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BigInt - npm Package Compare versions
Comparing version 5.4.5 to 5.5.0
| { | ||
| "name": "BigInt", | ||
| "version": "5.4.5", | ||
| "version": "5.5.0", | ||
| "description": "Big Integer Library in pure Javascript", | ||
@@ -5,0 +5,0 @@ "keywords": ["bigint"], |
2456
src/BigInt.js
| // Vjeux: Customized bigInt2str and str2bigInt in order to accept custom base. | ||
| //////////////////////////////////////////////////////////////////////////////////////// | ||
| // Big Integer Library v. 5.4 | ||
| // Created 2000, last modified 2009 | ||
| // Big Integer Library v. 5.5 | ||
| // Created 2000, last modified 2013 | ||
| // Leemon Baird | ||
@@ -10,2 +10,5 @@ // www.leemon.com | ||
| // Version history: | ||
| // v 5.5 17 Mar 2013 | ||
| // - two lines of a form like "if (x<0) x+=n" had the "if" changed to "while" to | ||
| // handle the case when x<-n. (Thanks to James Ansell for finding that bug) | ||
| // v 5.4 3 Oct 2009 | ||
@@ -23,3 +26,3 @@ // - added "var i" to greaterShift() so i is not global. (Thanks to P�ter Szab� for finding that bug) | ||
| // | ||
| // v 5.1 8 Oct 2007 | ||
| // v 5.1 8 Oct 2007 | ||
| // - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters | ||
@@ -31,22 +34,22 @@ // - added functions GCD and randBigInt, which call GCD_ and randBigInt_ | ||
| // This file is public domain. You can use it for any purpose without restriction. | ||
| // I do not guarantee that it is correct, so use it at your own risk. If you use | ||
| // it for something interesting, I'd appreciate hearing about it. If you find | ||
| // I do not guarantee that it is correct, so use it at your own risk. If you use | ||
| // it for something interesting, I'd appreciate hearing about it. If you find | ||
| // any bugs or make any improvements, I'd appreciate hearing about those too. | ||
| // It would also be nice if my name and URL were left in the comments. But none | ||
| // It would also be nice if my name and URL were left in the comments. But none | ||
| // of that is required. | ||
| // | ||
| // This code defines a bigInt library for arbitrary-precision integers. | ||
| // A bigInt is an array of integers storing the value in chunks of bpe bits, | ||
| // A bigInt is an array of integers storing the value in chunks of bpe bits, | ||
| // little endian (buff[0] is the least significant word). | ||
| // Negative bigInts are stored two's complement. Almost all the functions treat | ||
| // bigInts as nonnegative. The few that view them as two's complement say so | ||
| // in their comments. Some functions assume their parameters have at least one | ||
| // in their comments. Some functions assume their parameters have at least one | ||
| // leading zero element. Functions with an underscore at the end of the name put | ||
| // their answer into one of the arrays passed in, and have unpredictable behavior | ||
| // in case of overflow, so the caller must make sure the arrays are big enough to | ||
| // hold the answer. But the average user should never have to call any of the | ||
| // underscored functions. Each important underscored function has a wrapper function | ||
| // of the same name without the underscore that takes care of the details for you. | ||
| // For each underscored function where a parameter is modified, that same variable | ||
| // must not be used as another argument too. So, you cannot square x by doing | ||
| // their answer into one of the arrays passed in, and have unpredictable behavior | ||
| // in case of overflow, so the caller must make sure the arrays are big enough to | ||
| // hold the answer. But the average user should never have to call any of the | ||
| // underscored functions. Each important underscored function has a wrapper function | ||
| // of the same name without the underscore that takes care of the details for you. | ||
| // For each underscored function where a parameter is modified, that same variable | ||
| // must not be used as another argument too. So, you cannot square x by doing | ||
| // multMod_(x,x,n). You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n). | ||
@@ -63,16 +66,16 @@ // Or simply use the multMod(x,x,n) function without the underscore, where | ||
| // | ||
| // Note that for cryptographic purposes, the calls to Math.random() must | ||
| // Note that for cryptographic purposes, the calls to Math.random() must | ||
| // be replaced with calls to a better pseudorandom number generator. | ||
| // | ||
| // In the following, "bigInt" means a bigInt with at least one leading zero element, | ||
| // and "integer" means a nonnegative integer less than radix. In some cases, integer | ||
| // and "integer" means a nonnegative integer less than radix. In some cases, integer | ||
| // can be negative. Negative bigInts are 2s complement. | ||
| // | ||
| // | ||
| // The following functions do not modify their inputs. | ||
| // Those returning a bigInt, string, or Array will dynamically allocate memory for that value. | ||
| // Those returning a boolean will return the integer 0 (false) or 1 (true). | ||
| // Those returning boolean or int will not allocate memory except possibly on the first | ||
| // Those returning boolean or int will not allocate memory except possibly on the first | ||
| // time they're called with a given parameter size. | ||
| // | ||
| // bigInt add(x,y) //return (x+y) for bigInts x and y. | ||
| // | ||
| // bigInt add(x,y) //return (x+y) for bigInts x and y. | ||
| // bigInt addInt(x,n) //return (x+n) where x is a bigInt and n is an integer. | ||
@@ -110,4 +113,4 @@ // string bigInt2str(x,base) //return a string form of bigInt x in a given base, with 2 <= base <= 95 | ||
| // The following functions each have a non-underscored version, which most users should call instead. | ||
| // These functions each write to a single parameter, and the caller is responsible for ensuring the array | ||
| // passed in is large enough to hold the result. | ||
| // These functions each write to a single parameter, and the caller is responsible for ensuring the array | ||
| // passed in is large enough to hold the result. | ||
| // | ||
@@ -128,5 +131,5 @@ // void addInt_(x,n) //do x=x+n where x is a bigInt and n is an integer | ||
| // | ||
| // The following functions do NOT have a non-underscored version. | ||
| // The following functions do NOT have a non-underscored version. | ||
| // They each write a bigInt result to one or more parameters. The caller is responsible for | ||
| // ensuring the arrays passed in are large enough to hold the results. | ||
| // ensuring the arrays passed in are large enough to hold the results. | ||
| // | ||
@@ -186,805 +189,823 @@ // void addShift_(x,y,ys) //do x=x+(y<<(ys*bpe)) | ||
| //////////////////////////////////////////////////////////////////////////////////////// | ||
| (function(factory) { | ||
| if (typeof exports === 'object') { | ||
| // CommonJS | ||
| factory(require, exports, module); | ||
| } else if (typeof define === 'function') { | ||
| // AMD requirejs | ||
| define(factory); | ||
| } else { | ||
| // Plain script tag | ||
| var _module = {}; | ||
| _module.exports = {}; | ||
| var _require = function(name) { throw new Error("can't require"); } | ||
| factory(_require, _module.exports, _module); | ||
| window.BigInt = _module.exports; | ||
| } | ||
| })(function (require, exports, module) { | ||
| "use strict"; | ||
| (function () { | ||
| //globals | ||
| bpe=0; //bits stored per array element | ||
| mask=0; //AND this with an array element to chop it down to bpe bits | ||
| radix=mask+1; //equals 2^bpe. A single 1 bit to the left of the last bit of mask. | ||
| var trueRandom = function () { return Math.random(); }; | ||
| //the digits for converting to different bases | ||
| digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-'; | ||
| //globals | ||
| var bpe=0; //bits stored per array element | ||
| var mask=0; //AND this with an array element to chop it down to bpe bits | ||
| var radix=mask+1; //equals 2^bpe. A single 1 bit to the left of the last bit of mask. | ||
| //initialize the global variables | ||
| for (bpe=0; (1<<(bpe+1)) > (1<<bpe); bpe++); //bpe=number of bits in the mantissa on this platform | ||
| bpe>>=1; //bpe=number of bits in one element of the array representing the bigInt | ||
| mask=(1<<bpe)-1; //AND the mask with an integer to get its bpe least significant bits | ||
| radix=mask+1; //2^bpe. a single 1 bit to the left of the first bit of mask | ||
| one=int2bigInt(1,1,1); //constant used in powMod_() | ||
| //the digits for converting to different bases | ||
| var digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-'; | ||
| //the following global variables are scratchpad memory to | ||
| //reduce dynamic memory allocation in the inner loop | ||
| t=new Array(0); | ||
| ss=t; //used in mult_() | ||
| s0=t; //used in multMod_(), squareMod_() | ||
| s1=t; //used in powMod_(), multMod_(), squareMod_() | ||
| s2=t; //used in powMod_(), multMod_() | ||
| s3=t; //used in powMod_() | ||
| s4=t; s5=t; //used in mod_() | ||
| s6=t; //used in bigInt2str() | ||
| s7=t; //used in powMod_() | ||
| T=t; //used in GCD_() | ||
| sa=t; //used in mont_() | ||
| mr_x1=t; mr_r=t; mr_a=t; //used in millerRabin() | ||
| eg_v=t; eg_u=t; eg_A=t; eg_B=t; eg_C=t; eg_D=t; //used in eGCD_(), inverseMod_() | ||
| md_q1=t; md_q2=t; md_q3=t; md_r=t; md_r1=t; md_r2=t; md_tt=t; //used in mod_() | ||
| //initialize the global variables | ||
| for (bpe=0; (1<<(bpe+1)) > (1<<bpe); bpe++); //bpe=number of bits in the mantissa on this platform | ||
| bpe>>=1; //bpe=number of bits in one element of the array representing the bigInt | ||
| mask=(1<<bpe)-1; //AND the mask with an integer to get its bpe least significant bits | ||
| radix=mask+1; //2^bpe. a single 1 bit to the left of the first bit of mask | ||
| var one=int2bigInt(1,1,1); //constant used in powMod_() | ||
| primes=t; pows=t; s_i=t; s_i2=t; s_R=t; s_rm=t; s_q=t; s_n1=t; | ||
| 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_() | ||
| //the following global variables are scratchpad memory to | ||
| //reduce dynamic memory allocation in the inner loop | ||
| var t=new Array(0); | ||
| var ss=t; //used in mult_() | ||
| var s0=t; //used in multMod_(), squareMod_() | ||
| var s1=t; //used in powMod_(), multMod_(), squareMod_() | ||
| var s2=t; //used in powMod_(), multMod_() | ||
| var s3=t; //used in powMod_() | ||
| var s4= t, s5=t; //used in mod_() | ||
| var s6=t; //used in bigInt2str() | ||
| var s7=t; //used in powMod_() | ||
| var T=t; //used in GCD_() | ||
| var sa=t; //used in mont_() | ||
| var mr_x1= t, mr_r= t, mr_a=t; //used in millerRabin() | ||
| var eg_v= t, eg_u= t, eg_A=t, eg_B=t, eg_C=t, eg_D=t; //used in eGCD_(), inverseMod_() | ||
