[2847] | 1 | //////////////////////////////////////////////////////////////////////////////////////// |
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| 2 | // Big Integer Library v. 5.4 |
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| 3 | // Created 2000, last modified 2009 |
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| 4 | // Leemon Baird |
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| 5 | // www.leemon.com |
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| 6 | // |
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| 7 | // Version history: |
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| 8 | // v 5.4 3 Oct 2009 |
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| 9 | // - added "var i" to greaterShift() so i is not global. (Thanks to Pr Szabor finding that bug) |
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| 10 | // |
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| 11 | // v 5.3 21 Sep 2009 |
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| 12 | // - added randProbPrime(k) for probable primes |
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| 13 | // - unrolled loop in mont_ (slightly faster) |
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| 14 | // - millerRabin now takes a bigInt parameter rather than an int |
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| 15 | // |
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| 16 | // v 5.2 15 Sep 2009 |
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| 17 | // - fixed capitalization in call to int2bigInt in randBigInt |
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| 18 | // (thanks to Emili Evripidou, Reinhold Behringer, and Samuel Macaleese for finding that bug) |
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| 19 | // |
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| 20 | // v 5.1 8 Oct 2007 |
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| 21 | // - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters |
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| 22 | // - added functions GCD and randBigInt, which call GCD_ and randBigInt_ |
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| 23 | // - fixed a bug found by Rob Visser (see comment with his name below) |
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| 24 | // - improved comments |
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| 25 | // |
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| 26 | // This file is public domain. You can use it for any purpose without restriction. |
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| 27 | // I do not guarantee that it is correct, so use it at your own risk. If you use |
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| 28 | // it for something interesting, I'd appreciate hearing about it. If you find |
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| 29 | // any bugs or make any improvements, I'd appreciate hearing about those too. |
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| 30 | // It would also be nice if my name and URL were left in the comments. But none |
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| 31 | // of that is required. |
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| 32 | // |
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| 33 | // This code defines a bigInt library for arbitrary-precision integers. |
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| 34 | // A bigInt is an array of integers storing the value in chunks of bpe bits, |
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| 35 | // little endian (buff[0] is the least significant word). |
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| 36 | // Negative bigInts are stored two's complement. Almost all the functions treat |
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| 37 | // bigInts as nonnegative. The few that view them as two's complement say so |
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| 38 | // in their comments. Some functions assume their parameters have at least one |
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| 39 | // leading zero element. Functions with an underscore at the end of the name put |
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| 40 | // their answer into one of the arrays passed in, and have unpredictable behavior |
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| 41 | // in case of overflow, so the caller must make sure the arrays are big enough to |
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| 42 | // hold the answer. But the average user should never have to call any of the |
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| 43 | // underscored functions. Each important underscored function has a wrapper function |
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| 44 | // of the same name without the underscore that takes care of the details for you. |
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| 45 | // For each underscored function where a parameter is modified, that same variable |
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| 46 | // must not be used as another argument too. So, you cannot square x by doing |
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| 47 | // multMod_(x,x,n). You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n). |
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| 48 | // Or simply use the multMod(x,x,n) function without the underscore, where |
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| 49 | // such issues never arise, because non-underscored functions never change |
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| 50 | // their parameters; they always allocate new memory for the answer that is returned. |
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| 51 | // |
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| 52 | // These functions are designed to avoid frequent dynamic memory allocation in the inner loop. |
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| 53 | // For most functions, if it needs a BigInt as a local variable it will actually use |
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| 54 | // a global, and will only allocate to it only when it's not the right size. This ensures |
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| 55 | // that when a function is called repeatedly with same-sized parameters, it only allocates |
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| 56 | // memory on the first call. |
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| 57 | // |
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| 58 | // Note that for cryptographic purposes, the calls to Math.random() must |
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| 59 | // be replaced with calls to a better pseudorandom number generator. |
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| 60 | // |
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| 61 | // In the following, "bigInt" means a bigInt with at least one leading zero element, |
