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converse.js
Commit b8c12b1c authored by JC Brand's avatar JC Brand
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Remove unused 3rd party libs

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;(function (root, factory) {
if (typeof define === 'function' && define.amd) {
// XXX: Simply add an empty deps list here so that almond works.
define([], factory.bind(root, root.crypto || root.msCrypto))
} else if (typeof module !== 'undefined' && module.exports) {
module.exports = factory(require('crypto'))
} else {
root.BigInt = factory(root.crypto || root.msCrypto)
}
}(this, function (crypto) {
////////////////////////////////////////////////////////////////////////////////////////
// Big Integer Library v. 5.5
// Created 2000, last modified 2013
// Leemon Baird
// 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
// - added "var i" to greaterShift() so i is not global. (Thanks to Péter Szabó for finding that bug)
//
// v 5.3 21 Sep 2009
// - added randProbPrime(k) for probable primes
// - unrolled loop in mont_ (slightly faster)
// - millerRabin now takes a bigInt parameter rather than an int
//
// v 5.2 15 Sep 2009
// - fixed capitalization in call to int2bigInt in randBigInt
// (thanks to Emili Evripidou, Reinhold Behringer, and Samuel Macaleese for finding that bug)
//
// v 5.1 8 Oct 2007
// - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters
// - added functions GCD and randBigInt, which call GCD_ and randBigInt_
// - fixed a bug found by Rob Visser (see comment with his name below)
// - improved comments
//
// 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
// 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
// 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,
// 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
// 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
// multMod_(x,x,n). You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n).
// Or simply use the multMod(x,x,n) function without the underscore, where
// such issues never arise, because non-underscored functions never change
// their parameters; they always allocate new memory for the answer that is returned.
//
// These functions are designed to avoid frequent dynamic memory allocation in the inner loop.
// For most functions, if it needs a BigInt as a local variable it will actually use
// a global, and will only allocate to it only when it's not the right size. This ensures
// that when a function is called repeatedly with same-sized parameters, it only allocates
// memory on the first call.
//
// 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
// 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
// time they're called with a given parameter size.
//
// 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.
// string bigInt2str(x,base) //return a string form of bigInt x in a given base, with 2 <= base <= 95
// int bitSize(x) //return how many bits long the bigInt x is, not counting leading zeros
// bigInt dup(x) //return a copy of bigInt x
// boolean equals(x,y) //is the bigInt x equal to the bigint y?
// boolean equalsInt(x,y) //is bigint x equal to integer y?
// bigInt expand(x,n) //return a copy of x with at least n elements, adding leading zeros if needed
// Array findPrimes(n) //return array of all primes less than integer n
// bigInt GCD(x,y) //return greatest common divisor of bigInts x and y (each with same number of elements).
// boolean greater(x,y) //is x>y? (x and y are nonnegative bigInts)
// boolean greaterShift(x,y,shift)//is (x <<(shift*bpe)) > y?
// bigInt int2bigInt(t,n,m) //return a bigInt equal to integer t, with at least n bits and m array elements
// bigInt inverseMod(x,n) //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null
// int inverseModInt(x,n) //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse
// boolean isZero(x) //is the bigInt x equal to zero?
// boolean millerRabin(x,b) //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime? (b is bigInt, 1<b<x)
// boolean millerRabinInt(x,b) //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime? (b is int, 1<b<x)
// bigInt mod(x,n) //return a new bigInt equal to (x mod n) for bigInts x and n.
// int modInt(x,n) //return x mod n for bigInt x and integer n.
// bigInt mult(x,y) //return x*y for bigInts x and y. This is faster when y<x.
// bigInt multMod(x,y,n) //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x.
// boolean negative(x) //is bigInt x negative?
// bigInt powMod(x,y,n) //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n.
// bigInt randBigInt(n,s) //return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1.
// bigInt randTruePrime(k) //return a new, random, k-bit, true prime bigInt using Maurer's algorithm.
// bigInt randProbPrime(k) //return a new, random, k-bit, probable prime bigInt (probability it's composite less than 2^-80).
// bigInt str2bigInt(s,b,n,m) //return a bigInt for number represented in string s in base b with at least n bits and m array elements
// bigInt sub(x,y) //return (x-y) for bigInts x and y. Negative answers will be 2s complement
// bigInt trim(x,k) //return a copy of x with exactly k leading zero elements
//
//
// 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.
//
// void addInt_(x,n) //do x=x+n where x is a bigInt and n is an integer
// void add_(x,y) //do x=x+y for bigInts x and y
// void copy_(x,y) //do x=y on bigInts x and y
// void copyInt_(x,n) //do x=n on bigInt x and integer n
// void GCD_(x,y) //set x to the greatest common divisor of bigInts x and y, (y is destroyed). (This never overflows its array).
// boolean inverseMod_(x,n) //do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist
// void mod_(x,n) //do x=x mod n for bigInts x and n. (This never overflows its array).
// void mult_(x,y) //do x=x*y for bigInts x and y.
// void multMod_(x,y,n) //do x=x*y mod n for bigInts x,y,n.
// void powMod_(x,y,n) //do x=x**y mod n, where x,y,n are bigInts (n is odd) and ** is exponentiation. 0**0=1.
// void randBigInt_(b,n,s) //do b = an n-bit random BigInt. if s=1, then nth bit (most significant bit) is set to 1. n>=1.
// void randTruePrime_(ans,k) //do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb.
// void sub_(x,y) //do x=x-y for bigInts x and y. Negative answers will be 2s complement.
//
// 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.
//
// void addShift_(x,y,ys) //do x=x+(y<<(ys*bpe))
// void carry_(x) //do carries and borrows so each element of the bigInt x fits in bpe bits.
// void divide_(x,y,q,r) //divide x by y giving quotient q and remainder r
// int divInt_(x,n) //do x=floor(x/n) for bigInt x and integer n, and return the remainder. (This never overflows its array).
// int eGCD_(x,y,d,a,b) //sets a,b,d to positive bigInts such that d = GCD_(x,y) = a*x-b*y
// void halve_(x) //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement. (This never overflows its array).
// void leftShift_(x,n) //left shift bigInt x by n bits. n<bpe.
// void linComb_(x,y,a,b) //do x=a*x+b*y for bigInts x and y and integers a and b
// void linCombShift_(x,y,b,ys) //do x=x+b*(y<<(ys*bpe)) for bigInts x and y, and integers b and ys
// void mont_(x,y,n,np) //Montgomery multiplication (see comments where the function is defined)
// void multInt_(x,n) //do x=x*n where x is a bigInt and n is an integer.
