Mercurial > dropbear

annotate tomsfastmath/src/numtheory/fp_invmod.c @ 646:f10335e5e42f dropbear-tfm

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- More asm constraint fixes. Now seems to build OK on 32-bit OS X.
author Matt Johnston <matt@ucc.asn.au>
date Wed, 30 Nov 2011 23:03:47 +0800
parents a362b62d38b2
children
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1 /* TomsFastMath, a fast ISO C bignum library.
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2 *
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3 * This project is meant to fill in where LibTomMath
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4 * falls short. That is speed ;-)
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5 *
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6 * This project is public domain and free for all purposes.
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7 *
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8 * Tom St Denis, [email protected]
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9 */
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10 #include <tfm.h>
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11
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12 static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
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13 {
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14 fp_int x, y, u, v, A, B, C, D;
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15 int res;
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16
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17 /* b cannot be negative */
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18 if (b->sign == FP_NEG || fp_iszero(b) == 1) {
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19 return FP_VAL;
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20 }
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21
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22 /* init temps */
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23 fp_init(&x); fp_init(&y);
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24 fp_init(&u); fp_init(&v);
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25 fp_init(&A); fp_init(&B);
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26 fp_init(&C); fp_init(&D);
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27
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28 /* x = a, y = b */
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29 if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
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30 return res;
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31 }
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32 fp_copy(b, &y);
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33
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34 /* 2. [modified] if x,y are both even then return an error! */
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35 if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
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36 return FP_VAL;
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37 }
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38
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39 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
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40 fp_copy (&x, &u);
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41 fp_copy (&y, &v);
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42 fp_set (&A, 1);
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43 fp_set (&D, 1);
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44
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45 top:
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46 /* 4. while u is even do */
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47 while (fp_iseven (&u) == 1) {
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48 /* 4.1 u = u/2 */
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49 fp_div_2 (&u, &u);
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50
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51 /* 4.2 if A or B is odd then */
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52 if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
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53 /* A = (A+y)/2, B = (B-x)/2 */
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54 fp_add (&A, &y, &A);
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55 fp_sub (&B, &x, &B);
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56 }
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57 /* A = A/2, B = B/2 */
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58 fp_div_2 (&A, &A);
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59 fp_div_2 (&B, &B);
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60 }
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61
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62 /* 5. while v is even do */
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63 while (fp_iseven (&v) == 1) {
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64 /* 5.1 v = v/2 */
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65 fp_div_2 (&v, &v);
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66
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67 /* 5.2 if C or D is odd then */
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68 if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
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69 /* C = (C+y)/2, D = (D-x)/2 */
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70 fp_add (&C, &y, &C);
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71 fp_sub (&D, &x, &D);
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72 }
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73 /* C = C/2, D = D/2 */
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74 fp_div_2 (&C, &C);
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75 fp_div_2 (&D, &D);
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76 }
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77
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78 /* 6. if u >= v then */
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79 if (fp_cmp (&u, &v) != FP_LT) {
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80 /* u = u - v, A = A - C, B = B - D */
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81 fp_sub (&u, &v, &u);
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82 fp_sub (&A, &C, &A);
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83 fp_sub (&B, &D, &B);
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84 } else {
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85 /* v - v - u, C = C - A, D = D - B */
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86 fp_sub (&v, &u, &v);
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87 fp_sub (&C, &A, &C);
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88 fp_sub (&D, &B, &D);
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89 }
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90
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91 /* if not zero goto step 4 */
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92 if (fp_iszero (&u) == 0)
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93 goto top;
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94
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95 /* now a = C, b = D, gcd == g*v */
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96
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97 /* if v != 1 then there is no inverse */
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98 if (fp_cmp_d (&v, 1) != FP_EQ) {
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99 return FP_VAL;
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100 }
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101
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102 /* if its too low */
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103 while (fp_cmp_d(&C, 0) == FP_LT) {
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104 fp_add(&C, b, &C);
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105 }
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106
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107 /* too big */
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parents:
diff changeset
108 while (fp_cmp_mag(&C, b) != FP_LT) {
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parents:
diff changeset
109 fp_sub(&C, b, &C);
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parents:
diff changeset
110 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
111
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parents:
diff changeset
112 /* C is now the inverse */
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parents:
diff changeset
113 fp_copy(&C, c);
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parents:
diff changeset
114 return FP_OKAY;
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parents:
diff changeset
115 }
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parents:
diff changeset
116
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parents:
diff changeset
117 /* c = 1/a (mod b) for odd b only */
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parents:
diff changeset
118 int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
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parents:
diff changeset
119 {
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parents:
diff changeset
120 fp_int x, y, u, v, B, D;
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parents:
diff changeset
121 int neg;
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parents:
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122
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parents:
diff changeset
123 /* 2. [modified] b must be odd */
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parents:
diff changeset
124 if (fp_iseven (b) == FP_YES) {
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parents:
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125 return fp_invmod_slow(a,b,c);
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parents:
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126 }
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127
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parents:
diff changeset
128 /* init all our temps */
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parents:
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129 fp_init(&x); fp_init(&y);
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parents:
diff changeset
130 fp_init(&u); fp_init(&v);
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parents:
diff changeset
131 fp_init(&B); fp_init(&D);
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parents:
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132
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parents:
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133 /* x == modulus, y == value to invert */
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parents:
diff changeset
134 fp_copy(b, &x);
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parents:
diff changeset
135
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parents:
diff changeset
136 /* we need y = |a| */
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parents:
diff changeset
137 fp_abs(a, &y);
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parents:
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138
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parents:
diff changeset
139 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
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parents:
diff changeset
140 fp_copy(&x, &u);
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parents:
diff changeset
141 fp_copy(&y, &v);
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parents:
diff changeset
142 fp_set (&D, 1);
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parents:
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143
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parents:
diff changeset
144 top:
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parents:
diff changeset
145 /* 4. while u is even do */
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parents:
diff changeset
146 while (fp_iseven (&u) == FP_YES) {
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parents:
diff changeset
147 /* 4.1 u = u/2 */
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parents:
diff changeset
148 fp_div_2 (&u, &u);
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149
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parents:
diff changeset
150 /* 4.2 if B is odd then */
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parents:
diff changeset
151 if (fp_isodd (&B) == FP_YES) {
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parents:
diff changeset
152 fp_sub (&B, &x, &B);
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parents:
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153 }
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parents:
diff changeset
154 /* B = B/2 */
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parents:
diff changeset
155 fp_div_2 (&B, &B);
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parents:
diff changeset
156 }
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parents:
diff changeset
157
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parents:
diff changeset
158 /* 5. while v is even do */
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parents:
diff changeset
159 while (fp_iseven (&v) == FP_YES) {
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parents:
diff changeset
160 /* 5.1 v = v/2 */
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parents:
diff changeset
161 fp_div_2 (&v, &v);
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parents:
diff changeset
162
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parents:
diff changeset
163 /* 5.2 if D is odd then */
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parents:
diff changeset
164 if (fp_isodd (&D) == FP_YES) {
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parents:
diff changeset
165 /* D = (D-x)/2 */
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parents:
diff changeset
166 fp_sub (&D, &x, &D);
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parents:
diff changeset
167 }
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parents:
diff changeset
168 /* D = D/2 */
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parents:
diff changeset
169 fp_div_2 (&D, &D);
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parents:
diff changeset
170 }
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parents:
diff changeset
171
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parents:
diff changeset
172 /* 6. if u >= v then */
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parents:
diff changeset
173 if (fp_cmp (&u, &v) != FP_LT) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
174 /* u = u - v, B = B - D */
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parents:
diff changeset
175 fp_sub (&u, &v, &u);
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parents:
diff changeset
176 fp_sub (&B, &D, &B);
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parents:
diff changeset
177 } else {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
178 /* v - v - u, D = D - B */
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parents:
diff changeset
179 fp_sub (&v, &u, &v);
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parents:
diff changeset
180 fp_sub (&D, &B, &D);
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parents:
diff changeset
181 }
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parents:
diff changeset
182
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parents:
diff changeset
183 /* if not zero goto step 4 */
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parents:
diff changeset
184 if (fp_iszero (&u) == FP_NO) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
185 goto top;
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parents:
diff changeset
186 }
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parents:
diff changeset
187
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parents:
diff changeset
188 /* now a = C, b = D, gcd == g*v */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
189
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parents:
diff changeset
190 /* if v != 1 then there is no inverse */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
191 if (fp_cmp_d (&v, 1) != FP_EQ) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
192 return FP_VAL;
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parents:
diff changeset
193 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
194
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parents:
diff changeset
195 /* b is now the inverse */
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parents:
diff changeset
196 neg = a->sign;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
197 while (D.sign == FP_NEG) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
198 fp_add (&D, b, &D);
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parents:
diff changeset
199 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
200 fp_copy (&D, c);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
201 c->sign = neg;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
202 return FP_OKAY;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
203 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
204
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
205 /* $Source$ */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
206 /* $Revision$ */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
207 /* $Date$ */