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| 62 | // and "integer" means a nonnegative integer less than radix. In some cases, integer |
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| 63 | // can be negative. Negative bigInts are 2s complement. |
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| 64 | // |
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| 65 | // The following functions do not modify their inputs. |
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| 66 | // Those returning a bigInt, string, or Array will dynamically allocate memory for that value. |
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| 67 | // Those returning a boolean will return the integer 0 (false) or 1 (true). |
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| 68 | // Those returning boolean or int will not allocate memory except possibly on the first |
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| 69 | // time they're called with a given parameter size. |
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| 70 | |
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[2931] | 71 | |
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[2847] | 72 | //globals |
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| 73 | bpe=0; //bits stored per array element |
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| 74 | mask=0; //AND this with an array element to chop it down to bpe bits |
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| 75 | radix=mask+1; //equals 2^bpe. A single 1 bit to the left of the last bit of mask. |
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| 76 | |
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| 77 | //the digits for converting to different bases |
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| 78 | digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-'; |
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| 79 | |
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| 80 | //initialize the global variables |
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| 81 | for (bpe=0; (1<<(bpe+1)) > (1<<bpe); bpe++); //bpe=number of bits in the mantissa on this platform |
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| 82 | bpe>>=1; //bpe=number of bits in one element of the array representing the bigInt |
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| 83 | mask=(1<<bpe)-1; //AND the mask with an integer to get its bpe least significant bits |
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| 84 | radix=mask+1; //2^bpe. a single 1 bit to the left of the first bit of mask |
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| 85 | one=int2bigInt(1,1,1); //constant used in powMod_() |
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| 86 | |
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| 87 | //the following global variables are scratchpad memory to |
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| 88 | //reduce dynamic memory allocation in the inner loop |
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| 89 | t=new Array(0); |
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| 90 | ss=t; //used in mult_() |
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| 91 | s0=t; //used in multMod_(), squareMod_() |
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| 92 | s1=t; //used in powMod_(), multMod_(), squareMod_() |
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| 93 | s2=t; //used in powMod_(), multMod_() |
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| 94 | s3=t; //used in powMod_() |
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| 95 | s4=t; s5=t; //used in mod_() |
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| 96 | s6=t; //used in bigInt2str() |
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| 97 | s7=t; //used in powMod_() |
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| 98 | T=t; //used in GCD_() |
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| 99 | sa=t; //used in mont_() |
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| 100 | mr_x1=t; mr_r=t; mr_a=t; //used in millerRabin() |
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| 101 | eg_v=t; eg_u=t; eg_A=t; eg_B=t; eg_C=t; eg_D=t; //used in eGCD_(), inverseMod_() |
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| 102 | md_q1=t; md_q2=t; md_q3=t; md_r=t; md_r1=t; md_r2=t; md_tt=t; //used in mod_() |
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| 103 | |
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| 104 | primes=t; pows=t; s_i=t; s_i2=t; s_R=t; s_rm=t; s_q=t; s_n1=t; |
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| 105 | s_a=t; s_r2=t; s_n=t; s_b=t; s_d=t; s_x1=t; s_x2=t, s_aa=t; //used in randTruePrime_() |
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| 106 | |
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| 107 | rpprb=t; //used in randProbPrimeRounds() (which also uses "primes") |
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| 108 | |
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| 109 | //return a copy of x with at least n elements, adding leading zeros if needed |
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| 110 | function expand(x,n) { |
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| 111 | var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0); |
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| 112 | copy_(ans,x); |
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| 113 | return ans; |
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| 114 | } |
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| 115 | //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n. |
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| 116 | function powMod(x,y,n) { |
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| 117 | var ans=expand(x,n.length); |
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[2931] | 118 | powMod_(ans,bigintTrim(y,2),bigintTrim(n,2),0); //this should work without the bigintTrim, but doesn't |
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| 119 | return bigintTrim(ans,1); |
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[2847] | 120 | } |
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| 121 | |
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| 122 | //return (x-y) for bigInts x and y. Negative answers will be 2s complement |
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| 123 | function sub(x,y) { |
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| 124 | var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); |
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| 125 | sub_(ans,y); |
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[2931] | 126 | return bigintTrim(ans,1); |
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[2847] | 127 | } |
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| 128 | |
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| 129 | //return (x+y) for bigInts x and y. |
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| 130 | function add(x,y) { |
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| 131 | var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); |
