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annotate tomsfastmath/src/divide/fp_div.c @ 644:ff5cc422ba40 dropbear-tfm tomsfastmath

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Somehow Makefile.in went missing
author Matt Johnston <matt@ucc.asn.au>
date Wed, 23 Nov 2011 18:11:51 +0700
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 /* a/b => cb + d == a */
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13 int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
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14 {
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15 fp_int q, x, y, t1, t2;
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16 int n, t, i, norm, neg;
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17
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18 /* is divisor zero ? */
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19 if (fp_iszero (b) == 1) {
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20 return FP_VAL;
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21 }
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22
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23 /* if a < b then q=0, r = a */
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24 if (fp_cmp_mag (a, b) == FP_LT) {
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25 if (d != NULL) {
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26 fp_copy (a, d);
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27 }
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28 if (c != NULL) {
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29 fp_zero (c);
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30 }
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31 return FP_OKAY;
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32 }
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33
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34 fp_init(&q);
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35 q.used = a->used + 2;
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36
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37 fp_init(&t1);
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38 fp_init(&t2);
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39 fp_init_copy(&x, a);
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40 fp_init_copy(&y, b);
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41
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42 /* fix the sign */
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43 neg = (a->sign == b->sign) ? FP_ZPOS : FP_NEG;
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44 x.sign = y.sign = FP_ZPOS;
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45
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46 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
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47 norm = fp_count_bits(&y) % DIGIT_BIT;
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48 if (norm < (int)(DIGIT_BIT-1)) {
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49 norm = (DIGIT_BIT-1) - norm;
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50 fp_mul_2d (&x, norm, &x);
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51 fp_mul_2d (&y, norm, &y);
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52 } else {
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53 norm = 0;
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54 }
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55
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56 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
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57 n = x.used - 1;
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58 t = y.used - 1;
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59
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60 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
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61 fp_lshd (&y, n - t); /* y = y*b**{n-t} */
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62
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63 while (fp_cmp (&x, &y) != FP_LT) {
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64 ++(q.dp[n - t]);
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65 fp_sub (&x, &y, &x);
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66 }
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67
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68 /* reset y by shifting it back down */
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69 fp_rshd (&y, n - t);
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70
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71 /* step 3. for i from n down to (t + 1) */
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72 for (i = n; i >= (t + 1); i--) {
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73 if (i > x.used) {
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74 continue;
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75 }
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76
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77 /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
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78 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
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79 if (x.dp[i] == y.dp[t]) {
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80 q.dp[i - t - 1] = ((((fp_word)1) << DIGIT_BIT) - 1);
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81 } else {
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82 fp_word tmp;
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83 tmp = ((fp_word) x.dp[i]) << ((fp_word) DIGIT_BIT);
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84 tmp |= ((fp_word) x.dp[i - 1]);
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85 tmp /= ((fp_word) y.dp[t]);
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86 q.dp[i - t - 1] = (fp_digit) (tmp);
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87 }
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88
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89 /* while (q{i-t-1} * (yt * b + y{t-1})) >
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90 xi * b**2 + xi-1 * b + xi-2
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91
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92 do q{i-t-1} -= 1;
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93 */
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94 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1);
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95 do {
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96 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1);
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97
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98 /* find left hand */
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99 fp_zero (&t1);
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100 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
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101 t1.dp[1] = y.dp[t];
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102 t1.used = 2;
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103 fp_mul_d (&t1, q.dp[i - t - 1], &t1);
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104
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105 /* find right hand */
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106 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
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107 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
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108 t2.dp[2] = x.dp[i];
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109 t2.used = 3;
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110 } while (fp_cmp_mag(&t1, &t2) == FP_GT);
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111
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112 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
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113 fp_mul_d (&y, q.dp[i - t - 1], &t1);
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114 fp_lshd (&t1, i - t - 1);
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115 fp_sub (&x, &t1, &x);
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116
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117 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
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118 if (x.sign == FP_NEG) {
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119 fp_copy (&y, &t1);
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120 fp_lshd (&t1, i - t - 1);
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121 fp_add (&x, &t1, &x);
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122 q.dp[i - t - 1] = q.dp[i - t - 1] - 1;
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123 }
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124 }
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125
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126 /* now q is the quotient and x is the remainder
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127 * [which we have to normalize]
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128 */
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129
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130 /* get sign before writing to c */
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131 x.sign = x.used == 0 ? FP_ZPOS : a->sign;
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132
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133 if (c != NULL) {
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134 fp_clamp (&q);
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135 fp_copy (&q, c);
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136 c->sign = neg;
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137 }
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138
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139 if (d != NULL) {
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140 fp_div_2d (&x, norm, &x, NULL);
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141
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142 /* the following is a kludge, essentially we were seeing the right remainder but
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143 with excess digits that should have been zero
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144 */
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145 for (i = b->used; i < x.used; i++) {
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146 x.dp[i] = 0;
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147 }
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148 fp_clamp(&x);
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149 fp_copy (&x, d);
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150 }
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151
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152 return FP_OKAY;
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153 }
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154
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155 /* $Source$ */
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156 /* $Revision$ */
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157 /* $Date$ */