// void rightShift_(x,n) //right shift bigInt x by n bits. (This never overflows its array).
// void squareMod_(x,n) //do x=x*x mod n for bigInts x,n
// void subShift_(x,y,ys) //do x=x-(y<<(ys*bpe)). Negative answers will be 2s complement.
//
// The following functions are based on algorithms from the _Handbook of Applied Cryptography_
// powMod_() = algorithm 14.94, Montgomery exponentiation
// eGCD_,inverseMod_() = algorithm 14.61, Binary extended GCD_
// GCD_() = algorothm 14.57, Lehmer's algorithm
// mont_() = algorithm 14.36, Montgomery multiplication
// divide_() = algorithm 14.20 Multiple-precision division
// squareMod_() = algorithm 14.16 Multiple-precision squaring
// randTruePrime_() = algorithm 4.62, Maurer's algorithm
// millerRabin() = algorithm 4.24, Miller-Rabin algorithm
//
// Profiling shows:
// randTruePrime_() spends:
// 10% of its time in calls to powMod_()
// 85% of its time in calls to millerRabin()
// millerRabin() spends:
// 99% of its time in calls to powMod_() (always with a base of 2)
// powMod_() spends:
// 94% of its time in calls to mont_() (almost always with x==y)
//
// This suggests there are several ways to speed up this library slightly:
// - convert powMod_ to use a Montgomery form of k-ary window (or maybe a Montgomery form of sliding window)
// -- this should especially focus on being fast when raising 2 to a power mod n
// - convert randTruePrime_() to use a minimum r of 1/3 instead of 1/2 with the appropriate change to the test
// - tune the parameters in randTruePrime_(), including c, m, and recLimit
// - speed up the single loop in mont_() that takes 95% of the runtime, perhaps by reducing checking
// within the loop when all the parameters are the same length.
//
// There are several ideas that look like they wouldn't help much at all:
// - replacing trial division in randTruePrime_() with a sieve (that speeds up something taking almost no time anyway)
// - increase bpe from 15 to 30 (that would help if we had a 32*32->64 multiplier, but not with JavaScript's 32*32->32)
// - speeding up mont_(x,y,n,np) when x==y by doing a non-modular, non-Montgomery square
// followed by a Montgomery reduction. The intermediate answer will be twice as long as x, so that
// method would be slower. This is unfortunate because the code currently spends almost all of its time
// doing mont_(x,x,...), both for randTruePrime_() and powMod_(). A faster method for Montgomery squaring
// would have a large impact on the speed of randTruePrime_() and powMod_(). HAC has a couple of poorly-worded
// sentences that seem to imply it's faster to do a non-modular square followed by a single
// Montgomery reduction, but that's obviously wrong.
////////////////////////////////////////////////////////////////////////////////////////
//globals
// The number of significant bits in the fraction of a JavaScript
// floating-point number is 52, independent of platform.
// See: https://github.com/arlolra/otr/issues/41
var bpe = 26; // bits stored per array element
var radix = 1 << bpe; // equals 2^bpe
var mask = radix - 1; // AND this with an array element to chop it down to bpe bits
//the digits for converting to different bases
var digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-';
var one=int2bigInt(1,1,1); //constant used in powMod_()
//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_()
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;
}
//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 and b are bigInts with b<x
function millerRabin(x,b) {
var i,j,k,s;
if (mr_x1.length!=x.length) {
mr_x1=dup(x);
mr_r=dup(x);
mr_a=dup(x);
}
copy_(mr_a,b);
copy_(mr_r,x);
copy_(mr_x1,x);
addInt_(mr_r,-1);
addInt_(mr_x1,-1);
//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++;
*/
/* http://www.javascripter.net/math/primes/millerrabinbug-bigint54.htm */
if (isZero(mr_r)) return 0;
for (k=0; mr_r[k]==0; k++);
for (i=1,j=2; mr_r[k]%j==0; j*=2,i++ );
s = k*bpe + i - 1;
/* end */
if (s)
rightShift_(mr_r,s);
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;
}
}
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 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 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.
if (primes.length==0)
primes=findPrimes(30000); //check for divisibility by primes <=30000
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.
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;
}
//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;
}
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 (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 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.
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*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,w,m,pm,dd,j,r,B,divisible,z,zz,recSize,recLimit;
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/511.0-1.0);
}
}
//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 (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)) | randomBitInt(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;
}
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[randomBitInt(9)]; //r=Math.pow(2,Math.random()-1);
else
r=0.5;
//simulation suggests the more complex algorithm using r=.333 is only slightly faster.
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))
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]
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
//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 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;
}
//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]=randomBitInt(bpe);
}
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,qp;
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;
}
if (!sing) break; //quit when y all zero elements except possibly y[0]
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;
}
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);
if(!(x[0]&1) && !(n[0]&1)) { //if both inputs are even, then inverse doesn't exist
copyInt_(x,0);
return 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);
}
}
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);
}
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;
}
}
}
//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;
}
}
//this deprecated function is for backward compatibility only.
function inverseModInt_(x,n) {
return inverseModInt(x,n);
}
//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);
}
}
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 (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;
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=k-1;i>=0;i--)
if (x[i]>y[i])
return 1;
else if (x[i]<y[i])
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
//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
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]);
//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;
y2=y2 & mask;
c = (c - y2) / radix;
y1=c+q[i-ky]*y[ky-1];
c=y1;
y1=y1 & mask;
c = (c - y1) / radix;
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
}
//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 & mask;
b = -((c - b) / radix);
c+=b*radix;
}
x[i]=c & mask;
c = ((c - x[i]) / radix) - 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, buff;
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.
function str2bigInt(s,base,minSize) {
var d, i, j, 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;
}
// log2(base)*k
var bb = base, p = 0;
var b = base == 1 ? k : 0;
while (bb > 1) {
if (bb & 1) p = 1;
b += k;
bb >>= 1;
}
b += p*k;
x=int2bigInt(0,b,0);
for (i=0;i<k;i++) {
d=digitsStr.indexOf(s.substring(i,i+1),0);
if (base<=36 && d>=36) //convert lowercase to uppercase if base<=36
d-=26;
if (d>=base || d<0) { //stop at first illegal character
break;
}
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;
}
//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;
}
//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,base) {
var i,t,s="";
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);
s=digitsStr.substring(t,t+1)+s;
}
}
if (s.length==0)
s="0";
return s;
}
//returns a duplicate of bigInt x
function dup(x) {
var i, buff;
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 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 & mask;
b = -((c - b) / radix);
c+=b*radix;
}
x[i]=c & mask;
c = ((c - x[i]) / radix) - b;
if (!c) return; //stop carrying as soon as the carry is zero
}
}
//right shift bigInt x by n bits.