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| 132 | add_(ans,y); |
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[2931] | 133 | return bigintTrim(ans,1); |
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[2847] | 134 | } |
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| 135 | //Return the greatest common divisor of bigInts x and y (each with same number of elements). |
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| 136 | function GCD(x,y) { |
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| 137 | var xc,yc; |
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| 138 | xc=dup(x); |
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| 139 | yc=dup(y); |
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| 140 | GCD_(xc,yc); |
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| 141 | return xc; |
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| 142 | } |
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| 143 | |
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| 144 | //set x to the greatest common divisor of bigInts x and y (each with same number of elements). |
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| 145 | //y is destroyed. |
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| 146 | function GCD_(x,y) { |
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| 147 | var i,xp,yp,A,B,C,D,q,sing; |
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| 148 | if (T.length!=x.length) |
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| 149 | T=dup(x); |
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| 150 | |
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| 151 | sing=1; |
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| 152 | while (sing) { //while y has nonzero elements other than y[0] |
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| 153 | sing=0; |
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| 154 | for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0 |
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| 155 | if (y[i]) { |
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| 156 | sing=1; |
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| 157 | break; |
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| 158 | } |
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| 159 | if (!sing) break; //quit when y all zero elements except possibly y[0] |
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| 160 | |
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| 161 | for (i=x.length;!x[i] && i>=0;i--); //find most significant element of x |
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| 162 | xp=x[i]; |
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| 163 | yp=y[i]; |
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| 164 | A=1; B=0; C=0; D=1; |
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| 165 | while ((yp+C) && (yp+D)) { |
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| 166 | q =Math.floor((xp+A)/(yp+C)); |
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| 167 | qp=Math.floor((xp+B)/(yp+D)); |
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| 168 | if (q!=qp) |
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| 169 | break; |
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| 170 | t= A-q*C; A=C; C=t; // do (A,B,xp, C,D,yp) = (C,D,yp, A,B,xp) - q*(0,0,0, C,D,yp) |
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| 171 | t= B-q*D; B=D; D=t; |
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| 172 | t=xp-q*yp; xp=yp; yp=t; |
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| 173 | } |
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| 174 | if (B) { |
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| 175 | copy_(T,x); |
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| 176 | linComb_(x,y,A,B); //x=A*x+B*y |
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| 177 | linComb_(y,T,D,C); //y=D*y+C*T |
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| 178 | } else { |
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| 179 | mod_(x,y); |
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| 180 | copy_(T,x); |
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| 181 | copy_(x,y); |
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| 182 | copy_(y,T); |
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| 183 | } |
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| 184 | } |
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| 185 | if (y[0]==0) |
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| 186 | return; |
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| 187 | t=modInt(x,y[0]); |
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| 188 | copyInt_(x,y[0]); |
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| 189 | y[0]=t; |
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| 190 | while (y[0]) { |
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| 191 | x[0]%=y[0]; |
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| 192 | t=x[0]; x[0]=y[0]; y[0]=t; |
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| 193 | } |
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| 194 | } |
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| 195 | |
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| 196 | //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse |
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| 197 | function inverseModInt(x,n) { |
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| 198 | var a=1,b=0,t; |
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| 199 | for (;;) { |
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| 200 | if (x==1) return a; |
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| 201 | if (x==0) return 0; |
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| 202 | b-=a*Math.floor(n/x); |
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| 203 | n%=x; |
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| 204 | |
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| 205 | if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to += |
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| 206 | if (n==0) return 0; |
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| 207 | a-=b*Math.floor(x/n); |
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| 208 | x%=n; |
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| 209 | } |
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| 210 | } |
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| 211 | |
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| 212 | //this deprecated function is for backward compatibility only. |
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| 213 | function inverseModInt_(x,n) { |
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| 214 | return inverseModInt(x,n); |
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| 215 | } |
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| 216 | |
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| 217 | |
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| 218 | //Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that: |