| var md_q1=t, md_q2=t, md_q3=t, md_r=t, md_r1=t, md_r2=t, md_tt=t; //used in mod_() | ||
| rpprb=t; //used in randProbPrimeRounds() (which also uses "primes") | ||
| var primes=t, pows=t, s_i=t, s_i2=t, s_R=t, s_rm=t, s_q=t, s_n1=t; | ||
| var 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_() | ||
| //////////////////////////////////////////////////////////////////////////////////////// | ||
| var rpprb=t; //used in randProbPrimeRounds() (which also uses "primes") | ||
| //////////////////////////////////////////////////////////////////////////////////////// | ||
| //return array of all primes less than integer n | ||
| function findPrimes(n) { | ||
| var i,s,p,ans; | ||
| s=new Array(n); | ||
| for (i=0;i<n;i++) | ||
| s[i]=0; | ||
| s[0]=2; | ||
| p=0; //first p elements of s are primes, the rest are a sieve | ||
| for(;s[p]<n;) { //s[p] is the pth prime | ||
| for(i=s[p]*s[p]; i<n; i+=s[p]) //mark multiples of s[p] | ||
| s[i]=1; | ||
| p++; | ||
| s[p]=s[p-1]+1; | ||
| for(; s[p]<n && s[s[p]]; s[p]++); //find next prime (where s[p]==0) | ||
| } | ||
| ans=new Array(p); | ||
| for(i=0;i<p;i++) | ||
| ans[i]=s[i]; | ||
| return ans; | ||
| } | ||
| //return array of all primes less than integer n | ||
| function findPrimes(n) { | ||
| var i,s,p,ans; | ||
| s=new Array(n); | ||
| for (i=0;i<n;i++) | ||
| s[i]=0; | ||
| s[0]=2; | ||
| p=0; //first p elements of s are primes, the rest are a sieve | ||
| for(;s[p]<n;) { //s[p] is the pth prime | ||
| for(i=s[p]*s[p]; i<n; i+=s[p]) //mark multiples of s[p] | ||
| s[i]=1; | ||
| p++; | ||
| s[p]=s[p-1]+1; | ||
| for(; s[p]<n && s[s[p]]; s[p]++); //find next prime (where s[p]==0) | ||
| } | ||
| ans=new Array(p); | ||
| for(i=0;i<p;i++) | ||
| ans[i]=s[i]; | ||
| return ans; | ||
| } | ||
| //does a single round of Miller-Rabin base b consider x to be a possible prime? | ||
| //x is a bigInt, and b is an integer, with b<x | ||
| function millerRabinInt(x,b) { | ||
| if (mr_x1.length!=x.length) { | ||
| mr_x1=dup(x); | ||
| mr_r=dup(x); | ||
| mr_a=dup(x); | ||
| } | ||
| copyInt_(mr_a,b); | ||
| return millerRabin(x,mr_a); | ||
| } | ||
| //does a single round of Miller-Rabin base b consider x to be a possible prime? | ||
| //x is a bigInt, and b is an integer, with b<x | ||
| function millerRabinInt(x,b) { | ||
| if (mr_x1.length!=x.length) { | ||
| mr_x1=dup(x); | ||
| mr_r=dup(x); | ||
| mr_a=dup(x); | ||
| } | ||
| //does a single round of Miller-Rabin base b consider x to be a possible prime? | ||
| //x and b are bigInts with b<x | ||
| function millerRabin(x,b) { | ||
| var i,j,k,s; | ||
| copyInt_(mr_a,b); | ||
| return millerRabin(x,mr_a); | ||
| } | ||
| if (mr_x1.length!=x.length) { | ||
| mr_x1=dup(x); | ||
| mr_r=dup(x); | ||
| mr_a=dup(x); | ||
| } | ||
| //does a single round of Miller-Rabin base b consider x to be a possible prime? | ||
| //x and b are bigInts with b<x | ||
| function millerRabin(x,b) { | ||
| var i,j,k,s; | ||
| copy_(mr_a,b); | ||
| copy_(mr_r,x); | ||
| copy_(mr_x1,x); | ||
| if (mr_x1.length!=x.length) { | ||
| mr_x1=dup(x); | ||
| mr_r=dup(x); | ||
| mr_a=dup(x); | ||
| } | ||
| addInt_(mr_r,-1); | ||
| addInt_(mr_x1,-1); | ||
| copy_(mr_a,b); | ||
| copy_(mr_r,x); | ||
| copy_(mr_x1,x); | ||
| //s=the highest power of two that divides mr_r | ||
| k=0; | ||
| for (i=0;i<mr_r.length;i++) | ||
| for (j=1;j<mask;j<<=1) | ||
| if (x[i] & j) { | ||
| s=(k<mr_r.length+bpe ? k : 0); | ||
| i=mr_r.length; | ||
| j=mask; | ||
| } else | ||
| k++; | ||
| addInt_(mr_r,-1); | ||
| addInt_(mr_x1,-1); | ||
| if (s) | ||
| rightShift_(mr_r,s); | ||
| //s=the highest power of two that divides mr_r | ||
| k=0; | ||
| for (i=0;i<mr_r.length;i++) | ||
| for (j=1;j<mask;j<<=1) | ||
| if (x[i] & j) { | ||
| s=(k<mr_r.length+bpe ? k : 0); | ||
| i=mr_r.length; | ||
| j=mask; | ||
| } else | ||
| k++; | ||
| powMod_(mr_a,mr_r,x); | ||
| if (s) | ||
| rightShift_(mr_r,s); | ||
| if (!equalsInt(mr_a,1) && !equals(mr_a,mr_x1)) { | ||
| j=1; | ||
| while (j<=s-1 && !equals(mr_a,mr_x1)) { | ||
| squareMod_(mr_a,x); | ||
| if (equalsInt(mr_a,1)) { | ||
| return 0; | ||
| powMod_(mr_a,mr_r,x); | ||
| if (!equalsInt(mr_a,1) && !equals(mr_a,mr_x1)) { | ||
| j=1; | ||
| while (j<=s-1 && !equals(mr_a,mr_x1)) { | ||
| squareMod_(mr_a,x); | ||
| if (equalsInt(mr_a,1)) { | ||
| return 0; | ||
| } | ||
| j++; | ||
| } | ||
| if (!equals(mr_a,mr_x1)) { | ||
| return 0; | ||
| } | ||
| } | ||
| j++; | ||
| return 1; | ||
| } | ||
| if (!equals(mr_a,mr_x1)) { | ||
| return 0; | ||
| //returns how many bits long the bigInt is, not counting leading zeros. | ||
| function bitSize(x) { | ||
| var j,z,w; | ||
| for (j=x.length-1; (x[j]==0) && (j>0); j--); | ||
| for (z=0,w=x[j]; w; (w>>=1),z++); | ||
| z+=bpe*j; | ||
| return z; | ||
| } | ||
| } | ||
| return 1; | ||
| } | ||
| //returns how many bits long the bigInt is, not counting leading zeros. | ||
| function bitSize(x) { | ||
| var j,z,w; | ||
| for (j=x.length-1; (x[j]==0) && (j>0); j--); | ||
| for (z=0,w=x[j]; w; (w>>=1),z++); | ||
| z+=bpe*j; | ||
| return z; | ||
| } | ||
| //return a copy of x with at least n elements, adding leading zeros if needed | ||
| function expand(x,n) { | ||
| var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0); | ||
| copy_(ans,x); | ||
| return ans; | ||
| } | ||
| //return a copy of x with at least n elements, adding leading zeros if needed | ||
| function expand(x,n) { | ||
| var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0); | ||
| copy_(ans,x); | ||
| return ans; | ||
| } | ||
| //return a k-bit true random prime using Maurer's algorithm. | ||
| function randTruePrime(k) { | ||
| var ans=int2bigInt(0,k,0); | ||
| randTruePrime_(ans,k); | ||
| return trim(ans,1); | ||
| } | ||
| //return a k-bit true random prime using Maurer's algorithm. | ||
| function randTruePrime(k) { | ||
| var ans=int2bigInt(0,k,0); | ||
| randTruePrime_(ans,k); | ||
| return trim(ans,1); | ||
| } | ||
| //return a k-bit random probable prime with probability of error < 2^-80 | ||
| function randProbPrime(k) { | ||
| if (k>=600) return randProbPrimeRounds(k,2); //numbers from HAC table 4.3 | ||
| if (k>=550) return randProbPrimeRounds(k,4); | ||
| if (k>=500) return randProbPrimeRounds(k,5); | ||
| if (k>=400) return randProbPrimeRounds(k,6); | ||
| if (k>=350) return randProbPrimeRounds(k,7); | ||
| if (k>=300) return randProbPrimeRounds(k,9); | ||
| if (k>=250) return randProbPrimeRounds(k,12); //numbers from HAC table 4.4 | ||
| if (k>=200) return randProbPrimeRounds(k,15); | ||
| if (k>=150) return randProbPrimeRounds(k,18); | ||
| if (k>=100) return randProbPrimeRounds(k,27); | ||
| return randProbPrimeRounds(k,40); //number from HAC remark 4.26 (only an estimate) | ||
| } | ||
| //return a k-bit random probable prime with probability of error < 2^-80 | ||
| function randProbPrime(k) { | ||
| if (k>=600) return randProbPrimeRounds(k,2); //numbers from HAC table 4.3 | ||
| if (k>=550) return randProbPrimeRounds(k,4); | ||
| if (k>=500) return randProbPrimeRounds(k,5); | ||
| if (k>=400) return randProbPrimeRounds(k,6); | ||
| if (k>=350) return randProbPrimeRounds(k,7); | ||
| if (k>=300) return randProbPrimeRounds(k,9); | ||
| if (k>=250) return randProbPrimeRounds(k,12); //numbers from HAC table 4.4 | ||
| if (k>=200) return randProbPrimeRounds(k,15); | ||
| if (k>=150) return randProbPrimeRounds(k,18); | ||
| if (k>=100) return randProbPrimeRounds(k,27); | ||
| return randProbPrimeRounds(k,40); //number from HAC remark 4.26 (only an estimate) | ||
| } | ||
| //return a k-bit probable random prime using n rounds of Miller Rabin (after trial division with small primes) | ||
| function randProbPrimeRounds(k,n) { | ||
| var ans, i, divisible, B; | ||
| B=30000; //B is largest prime to use in trial division | ||
| ans=int2bigInt(0,k,0); | ||
| //return a k-bit probable random prime using n rounds of Miller Rabin (after trial division with small primes) | ||
| function randProbPrimeRounds(k,n) { | ||
| var ans, i, divisible, B; | ||
| B=30000; //B is largest prime to use in trial division | ||
| ans=int2bigInt(0,k,0); | ||
| //optimization: try larger and smaller B to find the best limit. | ||
| //optimization: try larger and smaller B to find the best limit. | ||
| if (primes.length==0) | ||
| primes=findPrimes(30000); //check for divisibility by primes <=30000 | ||
| if (primes.length==0) | ||
| primes=findPrimes(30000); //check for divisibility by primes <=30000 | ||
| if (rpprb.length!=ans.length) | ||
| rpprb=dup(ans); | ||
| if (rpprb.length!=ans.length) | ||
| rpprb=dup(ans); | ||
| for (;;) { //keep trying random values for ans until one appears to be prime | ||
| //optimization: pick a random number times L=2*3*5*...*p, plus a | ||
| // random element of the list of all numbers in [0,L) not divisible by any prime up to p. | ||
| // This can reduce the amount of random number generation. | ||
| for (;;) { //keep trying random values for ans until one appears to be prime | ||
| //optimization: pick a random number times L=2*3*5*...*p, plus a | ||
| // random element of the list of all numbers in [0,L) not divisible by any prime up to p. | ||
| // This can reduce the amount of random number generation. | ||
| randBigInt_(ans,k,0); //ans = a random odd number to check | ||
| ans[0] |= 1; | ||
| divisible=0; | ||
| randBigInt_(ans,k,0); //ans = a random odd number to check | ||
| ans[0] |= 1; | ||
| divisible=0; | ||
| //check ans for divisibility by small primes up to B | ||
| for (i=0; (i<primes.length) && (primes[i]<=B); i++) | ||
| if (modInt(ans,primes[i])==0 && !equalsInt(ans,primes[i])) { | ||
| divisible=1; | ||
| break; | ||
| } | ||
| //check ans for divisibility by small primes up to B | ||
| for (i=0; (i<primes.length) && (primes[i]<=B); i++) | ||
| if (modInt(ans,primes[i])==0 && !equalsInt(ans,primes[i])) { | ||
| divisible=1; | ||
| break; | ||
| } | ||
| //optimization: change millerRabin so the base can be bigger than the number being checked, then eliminate the while here. | ||
| //optimization: change millerRabin so the base can be bigger than the number being checked, then eliminate the while here. | ||
| //do n rounds of Miller Rabin, with random bases less than ans | ||
| for (i=0; i<n && !divisible; i++) { | ||
| randBigInt_(rpprb,k,0); | ||
| while(!greater(ans,rpprb)) //pick a random rpprb that's < ans | ||
| randBigInt_(rpprb,k,0); | ||
| if (!millerRabin(ans,rpprb)) | ||
| divisible=1; | ||
| } | ||
| //do n rounds of Miller Rabin, with random bases less than ans | ||
| for (i=0; i<n && !divisible; i++) { | ||
| randBigInt_(rpprb,k,0); | ||
| while(!greater(ans,rpprb)) //pick a random rpprb that's < ans | ||
| randBigInt_(rpprb,k,0); | ||
| if (!millerRabin(ans,rpprb)) | ||
| divisible=1; | ||
| if(!divisible) | ||
