1 | #include <tommath.h> |
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2 | |
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3 | #ifdef BN_MP_SQRT_C |
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4 | /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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5 | * |
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6 | * LibTomMath is a library that provides multiple-precision |
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7 | * integer arithmetic as well as number theoretic functionality. |
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8 | * |
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9 | * The library was designed directly after the MPI library by |
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10 | * Michael Fromberger but has been written from scratch with |
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11 | * additional optimizations in place. |
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12 | * |
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13 | * The library is free for all purposes without any express |
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14 | * guarantee it works. |
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15 | * |
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16 | * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com |
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17 | */ |
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18 | |
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19 | #ifndef NO_FLOATING_POINT |
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20 | #include <math.h> |
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21 | #endif |
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22 | |
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23 | /* this function is less generic than mp_n_root, simpler and faster */ |
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24 | int mp_sqrt(mp_int *arg, mp_int *ret) |
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25 | { |
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26 | int res; |
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27 | mp_int t1,t2; |
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28 | int i, j, k; |
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29 | #ifndef NO_FLOATING_POINT |
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30 | double d; |
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31 | mp_digit dig; |
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32 | #endif |
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33 | |
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34 | /* must be positive */ |
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35 | if (arg->sign == MP_NEG) { |
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36 | return MP_VAL; |
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37 | } |
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38 | |
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39 | /* easy out */ |
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40 | if (mp_iszero(arg) == MP_YES) { |
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41 | mp_zero(ret); |
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42 | return MP_OKAY; |
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43 | } |
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44 | |
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45 | i = (arg->used / 2) - 1; |
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46 | j = 2 * i; |
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47 | if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) { |
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48 | return res; |
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49 | } |
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50 | |
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51 | if ((res = mp_init(&t2)) != MP_OKAY) { |
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52 | goto E2; |
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53 | } |
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54 | |
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55 | for (k = 0; k < i; ++k) { |
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56 | t1.dp[k] = (mp_digit) 0; |
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57 | } |
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58 | |
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59 | #ifndef NO_FLOATING_POINT |
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60 | |
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61 | /* Estimate the square root using the hardware floating point unit. */ |
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62 | |
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63 | d = 0.0; |
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64 | for (k = arg->used-1; k >= j; --k) { |
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65 | d = ldexp(d, DIGIT_BIT) + (double) (arg->dp[k]); |
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66 | } |
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67 | d = sqrt(d); |
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68 | dig = (mp_digit) ldexp(d, -DIGIT_BIT); |
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69 | if (dig) { |
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70 | t1.used = i+2; |
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71 | d -= ldexp((double) dig, DIGIT_BIT); |
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72 | if (d != 0.0) { |
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73 | t1.dp[i+1] = dig; |
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74 | t1.dp[i] = ((mp_digit) d) - 1; |
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75 | } else { |
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76 | t1.dp[i+1] = dig-1; |
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77 | t1.dp[i] = MP_DIGIT_MAX; |
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78 | } |
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79 | } else { |
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80 | t1.used = i+1; |
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81 | t1.dp[i] = ((mp_digit) d) - 1; |
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82 | } |
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83 | |
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84 | #else |
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85 | |
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86 | /* Estimate the square root as having 1 in the most significant place. */ |
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87 | |
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88 | t1.used = i + 2; |
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89 | t1.dp[i+1] = (mp_digit) 1; |
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90 | t1.dp[i] = (mp_digit) 0; |
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91 | |
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92 | #endif |
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93 | |
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94 | /* t1 > 0 */ |
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95 | if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) { |
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96 | goto E1; |
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97 | } |
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98 | if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) { |
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99 | goto E1; |
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100 | } |
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101 | if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) { |
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102 | goto E1; |
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103 | } |
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104 | /* And now t1 > sqrt(arg) */ |
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105 | do { |
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106 | if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) { |
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107 | goto E1; |
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108 | } |
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109 | if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) { |
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110 | goto E1; |
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111 | } |
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112 | if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) { |
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113 | goto E1; |
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114 | } |
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115 | /* t1 >= sqrt(arg) >= t2 at this point */ |
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116 | } while (mp_cmp_mag(&t1,&t2) == MP_GT); |
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117 | |
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118 | mp_exch(&t1,ret); |
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119 | |
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120 | E1: mp_clear(&t2); |
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121 | E2: mp_clear(&t1); |
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122 | return res; |
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123 | } |
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124 | |
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125 | #endif |
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126 | |
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127 | /* $Source: /cvsroot/tcl/libtommath/bn_mp_sqrt.c,v $ */ |
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128 | /* Based on Tom's 1.3 */ |
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129 | /* $Revision: 1.5 $ */ |
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130 | /* $Date: 2006/12/01 05:48:23 $ */ |
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