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| 219 | // v = GCD_(x,y) = a*x-b*y |
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| 220 | //The bigInts v, a, b, must have exactly as many elements as the larger of x and y. |
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| 221 | function eGCD_(x,y,v,a,b) { |
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| 222 | var g=0; |
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| 223 | var k=Math.max(x.length,y.length); |
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| 224 | if (eg_u.length!=k) { |
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| 225 | eg_u=new Array(k); |
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| 226 | eg_A=new Array(k); |
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| 227 | eg_B=new Array(k); |
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| 228 | eg_C=new Array(k); |
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| 229 | eg_D=new Array(k); |
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| 230 | } |
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| 231 | while(!(x[0]&1) && !(y[0]&1)) { //while x and y both even |
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| 232 | halve_(x); |
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| 233 | halve_(y); |
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| 234 | g++; |
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| 235 | } |
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| 236 | copy_(eg_u,x); |
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| 237 | copy_(v,y); |
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| 238 | copyInt_(eg_A,1); |
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| 239 | copyInt_(eg_B,0); |
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| 240 | copyInt_(eg_C,0); |
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| 241 | copyInt_(eg_D,1); |
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| 242 | for (;;) { |
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| 243 | while(!(eg_u[0]&1)) { //while u is even |
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| 244 | halve_(eg_u); |
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| 245 | if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2 |
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| 246 | halve_(eg_A); |
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| 247 | halve_(eg_B); |
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| 248 | } else { |
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| 249 | add_(eg_A,y); halve_(eg_A); |
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| 250 | sub_(eg_B,x); halve_(eg_B); |
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| 251 | } |
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| 252 | } |
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| 253 | |
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| 254 | while (!(v[0]&1)) { //while v is even |
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| 255 | halve_(v); |
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| 256 | if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2 |
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| 257 | halve_(eg_C); |
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| 258 | halve_(eg_D); |
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| 259 | } else { |
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| 260 | add_(eg_C,y); halve_(eg_C); |
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| 261 | sub_(eg_D,x); halve_(eg_D); |
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| 262 | } |
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| 263 | } |
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| 264 | |
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| 265 | if (!greater(v,eg_u)) { //v<=u |
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| 266 | sub_(eg_u,v); |
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| 267 | sub_(eg_A,eg_C); |
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| 268 | sub_(eg_B,eg_D); |
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| 269 | } else { //v>u |
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| 270 | sub_(v,eg_u); |
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| 271 | sub_(eg_C,eg_A); |
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| 272 | sub_(eg_D,eg_B); |
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| 273 | } |
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| 274 | if (equalsInt(eg_u,0)) { |
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| 275 | if (negative(eg_C)) { //make sure a (C)is nonnegative |
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| 276 | add_(eg_C,y); |
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| 277 | sub_(eg_D,x); |
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| 278 | } |
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| 279 | multInt_(eg_D,-1); ///make sure b (D) is nonnegative |
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| 280 | copy_(a,eg_C); |
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| 281 | copy_(b,eg_D); |
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| 282 | leftShift_(v,g); |
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| 283 | return; |
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| 284 | } |
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| 285 | } |
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| 286 | } |
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| 287 | |
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| 288 | |
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| 289 | //is bigInt x negative? |
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| 290 | function negative(x) { |
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| 291 | return ((x[x.length-1]>>(bpe-1))&1); |
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| 292 | } |
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| 293 | |
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| 294 | |
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| 295 | //is (x << (shift*bpe)) > y? |
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| 296 | //x and y are nonnegative bigInts |
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| 297 | //shift is a nonnegative integer |
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| 298 | function greaterShift(x,y,shift) { |
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| 299 | var i, kx=x.length, ky=y.length; |
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| 300 | k=((kx+shift)<ky) ? (kx+shift) : ky; |
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| 301 | for (i=ky-1-shift; i<kx && i>=0; i++) |
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| 302 | if (x[i]>0) |
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| 303 | return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger |
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| 304 | for (i=kx-1+shift; i<ky; i++) |
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| 305 | if (y[i]>0) |