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
}
//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 & mask;
b = -((c - b) / radix);
c+=b*radix;
}
x[i]=c & mask;
c = ((c - x[i]) / radix) - 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 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 = (c - x[i]) / radix;
}
for (i=k;i<kk;i++) {
c+=a*x[i];
x[i]=c & mask;
c = (c - x[i]) / radix;
}
}
//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 = (c - x[i]) / radix;
}
for (i=k;c && i<kk;i++) {
c+=x[i];
x[i]=c & mask;
c = (c - x[i]) / radix;
}
}
//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 = (c - x[i]) / radix;
}
for (i=k;c && i<kk;i++) {
c+=x[i];
x[i]=c & mask;
c = (c - x[i]) / radix;
}
}
//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 = (c - x[i]) / radix;
}
for (i=k;c && i<kk;i++) {
c+=x[i];
x[i]=c & mask;
c = (c - x[i]) / radix;
}
}
//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 = (c - x[i]) / radix;
}
for (i=k;c && i<x.length;i++) {
c+=x[i];
x[i]=c & mask;
c = (c - x[i]) / radix;
}
}
//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 = (c - x[i]) / radix;
}
for (i=k;c && i<x.length;i++) {
c+=x[i];
x[i]=c & mask;
c = (c - x[i]) / radix;
}
}
//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*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 = (c - s0[2*i]) / radix;
for (j=i+1;j<kx;j++) {
c=s0[i+j]+2*x[i]*x[j]+c;
s0[i+j]=(c & mask);
c = (c - s0[i+j]) / radix;
}
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;
}
//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;
}
//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);
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);
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);
}
}
//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,t2,ks;
var kn=n.length;
var ky=y.length;
if (sa.length!=kn)
sa=new Array(kn);
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.
//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]);
c = (c - (c & mask)) / radix;
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]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]+t*y[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]+t*y[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]+t*y[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]+t*y[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
}
for (;j<ky;) {
c+=sa[j]+ui*n[j]+t*y[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
}
for (;j<kn-4;) {
c+=sa[j]+ui*n[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
c+=sa[j]+ui*n[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
}
for (;j<kn;) {
c+=sa[j]+ui*n[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
}
for (;j<ks;) {
c+=sa[j]; t2=sa[j-1]=c & mask; c=(c-t2)/radix; j++;
}
sa[j-1]=c & mask;
}
if (!greater(n,sa))
sub_(sa,n);
copy_(x,sa);
}
// otr.js additions
// computes num / den mod n
function divMod(num, den, n) {
return multMod(num, inverseMod(den, n), n)
}
// computes one - two mod n
function subMod(one, two, n) {
one = mod(one, n)
two = mod(two, n)
if (greater(two, one)) one = add(one, n)
return sub(one, two)
}
// computes 2^m as a bigInt
function twoToThe(m) {
var b = Math.floor(m / bpe) + 2
var t = new Array(b)
for (var i = 0; i < b; i++) t[i] = 0
t[b - 2] = 1 << (m % bpe)
return t
}
// cache these results for faster lookup
var _num2bin = (function () {
var i = 0, _num2bin= {}
for (; i < 0x100; ++i) {
_num2bin[i] = String.fromCharCode(i) // 0 -> "\00"
}
return _num2bin
}())
// serialize a bigInt to an ascii string
// padded up to pad length
function bigInt2bits(bi, pad) {
pad || (pad = 0)
bi = dup(bi)
var ba = ''
while (!isZero(bi)) {
ba = _num2bin[bi[0] & 0xff] + ba
rightShift_(bi, 8)
}
while (ba.length < pad) {
ba = '\x00' + ba
}
return ba
}
// converts a byte array to a bigInt
function ba2bigInt(data) {
var mpi = str2bigInt('0', 10, data.length)
data.forEach(function (d, i) {
if (i) leftShift_(mpi, 8)
mpi[0] |= d
})
return mpi
}
// returns a function that returns an array of n bytes
var randomBytes = (function () {
// in node
if ( typeof crypto !== 'undefined' &&
typeof crypto.randomBytes === 'function' ) {
return function (n) {
try {
var buf = crypto.randomBytes(n)
} catch (e) { throw e }
return Array.prototype.slice.call(buf, 0)
}
}
// in browser
else if ( typeof crypto !== 'undefined' &&
typeof crypto.getRandomValues === 'function' ) {
return function (n) {
var buf = new Uint8Array(n)
crypto.getRandomValues(buf)
return Array.prototype.slice.call(buf, 0)
}
}
// err
else {
console.log('Keys should not be generated without CSPRNG.');
return;
// throw new Error('Keys should not be generated without CSPRNG.')
}
}())
// Salsa 20 in webworker needs a 40 byte seed
function getSeed() {
return randomBytes(40)
}
// returns a single random byte
function randomByte() {
return randomBytes(1)[0]
}
// returns a k-bit random integer
function randomBitInt(k) {
if (k > 31) throw new Error("Too many bits.")
var i = 0, r = 0
var b = Math.floor(k / 8)
var mask = (1 << (k % 8)) - 1
if (mask) r = randomByte() & mask
for (; i < b; i++)
r = (256 * r) + randomByte()
return r
}
return {
str2bigInt : str2bigInt
, bigInt2str : bigInt2str
, int2bigInt : int2bigInt
, multMod : multMod
, powMod : powMod
, inverseMod : inverseMod
, randBigInt : randBigInt
, randBigInt_ : randBigInt_
, equals : equals
, equalsInt : equalsInt
, sub : sub
, mod : mod
, modInt : modInt
, mult : mult
, divInt_ : divInt_
, rightShift_ : rightShift_
, dup : dup
, greater : greater
, add : add
, isZero : isZero
, bitSize : bitSize
, millerRabin : millerRabin
, divide_ : divide_
, trim : trim
, primes : primes
, findPrimes : findPrimes
, getSeed : getSeed
, divMod : divMod
, subMod : subMod
, twoToThe : twoToThe
, bigInt2bits : bigInt2bits
, ba2bigInt : ba2bigInt
}
}))
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3rdparty/long.js deleted 100644 → 0
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/*
Copyright 2013 Daniel Wirtz <dcode@dcode.io>
Copyright 2009 The Closure Library Authors. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS-IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
/**
* @license long.js (c) 2013 Daniel Wirtz <dcode@dcode.io>
* Released under the Apache License, Version 2.0
* see: https://github.com/dcodeIO/long.js for details
*/
(function(global, factory) {
/* AMD */ if (typeof define === 'function' && define["amd"])
define([], factory);
/* CommonJS */ else if (typeof require === 'function' && typeof module === "object" && module && module["exports"])
module["exports"] = factory();
/* Global */ else
(global["dcodeIO"] = global["dcodeIO"] || {})["Long"] = factory();
})(this, function() {
"use strict";
/**
* Constructs a 64 bit two's-complement integer, given its low and high 32 bit values as *signed* integers.