| return ans; | ||
| } | ||
| } | ||
| if(!divisible) | ||
| return ans; | ||
| } | ||
| } | ||
| //return a new bigInt equal to (x mod n) for bigInts x and n. | ||
| function mod(x,n) { | ||
| var ans=dup(x); | ||
| mod_(ans,n); | ||
| return trim(ans,1); | ||
| } | ||
| //return a new bigInt equal to (x mod n) for bigInts x and n. | ||
| function mod(x,n) { | ||
| var ans=dup(x); | ||
| mod_(ans,n); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x+n) where x is a bigInt and n is an integer. | ||
| function addInt(x,n) { | ||
| var ans=expand(x,x.length+1); | ||
| addInt_(ans,n); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x+n) where x is a bigInt and n is an integer. | ||
| function addInt(x,n) { | ||
| var ans=expand(x,x.length+1); | ||
| addInt_(ans,n); | ||
| return trim(ans,1); | ||
| } | ||
| //return x*y for bigInts x and y. This is faster when y<x. | ||
| function mult(x,y) { | ||
| var ans=expand(x,x.length+y.length); | ||
| mult_(ans,y); | ||
| return trim(ans,1); | ||
| } | ||
| //return x*y for bigInts x and y. This is faster when y<x. | ||
| function mult(x,y) { | ||
| var ans=expand(x,x.length+y.length); | ||
| mult_(ans,y); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n. | ||
| function powMod(x,y,n) { | ||
| var ans=expand(x,n.length); | ||
| powMod_(ans,trim(y,2),trim(n,2),0); //this should work without the trim, but doesn't | ||
| return trim(ans,1); | ||
| } | ||
| //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n. | ||
| function powMod(x,y,n) { | ||
| var ans=expand(x,n.length); | ||
| powMod_(ans,trim(y,2),trim(n,2),0); //this should work without the trim, but doesn't | ||
| return trim(ans,1); | ||
| } | ||
| //return (x-y) for bigInts x and y. Negative answers will be 2s complement | ||
| function sub(x,y) { | ||
| var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); | ||
| sub_(ans,y); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x-y) for bigInts x and y. Negative answers will be 2s complement | ||
| function sub(x,y) { | ||
| var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); | ||
| sub_(ans,y); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x+y) for bigInts x and y. | ||
| function add(x,y) { | ||
| var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); | ||
| add_(ans,y); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x+y) for bigInts x and y. | ||
| function add(x,y) { | ||
| var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); | ||
| add_(ans,y); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null | ||
| function inverseMod(x,n) { | ||
| var ans=expand(x,n.length); | ||
| var s; | ||
| s=inverseMod_(ans,n); | ||
| return s ? trim(ans,1) : null; | ||
| } | ||
| //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null | ||
| function inverseMod(x,n) { | ||
| var ans=expand(x,n.length); | ||
| var s; | ||
| s=inverseMod_(ans,n); | ||
| return s ? trim(ans,1) : null; | ||
| } | ||
| //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x. | ||
| function multMod(x,y,n) { | ||
| var ans=expand(x,n.length); | ||
| multMod_(ans,y,n); | ||
| return trim(ans,1); | ||
| } | ||
| //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x. | ||
| function multMod(x,y,n) { | ||
| var ans=expand(x,n.length); | ||
| multMod_(ans,y,n); | ||
| return trim(ans,1); | ||
| } | ||
| //generate a k-bit true random prime using Maurer's algorithm, | ||
| //and put it into ans. The bigInt ans must be large enough to hold it. | ||
| function randTruePrime_(ans,k) { | ||
| var c,m,pm,dd,j,r,B,divisible,z,zz,recSize; | ||
| //generate a k-bit true random prime using Maurer's algorithm, | ||
| //and put it into ans. The bigInt ans must be large enough to hold it. | ||
| function randTruePrime_(ans,k) { | ||
| var c,m,pm,dd,j,r,B,divisible,z,zz,recSize; | ||
| if (primes.length==0) | ||
| primes=findPrimes(30000); //check for divisibility by primes <=30000 | ||
| if (primes.length==0) | ||
| primes=findPrimes(30000); //check for divisibility by primes <=30000 | ||
| if (pows.length==0) { | ||
| pows=new Array(512); | ||
| for (j=0;j<512;j++) { | ||
| pows[j]=Math.pow(2,j/511.-1.); | ||
| } | ||
| } | ||
| if (pows.length==0) { | ||
| pows=new Array(512); | ||
| for (j=0;j<512;j++) { | ||
| pows[j]=Math.pow(2,j/511.-1.); | ||
| } | ||
| } | ||
| //c and m should be tuned for a particular machine and value of k, to maximize speed | ||
| c=0.1; //c=0.1 in HAC | ||
| m=20; //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits | ||
| var recLimit=20; //stop recursion when k <=recLimit. Must have recLimit >= 2 | ||
| //c and m should be tuned for a particular machine and value of k, to maximize speed | ||
| c=0.1; //c=0.1 in HAC | ||
| m=20; //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits | ||
| recLimit=20; //stop recursion when k <=recLimit. Must have recLimit >= 2 | ||
| if (s_i2.length!=ans.length) { | ||
| s_i2=dup(ans); | ||
| s_R =dup(ans); | ||
| s_n1=dup(ans); | ||
| s_r2=dup(ans); | ||
| s_d =dup(ans); | ||
| s_x1=dup(ans); | ||
| s_x2=dup(ans); | ||
| s_b =dup(ans); | ||
| s_n =dup(ans); | ||
| s_i =dup(ans); | ||
| s_rm=dup(ans); | ||
| s_q =dup(ans); | ||
| s_a =dup(ans); | ||
| s_aa=dup(ans); | ||
| } | ||
| if (s_i2.length!=ans.length) { | ||
| s_i2=dup(ans); | ||
| s_R =dup(ans); | ||
| s_n1=dup(ans); | ||
| s_r2=dup(ans); | ||
| s_d =dup(ans); | ||
| s_x1=dup(ans); | ||
| s_x2=dup(ans); | ||
| s_b =dup(ans); | ||
| s_n =dup(ans); | ||
| s_i =dup(ans); | ||
| s_rm=dup(ans); | ||
| s_q =dup(ans); | ||
| s_a =dup(ans); | ||
| s_aa=dup(ans); | ||
| } | ||
| if (k <= recLimit) { //generate small random primes by trial division up to its square root | ||
| pm=(1<<((k+2)>>1))-1; //pm is binary number with all ones, just over sqrt(2^k) | ||
| copyInt_(ans,0); | ||
| for (dd=1;dd;) { | ||
| dd=0; | ||
| ans[0]= 1 | (1<<(k-1)) | Math.floor(Math.random()*(1<<k)); //random, k-bit, odd integer, with msb 1 | ||
| for (j=1;(j<primes.length) && ((primes[j]&pm)==primes[j]);j++) { //trial division by all primes 3...sqrt(2^k) | ||
| if (0==(ans[0]%primes[j])) { | ||
| dd=1; | ||
| break; | ||
| if (k <= recLimit) { //generate small random primes by trial division up to its square root | ||
| pm=(1<<((k+2)>>1))-1; //pm is binary number with all ones, just over sqrt(2^k) | ||
| copyInt_(ans,0); | ||
| for (dd=1;dd;) { | ||
| dd=0; | ||
| ans[0]= 1 | (1<<(k-1)) | Math.floor(trueRandom()*(1<<k)); //random, k-bit, odd integer, with msb 1 | ||
| for (j=1;(j<primes.length) && ((primes[j]&pm)==primes[j]);j++) { //trial division by all primes 3...sqrt(2^k) | ||
| if (0==(ans[0]%primes[j])) { | ||
| dd=1; | ||
| break; | ||
| } | ||
| } | ||
| } | ||
| carry_(ans); | ||
| return; | ||
| } | ||
| } | ||
| carry_(ans); | ||
| return; | ||
| } | ||
| B=c*k*k; //try small primes up to B (or all the primes[] array if the largest is less than B). | ||
| if (k>2*m) //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits | ||
| for (r=1; k-k*r<=m; ) | ||
| r=pows[Math.floor(Math.random()*512)]; //r=Math.pow(2,Math.random()-1); | ||
| else | ||
| r=.5; | ||
| B=c*k*k; //try small primes up to B (or all the primes[] array if the largest is less than B). | ||
| if (k>2*m) //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits | ||
| for (r=1; k-k*r<=m; ) | ||
| r=pows[Math.floor(trueRandom()*512)]; //r=Math.pow(2,Math.random()-1); | ||
| else | ||
| r=.5; | ||
| //simulation suggests the more complex algorithm using r=.333 is only slightly faster. | ||
| //simulation suggests the more complex algorithm using r=.333 is only slightly faster. | ||
| recSize=Math.floor(r*k)+1; | ||
| recSize=Math.floor(r*k)+1; | ||
| randTruePrime_(s_q,recSize); | ||
| copyInt_(s_i2,0); | ||
| s_i2[Math.floor((k-2)/bpe)] |= (1<<((k-2)%bpe)); //s_i2=2^(k-2) | ||
| divide_(s_i2,s_q,s_i,s_rm); //s_i=floor((2^(k-1))/(2q)) | ||
| randTruePrime_(s_q,recSize); | ||
| copyInt_(s_i2,0); | ||
| s_i2[Math.floor((k-2)/bpe)] |= (1<<((k-2)%bpe)); //s_i2=2^(k-2) | ||
| divide_(s_i2,s_q,s_i,s_rm); //s_i=floor((2^(k-1))/(2q)) | ||
| z=bitSize(s_i); | ||
| z=bitSize(s_i); | ||
| for (;;) { | ||
| for (;;) { //generate z-bit numbers until one falls in the range [0,s_i-1] | ||
| randBigInt_(s_R,z,0); | ||
| if (greater(s_i,s_R)) | ||
| break; | ||
| } //now s_R is in the range [0,s_i-1] | ||
| addInt_(s_R,1); //now s_R is in the range [1,s_i] | ||
| add_(s_R,s_i); //now s_R is in the range [s_i+1,2*s_i] | ||
| for (;;) { | ||
| for (;;) { //generate z-bit numbers until one falls in the range [0,s_i-1] | ||
| randBigInt_(s_R,z,0); | ||
| if (greater(s_i,s_R)) | ||
| break; | ||
| } //now s_R is in the range [0,s_i-1] | ||
| addInt_(s_R,1); //now s_R is in the range [1,s_i] | ||
| add_(s_R,s_i); //now s_R is in the range [s_i+1,2*s_i] | ||
| copy_(s_n,s_q); | ||
| mult_(s_n,s_R); | ||
| multInt_(s_n,2); | ||
| addInt_(s_n,1); //s_n=2*s_R*s_q+1 | ||
| copy_(s_n,s_q); | ||
| mult_(s_n,s_R); | ||
| multInt_(s_n,2); | ||
| addInt_(s_n,1); //s_n=2*s_R*s_q+1 | ||
| copy_(s_r2,s_R); | ||
| multInt_(s_r2,2); //s_r2=2*s_R | ||
| copy_(s_r2,s_R); | ||
| multInt_(s_r2,2); //s_r2=2*s_R | ||
| //check s_n for divisibility by small primes up to B | ||
| for (divisible=0,j=0; (j<primes.length) && (primes[j]<B); j++) | ||
| if (modInt(s_n,primes[j])==0 && !equalsInt(s_n,primes[j])) { | ||
| divisible=1; | ||
| break; | ||
| } | ||
| //check s_n for divisibility by small primes up to B | ||
| for (divisible=0,j=0; (j<primes.length) && (primes[j]<B); j++) | ||
| if (modInt(s_n,primes[j])==0 && !equalsInt(s_n,primes[j])) { | ||
| divisible=1; | ||
| break; | ||
| } | ||
| if (!divisible) //if it passes small primes check, then try a single Miller-Rabin base 2 | ||
| if (!millerRabinInt(s_n,2)) //this line represents 75% of the total runtime for randTruePrime_ | ||
| divisible=1; | ||
| if (!divisible) //if it passes small primes check, then try a single Miller-Rabin base 2 | ||
| if (!millerRabinInt(s_n,2)) //this line represents 75% of the total runtime for randTruePrime_ | ||
| divisible=1; | ||
| if (!divisible) { //if it passes that test, continue checking s_n | ||
| addInt_(s_n,-3); | ||
| for (j=s_n.length-1;(s_n[j]==0) && (j>0); j--); //strip leading zeros | ||
| for (zz=0,w=s_n[j]; w; (w>>=1),zz++); | ||
| zz+=bpe*j; //zz=number of bits in s_n, ignoring leading zeros | ||
| for (;;) { //generate z-bit numbers until one falls in the range [0,s_n-1] | ||
| randBigInt_(s_a,zz,0); | ||
| if (greater(s_n,s_a)) | ||
| break; | ||
| } //now s_a is in the range [0,s_n-1] | ||
| addInt_(s_n,3); //now s_a is in the range [0,s_n-4] | ||
| addInt_(s_a,2); //now s_a is in the range [2,s_n-2] | ||
| copy_(s_b,s_a); | ||
| copy_(s_n1,s_n); | ||
| addInt_(s_n1,-1); | ||
| powMod_(s_b,s_n1,s_n); //s_b=s_a^(s_n-1) modulo s_n | ||
| addInt_(s_b,-1); | ||
| if (isZero(s_b)) { | ||