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| 306 | return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger |
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| 307 | for (i=k-1; i>=shift; i--) |
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| 308 | if (x[i-shift]>y[i]) return 1; |
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| 309 | else if (x[i-shift]<y[i]) return 0; |
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| 310 | return 0; |
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| 311 | } |
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| 312 | |
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| 313 | //is x > y? (x and y both nonnegative) |
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| 314 | function greater(x,y) { |
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| 315 | var i; |
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| 316 | var k=(x.length<y.length) ? x.length : y.length; |
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| 317 | |
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| 318 | for (i=x.length;i<y.length;i++) |
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| 319 | if (y[i]) |
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| 320 | return 0; //y has more digits |
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| 321 | |
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| 322 | for (i=y.length;i<x.length;i++) |
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| 323 | if (x[i]) |
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| 324 | return 1; //x has more digits |
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| 325 | |
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| 326 | for (i=k-1;i>=0;i--) |
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| 327 | if (x[i]>y[i]) |
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| 328 | return 1; |
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| 329 | else if (x[i]<y[i]) |
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| 330 | return 0; |
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| 331 | return 0; |
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| 332 | } |
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| 333 | |
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| 334 | //divide x by y giving quotient q and remainder r. (q=floor(x/y), r=x mod y). All 4 are bigints. |
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| 335 | //x must have at least one leading zero element. |
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| 336 | //y must be nonzero. |
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| 337 | //q and r must be arrays that are exactly the same length as x. (Or q can have more). |
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| 338 | //Must have x.length >= y.length >= 2. |
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| 339 | function divide_(x,y,q,r) { |
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| 340 | var kx, ky; |
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| 341 | var i,j,y1,y2,c,a,b; |
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| 342 | copy_(r,x); |
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| 343 | for (ky=y.length;y[ky-1]==0;ky--); //ky is number of elements in y, not including leading zeros |
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| 344 | |
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| 345 | //normalize: ensure the most significant element of y has its highest bit set |
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| 346 | b=y[ky-1]; |
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| 347 | for (a=0; b; a++) |
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| 348 | b>>=1; |
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| 349 | a=bpe-a; //a is how many bits to shift so that the high order bit of y is leftmost in its array element |
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| 350 | leftShift_(y,a); //multiply both by 1<<a now, then divide both by that at the end |
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| 351 | leftShift_(r,a); |
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| 352 | |
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| 353 | //Rob Visser discovered a bug: the following line was originally just before the normalization. |
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| 354 | for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros |
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| 355 | |
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| 356 | copyInt_(q,0); // q=0 |
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| 357 | while (!greaterShift(y,r,kx-ky)) { // while (leftShift_(y,kx-ky) <= r) { |
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| 358 | subShift_(r,y,kx-ky); // r=r-leftShift_(y,kx-ky) |
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| 359 | q[kx-ky]++; // q[kx-ky]++; |
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| 360 | } // } |
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| 361 | |
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| 362 | for (i=kx-1; i>=ky; i--) { |
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| 363 | if (r[i]==y[ky-1]) |
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| 364 | q[i-ky]=mask; |
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| 365 | else |
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| 366 | q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]); |
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| 367 | |
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| 368 | //The following for(;;) loop is equivalent to the commented while loop, |
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| 369 | //except that the uncommented version avoids overflow. |
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| 370 | //The commented loop comes from HAC, which assumes r[-1]==y[-1]==0 |
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| 371 | // while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2]) |
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| 372 | // q[i-ky]--; |
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| 373 | for (;;) { |
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| 374 | y2=(ky>1 ? y[ky-2] : 0)*q[i-ky]; |
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| 375 | c=y2>>bpe; |
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| 376 | y2=y2 & mask; |
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| 377 | y1=c+q[i-ky]*y[ky-1]; |
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| 378 | c=y1>>bpe; |
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| 379 | y1=y1 & mask; |
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| 380 | |
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| 381 | if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) |
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| 382 | q[i-ky]--; |
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| 383 | else |