* See the from* functions below for more convenient ways of constructing Longs.
* @exports Long
* @class A Long class for representing a 64 bit two's-complement integer value.
* @param {number} low The low (signed) 32 bits of the long
* @param {number} high The high (signed) 32 bits of the long
* @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
* @constructor
*/
function Long(low, high, unsigned) {
/**
* The low 32 bits as a signed value.
* @type {number}
*/
this.low = low | 0;
/**
* The high 32 bits as a signed value.
* @type {number}
*/
this.high = high | 0;
/**
* Whether unsigned or not.
* @type {boolean}
*/
this.unsigned = !!unsigned;
}
// The internal representation of a long is the two given signed, 32-bit values.
// We use 32-bit pieces because these are the size of integers on which
// Javascript performs bit-operations. For operations like addition and
// multiplication, we split each number into 16 bit pieces, which can easily be
// multiplied within Javascript's floating-point representation without overflow
// or change in sign.
//
// In the algorithms below, we frequently reduce the negative case to the
// positive case by negating the input(s) and then post-processing the result.
// Note that we must ALWAYS check specially whether those values are MIN_VALUE
// (-2^63) because -MIN_VALUE == MIN_VALUE (since 2^63 cannot be represented as
// a positive number, it overflows back into a negative). Not handling this
// case would often result in infinite recursion.
//
// Common constant values ZERO, ONE, NEG_ONE, etc. are defined below the from*
// methods on which they depend.
/**
* An indicator used to reliably determine if an object is a Long or not.
* @type {boolean}
* @const
* @private
*/
Long.prototype.__isLong__;
Object.defineProperty(Long.prototype, "__isLong__", {
value: true,
enumerable: false,
configurable: false
});
/**
* @function
* @param {*} obj Object
* @returns {boolean}
* @inner
*/
function isLong(obj) {
return (obj && obj["__isLong__"]) === true;
}
/**
* Tests if the specified object is a Long.
* @function
* @param {*} obj Object
* @returns {boolean}
*/
Long.isLong = isLong;
/**
* A cache of the Long representations of small integer values.
* @type {!Object}
* @inner
*/
var INT_CACHE = {};
/**
* A cache of the Long representations of small unsigned integer values.
* @type {!Object}
* @inner
*/
var UINT_CACHE = {};
/**
* @param {number} value
* @param {boolean=} unsigned
* @returns {!Long}
* @inner
*/
function fromInt(value, unsigned) {
var obj, cachedObj, cache;
if (unsigned) {
value >>>= 0;
if (cache = (0 <= value && value < 256)) {
cachedObj = UINT_CACHE[value];
if (cachedObj)
return cachedObj;
}
obj = fromBits(value, (value | 0) < 0 ? -1 : 0, true);
if (cache)
UINT_CACHE[value] = obj;
return obj;
} else {
value |= 0;
if (cache = (-128 <= value && value < 128)) {
cachedObj = INT_CACHE[value];
if (cachedObj)
return cachedObj;
}
obj = fromBits(value, value < 0 ? -1 : 0, false);
if (cache)
INT_CACHE[value] = obj;
return obj;
}
}
/**
* Returns a Long representing the given 32 bit integer value.
* @function
* @param {number} value The 32 bit integer in question
* @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
* @returns {!Long} The corresponding Long value
*/
Long.fromInt = fromInt;
/**
* @param {number} value
* @param {boolean=} unsigned
* @returns {!Long}
* @inner
*/
function fromNumber(value, unsigned) {
if (isNaN(value) || !isFinite(value))
return unsigned ? UZERO : ZERO;
if (unsigned) {
if (value < 0)
return UZERO;
if (value >= TWO_PWR_64_DBL)
return MAX_UNSIGNED_VALUE;
} else {
if (value <= -TWO_PWR_63_DBL)
return MIN_VALUE;
if (value + 1 >= TWO_PWR_63_DBL)
return MAX_VALUE;
}
if (value < 0)
return fromNumber(-value, unsigned).neg();
return fromBits((value % TWO_PWR_32_DBL) | 0, (value / TWO_PWR_32_DBL) | 0, unsigned);
}
/**
* Returns a Long representing the given value, provided that it is a finite number. Otherwise, zero is returned.
* @function
* @param {number} value The number in question
* @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
* @returns {!Long} The corresponding Long value
*/
Long.fromNumber = fromNumber;
/**
* @param {number} lowBits
* @param {number} highBits
* @param {boolean=} unsigned
* @returns {!Long}
* @inner
*/
function fromBits(lowBits, highBits, unsigned) {
return new Long(lowBits, highBits, unsigned);
}
/**
* Returns a Long representing the 64 bit integer that comes by concatenating the given low and high bits. Each is
* assumed to use 32 bits.
* @function
* @param {number} lowBits The low 32 bits
* @param {number} highBits The high 32 bits
* @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
* @returns {!Long} The corresponding Long value
*/
Long.fromBits = fromBits;
/**
* @function
* @param {number} base
* @param {number} exponent
* @returns {number}
* @inner
*/
var pow_dbl = Math.pow; // Used 4 times (4*8 to 15+4)
/**
* @param {string} str
* @param {(boolean|number)=} unsigned
* @param {number=} radix
* @returns {!Long}
* @inner
*/
function fromString(str, unsigned, radix) {
if (str.length === 0)
throw Error('empty string');
if (str === "NaN" || str === "Infinity" || str === "+Infinity" || str === "-Infinity")
return ZERO;
if (typeof unsigned === 'number') {
// For goog.math.long compatibility
radix = unsigned,
unsigned = false;
} else {
unsigned = !! unsigned;
}
radix = radix || 10;
if (radix < 2 || 36 < radix)
throw RangeError('radix');
var p;
if ((p = str.indexOf('-')) > 0)
throw Error('interior hyphen');
else if (p === 0) {
return fromString(str.substring(1), unsigned, radix).neg();
}
// Do several (8) digits each time through the loop, so as to
// minimize the calls to the very expensive emulated div.
var radixToPower = fromNumber(pow_dbl(radix, 8));
var result = ZERO;
for (var i = 0; i < str.length; i += 8) {
var size = Math.min(8, str.length - i),
value = parseInt(str.substring(i, i + size), radix);
if (size < 8) {
var power = fromNumber(pow_dbl(radix, size));
result = result.mul(power).add(fromNumber(value));
} else {
result = result.mul(radixToPower);
result = result.add(fromNumber(value));
}
}
result.unsigned = unsigned;
return result;
}
/**
* Returns a Long representation of the given string, written using the specified radix.
