >= v then */
   if (fp_cmp (&u, &v) != FP_LT) {
     /* u = u - v, A = A - C, B = B - D */
     fp_sub (&u, &v, &u);
     fp_sub (&A, &C, &A);
     fp_sub (&B, &D, &B);
   } else {
     /* v - v - u, C = C - A, D = D - B */
     fp_sub (&v, &u, &v);
     fp_sub (&C, &A, &C);
     fp_sub (&D, &B, &D);
   }
 
   /* if not zero goto step 4 */
   if (fp_iszero (&u) == 0)
     goto top;
 
   /* now a = C, b = D, gcd == g*v */
 
   /* if v != 1 then there is no inverse */
   if (fp_cmp_d (&v, 1) != FP_EQ) {
     return FP_VAL;
   }
 
   /* if its too low */
   while (fp_cmp_d(&C, 0) == FP_LT) {
       fp_add(&C, b, &C);
   }
   
   /* too big */
   while (fp_cmp_mag(&C, b) != FP_LT) {
       fp_sub(&C, b, &C);
   }
   
   /* C is now the inverse */
   fp_copy(&C, c);
   return FP_OKAY;
 }
 
 /* c = 1/a (mod b) for odd b only */
 int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
 {
   fp_int  x, y, u, v, B, D;
   int     neg;
 
   /* 2. [modified] b must be odd   */
   if (fp_iseven (b) == FP_YES) {
     return fp_invmod_slow(a,b,c);
   }
 
   /* init all our temps */
   fp_init(&x);  fp_init(&y);
   fp_init(&u);  fp_init(&v);
   fp_init(&B);  fp_init(&D);
 
   /* x == modulus, y == value to invert */
   fp_copy(b, &x);
 
   /* we need y = |a| */
   fp_abs(a, &y);
 
   /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
   fp_copy(&x, &u);
   fp_copy(&y, &v);
   fp_set (&D, 1);
 
 top:
   /* 4.  while u is even do */
   while (fp_iseven (&u) == FP_YES) {
     /* 4.1 u = u/2 */
     fp_div_2 (&u, &u);
 
     /* 4.2 if B is odd then */
     if (fp_isodd (&B) == FP_YES) {
       fp_sub (&B, &x, &B);
     }
     /* B = B/2 */
     fp_div_2 (&B, &B);
   }
 
   /* 5.  while v is even do */
   while (fp_iseven (&v) == FP_YES) {
     /* 5.1 v = v/2 */
     fp_div_2 (&v, &v);
 
     /* 5.2 if D is odd then */
     if (fp_isodd (&D) == FP_YES) {
       /* D = (D-x)/2 */
       fp_sub (&D, &x, &D);
     }
     /* D = D/2 */
     fp_div_2 (&D, &D);
   }
 
   /* 6.  if u >= v then */
   if (fp_cmp (&u, &v) != FP_LT) {
     /* u = u - v, B = B - D */
     fp_sub (&u, &v, &u);
     fp_sub (&B, &D, &B);
   } else {
     /* v - v - u, D = D - B */
     fp_sub (&v, &u, &v);
     fp_sub (&D, &B, &D);
   }
 
   /* if not zero goto step 4 */
   if (fp_iszero (&u) == FP_NO) {
     goto top;
   }
 
   /* now a = C, b = D, gcd == g*v */
 
   /* if v != 1 then there is no inverse */
   if (fp_cmp_d (&v, 1) != FP_EQ) {
     return FP_VAL;
   }
 
   /* b is now the inverse */
   neg = a->sign;
   while (D.sign == FP_NEG) {
     fp_add (&D, b, &D);
   }
   fp_copy (&D, c);
   c->sign = neg;
   return FP_OKAY;
 }
 
 /* $Source: /cvs/libtom/tomsfastmath/src/numtheory/fp_invmod.c,v $ */
 /* $Revision: 1.1 $ */
 /* $Date: 2007/01/24 21:25:19 $ */