| copy_(s_b,s_a); | ||
| powMod_(s_b,s_r2,s_n); | ||
| addInt_(s_b,-1); | ||
| copy_(s_aa,s_n); | ||
| copy_(s_d,s_b); | ||
| GCD_(s_d,s_n); //if s_b and s_n are relatively prime, then s_n is a prime | ||
| if (equalsInt(s_d,1)) { | ||
| copy_(ans,s_aa); | ||
| return; //if we've made it this far, then s_n is absolutely guaranteed to be prime | ||
| if (!divisible) { //if it passes that test, continue checking s_n | ||
| addInt_(s_n,-3); | ||
| for (j=s_n.length-1;(s_n[j]==0) && (j>0); j--); //strip leading zeros | ||
| for (zz=0,w=s_n[j]; w; (w>>=1),zz++); | ||
| zz+=bpe*j; //zz=number of bits in s_n, ignoring leading zeros | ||
| for (;;) { //generate z-bit numbers until one falls in the range [0,s_n-1] | ||
| randBigInt_(s_a,zz,0); | ||
| if (greater(s_n,s_a)) | ||
| break; | ||
| } //now s_a is in the range [0,s_n-1] | ||
| addInt_(s_n,3); //now s_a is in the range [0,s_n-4] | ||
| addInt_(s_a,2); //now s_a is in the range [2,s_n-2] | ||
| copy_(s_b,s_a); | ||
| copy_(s_n1,s_n); | ||
| addInt_(s_n1,-1); | ||
| powMod_(s_b,s_n1,s_n); //s_b=s_a^(s_n-1) modulo s_n | ||
| addInt_(s_b,-1); | ||
| if (isZero(s_b)) { | ||
| copy_(s_b,s_a); | ||
| powMod_(s_b,s_r2,s_n); | ||
| addInt_(s_b,-1); | ||
| copy_(s_aa,s_n); | ||
| copy_(s_d,s_b); | ||
| GCD_(s_d,s_n); //if s_b and s_n are relatively prime, then s_n is a prime | ||
| if (equalsInt(s_d,1)) { | ||
| copy_(ans,s_aa); | ||
| return; //if we've made it this far, then s_n is absolutely guaranteed to be prime | ||
| } | ||
| } | ||
| } | ||
| } | ||
| } | ||
| } | ||
| } | ||
| //Return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1. | ||
| function randBigInt(n,s) { | ||
| var a,b; | ||
| a=Math.floor((n-1)/bpe)+2; //# array elements to hold the BigInt with a leading 0 element | ||
| b=int2bigInt(0,0,a); | ||
| randBigInt_(b,n,s); | ||
| return b; | ||
| } | ||
| //Return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1. | ||
| function randBigInt(n,s) { | ||
| var a,b; | ||
| a=Math.floor((n-1)/bpe)+2; //# array elements to hold the BigInt with a leading 0 element | ||
| b=int2bigInt(0,0,a); | ||
| randBigInt_(b,n,s); | ||
| return b; | ||
| } | ||
| //Set b to an n-bit random BigInt. If s=1, then the most significant of those n bits is set to 1. | ||
| //Array b must be big enough to hold the result. Must have n>=1 | ||
| function randBigInt_(b,n,s) { | ||
| var i,a; | ||
| for (i=0;i<b.length;i++) | ||
| b[i]=0; | ||
| a=Math.floor((n-1)/bpe)+1; //# array elements to hold the BigInt | ||
| for (i=0;i<a;i++) { | ||
| b[i]=Math.floor(Math.random()*(1<<(bpe-1))); | ||
| } | ||
| b[a-1] &= (2<<((n-1)%bpe))-1; | ||
| if (s==1) | ||
| b[a-1] |= (1<<((n-1)%bpe)); | ||
| } | ||
| //Return the greatest common divisor of bigInts x and y (each with same number of elements). | ||
| function GCD(x,y) { | ||
| var xc,yc; | ||
| xc=dup(x); | ||
| yc=dup(y); | ||
| GCD_(xc,yc); | ||
| return xc; | ||
| } | ||
| //set x to the greatest common divisor of bigInts x and y (each with same number of elements). | ||
| //y is destroyed. | ||
| function GCD_(x,y) { | ||
| var i,xp,yp,A,B,C,D,q,sing; | ||
| if (T.length!=x.length) | ||
| T=dup(x); | ||
| sing=1; | ||
| while (sing) { //while y has nonzero elements other than y[0] | ||
| sing=0; | ||
| for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0 | ||
| if (y[i]) { | ||
| sing=1; | ||
| break; | ||
| //Set b to an n-bit random BigInt. If s=1, then the most significant of those n bits is set to 1. | ||
| //Array b must be big enough to hold the result. Must have n>=1 | ||
| function randBigInt_(b,n,s) { | ||
| var i,a; | ||
| for (i=0;i<b.length;i++) | ||
| b[i]=0; | ||
| a=Math.floor((n-1)/bpe)+1; //# array elements to hold the BigInt | ||
| for (i=0;i<a;i++) { | ||
| b[i]=Math.floor(trueRandom()*(1<<(bpe-1))); | ||
| } | ||
| if (!sing) break; //quit when y all zero elements except possibly y[0] | ||
| b[a-1] &= (2<<((n-1)%bpe))-1; | ||
| if (s==1) | ||
| b[a-1] |= (1<<((n-1)%bpe)); | ||
| } | ||
| for (i=x.length;!x[i] && i>=0;i--); //find most significant element of x | ||
| xp=x[i]; | ||
| yp=y[i]; | ||
| A=1; B=0; C=0; D=1; | ||
| while ((yp+C) && (yp+D)) { | ||
| q =Math.floor((xp+A)/(yp+C)); | ||
| qp=Math.floor((xp+B)/(yp+D)); | ||
| if (q!=qp) | ||
| break; | ||
| 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) | ||
| t= B-q*D; B=D; D=t; | ||
| t=xp-q*yp; xp=yp; yp=t; | ||
| //Return the greatest common divisor of bigInts x and y (each with same number of elements). | ||
| function GCD(x,y) { | ||
| var xc,yc; | ||
| xc=dup(x); | ||
| yc=dup(y); | ||
| GCD_(xc,yc); | ||
| return xc; | ||
| } | ||
| if (B) { | ||
| copy_(T,x); | ||
| linComb_(x,y,A,B); //x=A*x+B*y | ||
| linComb_(y,T,D,C); //y=D*y+C*T | ||
| } else { | ||
| mod_(x,y); | ||
| copy_(T,x); | ||
| copy_(x,y); | ||
| copy_(y,T); | ||
| } | ||
| } | ||
| if (y[0]==0) | ||
| return; | ||
| t=modInt(x,y[0]); | ||
| copyInt_(x,y[0]); | ||
| y[0]=t; | ||
| while (y[0]) { | ||
| x[0]%=y[0]; | ||
| t=x[0]; x[0]=y[0]; y[0]=t; | ||
| } | ||
| } | ||
| //do x=x**(-1) mod n, for bigInts x and n. | ||
| //If no inverse exists, it sets x to zero and returns 0, else it returns 1. | ||
| //The x array must be at least as large as the n array. | ||
| function inverseMod_(x,n) { | ||
| var k=1+2*Math.max(x.length,n.length); | ||
| //set x to the greatest common divisor of bigInts x and y (each with same number of elements). | ||
| //y is destroyed. | ||
| function GCD_(x,y) { | ||
| var i,xp,yp,A,B,C,D,q,sing; | ||
| if (T.length!=x.length) | ||
| T=dup(x); | ||
| if(!(x[0]&1) && !(n[0]&1)) { //if both inputs are even, then inverse doesn't exist | ||
| copyInt_(x,0); | ||
| return 0; | ||
| } | ||
| sing=1; | ||
| while (sing) { //while y has nonzero elements other than y[0] | ||
| sing=0; | ||
| for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0 | ||
| if (y[i]) { | ||
| sing=1; | ||
| break; | ||
| } | ||
| if (!sing) break; //quit when y all zero elements except possibly y[0] | ||
| if (eg_u.length!=k) { | ||
| eg_u=new Array(k); | ||
| eg_v=new Array(k); | ||
| eg_A=new Array(k); | ||
| eg_B=new Array(k); | ||
| eg_C=new Array(k); | ||
| eg_D=new Array(k); | ||
| } | ||
| copy_(eg_u,x); | ||
| copy_(eg_v,n); | ||
| copyInt_(eg_A,1); | ||
| copyInt_(eg_B,0); | ||
| copyInt_(eg_C,0); | ||
| copyInt_(eg_D,1); | ||
| for (;;) { | ||
| while(!(eg_u[0]&1)) { //while eg_u is even | ||
| halve_(eg_u); | ||
| if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if eg_A==eg_B==0 mod 2 | ||
| halve_(eg_A); | ||
| halve_(eg_B); | ||
| } else { | ||
| add_(eg_A,n); halve_(eg_A); | ||
| sub_(eg_B,x); halve_(eg_B); | ||
| for (i=x.length;!x[i] && i>=0;i--); //find most significant element of x | ||
| xp=x[i]; | ||
| yp=y[i]; | ||
| A=1; B=0; C=0; D=1; | ||
| while ((yp+C) && (yp+D)) { | ||
| q =Math.floor((xp+A)/(yp+C)); | ||
| var qp=Math.floor((xp+B)/(yp+D)); | ||
| if (q!=qp) | ||
| break; | ||
| 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) | ||
| t= B-q*D; B=D; D=t; | ||
| t=xp-q*yp; xp=yp; yp=t; | ||
| } | ||
| if (B) { | ||
| copy_(T,x); | ||
| linComb_(x,y,A,B); //x=A*x+B*y | ||
| linComb_(y,T,D,C); //y=D*y+C*T | ||
| } else { | ||
| mod_(x,y); | ||
| copy_(T,x); | ||
| copy_(x,y); | ||
| copy_(y,T); | ||
| } | ||
| } | ||
| } | ||
| while (!(eg_v[0]&1)) { //while eg_v is even | ||
| halve_(eg_v); | ||
| if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if eg_C==eg_D==0 mod 2 | ||
| halve_(eg_C); | ||
| halve_(eg_D); | ||
| } else { | ||
| add_(eg_C,n); halve_(eg_C); | ||
| sub_(eg_D,x); halve_(eg_D); | ||
| if (y[0]==0) | ||
| return; | ||
| t=modInt(x,y[0]); | ||
| copyInt_(x,y[0]); | ||
| y[0]=t; | ||
| while (y[0]) { | ||
| x[0]%=y[0]; | ||
| t=x[0]; x[0]=y[0]; y[0]=t; | ||
| } | ||
| } | ||
| if (!greater(eg_v,eg_u)) { //eg_v <= eg_u | ||
| sub_(eg_u,eg_v); | ||
| sub_(eg_A,eg_C); | ||
| sub_(eg_B,eg_D); | ||
| } else { //eg_v > eg_u | ||
| sub_(eg_v,eg_u); | ||
| sub_(eg_C,eg_A); | ||
| sub_(eg_D,eg_B); | ||
| } | ||
| //do x=x**(-1) mod n, for bigInts x and n. | ||
| //If no inverse exists, it sets x to zero and returns 0, else it returns 1. | ||
| //The x array must be at least as large as the n array. | ||
| function inverseMod_(x,n) { | ||
| var k=1+2*Math.max(x.length,n.length); | ||
| if (equalsInt(eg_u,0)) { | ||
| if (negative(eg_C)) //make sure answer is nonnegative | ||
| add_(eg_C,n); | ||
| copy_(x,eg_C); | ||
| if (!equalsInt(eg_v,1)) { //if GCD_(x,n)!=1, then there is no inverse | ||
| if(!(x[0]&1) && !(n[0]&1)) { //if both inputs are even, then inverse doesn't exist | ||
| copyInt_(x,0); | ||
| return 0; | ||
| } | ||
| return 1; | ||
| } | ||
| } | ||
| } | ||
| //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse | ||
| function inverseModInt(x,n) { | ||
| var a=1,b=0,t; | ||
| for (;;) { | ||
| if (x==1) return a; | ||
| if (x==0) return 0; | ||
| b-=a*Math.floor(n/x); | ||
| n%=x; | ||
| if (eg_u.length!=k) { | ||
| eg_u=new Array(k); | ||
| eg_v=new Array(k); | ||
| eg_A=new Array(k); | ||
| eg_B=new Array(k); | ||
| eg_C=new Array(k); | ||
| eg_D=new Array(k); | ||
| } | ||
| if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to += | ||
| if (n==0) return 0; | ||
| a-=b*Math.floor(x/n); | ||
| x%=n; | ||
| } | ||
| } | ||
| copy_(eg_u,x); | ||
| copy_(eg_v,n); | ||
| copyInt_(eg_A,1); | ||
| copyInt_(eg_B,0); | ||
| copyInt_(eg_C,0); | ||
| copyInt_(eg_D,1); | ||
| for (;;) { | ||
| while(!(eg_u[0]&1)) { //while eg_u is even | ||
| halve_(eg_u); | ||
| if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if eg_A==eg_B==0 mod 2 | ||
| halve_(eg_A); | ||
| halve_(eg_B); | ||
| } else { | ||
| add_(eg_A,n); halve_(eg_A); | ||
| sub_(eg_B,x); halve_(eg_B); | ||
| } | ||
| } | ||
| //this deprecated function is for backward compatibility only. | ||
| function inverseModInt_(x,n) { | ||
| return inverseModInt(x,n); | ||
| } | ||
| while (!(eg_v[0]&1)) { //while eg_v is even | ||
| halve_(eg_v); | ||
| if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if eg_C==eg_D==0 mod 2 | ||
| halve_(eg_C); | ||
| halve_(eg_D); | ||
| } else { | ||
| add_(eg_C,n); halve_(eg_C); | ||
| sub_(eg_D,x); halve_(eg_D); | ||
| } | ||
| } | ||
| if (!greater(eg_v,eg_u)) { //eg_v <= eg_u | ||
| sub_(eg_u,eg_v); | ||
| sub_(eg_A,eg_C); | ||
| sub_(eg_B,eg_D); | ||
| } else { //eg_v > eg_u | ||
| sub_(eg_v,eg_u); | ||
| sub_(eg_C,eg_A); | ||
| sub_(eg_D,eg_B); | ||
| } | ||
| //Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that: | ||
| // v = GCD_(x,y) = a*x-b*y | ||
| //The bigInts v, a, b, must have exactly as many elements as the larger of x and y. | ||
| function eGCD_(x,y,v,a,b) { | ||
| var g=0; | ||
| var k=Math.max(x.length,y.length); | ||
| if (eg_u.length!=k) { | ||
| eg_u=new Array(k); | ||
| eg_A=new Array(k); | ||
| eg_B=new Array(k); | ||
| eg_C=new Array(k); | ||
| eg_D=new Array(k); | ||