* @function
* @param {string} str The textual representation of the Long
* @param {(boolean|number)=} unsigned Whether unsigned or not, defaults to `false` for signed
* @param {number=} radix The radix in which the text is written (2-36), defaults to 10
* @returns {!Long} The corresponding Long value
*/
Long.fromString = fromString;
/**
* @function
* @param {!Long|number|string|!{low: number, high: number, unsigned: boolean}} val
* @returns {!Long}
* @inner
*/
function fromValue(val) {
if (val /* is compatible */ instanceof Long)
return val;
if (typeof val === 'number')
return fromNumber(val);
if (typeof val === 'string')
return fromString(val);
// Throws for non-objects, converts non-instanceof Long:
return fromBits(val.low, val.high, val.unsigned);
}
/**
* Converts the specified value to a Long.
* @function
* @param {!Long|number|string|!{low: number, high: number, unsigned: boolean}} val Value
* @returns {!Long}
*/
Long.fromValue = fromValue;
// NOTE: the compiler should inline these constant values below and then remove these variables, so there should be
// no runtime penalty for these.
/**
* @type {number}
* @const
* @inner
*/
var TWO_PWR_16_DBL = 1 << 16;
/**
* @type {number}
* @const
* @inner
*/
var TWO_PWR_24_DBL = 1 << 24;
/**
* @type {number}
* @const
* @inner
*/
var TWO_PWR_32_DBL = TWO_PWR_16_DBL * TWO_PWR_16_DBL;
/**
* @type {number}
* @const
* @inner
*/
var TWO_PWR_64_DBL = TWO_PWR_32_DBL * TWO_PWR_32_DBL;
/**
* @type {number}
* @const
* @inner
*/
var TWO_PWR_63_DBL = TWO_PWR_64_DBL / 2;
/**
* @type {!Long}
* @const
* @inner
*/
var TWO_PWR_24 = fromInt(TWO_PWR_24_DBL);
/**
* @type {!Long}
* @inner
*/
var ZERO = fromInt(0);
/**
* Signed zero.
* @type {!Long}
*/
Long.ZERO = ZERO;
/**
* @type {!Long}
* @inner
*/
var UZERO = fromInt(0, true);
/**
* Unsigned zero.
* @type {!Long}
*/
Long.UZERO = UZERO;
/**
* @type {!Long}
* @inner
*/
var ONE = fromInt(1);
/**
* Signed one.
* @type {!Long}
*/
Long.ONE = ONE;
/**
* @type {!Long}
* @inner
*/
var UONE = fromInt(1, true);
/**
* Unsigned one.
* @type {!Long}
*/
Long.UONE = UONE;
/**
* @type {!Long}
* @inner
*/
var NEG_ONE = fromInt(-1);
/**
* Signed negative one.
* @type {!Long}
*/
Long.NEG_ONE = NEG_ONE;
/**
* @type {!Long}
* @inner
*/
var MAX_VALUE = fromBits(0xFFFFFFFF|0, 0x7FFFFFFF|0, false);
/**
* Maximum signed value.
* @type {!Long}
*/
Long.MAX_VALUE = MAX_VALUE;
/**
* @type {!Long}
* @inner
*/
var MAX_UNSIGNED_VALUE = fromBits(0xFFFFFFFF|0, 0xFFFFFFFF|0, true);
/**
* Maximum unsigned value.
* @type {!Long}
*/
Long.MAX_UNSIGNED_VALUE = MAX_UNSIGNED_VALUE;
/**
* @type {!Long}
* @inner
*/
var MIN_VALUE = fromBits(0, 0x80000000|0, false);
/**
* Minimum signed value.
* @type {!Long}
*/
Long.MIN_VALUE = MIN_VALUE;
/**
* @alias Long.prototype
* @inner
*/
var LongPrototype = Long.prototype;
/**
* Converts the Long to a 32 bit integer, assuming it is a 32 bit integer.
* @returns {number}
*/
LongPrototype.toInt = function toInt() {
return this.unsigned ? this.low >>> 0 : this.low;
};
/**
* Converts the Long to a the nearest floating-point representation of this value (double, 53 bit mantissa).
* @returns {number}
*/
LongPrototype.toNumber = function toNumber() {
if (this.unsigned)
return ((this.high >>> 0) * TWO_PWR_32_DBL) + (this.low >>> 0);
return this.high * TWO_PWR_32_DBL + (this.low >>> 0);
};
/**
* Converts the Long to a string written in the specified radix.
* @param {number=} radix Radix (2-36), defaults to 10
* @returns {string}
* @override
* @throws {RangeError} If `radix` is out of range
*/
LongPrototype.toString = function toString(radix) {
radix = radix || 10;
if (radix < 2 || 36 < radix)
throw RangeError('radix');
if (this.isZero())
return '0';
if (this.isNegative()) { // Unsigned Longs are never negative
if (this.eq(MIN_VALUE)) {
// We need to change the Long value before it can be negated, so we remove
// the bottom-most digit in this base and then recurse to do the rest.
var radixLong = fromNumber(radix),
div = this.div(radixLong),
rem1 = div.mul(radixLong).sub(this);
return div.toString(radix) + rem1.toInt().toString(radix);
} else
return '-' + this.neg().toString(radix);
}
// Do several (6) digits each time through the loop, so as to
// minimize the calls to the very expensive emulated div.
var radixToPower = fromNumber(pow_dbl(radix, 6), this.unsigned),
rem = this;
var result = '';
while (true) {
var remDiv = rem.div(radixToPower),
intval = rem.sub(remDiv.mul(radixToPower)).toInt() >>> 0,
digits = intval.toString(radix);
rem = remDiv;
if (rem.isZero())
return digits + result;
else {
while (digits.length < 6)
digits = '0' + digits;
result = '' + digits + result;
}
}
};
/**
* Gets the high 32 bits as a signed integer.
* @returns {number} Signed high bits
*/
LongPrototype.getHighBits = function getHighBits() {
return this.high;
};
/**
* Gets the high 32 bits as an unsigned integer.