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| 384 | break; |
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| 385 | } |
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| 386 | |
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| 387 | linCombShift_(r,y,-q[i-ky],i-ky); //r=r-q[i-ky]*leftShift_(y,i-ky) |
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| 388 | if (negative(r)) { |
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| 389 | addShift_(r,y,i-ky); //r=r+leftShift_(y,i-ky) |
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| 390 | q[i-ky]--; |
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| 391 | } |
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| 392 | } |
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| 393 | |
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| 394 | rightShift_(y,a); //undo the normalization step |
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| 395 | rightShift_(r,a); //undo the normalization step |
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| 396 | } |
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| 397 | |
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| 398 | //do carries and borrows so each element of the bigInt x fits in bpe bits. |
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| 399 | function carry_(x) { |
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| 400 | var i,k,c,b; |
---|
| 401 | k=x.length; |
---|
| 402 | c=0; |
---|
| 403 | for (i=0;i<k;i++) { |
---|
| 404 | c+=x[i]; |
---|
| 405 | b=0; |
---|
| 406 | if (c<0) { |
---|
| 407 | b=-(c>>bpe); |
---|
| 408 | c+=b*radix; |
---|
| 409 | } |
---|
| 410 | x[i]=c & mask; |
---|
| 411 | c=(c>>bpe)-b; |
---|
| 412 | } |
---|
| 413 | } |
---|
| 414 | |
---|
| 415 | //return x mod n for bigInt x and integer n. |
---|
| 416 | function modInt(x,n) { |
---|
| 417 | var i,c=0; |
---|
| 418 | for (i=x.length-1; i>=0; i--) |
---|
| 419 | c=(c*radix+x[i])%n; |
---|
| 420 | return c; |
---|
| 421 | } |
---|
| 422 | |
---|
| 423 | //convert the integer t into a bigInt with at least the given number of bits. |
---|
| 424 | //the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word) |
---|
| 425 | //Pad the array with leading zeros so that it has at least minSize elements. |
---|
| 426 | //There will always be at least one leading 0 element. |
---|
| 427 | function int2bigInt(t,bits,minSize) { |
---|
| 428 | var i,k; |
---|
| 429 | k=Math.ceil(bits/bpe)+1; |
---|
| 430 | k=minSize>k ? minSize : k; |
---|
| 431 | buff=new Array(k); |
---|
| 432 | copyInt_(buff,t); |
---|
| 433 | return buff; |
---|
| 434 | } |
---|
| 435 | |
---|
| 436 | //return the bigInt given a string representation in a given base. |
---|
| 437 | //Pad the array with leading zeros so that it has at least minSize elements. |
---|
| 438 | //If base=-1, then it reads in a space-separated list of array elements in decimal. |
---|
| 439 | //The array will always have at least one leading zero, unless base=-1. |
---|
| 440 | function str2bigInt(s,base,minSize) { |
---|
| 441 | var d, i, j, x, y, kk; |
---|
| 442 | var k=s.length; |
---|
| 443 | if (base==-1) { //comma-separated list of array elements in decimal |
---|
| 444 | x=new Array(0); |
---|
| 445 | for (;;) { |
---|
| 446 | y=new Array(x.length+1); |
---|
| 447 | for (i=0;i<x.length;i++) |
---|
| 448 | y[i+1]=x[i]; |
---|
| 449 | y[0]=parseInt(s,10); |
---|
| 450 | x=y; |
---|
| 451 | d=s.indexOf(',',0); |
---|
| 452 | if (d<1) |
---|
| 453 | break; |
---|
| 454 | s=s.substring(d+1); |
---|
| 455 | if (s.length==0) |
---|
| 456 | break; |
---|
| 457 | } |
---|
| 458 | if (x.length<minSize) { |
---|
| 459 | y=new Array(minSize); |
---|
| 460 | copy_(y,x); |
---|
| 461 | return y; |
---|
| 462 | } |
---|
| 463 | return x; |
---|
| 464 | } |
---|
| 465 | |
---|
| 466 | x=int2bigInt(0,base*k,0); |
---|
| 467 | for (i=0;i<k;i++) { |
---|
| 468 | d=digitsStr.indexOf(s.substring(i,i+1),0); |
---|
| 469 | if (base<=36 && d>=36) //convert lowercase to uppercase if base<=36 |
---|
| 470 | d-=26; |
---|
| 471 | if (d>=base || d<0) { //stop at first illegal character |
---|
| 472 | break; |
---|
| 473 | } |
---|
| 474 | multInt_(x,base); |
---|
| 475 | addInt_(x,d); |
---|
| 476 | } |
---|
| 477 | |
---|
| 478 | for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros |
---|
| 479 | k=minSize>k+1 ? minSize : k+1; |
---|
| 480 | y=new Array(k); |
---|
| 481 | kk=k<x.length ? k : x.length; |
---|
| 482 | for (i=0;i<kk;i++) |
---|
| 483 | y[i]=x[i]; |
---|
| 484 | for (;i<k;i++) |
---|
| 485 | y[i]=0; |
---|
| 486 | return y; |
---|
| 487 | } |
---|
| 488 | |
---|
| 489 | //is bigint x equal to integer y? |
---|
| 490 | //y must have less than bpe bits |
---|
| 491 | function equalsInt(x,y) { |
---|
| 492 | var i; |
---|
| 493 | if (x[0]!=y) |
---|
| 494 | return 0; |
---|
| 495 | for (i=1;i<x.length;i++) |
---|
| 496 | if (x[i]) |
---|
| 497 | return 0; |
---|
| 498 | return 1; |
---|
| 499 | } |
---|
| 500 | |
---|
| 501 | //are bigints x and y equal? |
---|
| 502 | //this works even if x and y are different lengths and have arbitrarily many leading zeros |
---|
| 503 | function equals(x,y) { |
---|
| 504 | var i; |
---|
| 505 | var k=x.length<y.length ? x.length : y.length; |
---|
| 506 | for (i=0;i<k;i++) |
---|
| 507 | if (x[i]!=y[i]) |
---|
| 508 | return 0; |
---|
| 509 | if (x.length>y.length) { |
---|
| 510 | for (;i<x.length;i++) |
---|
| 511 | if (x[i]) |
---|
| 512 | return 0; |
---|
| 513 | } else { |
---|
| 514 | for (;i<y.length;i++) |
---|
| 515 | if (y[i]) |
---|
| 516 | return 0; |
---|
| 517 | } |
---|
| 518 | return 1; |
---|
| 519 | } |
---|
| 520 | |
---|
| 521 | //is the bigInt x equal to zero? |
---|
| 522 | function isZero(x) { |
---|
| 523 | var i; |
---|
| 524 | for (i=0;i<x.length;i++) |
---|
| 525 | if (x[i]) |
---|
| 526 | return 0; |
---|
| 527 | return 1; |
---|
| 528 | } |
---|
| 529 | |
---|
| 530 | //convert a bigInt into a string in a given base, from base 2 up to base 95. |
---|
| 531 | //Base -1 prints the contents of the array representing the number. |
---|
| 532 | function bigInt2str(x,base) { |
---|
| 533 | var i,t,s=""; |
---|
| 534 | |
---|
| 535 | if (s6.length!=x.length) |
---|
| 536 | s6=dup(x); |
---|
| 537 | else |
---|
| 538 | copy_(s6,x); |
---|
| 539 | |
---|
| 540 | if (base==-1) { //return the list of array contents |
---|
| 541 | for (i=x.length-1;i>0;i--) |
---|
| 542 | s+=x[i]+','; |
---|
| 543 | s+=x[0]; |
---|
| 544 | } |
---|
| 545 | else { //return it in the given base |
---|
| 546 | while (!isZero(s6)) { |
---|
| 547 | t=divInt_(s6,base); //t=s6 % base; s6=floor(s6/base); |
---|
| 548 | s=digitsStr.substring(t,t+1)+s; |
---|
| 549 | } |
---|
| 550 | } |
---|
| 551 | if (s.length==0) |
---|
| 552 | s="0"; |
---|
| 553 | return s; |
---|
| 554 | } |
---|
| 555 | |
---|
| 556 | //returns a duplicate of bigInt x |
---|
| 557 | function dup(x) { |
---|
| 558 | var i; |
---|
| 559 | buff=new Array(x.length); |
---|
| 560 | copy_(buff,x); |
---|
| 561 | return buff; |
---|
| 562 | } |
---|
| 563 | |
---|
| 564 | //do x=y on bigInts x and y. x must be an array at least as big as y (not counting the leading zeros in y). |
---|
| 565 | function copy_(x,y) { |