| } | ||
| while(!(x[0]&1) && !(y[0]&1)) { //while x and y both even | ||
| halve_(x); | ||
| halve_(y); | ||
| g++; | ||
| } | ||
| copy_(eg_u,x); | ||
| copy_(v,y); | ||
| copyInt_(eg_A,1); | ||
| copyInt_(eg_B,0); | ||
| copyInt_(eg_C,0); | ||
| copyInt_(eg_D,1); | ||
| for (;;) { | ||
| while(!(eg_u[0]&1)) { //while u is even | ||
| halve_(eg_u); | ||
| if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2 | ||
| halve_(eg_A); | ||
| halve_(eg_B); | ||
| } else { | ||
| add_(eg_A,y); halve_(eg_A); | ||
| sub_(eg_B,x); halve_(eg_B); | ||
| if (equalsInt(eg_u,0)) { | ||
| while (negative(eg_C)) //make sure answer is nonnegative | ||
| add_(eg_C,n); | ||
| copy_(x,eg_C); | ||
| if (!equalsInt(eg_v,1)) { //if GCD_(x,n)!=1, then there is no inverse | ||
| copyInt_(x,0); | ||
| return 0; | ||
| } | ||
| return 1; | ||
| } | ||
| } | ||
| } | ||
| while (!(v[0]&1)) { //while v is even | ||
| halve_(v); | ||
| if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2 | ||
| halve_(eg_C); | ||
| halve_(eg_D); | ||
| } else { | ||
| add_(eg_C,y); halve_(eg_C); | ||
| sub_(eg_D,x); halve_(eg_D); | ||
| //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse | ||
| function inverseModInt(x,n) { | ||
| var a=1,b=0,t; | ||
| for (;;) { | ||
| if (x==1) return a; | ||
| if (x==0) return 0; | ||
| b-=a*Math.floor(n/x); | ||
| n%=x; | ||
| if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to += | ||
| if (n==0) return 0; | ||
| a-=b*Math.floor(x/n); | ||
| x%=n; | ||
| } | ||
| } | ||
| if (!greater(v,eg_u)) { //v<=u | ||
| sub_(eg_u,v); | ||
| sub_(eg_A,eg_C); | ||
| sub_(eg_B,eg_D); | ||
| } else { //v>u | ||
| sub_(v,eg_u); | ||
| sub_(eg_C,eg_A); | ||
| sub_(eg_D,eg_B); | ||
| //this deprecated function is for backward compatibility only. | ||
| function inverseModInt_(x,n) { | ||
| return inverseModInt(x,n); | ||
| } | ||
| if (equalsInt(eg_u,0)) { | ||
| if (negative(eg_C)) { //make sure a (C)is nonnegative | ||
| add_(eg_C,y); | ||
| sub_(eg_D,x); | ||
| //Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that: | ||
| // v = GCD_(x,y) = a*x-b*y | ||
| //The bigInts v, a, b, must have exactly as many elements as the larger of x and y. | ||
| function eGCD_(x,y,v,a,b) { | ||
| var g=0; | ||
| var k=Math.max(x.length,y.length); | ||
| if (eg_u.length!=k) { | ||
| eg_u=new Array(k); | ||
| eg_A=new Array(k); | ||
| eg_B=new Array(k); | ||
| eg_C=new Array(k); | ||
| eg_D=new Array(k); | ||
| } | ||
| multInt_(eg_D,-1); ///make sure b (D) is nonnegative | ||
| copy_(a,eg_C); | ||
| copy_(b,eg_D); | ||
| leftShift_(v,g); | ||
| return; | ||
| while(!(x[0]&1) && !(y[0]&1)) { //while x and y both even | ||
| halve_(x); | ||
| halve_(y); | ||
| g++; | ||
| } | ||
| copy_(eg_u,x); | ||
| copy_(v,y); | ||
| copyInt_(eg_A,1); | ||
| copyInt_(eg_B,0); | ||
| copyInt_(eg_C,0); | ||
| copyInt_(eg_D,1); | ||
| for (;;) { | ||
| while(!(eg_u[0]&1)) { //while u is even | ||
| halve_(eg_u); | ||
| if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2 | ||
| halve_(eg_A); | ||
| halve_(eg_B); | ||
| } else { | ||
| add_(eg_A,y); halve_(eg_A); | ||
| sub_(eg_B,x); halve_(eg_B); | ||
| } | ||
| } | ||
| while (!(v[0]&1)) { //while v is even | ||
| halve_(v); | ||
| if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2 | ||
| halve_(eg_C); | ||
| halve_(eg_D); | ||
| } else { | ||
| add_(eg_C,y); halve_(eg_C); | ||
| sub_(eg_D,x); halve_(eg_D); | ||
| } | ||
| } | ||
| if (!greater(v,eg_u)) { //v<=u | ||
| sub_(eg_u,v); | ||
| sub_(eg_A,eg_C); | ||
| sub_(eg_B,eg_D); | ||
| } else { //v>u | ||
| sub_(v,eg_u); | ||
| sub_(eg_C,eg_A); | ||
| sub_(eg_D,eg_B); | ||
| } | ||
| if (equalsInt(eg_u,0)) { | ||
| while (negative(eg_C)) { //make sure a (C) is nonnegative | ||
| add_(eg_C,y); | ||
| sub_(eg_D,x); | ||
| } | ||
| multInt_(eg_D,-1); ///make sure b (D) is nonnegative | ||
| copy_(a,eg_C); | ||
| copy_(b,eg_D); | ||
| leftShift_(v,g); | ||
| return; | ||
| } | ||
| } | ||
| } | ||
| } | ||
| } | ||
| //is bigInt x negative? | ||
| function negative(x) { | ||
| return ((x[x.length-1]>>(bpe-1))&1); | ||
| } | ||
| //is bigInt x negative? | ||
| function negative(x) { | ||
| return ((x[x.length-1]>>(bpe-1))&1); | ||
| } | ||
| //is (x << (shift*bpe)) > y? | ||
| //x and y are nonnegative bigInts | ||
| //shift is a nonnegative integer | ||
| function greaterShift(x,y,shift) { | ||
| var i, kx=x.length, ky=y.length; | ||
| k=((kx+shift)<ky) ? (kx+shift) : ky; | ||
| for (i=ky-1-shift; i<kx && i>=0; i++) | ||
| if (x[i]>0) | ||
| return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger | ||
| for (i=kx-1+shift; i<ky; i++) | ||
| if (y[i]>0) | ||
| return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger | ||
| for (i=k-1; i>=shift; i--) | ||
| if (x[i-shift]>y[i]) return 1; | ||
| else if (x[i-shift]<y[i]) return 0; | ||
| return 0; | ||
| } | ||
| //is (x << (shift*bpe)) > y? | ||
| //x and y are nonnegative bigInts | ||
| //shift is a nonnegative integer | ||
| function greaterShift(x,y,shift) { | ||
| var i, kx=x.length, ky=y.length; | ||
| var k=((kx+shift)<ky) ? (kx+shift) : ky; | ||
| for (i=ky-1-shift; i<kx && i>=0; i++) | ||
| if (x[i]>0) | ||
| return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger | ||
| for (i=kx-1+shift; i<ky; i++) | ||
| if (y[i]>0) | ||
| return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger | ||
| for (i=k-1; i>=shift; i--) | ||
| if (x[i-shift]>y[i]) return 1; | ||
| else if (x[i-shift]<y[i]) return 0; | ||
| return 0; | ||
| } | ||
| //is x > y? (x and y both nonnegative) | ||
| function greater(x,y) { | ||
| var i; | ||
| var k=(x.length<y.length) ? x.length : y.length; | ||
| //is x > y? (x and y both nonnegative) | ||
| function greater(x,y) { | ||
| var i; | ||
| var k=(x.length<y.length) ? x.length : y.length; | ||
| for (i=x.length;i<y.length;i++) | ||
| if (y[i]) | ||
| return 0; //y has more digits | ||
| for (i=x.length;i<y.length;i++) | ||
| if (y[i]) | ||
| return 0; //y has more digits | ||
| for (i=y.length;i<x.length;i++) | ||
| if (x[i]) | ||
| return 1; //x has more digits | ||
| for (i=y.length;i<x.length;i++) | ||
| if (x[i]) | ||
| return 1; //x has more digits | ||
| for (i=k-1;i>=0;i--) | ||
| if (x[i]>y[i]) | ||
| return 1; | ||
| else if (x[i]<y[i]) | ||
| for (i=k-1;i>=0;i--) | ||
| if (x[i]>y[i]) | ||
| return 1; | ||
| else if (x[i]<y[i]) | ||
| return 0; | ||
| return 0; | ||
| return 0; | ||
| } | ||
| } | ||
| //divide x by y giving quotient q and remainder r. (q=floor(x/y), r=x mod y). All 4 are bigints. | ||
| //x must have at least one leading zero element. | ||
| //y must be nonzero. | ||
| //q and r must be arrays that are exactly the same length as x. (Or q can have more). | ||
| //Must have x.length >= y.length >= 2. | ||
| function divide_(x,y,q,r) { | ||
| var kx, ky; | ||
| var i,j,y1,y2,c,a,b; | ||
| copy_(r,x); | ||
| for (ky=y.length;y[ky-1]==0;ky--); //ky is number of elements in y, not including leading zeros | ||
| //divide x by y giving quotient q and remainder r. (q=floor(x/y), r=x mod y). All 4 are bigints. | ||
| //x must have at least one leading zero element. | ||
| //y must be nonzero. | ||
| //q and r must be arrays that are exactly the same length as x. (Or q can have more). | ||
| //Must have x.length >= y.length >= 2. | ||
| function divide_(x,y,q,r) { | ||
| var kx, ky; | ||
| var i,j,y1,y2,c,a,b; | ||
| copy_(r,x); | ||
| for (ky=y.length;y[ky-1]==0;ky--); //ky is number of elements in y, not including leading zeros | ||
| //normalize: ensure the most significant element of y has its highest bit set | ||
| b=y[ky-1]; | ||
| for (a=0; b; a++) | ||
| b>>=1; | ||
| a=bpe-a; //a is how many bits to shift so that the high order bit of y is leftmost in its array element | ||
| leftShift_(y,a); //multiply both by 1<<a now, then divide both by that at the end | ||
| leftShift_(r,a); | ||
| //normalize: ensure the most significant element of y has its highest bit set | ||
| b=y[ky-1]; | ||
| for (a=0; b; a++) | ||
| b>>=1; | ||
| a=bpe-a; //a is how many bits to shift so that the high order bit of y is leftmost in its array element | ||
| leftShift_(y,a); //multiply both by 1<<a now, then divide both by that at the end | ||
| leftShift_(r,a); | ||
| //Rob Visser discovered a bug: the following line was originally just before the normalization. | ||
| for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros | ||
| //Rob Visser discovered a bug: the following line was originally just before the normalization. | ||
| for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros | ||
| copyInt_(q,0); // q=0 | ||
| while (!greaterShift(y,r,kx-ky)) { // while (leftShift_(y,kx-ky) <= r) { | ||
| subShift_(r,y,kx-ky); // r=r-leftShift_(y,kx-ky) | ||
| q[kx-ky]++; // q[kx-ky]++; | ||
| } // } | ||
| copyInt_(q,0); // q=0 | ||
| while (!greaterShift(y,r,kx-ky)) { // while (leftShift_(y,kx-ky) <= r) { | ||
| subShift_(r,y,kx-ky); // r=r-leftShift_(y,kx-ky) | ||
| q[kx-ky]++; // q[kx-ky]++; | ||
| } // } | ||
| for (i=kx-1; i>=ky; i--) { | ||
| if (r[i]==y[ky-1]) | ||
| q[i-ky]=mask; | ||
| else | ||
| q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]); | ||
| for (i=kx-1; i>=ky; i--) { | ||
| if (r[i]==y[ky-1]) | ||
| q[i-ky]=mask; | ||
| else | ||
| q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]); | ||
| //The following for(;;) loop is equivalent to the commented while loop, | ||
| //except that the uncommented version avoids overflow. | ||
| //The commented loop comes from HAC, which assumes r[-1]==y[-1]==0 | ||
| // while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2]) | ||
| // q[i-ky]--; | ||
| for (;;) { | ||
| y2=(ky>1 ? y[ky-2] : 0)*q[i-ky]; | ||
| c=y2>>bpe; | ||
| y2=y2 & mask; | ||
| y1=c+q[i-ky]*y[ky-1]; | ||
| c=y1>>bpe; | ||
| y1=y1 & mask; | ||
| //The following for(;;) loop is equivalent to the commented while loop, | ||
| //except that the uncommented version avoids overflow. | ||
| //The commented loop comes from HAC, which assumes r[-1]==y[-1]==0 | ||
| // while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2]) | ||
| // q[i-ky]--; | ||
| for (;;) { | ||
| y2=(ky>1 ? y[ky-2] : 0)*q[i-ky]; | ||
| c=y2>>bpe; | ||
| y2=y2 & mask; | ||
| y1=c+q[i-ky]*y[ky-1]; | ||
| c=y1>>bpe; | ||
| y1=y1 & mask; | ||
| if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) | ||
| q[i-ky]--; | ||
| else | ||
| break; | ||
| if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) | ||
| q[i-ky]--; | ||
| else | ||
| break; | ||
| } | ||
| linCombShift_(r,y,-q[i-ky],i-ky); //r=r-q[i-ky]*leftShift_(y,i-ky) | ||
| if (negative(r)) { | ||
| addShift_(r,y,i-ky); //r=r+leftShift_(y,i-ky) | ||
| q[i-ky]--; | ||
| } | ||
| } | ||
| rightShift_(y,a); //undo the normalization step | ||
| rightShift_(r,a); //undo the normalization step | ||
| } | ||