* @returns {number} Unsigned high bits
*/
LongPrototype.getHighBitsUnsigned = function getHighBitsUnsigned() {
return this.high >>> 0;
};
/**
* Gets the low 32 bits as a signed integer.
* @returns {number} Signed low bits
*/
LongPrototype.getLowBits = function getLowBits() {
return this.low;
};
/**
* Gets the low 32 bits as an unsigned integer.
* @returns {number} Unsigned low bits
*/
LongPrototype.getLowBitsUnsigned = function getLowBitsUnsigned() {
return this.low >>> 0;
};
/**
* Gets the number of bits needed to represent the absolute value of this Long.
* @returns {number}
*/
LongPrototype.getNumBitsAbs = function getNumBitsAbs() {
if (this.isNegative()) // Unsigned Longs are never negative
return this.eq(MIN_VALUE) ? 64 : this.neg().getNumBitsAbs();
var val = this.high != 0 ? this.high : this.low;
for (var bit = 31; bit > 0; bit--)
if ((val & (1 << bit)) != 0)
break;
return this.high != 0 ? bit + 33 : bit + 1;
};
/**
* Tests if this Long's value equals zero.
* @returns {boolean}
*/
LongPrototype.isZero = function isZero() {
return this.high === 0 && this.low === 0;
};
/**
* Tests if this Long's value is negative.
* @returns {boolean}
*/
LongPrototype.isNegative = function isNegative() {
return !this.unsigned && this.high < 0;
};
/**
* Tests if this Long's value is positive.
* @returns {boolean}
*/
LongPrototype.isPositive = function isPositive() {
return this.unsigned || this.high >= 0;
};
/**
* Tests if this Long's value is odd.
* @returns {boolean}
*/
LongPrototype.isOdd = function isOdd() {
return (this.low & 1) === 1;
};
/**
* Tests if this Long's value is even.
* @returns {boolean}
*/
LongPrototype.isEven = function isEven() {
return (this.low & 1) === 0;
};
/**
* Tests if this Long's value equals the specified's.
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.equals = function equals(other) {
if (!isLong(other))
other = fromValue(other);
if (this.unsigned !== other.unsigned && (this.high >>> 31) === 1 && (other.high >>> 31) === 1)
return false;
return this.high === other.high && this.low === other.low;
};
/**
* Tests if this Long's value equals the specified's. This is an alias of {@link Long#equals}.
* @function
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.eq = LongPrototype.equals;
/**
* Tests if this Long's value differs from the specified's.
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.notEquals = function notEquals(other) {
return !this.eq(/* validates */ other);
};
/**
* Tests if this Long's value differs from the specified's. This is an alias of {@link Long#notEquals}.
* @function
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.neq = LongPrototype.notEquals;
/**
* Tests if this Long's value is less than the specified's.
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.lessThan = function lessThan(other) {
return this.comp(/* validates */ other) < 0;
};
/**
* Tests if this Long's value is less than the specified's. This is an alias of {@link Long#lessThan}.
* @function
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.lt = LongPrototype.lessThan;
/**
* Tests if this Long's value is less than or equal the specified's.
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.lessThanOrEqual = function lessThanOrEqual(other) {
return this.comp(/* validates */ other) <= 0;
};
/**
* Tests if this Long's value is less than or equal the specified's. This is an alias of {@link Long#lessThanOrEqual}.
* @function
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.lte = LongPrototype.lessThanOrEqual;
/**
* Tests if this Long's value is greater than the specified's.
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.greaterThan = function greaterThan(other) {
return this.comp(/* validates */ other) > 0;
};
/**
* Tests if this Long's value is greater than the specified's. This is an alias of {@link Long#greaterThan}.
* @function
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.gt = LongPrototype.greaterThan;
/**
* Tests if this Long's value is greater than or equal the specified's.
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.greaterThanOrEqual = function greaterThanOrEqual(other) {
return this.comp(/* validates */ other) >= 0;
};
/**
* Tests if this Long's value is greater than or equal the specified's. This is an alias of {@link Long#greaterThanOrEqual}.
* @function
* @param {!Long|number|string} other Other value
* @returns {boolean}
*/
LongPrototype.gte = LongPrototype.greaterThanOrEqual;
/**
* Compares this Long's value with the specified's.
* @param {!Long|number|string} other Other value
* @returns {number} 0 if they are the same, 1 if the this is greater and -1
* if the given one is greater
*/
LongPrototype.compare = function compare(other) {
if (!isLong(other))
other = fromValue(other);
if (this.eq(other))
return 0;
var thisNeg = this.isNegative(),
otherNeg = other.isNegative();
if (thisNeg && !otherNeg)
return -1;
if (!thisNeg && otherNeg)
return 1;
// At this point the sign bits are the same
if (!this.unsigned)
return this.sub(other).isNegative() ? -1 : 1;
// Both are positive if at least one is unsigned
return (other.high >>> 0) > (this.high >>> 0) || (other.high === this.high && (other.low >>> 0) > (this.low >>> 0)) ? -1 : 1;
};
/**
* Compares this Long's value with the specified's. This is an alias of {@link Long#compare}.
* @function
* @param {!Long|number|string} other Other value
* @returns {number} 0 if they are the same, 1 if the this is greater and -1
* if the given one is greater
*/
LongPrototype.comp = LongPrototype.compare;
/**
* Negates this Long's value.
* @returns {!Long} Negated Long
*/
LongPrototype.negate = function negate() {
if (!this.unsigned && this.eq(MIN_VALUE))
return MIN_VALUE;
return this.not().add(ONE);
};
/**
* Negates this Long's value. This is an alias of {@link Long#negate}.
* @function
* @returns {!Long} Negated Long
*/
LongPrototype.neg = LongPrototype.negate;
/**
* Returns the sum of this and the specified Long.
* @param {!Long|number|string} addend Addend
* @returns {!Long} Sum
*/
LongPrototype.add = function add(addend) {
if (!isLong(addend))
addend = fromValue(addend);
// Divide each number into 4 chunks of 16 bits, and then sum the chunks.
var a48 = this.high >>> 16;
var a32 = this.high & 0xFFFF;
var a16 = this.low >>> 16;
var a00 = this.low & 0xFFFF;
var b48 = addend.high >>> 16;
var b32 = addend.high & 0xFFFF;
var b16 = addend.low >>> 16;
var b00 = addend.low & 0xFFFF;
var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
c00 += a00 + b00;
c16 += c00 >>> 16;
c00 &= 0xFFFF;
c16 += a16 + b16;
c32 += c16 >>> 16;
c16 &= 0xFFFF;
c32 += a32 + b32;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c48 += a48 + b48;
c48 &= 0xFFFF;
return fromBits((c16 << 16) | c00, (c48 << 16) | c32, this.unsigned);
};
/**
* Returns the difference of this and the specified Long.