---|
| 566 | var i; |
---|
| 567 | var k=x.length<y.length ? x.length : y.length; |
---|
| 568 | for (i=0;i<k;i++) |
---|
| 569 | x[i]=y[i]; |
---|
| 570 | for (i=k;i<x.length;i++) |
---|
| 571 | x[i]=0; |
---|
| 572 | } |
---|
| 573 | |
---|
| 574 | //do x=y on bigInt x and integer y. |
---|
| 575 | function copyInt_(x,n) { |
---|
| 576 | var i,c; |
---|
| 577 | for (c=n,i=0;i<x.length;i++) { |
---|
| 578 | x[i]=c & mask; |
---|
| 579 | c>>=bpe; |
---|
| 580 | } |
---|
| 581 | } |
---|
| 582 | |
---|
| 583 | //do x=x+n where x is a bigInt and n is an integer. |
---|
| 584 | //x must be large enough to hold the result. |
---|
| 585 | function addInt_(x,n) { |
---|
| 586 | var i,k,c,b; |
---|
| 587 | x[0]+=n; |
---|
| 588 | k=x.length; |
---|
| 589 | c=0; |
---|
| 590 | for (i=0;i<k;i++) { |
---|
| 591 | c+=x[i]; |
---|
| 592 | b=0; |
---|
| 593 | if (c<0) { |
---|
| 594 | b=-(c>>bpe); |
---|
| 595 | c+=b*radix; |
---|
| 596 | } |
---|
| 597 | x[i]=c & mask; |
---|
| 598 | c=(c>>bpe)-b; |
---|
| 599 | if (!c) return; //stop carrying as soon as the carry is zero |
---|
| 600 | } |
---|
| 601 | } |
---|
| 602 | |
---|
| 603 | //right shift bigInt x by n bits. 0 <= n < bpe. |
---|
| 604 | function rightShift_(x,n) { |
---|
| 605 | var i; |
---|
| 606 | var k=Math.floor(n/bpe); |
---|
| 607 | if (k) { |
---|
| 608 | for (i=0;i<x.length-k;i++) //right shift x by k elements |
---|
| 609 | x[i]=x[i+k]; |
---|
| 610 | for (;i<x.length;i++) |
---|
| 611 | x[i]=0; |
---|
| 612 | n%=bpe; |
---|
| 613 | } |
---|
| 614 | for (i=0;i<x.length-1;i++) { |
---|
| 615 | x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n)); |
---|
| 616 | } |
---|
| 617 | x[i]>>=n; |
---|
| 618 | } |
---|
| 619 | |
---|
| 620 | //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement |
---|
| 621 | function halve_(x) { |
---|
| 622 | var i; |
---|
| 623 | for (i=0;i<x.length-1;i++) { |
---|
| 624 | x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1)); |
---|
| 625 | } |
---|
| 626 | x[i]=(x[i]>>1) | (x[i] & (radix>>1)); //most significant bit stays the same |
---|
| 627 | } |
---|
| 628 | |
---|
| 629 | //left shift bigInt x by n bits. |
---|
| 630 | function leftShift_(x,n) { |
---|
| 631 | var i; |
---|
| 632 | var k=Math.floor(n/bpe); |
---|
| 633 | if (k) { |
---|
| 634 | for (i=x.length; i>=k; i--) //left shift x by k elements |
---|
| 635 | x[i]=x[i-k]; |
---|
| 636 | for (;i>=0;i--) |
---|
| 637 | x[i]=0; |
---|
| 638 | n%=bpe; |
---|
| 639 | } |
---|
| 640 | if (!n) |
---|
| 641 | return; |
---|
| 642 | for (i=x.length-1;i>0;i--) { |
---|
| 643 | x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n))); |
---|
| 644 | } |
---|
| 645 | x[i]=mask & (x[i]<<n); |
---|
| 646 | } |
---|
| 647 | |
---|
| 648 | //do x=x*n where x is a bigInt and n is an integer. |
---|
| 649 | //x must be large enough to hold the result. |
---|
| 650 | function multInt_(x,n) { |
---|
| 651 | var i,k,c,b; |
---|
| 652 | if (!n) |
---|
| 653 | return; |
---|
| 654 | k=x.length; |
---|
| 655 | c=0; |
---|
| 656 | for (i=0;i<k;i++) { |
---|
| 657 | c+=x[i]*n; |
---|
| 658 | b=0; |
---|
| 659 | if (c<0) { |
---|
| 660 | b=-(c>>bpe); |
---|
| 661 | c+=b*radix; |
---|
| 662 | } |
---|
| 663 | x[i]=c & mask; |
---|
| 664 | c=(c>>bpe)-b; |
---|
| 665 | } |
---|
| 666 | } |
---|
| 667 | |
---|
| 668 | //do x=floor(x/n) for bigInt x and integer n, and return the remainder |
---|
| 669 | function divInt_(x,n) { |
---|
| 670 | var i,r=0,s; |
---|
| 671 | for (i=x.length-1;i>=0;i--) { |
---|
| 672 | s=r*radix+x[i]; |
---|
| 673 | x[i]=Math.floor(s/n); |
---|
| 674 | r=s%n; |
---|
| 675 | } |
---|
| 676 | return r; |
---|
| 677 | } |
---|
| 678 | |
---|
| 679 | //do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b. |
---|
| 680 | //x must be large enough to hold the answer. |
---|
| 681 | function linComb_(x,y,a,b) { |
---|
| 682 | var i,c,k,kk; |
---|
| 683 | k=x.length<y.length ? x.length : y.length; |
---|
| 684 | kk=x.length; |
---|
| 685 | for (c=0,i=0;i<k;i++) { |
---|
| 686 | c+=a*x[i]+b*y[i]; |
---|
| 687 | x[i]=c & mask; |
---|
| 688 | c>>=bpe; |
---|
| 689 | } |
---|
| 690 | for (i=k;i<kk;i++) { |
---|
| 691 | c+=a*x[i]; |
---|
| 692 | x[i]=c & mask; |
---|
| 693 | c>>=bpe; |
---|
| 694 | } |
---|
| 695 | } |
---|
| 696 | |
---|
| 697 | //do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys. |
---|
| 698 | //x must be large enough to hold the answer. |
---|
| 699 | function linCombShift_(x,y,b,ys) { |
---|
| 700 | var i,c,k,kk; |
---|
| 701 | k=x.length<ys+y.length ? x.length : ys+y.length; |
---|
| 702 | kk=x.length; |
---|
| 703 | for (c=0,i=ys;i<k;i++) { |
---|
| 704 | c+=x[i]+b*y[i-ys]; |
---|
| 705 | x[i]=c & mask; |
---|
| 706 | c>>=bpe; |
---|
| 707 | } |
---|
| 708 | for (i=k;c && i<kk;i++) { |
---|
| 709 | c+=x[i]; |
---|
| 710 | x[i]=c & mask; |
---|
| 711 | c>>=bpe; |
---|
| 712 | } |
---|
| 713 | } |
---|
| 714 | |
---|
| 715 | //do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. |
---|
| 716 | //x must be large enough to hold the answer. |
---|
| 717 | function addShift_(x,y,ys) { |
---|
| 718 | var i,c,k,kk; |
---|
| 719 | k=x.length<ys+y.length ? x.length : ys+y.length; |
---|
| 720 | kk=x.length; |
---|
| 721 | for (c=0,i=ys;i<k;i++) { |
---|
| 722 | c+=x[i]+y[i-ys]; |
---|
| 723 | x[i]=c & mask; |
---|
| 724 | c>>=bpe; |
---|
| 725 | } |
---|
| 726 | for (i=k;c && i<kk;i++) { |
---|
| 727 | c+=x[i]; |
---|
| 728 | x[i]=c & mask; |
---|
| 729 | c>>=bpe; |
---|
| 730 | } |
---|
| 731 | } |
---|
| 732 | |
---|
| 733 | //do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. |
---|
| 734 | //x must be large enough to hold the answer. |
---|
| 735 | function subShift_(x,y,ys) { |
---|
| 736 | var i,c,k,kk; |
---|
| 737 | k=x.length<ys+y.length ? x.length : ys+y.length; |
---|
| 738 | kk=x.length; |
---|
| 739 | for (c=0,i=ys;i<k;i++) { |
---|
| 740 | c+=x[i]-y[i-ys]; |
---|
| 741 | x[i]=c & mask; |
---|
| 742 | c>>=bpe; |
---|
| 743 | } |
---|
| 744 | for (i=k;c && i<kk;i++) { |
---|
| 745 | c+=x[i]; |
---|
| 746 | x[i]=c & mask; |
---|
| 747 | c>>=bpe; |
---|
| 748 | } |
---|
| 749 | } |
---|
| 750 | |
---|
| 751 | //do x=x-y for bigInts x and y. |
---|
| 752 | //x must be large enough to hold the answer. |
---|
| 753 | //negative answers will be 2s complement |
---|
| 754 | function sub_(x,y) { |
---|
| 755 | var i,c,k,kk; |
---|
| 756 | k=x.length<y.length ? x.length : y.length; |
---|
| 757 | for (c=0,i=0;i<k;i++) { |
---|
| 758 | c+=x[i]-y[i]; |
---|
| 759 | x[i]=c & mask; |
---|
| 760 | c>>=bpe; |
---|
| 761 | } |
---|
| 762 | for (i=k;c && i<x.length;i++) { |
---|
| 763 | c+=x[i]; |
---|
| 764 | x[i]=c & mask; |
---|
| 765 | c>>=bpe; |
---|
| 766 | } |
---|
| 767 | } |
---|
| 768 | |
---|
| 769 | //do x=x+y for bigInts x and y. |
---|
| 770 | //x must be large enough to hold the answer. |
---|
| 771 | function add_(x,y) { |
---|
| 772 | var i,c,k,kk; |
---|
| 773 | k=x.length<y.length ? x.length : y.length; |
---|
| 774 | for (c=0,i=0;i<k;i++) { |
---|
| 775 | c+=x[i]+y[i]; |
---|
| 776 | x[i]=c & mask; |
---|
| 777 | c>>=bpe; |
---|
| 778 | } |
---|
| 779 | for (i=k;c && i<x.length;i++) { |
---|
| 780 | c+=x[i]; |
---|
| 781 | x[i]=c & mask; |
---|
| 782 | c>>=bpe; |