| linCombShift_(r,y,-q[i-ky],i-ky); //r=r-q[i-ky]*leftShift_(y,i-ky) | ||
| if (negative(r)) { | ||
| addShift_(r,y,i-ky); //r=r+leftShift_(y,i-ky) | ||
| q[i-ky]--; | ||
| //do carries and borrows so each element of the bigInt x fits in bpe bits. | ||
| function carry_(x) { | ||
| var i,k,c,b; | ||
| k=x.length; | ||
| c=0; | ||
| for (i=0;i<k;i++) { | ||
| c+=x[i]; | ||
| b=0; | ||
| if (c<0) { | ||
| b=-(c>>bpe); | ||
| c+=b*radix; | ||
| } | ||
| x[i]=c & mask; | ||
| c=(c>>bpe)-b; | ||
| } | ||
| } | ||
| } | ||
| rightShift_(y,a); //undo the normalization step | ||
| rightShift_(r,a); //undo the normalization step | ||
| } | ||
| //return x mod n for bigInt x and integer n. | ||
| function modInt(x,n) { | ||
| var i,c=0; | ||
| for (i=x.length-1; i>=0; i--) | ||
| c=(c*radix+x[i])%n; | ||
| return c; | ||
| } | ||
| //do carries and borrows so each element of the bigInt x fits in bpe bits. | ||
| function carry_(x) { | ||
| var i,k,c,b; | ||
| k=x.length; | ||
| c=0; | ||
| for (i=0;i<k;i++) { | ||
| c+=x[i]; | ||
| b=0; | ||
| if (c<0) { | ||
| b=-(c>>bpe); | ||
| c+=b*radix; | ||
| //convert the integer t into a bigInt with at least the given number of bits. | ||
| //the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word) | ||
| //Pad the array with leading zeros so that it has at least minSize elements. | ||
| //There will always be at least one leading 0 element. | ||
| function int2bigInt(t,bits,minSize) { | ||
| var i,k; | ||
| k=Math.ceil(bits/bpe)+1; | ||
| k=minSize>k ? minSize : k; | ||
| var buff=new Array(k); | ||
| copyInt_(buff,t); | ||
| return buff; | ||
| } | ||
| x[i]=c & mask; | ||
| c=(c>>bpe)-b; | ||
| } | ||
| } | ||
| //return x mod n for bigInt x and integer n. | ||
| function modInt(x,n) { | ||
| var i,c=0; | ||
| for (i=x.length-1; i>=0; i--) | ||
| c=(c*radix+x[i])%n; | ||
| return c; | ||
| } | ||
| //convert the integer t into a bigInt with at least the given number of bits. | ||
| //the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word) | ||
| //Pad the array with leading zeros so that it has at least minSize elements. | ||
| //There will always be at least one leading 0 element. | ||
| function int2bigInt(t,bits,minSize) { | ||
| var i,k; | ||
| k=Math.ceil(bits/bpe)+1; | ||
| k=minSize>k ? minSize : k; | ||
| buff=new Array(k); | ||
| copyInt_(buff,t); | ||
| return buff; | ||
| } | ||
| //return the bigInt given a string representation in a given base. | ||
| //Pad the array with leading zeros so that it has at least minSize elements. | ||
| //If base=-1, then it reads in a space-separated list of array elements in decimal. | ||
| //The array will always have at least one leading zero, unless base=-1. | ||
| //return the bigInt given a string representation in a given base. | ||
| //Pad the array with leading zeros so that it has at least minSize elements. | ||
| //If base=-1, then it reads in a space-separated list of array elements in decimal. | ||
| //The array will always have at least one leading zero, unless base=-1. | ||
| function str2bigInt(s,b,minSize) { | ||
@@ -999,28 +1020,28 @@ var d, i, j, base, str, x, y, kk; | ||
| } | ||
| var k=s.length; | ||
| if (base==-1) { //comma-separated list of array elements in decimal | ||
| x=new Array(0); | ||
| for (;;) { | ||
| y=new Array(x.length+1); | ||
| for (i=0;i<x.length;i++) | ||
| y[i+1]=x[i]; | ||
| y[0]=parseInt(s,10); | ||
| x=y; | ||
| d=s.indexOf(',',0); | ||
| if (d<1) | ||
| break; | ||
| s=s.substring(d+1); | ||
| if (s.length==0) | ||
| break; | ||
| } | ||
| if (x.length<minSize) { | ||
| y=new Array(minSize); | ||
| copy_(y,x); | ||
| return y; | ||
| } | ||
| return x; | ||
| } | ||
| var k=s.length; | ||
| if (base==-1) { //comma-separated list of array elements in decimal | ||
| x=new Array(0); | ||
| for (;;) { | ||
| y=new Array(x.length+1); | ||
| for (i=0;i<x.length;i++) | ||
| y[i+1]=x[i]; | ||
| y[0]=parseInt(s,10); | ||
| x=y; | ||
| d=s.indexOf(',',0); | ||
| if (d<1) | ||
| break; | ||
| s=s.substring(d+1); | ||
| if (s.length==0) | ||
| break; | ||
| } | ||
| if (x.length<minSize) { | ||
| y=new Array(minSize); | ||
| copy_(y,x); | ||
| return y; | ||
| } | ||
| return x; | ||
| } | ||
| x=int2bigInt(0,base*k,0); | ||
| for (i=0;i<k;i++) { | ||
| x=int2bigInt(0,base*k,0); | ||
| for (i=0;i<k;i++) { | ||
| d=str.indexOf(s.substring(i,i+1),0); | ||
@@ -1031,61 +1052,61 @@ // if (base<=36 && d>=36) //convert lowercase to uppercase if base<=36 | ||
| continue; | ||
| } | ||
| multInt_(x,base); | ||
| addInt_(x,d); | ||
| } | ||
| for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros | ||
| k=minSize>k+1 ? minSize : k+1; | ||
| y=new Array(k); | ||
| kk=k<x.length ? k : x.length; | ||
| for (i=0;i<kk;i++) | ||
| y[i]=x[i]; | ||
| for (;i<k;i++) | ||
| y[i]=0; | ||
| return y; | ||
| } | ||
| multInt_(x,base); | ||
| addInt_(x,d); | ||
| } | ||
| for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros | ||
| k=minSize>k+1 ? minSize : k+1; | ||
| y=new Array(k); | ||
| kk=k<x.length ? k : x.length; | ||
| for (i=0;i<kk;i++) | ||
| y[i]=x[i]; | ||
| for (;i<k;i++) | ||
| y[i]=0; | ||
| return y; | ||
| } | ||
| //is bigint x equal to integer y? | ||
| //y must have less than bpe bits | ||
| function equalsInt(x,y) { | ||
| var i; | ||
| if (x[0]!=y) | ||
| return 0; | ||
| for (i=1;i<x.length;i++) | ||
| if (x[i]) | ||
| return 0; | ||
| return 1; | ||
| } | ||
| //is bigint x equal to integer y? | ||
| //y must have less than bpe bits | ||
| function equalsInt(x,y) { | ||
| var i; | ||
| if (x[0]!=y) | ||
| return 0; | ||
| for (i=1;i<x.length;i++) | ||
| if (x[i]) | ||
| return 0; | ||
| return 1; | ||
| } | ||
| //are bigints x and y equal? | ||
| //this works even if x and y are different lengths and have arbitrarily many leading zeros | ||
| function equals(x,y) { | ||
| var i; | ||
| var k=x.length<y.length ? x.length : y.length; | ||
| for (i=0;i<k;i++) | ||
| if (x[i]!=y[i]) | ||
| return 0; | ||
| if (x.length>y.length) { | ||
| for (;i<x.length;i++) | ||
| if (x[i]) | ||
| return 0; | ||
| } else { | ||
| for (;i<y.length;i++) | ||
| if (y[i]) | ||
| return 0; | ||
| } | ||
| return 1; | ||
| } | ||
| //are bigints x and y equal? | ||
| //this works even if x and y are different lengths and have arbitrarily many leading zeros | ||
| function equals(x,y) { | ||
| var i; | ||
| var k=x.length<y.length ? x.length : y.length; | ||
| for (i=0;i<k;i++) | ||
| if (x[i]!=y[i]) | ||
| return 0; | ||
| if (x.length>y.length) { | ||
| for (;i<x.length;i++) | ||
| if (x[i]) | ||
| return 0; | ||
| } else { | ||
| for (;i<y.length;i++) | ||
| if (y[i]) | ||
| return 0; | ||
| } | ||
| return 1; | ||
| } | ||
| //is the bigInt x equal to zero? | ||
| function isZero(x) { | ||
| var i; | ||
| for (i=0;i<x.length;i++) | ||
| if (x[i]) | ||
| return 0; | ||
| return 1; | ||
| } | ||
| //is the bigInt x equal to zero? | ||
| function isZero(x) { | ||
| var i; | ||
| for (i=0;i<x.length;i++) | ||
| if (x[i]) | ||
| return 0; | ||
| return 1; | ||
| } | ||
| //convert a bigInt into a string in a given base, from base 2 up to base 95. | ||
| //Base -1 prints the contents of the array representing the number. | ||
| //convert a bigInt into a string in a given base, from base 2 up to base 95. | ||
| //Base -1 prints the contents of the array representing the number. | ||
| function bigInt2str(x,b) { | ||
@@ -1101,459 +1122,492 @@ var i,t,base,str,s=""; | ||
| if (s6.length!=x.length) | ||
| s6=dup(x); | ||
| else | ||
| copy_(s6,x); | ||
| if (s6.length!=x.length) | ||
| s6=dup(x); | ||
| else | ||
| copy_(s6,x); | ||
| if (base==-1) { //return the list of array contents | ||
| for (i=x.length-1;i>0;i--) | ||
| s+=x[i]+','; | ||
| s+=x[0]; | ||
| } | ||
| else { //return it in the given base | ||
| while (!isZero(s6)) { | ||
| t=divInt_(s6,base); //t=s6 % base; s6=floor(s6/base); | ||
| if (base==-1) { //return the list of array contents | ||
| for (i=x.length-1;i>0;i--) | ||
| s+=x[i]+','; | ||
| s+=x[0]; | ||
| } | ||
| else { //return it in the given base | ||
| while (!isZero(s6)) { | ||
| t=divInt_(s6,base); //t=s6 % base; s6=floor(s6/base); | ||
| s=str.substring(t,t+1)+s; | ||
| } | ||
| } | ||
| if (s.length==0) | ||
| s=str[0]; | ||
| return s; | ||
| } | ||
| } | ||
| if (s.length==0) | ||
| s=str[0]; | ||
| return s; | ||
| } | ||
| //returns a duplicate of bigInt x | ||
| function dup(x) { | ||
| var i; | ||
| buff=new Array(x.length); | ||
| copy_(buff,x); | ||
| return buff; | ||
| } | ||
| //returns a duplicate of bigInt x | ||
| function dup(x) { | ||
| var i; | ||
| var buff=new Array(x.length); | ||
| copy_(buff,x); | ||
| return buff; | ||
| } | ||
| //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). | ||
| function copy_(x,y) { | ||
| var i; | ||
| var k=x.length<y.length ? x.length : y.length; | ||
| for (i=0;i<k;i++) | ||
| x[i]=y[i]; | ||
| for (i=k;i<x.length;i++) | ||
| x[i]=0; | ||
| } | ||
| //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). | ||
| function copy_(x,y) { | ||
| var i; | ||
| var k=x.length<y.length ? x.length : y.length; | ||
| for (i=0;i<k;i++) | ||
| x[i]=y[i]; | ||
| for (i=k;i<x.length;i++) | ||
| x[i]=0; | ||
| } | ||
| //do x=y on bigInt x and integer y. | ||
| function copyInt_(x,n) { | ||
| var i,c; | ||
| for (c=n,i=0;i<x.length;i++) { | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=y on bigInt x and integer y. | ||
| function copyInt_(x,n) { | ||
| var i,c; | ||
| for (c=n,i=0;i<x.length;i++) { | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x+n where x is a bigInt and n is an integer. | ||
| //x must be large enough to hold the result. | ||
| function addInt_(x,n) { | ||
| var i,k,c,b; | ||
| x[0]+=n; | ||
| k=x.length; | ||
| c=0; | ||
| for (i=0;i<k;i++) { | ||
| c+=x[i]; | ||
| b=0; | ||
| if (c<0) { | ||
| b=-(c>>bpe); | ||
| c+=b*radix; | ||
| //do x=x+n where x is a bigInt and n is an integer. | ||
| //x must be large enough to hold the result. | ||
| function addInt_(x,n) { | ||
| var i,k,c,b; | ||
| x[0]+=n; | ||
| k=x.length; | ||
| c=0; | ||
| for (i=0;i<k;i++) { | ||
| c+=x[i]; | ||
| b=0; | ||
| if (c<0) { | ||
| b=-(c>>bpe); | ||
| c+=b*radix; | ||
| } | ||
| x[i]=c & mask; | ||
| c=(c>>bpe)-b; | ||
| if (!c) return; //stop carrying as soon as the carry is zero | ||
| } | ||
| } | ||
| x[i]=c & mask; | ||
| c=(c>>bpe)-b; | ||
| if (!c) return; //stop carrying as soon as the carry is zero | ||
| } | ||
| } | ||
| //right shift bigInt x by n bits. 0 <= n < bpe. | ||
| function rightShift_(x,n) { | ||
| var i; | ||
| var k=Math.floor(n/bpe); | ||
| if (k) { | ||
| for (i=0;i<x.length-k;i++) //right shift x by k elements | ||
| x[i]=x[i+k]; | ||
| for (;i<x.length;i++) | ||
| x[i]=0; | ||
| n%=bpe; | ||
| } | ||
| for (i=0;i<x.length-1;i++) { | ||
| x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n)); | ||