* @param {!Long|number|string} subtrahend Subtrahend
* @returns {!Long} Difference
*/
LongPrototype.subtract = function subtract(subtrahend) {
if (!isLong(subtrahend))
subtrahend = fromValue(subtrahend);
return this.add(subtrahend.neg());
};
/**
* Returns the difference of this and the specified Long. This is an alias of {@link Long#subtract}.
* @function
* @param {!Long|number|string} subtrahend Subtrahend
* @returns {!Long} Difference
*/
LongPrototype.sub = LongPrototype.subtract;
/**
* Returns the product of this and the specified Long.
* @param {!Long|number|string} multiplier Multiplier
* @returns {!Long} Product
*/
LongPrototype.multiply = function multiply(multiplier) {
if (this.isZero())
return ZERO;
if (!isLong(multiplier))
multiplier = fromValue(multiplier);
if (multiplier.isZero())
return ZERO;
if (this.eq(MIN_VALUE))
return multiplier.isOdd() ? MIN_VALUE : ZERO;
if (multiplier.eq(MIN_VALUE))
return this.isOdd() ? MIN_VALUE : ZERO;
if (this.isNegative()) {
if (multiplier.isNegative())
return this.neg().mul(multiplier.neg());
else
return this.neg().mul(multiplier).neg();
} else if (multiplier.isNegative())
return this.mul(multiplier.neg()).neg();
// If both longs are small, use float multiplication
if (this.lt(TWO_PWR_24) && multiplier.lt(TWO_PWR_24))
return fromNumber(this.toNumber() * multiplier.toNumber(), this.unsigned);
// Divide each long into 4 chunks of 16 bits, and then add up 4x4 products.
// We can skip products that would overflow.
var a48 = this.high >>> 16;
var a32 = this.high & 0xFFFF;
var a16 = this.low >>> 16;
var a00 = this.low & 0xFFFF;
var b48 = multiplier.high >>> 16;
var b32 = multiplier.high & 0xFFFF;
var b16 = multiplier.low >>> 16;
var b00 = multiplier.low & 0xFFFF;
var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
c00 += a00 * b00;
c16 += c00 >>> 16;
c00 &= 0xFFFF;
c16 += a16 * b00;
c32 += c16 >>> 16;
c16 &= 0xFFFF;
c16 += a00 * b16;
c32 += c16 >>> 16;
c16 &= 0xFFFF;
c32 += a32 * b00;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c32 += a16 * b16;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c32 += a00 * b32;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c48 += a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48;
c48 &= 0xFFFF;
return fromBits((c16 << 16) | c00, (c48 << 16) | c32, this.unsigned);
};
/**
* Returns the product of this and the specified Long. This is an alias of {@link Long#multiply}.
* @function
* @param {!Long|number|string} multiplier Multiplier
* @returns {!Long} Product
*/
LongPrototype.mul = LongPrototype.multiply;
/**
* Returns this Long divided by the specified. The result is signed if this Long is signed or
* unsigned if this Long is unsigned.
* @param {!Long|number|string} divisor Divisor
* @returns {!Long} Quotient
*/
LongPrototype.divide = function divide(divisor) {
if (!isLong(divisor))
divisor = fromValue(divisor);
if (divisor.isZero())
throw Error('division by zero');
if (this.isZero())
return this.unsigned ? UZERO : ZERO;
var approx, rem, res;
if (!this.unsigned) {
// This section is only relevant for signed longs and is derived from the
// closure library as a whole.
if (this.eq(MIN_VALUE)) {
if (divisor.eq(ONE) || divisor.eq(NEG_ONE))
return MIN_VALUE; // recall that -MIN_VALUE == MIN_VALUE
else if (divisor.eq(MIN_VALUE))
return ONE;
else {
// At this point, we have |other| >= 2, so |this/other| < |MIN_VALUE|.
var halfThis = this.shr(1);
approx = halfThis.div(divisor).shl(1);
if (approx.eq(ZERO)) {
return divisor.isNegative() ? ONE : NEG_ONE;
} else {
rem = this.sub(divisor.mul(approx));
res = approx.add(rem.div(divisor));
return res;
}
}
} else if (divisor.eq(MIN_VALUE))
return this.unsigned ? UZERO : ZERO;
if (this.isNegative()) {
if (divisor.isNegative())
return this.neg().div(divisor.neg());
return this.neg().div(divisor).neg();
} else if (divisor.isNegative())
return this.div(divisor.neg()).neg();
res = ZERO;
} else {
// The algorithm below has not been made for unsigned longs. It's therefore
// required to take special care of the MSB prior to running it.
if (!divisor.unsigned)
divisor = divisor.toUnsigned();
if (divisor.gt(this))
return UZERO;
if (divisor.gt(this.shru(1))) // 15 >>> 1 = 7 ; with divisor = 8 ; true
return UONE;
res = UZERO;
}
// Repeat the following until the remainder is less than other: find a
// floating-point that approximates remainder / other *from below*, add this
// into the result, and subtract it from the remainder. It is critical that
// the approximate value is less than or equal to the real value so that the
// remainder never becomes negative.
rem = this;
while (rem.gte(divisor)) {
// Approximate the result of division. This may be a little greater or
// smaller than the actual value.
approx = Math.max(1, Math.floor(rem.toNumber() / divisor.toNumber()));
// We will tweak the approximate result by changing it in the 48-th digit or
// the smallest non-fractional digit, whichever is larger.
var log2 = Math.ceil(Math.log(approx) / Math.LN2),
delta = (log2 <= 48) ? 1 : pow_dbl(2, log2 - 48),
// Decrease the approximation until it is smaller than the remainder. Note
// that if it is too large, the product overflows and is negative.
approxRes = fromNumber(approx),
approxRem = approxRes.mul(divisor);
while (approxRem.isNegative() || approxRem.gt(rem)) {
approx -= delta;
approxRes = fromNumber(approx, this.unsigned);
approxRem = approxRes.mul(divisor);
}
// We know the answer can't be zero... and actually, zero would cause
// infinite recursion since we would make no progress.
if (approxRes.isZero())
approxRes = ONE;
res = res.add(approxRes);
rem = rem.sub(approxRem);
}
return res;
};
/**
* Returns this Long divided by the specified. This is an alias of {@link Long#divide}.