---|
| 783 | } |
---|
| 784 | } |
---|
| 785 | |
---|
| 786 | //do x=x*y for bigInts x and y. This is faster when y<x. |
---|
| 787 | function mult_(x,y) { |
---|
| 788 | var i; |
---|
| 789 | if (ss.length!=2*x.length) |
---|
| 790 | ss=new Array(2*x.length); |
---|
| 791 | copyInt_(ss,0); |
---|
| 792 | for (i=0;i<y.length;i++) |
---|
| 793 | if (y[i]) |
---|
| 794 | linCombShift_(ss,x,y[i],i); //ss=1*ss+y[i]*(x<<(i*bpe)) |
---|
| 795 | copy_(x,ss); |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | //do x=x mod n for bigInts x and n. |
---|
| 799 | function mod_(x,n) { |
---|
| 800 | if (s4.length!=x.length) |
---|
| 801 | s4=dup(x); |
---|
| 802 | else |
---|
| 803 | copy_(s4,x); |
---|
| 804 | if (s5.length!=x.length) |
---|
| 805 | s5=dup(x); |
---|
| 806 | divide_(s4,n,s5,x); //x = remainder of s4 / n |
---|
| 807 | } |
---|
| 808 | |
---|
| 809 | //do x=x*y mod n for bigInts x,y,n. |
---|
| 810 | //for greater speed, let y<x. |
---|
| 811 | function multMod_(x,y,n) { |
---|
| 812 | var i; |
---|
| 813 | if (s0.length!=2*x.length) |
---|
| 814 | s0=new Array(2*x.length); |
---|
| 815 | copyInt_(s0,0); |
---|
| 816 | for (i=0;i<y.length;i++) |
---|
| 817 | if (y[i]) |
---|
| 818 | linCombShift_(s0,x,y[i],i); //s0=1*s0+y[i]*(x<<(i*bpe)) |
---|
| 819 | mod_(s0,n); |
---|
| 820 | copy_(x,s0); |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | //do x=x*x mod n for bigInts x,n. |
---|
| 824 | function squareMod_(x,n) { |
---|
| 825 | var i,j,d,c,kx,kn,k; |
---|
| 826 | for (kx=x.length; kx>0 && !x[kx-1]; kx--); //ignore leading zeros in x |
---|
| 827 | k=kx>n.length ? 2*kx : 2*n.length; //k=# elements in the product, which is twice the elements in the larger of x and n |
---|
| 828 | if (s0.length!=k) |
---|
| 829 | s0=new Array(k); |
---|
| 830 | copyInt_(s0,0); |
---|
| 831 | for (i=0;i<kx;i++) { |
---|
| 832 | c=s0[2*i]+x[i]*x[i]; |
---|
| 833 | s0[2*i]=c & mask; |
---|
| 834 | c>>=bpe; |
---|
| 835 | for (j=i+1;j<kx;j++) { |
---|
| 836 | c=s0[i+j]+2*x[i]*x[j]+c; |
---|
| 837 | s0[i+j]=(c & mask); |
---|
| 838 | c>>=bpe; |
---|
| 839 | } |
---|
| 840 | s0[i+kx]=c; |
---|
| 841 | } |
---|
| 842 | mod_(s0,n); |
---|
| 843 | copy_(x,s0); |
---|
| 844 | } |
---|
| 845 | |
---|
| 846 | //return x with exactly k leading zero elements |
---|
[2931] | 847 | function bigintTrim(x,k) { |
---|
[2847] | 848 | var i,y; |
---|
| 849 | for (i=x.length; i>0 && !x[i-1]; i--); |
---|
| 850 | y=new Array(i+k); |
---|
| 851 | copy_(y,x); |
---|
| 852 | return y; |
---|
| 853 | } |
---|
| 854 | |
---|
| 855 | //do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation. 0**0=1. |
---|
| 856 | //this is faster when n is odd. x usually needs to have as many elements as n. |
---|
| 857 | function powMod_(x,y,n) { |
---|
| 858 | var k1,k2,kn,np; |
---|
| 859 | if(s7.length!=n.length) |
---|
| 860 | s7=dup(n); |
---|
| 861 | |
---|
| 862 | //for even modulus, use a simple square-and-multiply algorithm, |
---|
| 863 | //rather than using the more complex Montgomery algorithm. |
---|
| 864 | if ((n[0]&1)==0) { |
---|
| 865 | copy_(s7,x); |
---|
| 866 | copyInt_(x,1); |
---|
| 867 | while(!equalsInt(y,0)) { |
---|
| 868 | if (y[0]&1) |
---|
| 869 | multMod_(x,s7,n); |
---|
| 870 | divInt_(y,2); |
---|
| 871 | squareMod_(s7,n); |
---|
| 872 | } |
---|
| 873 | return; |
---|
| 874 | } |
---|
| 875 | |
---|
| 876 | //calculate np from n for the Montgomery multiplications |
---|
| 877 | copyInt_(s7,0); |
---|
| 878 | for (kn=n.length;kn>0 && !n[kn-1];kn--); |
---|
| 879 | np=radix-inverseModInt(modInt(n,radix),radix); |
---|
| 880 | s7[kn]=1; |
---|
| 881 | multMod_(x ,s7,n); // x = x * 2**(kn*bp) mod n |
---|
| 882 | |
---|
| 883 | if (s3.length!=x.length) |
---|
| 884 | s3=dup(x); |
---|
| 885 | else |
---|
| 886 | copy_(s3,x); |
---|
| 887 | |
---|
| 888 | for (k1=y.length-1;k1>0 & !y[k1]; k1--); //k1=first nonzero element of y |
---|
| 889 | if (y[k1]==0) { //anything to the 0th power is 1 |
---|
| 890 | copyInt_(x,1); |
---|
| 891 | return; |
---|
| 892 | } |
---|
| 893 | for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1); //k2=position of first 1 bit in y[k1] |
---|
| 894 | for (;;) { |
---|
| 895 | if (!(k2>>=1)) { //look at next bit of y |
---|
| 896 | k1--; |
---|
| 897 | if (k1<0) { |
---|
| 898 | mont_(x,one,n,np); |
---|
| 899 | return; |
---|
| 900 | } |
---|
| 901 | k2=1<<(bpe-1); |
---|
| 902 | } |
---|
| 903 | mont_(x,x,n,np); |
---|
| 904 | |
---|
| 905 | if (k2 & y[k1]) //if next bit is a 1 |
---|
| 906 | mont_(x,s3,n,np); |
---|
| 907 | } |
---|
| 908 | } |
---|
| 909 | |
---|
| 910 | |
---|
| 911 | //do x=x*y*Ri mod n for bigInts x,y,n, |
---|
| 912 | // where Ri = 2**(-kn*bpe) mod n, and kn is the |
---|
| 913 | // number of elements in the n array, not |
---|
| 914 | // counting leading zeros. |
---|
| 915 | //x array must have at least as many elemnts as the n array |
---|
| 916 | //It's OK if x and y are the same variable. |
---|
| 917 | //must have: |
---|
| 918 | // x,y < n |
---|
| 919 | // n is odd |
---|
| 920 | // np = -(n^(-1)) mod radix |
---|
| 921 | function mont_(x,y,n,np) { |
---|
| 922 | var i,j,c,ui,t,ks; |
---|
| 923 | var kn=n.length; |
---|
| 924 | var ky=y.length; |
---|
| 925 | |
---|
| 926 | if (sa.length!=kn) |
---|
| 927 | sa=new Array(kn); |
---|
| 928 | |
---|
| 929 | copyInt_(sa,0); |
---|
| 930 | |
---|
| 931 | for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n |
---|
| 932 | for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y |
---|
| 933 | ks=sa.length-1; //sa will never have more than this many nonzero elements. |
---|
| 934 | |
---|
| 935 | //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large numbers |
---|
| 936 | for (i=0; i<kn; i++) { |
---|
| 937 | t=sa[0]+x[i]*y[0]; |
---|
| 938 | ui=((t & mask) * np) & mask; //the inner "& mask" was needed on Safari (but not MSIE) at one time |
---|
| 939 | c=(t+ui*n[0]) >> bpe; |
---|
| 940 | t=x[i]; |
---|
| 941 | |
---|
| 942 | //do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe. Loop is unrolled 5-fold for speed |
---|
| 943 | j=1; |
---|
| 944 | for (;j<ky-4;) { c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 945 | c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 946 | c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 947 | c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 948 | c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; } |
---|
| 949 | for (;j<ky;) { c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; } |
---|
| 950 | for (;j<kn-4;) { c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 951 | c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 952 | c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 953 | c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; |
---|
| 954 | c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; } |
---|
| 955 | for (;j<kn;) { c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; } |
---|
| 956 | for (;j<ks;) { c+=sa[j]; sa[j-1]=c & mask; c>>=bpe; j++; } |
---|
| 957 | sa[j-1]=c & mask; |
---|
| 958 | } |
---|
| 959 | |
---|
| 960 | if (!greater(n,sa)) |
---|
| 961 | sub_(sa,n); |
---|
| 962 | copy_(x,sa); |
---|
| 963 | } |
---|
| 964 | |
---|
| 965 | |
---|