| } | ||
| x[i]>>=n; | ||
| } | ||
| //right shift bigInt x by n bits. 0 <= n < bpe. | ||
| function rightShift_(x,n) { | ||
| var i; | ||
| var k=Math.floor(n/bpe); | ||
| if (k) { | ||
| for (i=0;i<x.length-k;i++) //right shift x by k elements | ||
| x[i]=x[i+k]; | ||
| for (;i<x.length;i++) | ||
| x[i]=0; | ||
| n%=bpe; | ||
| } | ||
| for (i=0;i<x.length-1;i++) { | ||
| x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n)); | ||
| } | ||
| x[i]>>=n; | ||
| } | ||
| //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement | ||
| function halve_(x) { | ||
| var i; | ||
| for (i=0;i<x.length-1;i++) { | ||
| x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1)); | ||
| } | ||
| x[i]=(x[i]>>1) | (x[i] & (radix>>1)); //most significant bit stays the same | ||
| } | ||
| //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement | ||
| function halve_(x) { | ||
| var i; | ||
| for (i=0;i<x.length-1;i++) { | ||
| x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1)); | ||
| } | ||
| x[i]=(x[i]>>1) | (x[i] & (radix>>1)); //most significant bit stays the same | ||
| } | ||
| //left shift bigInt x by n bits. | ||
| function leftShift_(x,n) { | ||
| var i; | ||
| var k=Math.floor(n/bpe); | ||
| if (k) { | ||
| for (i=x.length; i>=k; i--) //left shift x by k elements | ||
| x[i]=x[i-k]; | ||
| for (;i>=0;i--) | ||
| x[i]=0; | ||
| n%=bpe; | ||
| } | ||
| if (!n) | ||
| return; | ||
| for (i=x.length-1;i>0;i--) { | ||
| x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n))); | ||
| } | ||
| x[i]=mask & (x[i]<<n); | ||
| } | ||
| //left shift bigInt x by n bits. | ||
| function leftShift_(x,n) { | ||
| var i; | ||
| var k=Math.floor(n/bpe); | ||
| if (k) { | ||
| for (i=x.length; i>=k; i--) //left shift x by k elements | ||
| x[i]=x[i-k]; | ||
| for (;i>=0;i--) | ||
| x[i]=0; | ||
| n%=bpe; | ||
| } | ||
| if (!n) | ||
| return; | ||
| for (i=x.length-1;i>0;i--) { | ||
| x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n))); | ||
| } | ||
| x[i]=mask & (x[i]<<n); | ||
| } | ||
| //do x=x*n where x is a bigInt and n is an integer. | ||
| //x must be large enough to hold the result. | ||
| function multInt_(x,n) { | ||
| var i,k,c,b; | ||
| if (!n) | ||
| return; | ||
| k=x.length; | ||
| c=0; | ||
| for (i=0;i<k;i++) { | ||
| c+=x[i]*n; | ||
| b=0; | ||
| if (c<0) { | ||
| b=-(c>>bpe); | ||
| c+=b*radix; | ||
| //do x=x*n where x is a bigInt and n is an integer. | ||
| //x must be large enough to hold the result. | ||
| function multInt_(x,n) { | ||
| var i,k,c,b; | ||
| if (!n) | ||
| return; | ||
| k=x.length; | ||
| c=0; | ||
| for (i=0;i<k;i++) { | ||
| c+=x[i]*n; | ||
| b=0; | ||
| if (c<0) { | ||
| b=-(c>>bpe); | ||
| c+=b*radix; | ||
| } | ||
| x[i]=c & mask; | ||
| c=(c>>bpe)-b; | ||
| } | ||
| } | ||
| x[i]=c & mask; | ||
| c=(c>>bpe)-b; | ||
| } | ||
| } | ||
| //do x=floor(x/n) for bigInt x and integer n, and return the remainder | ||
| function divInt_(x,n) { | ||
| var i,r=0,s; | ||
| for (i=x.length-1;i>=0;i--) { | ||
| s=r*radix+x[i]; | ||
| x[i]=Math.floor(s/n); | ||
| r=s%n; | ||
| } | ||
| return r; | ||
| } | ||
| //do x=floor(x/n) for bigInt x and integer n, and return the remainder | ||
| function divInt_(x,n) { | ||
| var i,r=0,s; | ||
| for (i=x.length-1;i>=0;i--) { | ||
| s=r*radix+x[i]; | ||
| x[i]=Math.floor(s/n); | ||
| r=s%n; | ||
| } | ||
| return r; | ||
| } | ||
| //do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b. | ||
| //x must be large enough to hold the answer. | ||
| function linComb_(x,y,a,b) { | ||
| var i,c,k,kk; | ||
| k=x.length<y.length ? x.length : y.length; | ||
| kk=x.length; | ||
| for (c=0,i=0;i<k;i++) { | ||
| c+=a*x[i]+b*y[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;i<kk;i++) { | ||
| c+=a*x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b. | ||
| //x must be large enough to hold the answer. | ||
| function linComb_(x,y,a,b) { | ||
| var i,c,k,kk; | ||
| k=x.length<y.length ? x.length : y.length; | ||
| kk=x.length; | ||
| for (c=0,i=0;i<k;i++) { | ||
| c+=a*x[i]+b*y[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;i<kk;i++) { | ||
| c+=a*x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys. | ||
| //x must be large enough to hold the answer. | ||
| function linCombShift_(x,y,b,ys) { | ||
| var i,c,k,kk; | ||
| k=x.length<ys+y.length ? x.length : ys+y.length; | ||
| kk=x.length; | ||
| for (c=0,i=ys;i<k;i++) { | ||
| c+=x[i]+b*y[i-ys]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<kk;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys. | ||
| //x must be large enough to hold the answer. | ||
| function linCombShift_(x,y,b,ys) { | ||
| var i,c,k,kk; | ||
| k=x.length<ys+y.length ? x.length : ys+y.length; | ||
| kk=x.length; | ||
| for (c=0,i=ys;i<k;i++) { | ||
| c+=x[i]+b*y[i-ys]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<kk;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. | ||
| //x must be large enough to hold the answer. | ||
| function addShift_(x,y,ys) { | ||
| var i,c,k,kk; | ||
| k=x.length<ys+y.length ? x.length : ys+y.length; | ||
| kk=x.length; | ||
| for (c=0,i=ys;i<k;i++) { | ||
| c+=x[i]+y[i-ys]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<kk;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. | ||
| //x must be large enough to hold the answer. | ||
| function addShift_(x,y,ys) { | ||
| var i,c,k,kk; | ||
| k=x.length<ys+y.length ? x.length : ys+y.length; | ||
| kk=x.length; | ||
| for (c=0,i=ys;i<k;i++) { | ||
| c+=x[i]+y[i-ys]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<kk;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. | ||
| //x must be large enough to hold the answer. | ||
| function subShift_(x,y,ys) { | ||
| var i,c,k,kk; | ||
| k=x.length<ys+y.length ? x.length : ys+y.length; | ||
| kk=x.length; | ||
| for (c=0,i=ys;i<k;i++) { | ||
| c+=x[i]-y[i-ys]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<kk;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. | ||
| //x must be large enough to hold the answer. | ||
| function subShift_(x,y,ys) { | ||
| var i,c,k,kk; | ||
| k=x.length<ys+y.length ? x.length : ys+y.length; | ||
| kk=x.length; | ||
| for (c=0,i=ys;i<k;i++) { | ||
| c+=x[i]-y[i-ys]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<kk;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x-y for bigInts x and y. | ||
| //x must be large enough to hold the answer. | ||
| //negative answers will be 2s complement | ||
| function sub_(x,y) { | ||
| var i,c,k,kk; | ||
| k=x.length<y.length ? x.length : y.length; | ||
| for (c=0,i=0;i<k;i++) { | ||
| c+=x[i]-y[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<x.length;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x-y for bigInts x and y. | ||
| //x must be large enough to hold the answer. | ||
| //negative answers will be 2s complement | ||
| function sub_(x,y) { | ||
| var i,c,k,kk; | ||
| k=x.length<y.length ? x.length : y.length; | ||
| for (c=0,i=0;i<k;i++) { | ||
| c+=x[i]-y[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<x.length;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x+y for bigInts x and y. | ||
| //x must be large enough to hold the answer. | ||
| function add_(x,y) { | ||
| var i,c,k,kk; | ||
| k=x.length<y.length ? x.length : y.length; | ||
| for (c=0,i=0;i<k;i++) { | ||
| c+=x[i]+y[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<x.length;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x+y for bigInts x and y. | ||
| //x must be large enough to hold the answer. | ||
| function add_(x,y) { | ||
| var i,c,k,kk; | ||
| k=x.length<y.length ? x.length : y.length; | ||
| for (c=0,i=0;i<k;i++) { | ||
| c+=x[i]+y[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| for (i=k;c && i<x.length;i++) { | ||
| c+=x[i]; | ||
| x[i]=c & mask; | ||
| c>>=bpe; | ||
| } | ||
| } | ||
| //do x=x*y for bigInts x and y. This is faster when y<x. | ||
| function mult_(x,y) { | ||
| var i; | ||
| if (ss.length!=2*x.length) | ||
| ss=new Array(2*x.length); | ||
| copyInt_(ss,0); | ||
| for (i=0;i<y.length;i++) | ||
| if (y[i]) | ||
| linCombShift_(ss,x,y[i],i); //ss=1*ss+y[i]*(x<<(i*bpe)) | ||
| copy_(x,ss); | ||
| } | ||
| //do x=x*y for bigInts x and y. This is faster when y<x. | ||
| function mult_(x,y) { | ||
| var i; | ||
| if (ss.length!=2*x.length) | ||
| ss=new Array(2*x.length); | ||
| copyInt_(ss,0); | ||
| for (i=0;i<y.length;i++) | ||
| if (y[i]) | ||
| linCombShift_(ss,x,y[i],i); //ss=1*ss+y[i]*(x<<(i*bpe)) | ||
| copy_(x,ss); | ||
| } | ||
| //do x=x mod n for bigInts x and n. | ||
| function mod_(x,n) { | ||
| if (s4.length!=x.length) | ||
| s4=dup(x); | ||
| else | ||
| copy_(s4,x); | ||
| if (s5.length!=x.length) | ||
| s5=dup(x); | ||
| divide_(s4,n,s5,x); //x = remainder of s4 / n | ||
| } | ||
| //do x=x mod n for bigInts x and n. | ||
| function mod_(x,n) { | ||
| if (s4.length!=x.length) | ||
| s4=dup(x); | ||
| else | ||
| copy_(s4,x); | ||
| if (s5.length!=x.length) | ||
| s5=dup(x); | ||
| divide_(s4,n,s5,x); //x = remainder of s4 / n | ||
| } | ||
| //do x=x*y mod n for bigInts x,y,n. | ||
| //for greater speed, let y<x. | ||
| function multMod_(x,y,n) { | ||
| var i; | ||
| if (s0.length!=2*x.length) | ||
| s0=new Array(2*x.length); | ||
| copyInt_(s0,0); | ||
| for (i=0;i<y.length;i++) | ||
| if (y[i]) | ||
| linCombShift_(s0,x,y[i],i); //s0=1*s0+y[i]*(x<<(i*bpe)) | ||
| mod_(s0,n); | ||
| copy_(x,s0); | ||
| } | ||
| //do x=x*y mod n for bigInts x,y,n. | ||
| //for greater speed, let y<x. | ||
| function multMod_(x,y,n) { | ||
| var i; | ||
| if (s0.length!=2*x.length) | ||
| s0=new Array(2*x.length); | ||
| copyInt_(s0,0); | ||
| for (i=0;i<y.length;i++) | ||
| if (y[i]) | ||
| linCombShift_(s0,x,y[i],i); //s0=1*s0+y[i]*(x<<(i*bpe)) | ||
| mod_(s0,n); | ||
| copy_(x,s0); | ||
| } | ||
| //do x=x*x mod n for bigInts x,n. | ||
| function squareMod_(x,n) { | ||
| var i,j,d,c,kx,kn,k; | ||
| for (kx=x.length; kx>0 && !x[kx-1]; kx--); //ignore leading zeros in x | ||
| 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 | ||
| if (s0.length!=k) | ||
| s0=new Array(k); | ||
| copyInt_(s0,0); | ||
| for (i=0;i<kx;i++) { | ||
| c=s0[2*i]+x[i]*x[i]; | ||
| s0[2*i]=c & mask; | ||
| c>>=bpe; | ||
| for (j=i+1;j<kx;j++) { | ||
| c=s0[i+j]+2*x[i]*x[j]+c; | ||
| s0[i+j]=(c & mask); | ||
| c>>=bpe; | ||
| //do x=x*x mod n for bigInts x,n. | ||
| function squareMod_(x,n) { | ||
| var i,j,d,c,kx,kn,k; | ||
| for (kx=x.length; kx>0 && !x[kx-1]; kx--); //ignore leading zeros in x | ||
| 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 | ||
| if (s0.length!=k) | ||
| s0=new Array(k); | ||
| copyInt_(s0,0); | ||
| for (i=0;i<kx;i++) { | ||
| c=s0[2*i]+x[i]*x[i]; | ||
| s0[2*i]=c & mask; | ||
| c>>=bpe; | ||
| for (j=i+1;j<kx;j++) { | ||
| c=s0[i+j]+2*x[i]*x[j]+c; | ||
| s0[i+j]=(c & mask); | ||
| c>>=bpe; | ||
| } | ||