* @function
* @param {!Long|number|string} divisor Divisor
* @returns {!Long} Quotient
*/
LongPrototype.div = LongPrototype.divide;
/**
* Returns this Long modulo the specified.
* @param {!Long|number|string} divisor Divisor
* @returns {!Long} Remainder
*/
LongPrototype.modulo = function modulo(divisor) {
if (!isLong(divisor))
divisor = fromValue(divisor);
return this.sub(this.div(divisor).mul(divisor));
};
/**
* Returns this Long modulo the specified. This is an alias of {@link Long#modulo}.
* @function
* @param {!Long|number|string} divisor Divisor
* @returns {!Long} Remainder
*/
LongPrototype.mod = LongPrototype.modulo;
/**
* Returns the bitwise NOT of this Long.
* @returns {!Long}
*/
LongPrototype.not = function not() {
return fromBits(~this.low, ~this.high, this.unsigned);
};
/**
* Returns the bitwise AND of this Long and the specified.
* @param {!Long|number|string} other Other Long
* @returns {!Long}
*/
LongPrototype.and = function and(other) {
if (!isLong(other))
other = fromValue(other);
return fromBits(this.low & other.low, this.high & other.high, this.unsigned);
};
/**
* Returns the bitwise OR of this Long and the specified.
* @param {!Long|number|string} other Other Long
* @returns {!Long}
*/
LongPrototype.or = function or(other) {
if (!isLong(other))
other = fromValue(other);
return fromBits(this.low | other.low, this.high | other.high, this.unsigned);
};
/**
* Returns the bitwise XOR of this Long and the given one.
* @param {!Long|number|string} other Other Long
* @returns {!Long}
*/
LongPrototype.xor = function xor(other) {
if (!isLong(other))
other = fromValue(other);
return fromBits(this.low ^ other.low, this.high ^ other.high, this.unsigned);
};
/**
* Returns this Long with bits shifted to the left by the given amount.
* @param {number|!Long} numBits Number of bits
* @returns {!Long} Shifted Long
*/
LongPrototype.shiftLeft = function shiftLeft(numBits) {
if (isLong(numBits))
numBits = numBits.toInt();
if ((numBits &= 63) === 0)
return this;
else if (numBits < 32)
return fromBits(this.low << numBits, (this.high << numBits) | (this.low >>> (32 - numBits)), this.unsigned);
else
return fromBits(0, this.low << (numBits - 32), this.unsigned);
};
/**
* Returns this Long with bits shifted to the left by the given amount. This is an alias of {@link Long#shiftLeft}.
* @function
* @param {number|!Long} numBits Number of bits
* @returns {!Long} Shifted Long
*/
LongPrototype.shl = LongPrototype.shiftLeft;
/**
* Returns this Long with bits arithmetically shifted to the right by the given amount.
* @param {number|!Long} numBits Number of bits
* @returns {!Long} Shifted Long
*/
LongPrototype.shiftRight = function shiftRight(numBits) {
if (isLong(numBits))
numBits = numBits.toInt();
if ((numBits &= 63) === 0)
return this;
else if (numBits < 32)
return fromBits((this.low >>> numBits) | (this.high << (32 - numBits)), this.high >> numBits, this.unsigned);
else
return fromBits(this.high >> (numBits - 32), this.high >= 0 ? 0 : -1, this.unsigned);
};
/**
* Returns this Long with bits arithmetically shifted to the right by the given amount. This is an alias of {@link Long#shiftRight}.
* @function
* @param {number|!Long} numBits Number of bits
* @returns {!Long} Shifted Long
*/
LongPrototype.shr = LongPrototype.shiftRight;
/**
* Returns this Long with bits logically shifted to the right by the given amount.
* @param {number|!Long} numBits Number of bits
* @returns {!Long} Shifted Long
*/
LongPrototype.shiftRightUnsigned = function shiftRightUnsigned(numBits) {
if (isLong(numBits))
numBits = numBits.toInt();
numBits &= 63;
if (numBits === 0)
return this;
else {
var high = this.high;
if (numBits < 32) {
var low = this.low;
return fromBits((low >>> numBits) | (high << (32 - numBits)), high >>> numBits, this.unsigned);
} else if (numBits === 32)
return fromBits(high, 0, this.unsigned);
else
return fromBits(high >>> (numBits - 32), 0, this.unsigned);
}
};
/**
* Returns this Long with bits logically shifted to the right by the given amount. This is an alias of {@link Long#shiftRightUnsigned}.
* @function
* @param {number|!Long} numBits Number of bits
* @returns {!Long} Shifted Long
*/
LongPrototype.shru = LongPrototype.shiftRightUnsigned;
/**
* Converts this Long to signed.
* @returns {!Long} Signed long
*/
LongPrototype.toSigned = function toSigned() {
if (!this.unsigned)
return this;
return fromBits(this.low, this.high, false);
};
/**
* Converts this Long to unsigned.
* @returns {!Long} Unsigned long
*/
LongPrototype.toUnsigned = function toUnsigned() {
if (this.unsigned)
return this;
return fromBits(this.low, this.high, true);
};
/**
* Converts this Long to its byte representation.
* @param {boolean=} le Whether little or big endian, defaults to big endian
* @returns {!Array.<number>} Byte representation
*/
LongPrototype.toBytes = function(le) {
return le ? this.toBytesLE() : this.toBytesBE();
}
/**
* Converts this Long to its little endian byte representation.
* @returns {!Array.<number>} Little endian byte representation
*/
LongPrototype.toBytesLE = function() {
var hi = this.high,
lo = this.low;
return [
lo & 0xff,
(lo >>> 8) & 0xff,
(lo >>> 16) & 0xff,
(lo >>> 24) & 0xff,
hi & 0xff,
(hi >>> 8) & 0xff,
(hi >>> 16) & 0xff,
(hi >>> 24) & 0xff
];
}
/**
* Converts this Long to its big endian byte representation.
* @returns {!Array.<number>} Big endian byte representation
*/
LongPrototype.toBytesBE = function() {
var hi = this.high,
lo = this.low;
return [
(hi >>> 24) & 0xff,
(hi >>> 16) & 0xff,
(hi >>> 8) & 0xff,
hi & 0xff,
(lo >>> 24) & 0xff,
(lo >>> 16) & 0xff,
(lo >>> 8) & 0xff,
lo & 0xff
];
}
return Long;
});
3rdparty/protobuf.js deleted 100644 → 0
View file @ 0b1e5c63
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