| s0[i+kx]=c; | ||
| } | ||
| mod_(s0,n); | ||
| copy_(x,s0); | ||
| } | ||
| s0[i+kx]=c; | ||
| } | ||
| mod_(s0,n); | ||
| copy_(x,s0); | ||
| } | ||
| //return x with exactly k leading zero elements | ||
| function trim(x,k) { | ||
| var i,y; | ||
| for (i=x.length; i>0 && !x[i-1]; i--); | ||
| y=new Array(i+k); | ||
| copy_(y,x); | ||
| return y; | ||
| } | ||
| //return x with exactly k leading zero elements | ||
| function trim(x,k) { | ||
| var i,y; | ||
| for (i=x.length; i>0 && !x[i-1]; i--); | ||
| y=new Array(i+k); | ||
| copy_(y,x); | ||
| return y; | ||
| } | ||
| //do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation. 0**0=1. | ||
| //this is faster when n is odd. x usually needs to have as many elements as n. | ||
| function powMod_(x,y,n) { | ||
| var k1,k2,kn,np; | ||
| if(s7.length!=n.length) | ||
| s7=dup(n); | ||
| //do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation. 0**0=1. | ||
| //this is faster when n is odd. x usually needs to have as many elements as n. | ||
| function powMod_(x,y,n) { | ||
| var k1,k2,kn,np; | ||
| if(s7.length!=n.length) | ||
| s7=dup(n); | ||
| //for even modulus, use a simple square-and-multiply algorithm, | ||
| //rather than using the more complex Montgomery algorithm. | ||
| if ((n[0]&1)==0) { | ||
| copy_(s7,x); | ||
| copyInt_(x,1); | ||
| while(!equalsInt(y,0)) { | ||
| if (y[0]&1) | ||
| multMod_(x,s7,n); | ||
| divInt_(y,2); | ||
| squareMod_(s7,n); | ||
| } | ||
| return; | ||
| } | ||
| //for even modulus, use a simple square-and-multiply algorithm, | ||
| //rather than using the more complex Montgomery algorithm. | ||
| if ((n[0]&1)==0) { | ||
| copy_(s7,x); | ||
| copyInt_(x,1); | ||
| while(!equalsInt(y,0)) { | ||
| if (y[0]&1) | ||
| multMod_(x,s7,n); | ||
| divInt_(y,2); | ||
| squareMod_(s7,n); | ||
| } | ||
| return; | ||
| } | ||
| //calculate np from n for the Montgomery multiplications | ||
| copyInt_(s7,0); | ||
| for (kn=n.length;kn>0 && !n[kn-1];kn--); | ||
| np=radix-inverseModInt(modInt(n,radix),radix); | ||
| s7[kn]=1; | ||
| multMod_(x ,s7,n); // x = x * 2**(kn*bp) mod n | ||
| //calculate np from n for the Montgomery multiplications | ||
| copyInt_(s7,0); | ||
| for (kn=n.length;kn>0 && !n[kn-1];kn--); | ||
| np=radix-inverseModInt(modInt(n,radix),radix); | ||
| s7[kn]=1; | ||
| multMod_(x ,s7,n); // x = x * 2**(kn*bp) mod n | ||
| if (s3.length!=x.length) | ||
| s3=dup(x); | ||
| else | ||
| copy_(s3,x); | ||
| if (s3.length!=x.length) | ||
| s3=dup(x); | ||
| else | ||
| copy_(s3,x); | ||
| for (k1=y.length-1;k1>0 & !y[k1]; k1--); //k1=first nonzero element of y | ||
| if (y[k1]==0) { //anything to the 0th power is 1 | ||
| copyInt_(x,1); | ||
| return; | ||
| } | ||
| for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1); //k2=position of first 1 bit in y[k1] | ||
| for (;;) { | ||
| if (!(k2>>=1)) { //look at next bit of y | ||
| k1--; | ||
| if (k1<0) { | ||
| mont_(x,one,n,np); | ||
| for (k1=y.length-1;k1>0 & !y[k1]; k1--); //k1=first nonzero element of y | ||
| if (y[k1]==0) { //anything to the 0th power is 1 | ||
| copyInt_(x,1); | ||
| return; | ||
| } | ||
| k2=1<<(bpe-1); | ||
| for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1); //k2=position of first 1 bit in y[k1] | ||
| for (;;) { | ||
| if (!(k2>>=1)) { //look at next bit of y | ||
| k1--; | ||
| if (k1<0) { | ||
| mont_(x,one,n,np); | ||
| return; | ||
| } | ||
| k2=1<<(bpe-1); | ||
| } | ||
| mont_(x,x,n,np); | ||
| if (k2 & y[k1]) //if next bit is a 1 | ||
| mont_(x,s3,n,np); | ||
| } | ||
| } | ||
| mont_(x,x,n,np); | ||
| if (k2 & y[k1]) //if next bit is a 1 | ||
| mont_(x,s3,n,np); | ||
| } | ||
| } | ||
| //do x=x*y*Ri mod n for bigInts x,y,n, | ||
| // where Ri = 2**(-kn*bpe) mod n, and kn is the | ||
| // number of elements in the n array, not | ||
| // counting leading zeros. | ||
| //x array must have at least as many elemnts as the n array | ||
| //It's OK if x and y are the same variable. | ||
| //must have: | ||
| // x,y < n | ||
| // n is odd | ||
| // np = -(n^(-1)) mod radix | ||
| function mont_(x,y,n,np) { | ||
| var i,j,c,ui,t,ks; | ||
| var kn=n.length; | ||
| var ky=y.length; | ||
| //do x=x*y*Ri mod n for bigInts x,y,n, | ||
| // where Ri = 2**(-kn*bpe) mod n, and kn is the | ||
| // number of elements in the n array, not | ||
| // counting leading zeros. | ||
| //x array must have at least as many elemnts as the n array | ||
| //It's OK if x and y are the same variable. | ||
| //must have: | ||
| // x,y < n | ||
| // n is odd | ||
| // np = -(n^(-1)) mod radix | ||
| function mont_(x,y,n,np) { | ||
| var i,j,c,ui,t,ks; | ||
| var kn=n.length; | ||
| var ky=y.length; | ||
| if (sa.length!=kn) | ||
| sa=new Array(kn); | ||
| if (sa.length!=kn) | ||
| sa=new Array(kn); | ||
| copyInt_(sa,0); | ||
| copyInt_(sa,0); | ||
| for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n | ||
| for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y | ||
| ks=sa.length-1; //sa will never have more than this many nonzero elements. | ||
| for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n | ||
| for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y | ||
| ks=sa.length-1; //sa will never have more than this many nonzero elements. | ||
| //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large numbers | ||
| for (i=0; i<kn; i++) { | ||
| t=sa[0]+x[i]*y[0]; | ||
| ui=((t & mask) * np) & mask; //the inner "& mask" was needed on Safari (but not MSIE) at one time | ||
| c=(t+ui*n[0]) >> bpe; | ||
| t=x[i]; | ||
| //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large numbers | ||
| for (i=0; i<kn; i++) { | ||
| t=sa[0]+x[i]*y[0]; | ||
| ui=((t & mask) * np) & mask; //the inner "& mask" was needed on Safari (but not MSIE) at one time | ||
| c=(t+ui*n[0]) >> bpe; | ||
| t=x[i]; | ||
| //do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe. Loop is unrolled 5-fold for speed | ||
| j=1; | ||
| for (;j<ky-4;) { c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<ky;) { c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<kn-4;) { c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<kn;) { c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<ks;) { c+=sa[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| sa[j-1]=c & mask; | ||
| } | ||
| //do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe. Loop is unrolled 5-fold for speed | ||
| j=1; | ||
| for (;j<ky-4;) { c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<ky;) { c+=sa[j]+ui*n[j]+t*y[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<kn-4;) { c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; | ||
| c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<kn;) { c+=sa[j]+ui*n[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| for (;j<ks;) { c+=sa[j]; sa[j-1]=c & mask; c>>=bpe; j++; } | ||
| sa[j-1]=c & mask; | ||
| } | ||
| if (!greater(n,sa)) | ||
| sub_(sa,n); | ||
| copy_(x,sa); | ||
| } | ||
| if (!greater(n,sa)) | ||
| sub_(sa,n); | ||
| copy_(x,sa); | ||
| } | ||
| module.exports = { | ||
| 'add': add, | ||
| 'addInt': addInt, | ||
| 'bigInt2str': bigInt2str, | ||
| 'bitSize': bitSize, | ||
| 'dup': dup, | ||
| 'equals': equals, | ||
| 'equalsInt': equalsInt, | ||
| 'expand': expand, | ||
| 'findPrimes': findPrimes, | ||
| 'GCD': GCD, | ||
| 'greater': greater, | ||
| 'greaterShift': greaterShift, | ||
| 'int2bigInt': int2bigInt, | ||
| 'inverseMod': inverseMod, | ||
| 'inverseModInt': inverseModInt, | ||
| 'isZero': isZero, | ||
| 'millerRabin': millerRabin, | ||
| 'millerRabinInt': millerRabinInt, | ||
| 'mod': mod, | ||
| 'modInt': modInt, | ||
| 'mult': mult, | ||
| 'multMod': multMod, | ||
| 'negative': negative, | ||
| 'powMod': powMod, | ||
| 'randBigInt': randBigInt, | ||
| 'randTruePrime': randTruePrime, | ||
| 'randProbPrime': randProbPrime, | ||
| 'str2bigInt': str2bigInt, | ||
| 'sub': sub, | ||
| 'trim': trim, | ||
| 'addInt_': addInt_, | ||
| 'add_': add_, | ||
| 'copy_': copy_, | ||
| 'copyInt_': copyInt_, | ||
| 'GCD_': GCD_, | ||
| 'inverseMod_': inverseMod_, | ||
| 'mod_': mod_, | ||
| 'mult_': mult_, | ||
| 'multMod_': multMod_, | ||
| 'powMod_': powMod_, | ||
| 'randBigInt_': randBigInt_, | ||
| 'randTruePrime_': randTruePrime_, | ||
| 'sub_': sub_, | ||
| 'addShift_': addShift_, | ||
| 'carry_': carry_, | ||
| 'divide_': divide_, | ||
| 'divInt_': divInt_, | ||
| 'eGCD_': eGCD_, | ||
| 'halve_': halve_, | ||
| 'leftShift_': leftShift_, | ||
| 'linComb_': linComb_, | ||
| 'linCombShift_': linCombShift_, | ||
| 'mont_': mont_, | ||
| 'multInt_': multInt_, | ||
| 'rightShift_': rightShift_, | ||
| 'squareMod_': squareMod_, | ||
| 'subShift_': subShift_, | ||
| }; | ||
| if (typeof module === 'undefined') { | ||
| module = {}; | ||
| } | ||
| BigInt = module.exports = { | ||
| 'add': add, 'addInt': addInt, 'bigInt2str': bigInt2str, 'bitSize': bitSize, | ||
| 'dup': dup, 'equals': equals, 'equalsInt': equalsInt, 'expand': expand, | ||
| 'findPrimes': findPrimes, 'GCD': GCD, 'greater': greater, | ||
| 'greaterShift': greaterShift, 'int2bigInt': int2bigInt, | ||
| 'inverseMod': inverseMod, 'inverseModInt': inverseModInt, 'isZero': isZero, | ||
| 'millerRabin': millerRabin, 'millerRabinInt': millerRabinInt, 'mod': mod, | ||
| 'modInt': modInt, 'mult': mult, 'multMod': multMod, 'negative': negative, | ||
| 'powMod': powMod, 'randBigInt': randBigInt, 'randTruePrime': randTruePrime, | ||
| 'randProbPrime': randProbPrime, 'str2bigInt': str2bigInt, 'sub': sub, | ||
| 'trim': trim, 'addInt_': addInt_, 'add_': add_, 'copy_': copy_, | ||
| 'copyInt_': copyInt_, 'GCD_': GCD_, 'inverseMod_': inverseMod_, 'mod_': mod_, | ||
| 'mult_': mult_, 'multMod_': multMod_, 'powMod_': powMod_, | ||
| 'randBigInt_': randBigInt_, 'randTruePrime_': randTruePrime_, 'sub_': sub_, | ||
| 'addShift_': addShift_, 'carry_': carry_, 'divide_': divide_, | ||
| 'divInt_': divInt_, 'eGCD_': eGCD_, 'halve_': halve_, 'leftShift_': leftShift_, | ||
| 'linComb_': linComb_, 'linCombShift_': linCombShift_, 'mont_': mont_, | ||
| 'multInt_': multInt_, 'rightShift_': rightShift_, 'squareMod_': squareMod_, | ||
| 'subShift_': subShift_, 'powMod_': powMod_, 'eGCD_': eGCD_, | ||
| 'inverseMod_': inverseMod_, 'GCD_': GCD_, 'mont_': mont_, 'divide_': divide_, | ||
| 'squareMod_': squareMod_, 'randTruePrime_': randTruePrime_, | ||
| 'millerRabin': millerRabin | ||
| }; | ||
| })(); | ||
| }); |
Fixed alerts
No README
QualityPackage does not have a README. This may indicate a failed publish or a low quality package.
Found 1 instance in 1 package
Improved metrics
- Total package byte prevSize
- increased by11.96%
57060
- Number of package files
- increased by50%
3
- Lines of code
- increased by3.71%
1455
- Number of medium quality alerts
- decreased by-50%
1
- Number of lines in readme file
- increased byInfinity%
11
No dependency changes