From 1086c1fac6fcbd8f7455aa78d4e7e66d6c1e9051 Mon Sep 17 00:00:00 2001 From: Evgenus Date: Sun, 3 Aug 2014 15:16:57 +0300 Subject: [PATCH] definitions for BigInt by Baird Leemon. distribution source: https://github.com/Evgenus/BigInt original source: http://www.leemon.com/crypto/BigInt.html --- CONTRIBUTORS.md | 1 + bigint/bigint-tests.ts | 81 ++++++++++++++ bigint/bigint.d.ts | 245 +++++++++++++++++++++++++++++++++++++++++ 3 files changed, 327 insertions(+) create mode 100644 bigint/bigint-tests.ts create mode 100644 bigint/bigint.d.ts diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md index af326634b1..eab14f2c50 100644 --- a/CONTRIBUTORS.md +++ b/CONTRIBUTORS.md @@ -31,6 +31,7 @@ All definitions files include a header with the author and editors, so at some p * [Backbone.js](http://backbonejs.org/) (by [Boris Yankov](https://github.com/borisyankov)) * [Backbone Relational](http://backbonerelational.org/) (by [Eirik Hoem](https://github.com/eirikhm)) * [big.js](https://github.com/MikeMcl/big.js) (by [Steve Ognibene](https://github.com/nycdotnet)) +* [BigInt](https://github.com/Evgenus/BigInt) (by [Eugene Chernyshov](https://github.com/Evgenus)) * [BigInteger](https://github.com/peterolson/BigInteger.js) (by [Ingo Bürk](https://github.com/Airblader)) * [BigScreen](http://brad.is/coding/BigScreen/) (by [Douglas Eichelberger](https://github.com/dduugg)) * [Bluebird](https://github.com/petkaantonov/bluebird) (by [Bart van der Schoor](https://github.com/Bartvds)) diff --git a/bigint/bigint-tests.ts b/bigint/bigint-tests.ts new file mode 100644 index 0000000000..8ccf2ba4b9 --- /dev/null +++ b/bigint/bigint-tests.ts @@ -0,0 +1,81 @@ +/// + +var bi: BigInt.BigInt; +var num: number; +var str: string; +var b: boolean; + +BigInt.setRandom(() => { return 0; }); + +bi = BigInt.add(bi, bi); +bi = BigInt.addInt(bi, num); +str = BigInt.bigInt2str(bi, num); +str = BigInt.bigInt2str(bi, str); +num = BigInt.bitSize(bi); +bi = BigInt.dup(bi); +b = BigInt.equals(bi, bi); +b = BigInt.equalsInt(bi, num); +bi = BigInt.expand(bi, num); +var nums: number[] = BigInt.findPrimes(num); +bi = BigInt.GCD(bi, bi); +b = BigInt.greater(bi, bi); +b = BigInt.greaterShift(bi, bi, num); +bi = BigInt.int2bigInt(0); +bi = BigInt.int2bigInt(0, 0); +bi = BigInt.int2bigInt(0, 0, 0); +bi = BigInt.inverseMod(bi, bi); +bi = BigInt.inverseModInt(num, num); +b = BigInt.isZero(bi); +b = BigInt.millerRabin(bi, bi); +b = BigInt.millerRabinInt(num, num); +bi = BigInt.mod(bi, bi); +num = BigInt.modInt(bi, num); +bi = BigInt.mult(bi, bi); +bi = BigInt.multMod(bi, bi, bi); +b = BigInt.negative(bi); +bi = BigInt.powMod(bi, bi, bi); +bi = BigInt.randBigInt(num, num); +bi = BigInt.randTruePrime(num); +bi = BigInt.randProbPrime(num); +bi = BigInt.str2bigInt(str, num); +bi = BigInt.str2bigInt(str, num, 0); +bi = BigInt.str2bigInt(str, num, 0, 0); +bi = BigInt.str2bigInt(str, str); +bi = BigInt.str2bigInt(str, str, 0); +bi = BigInt.str2bigInt(str, str, 0, 0); +bi = BigInt.sub(bi, bi); +bi = BigInt.trim(bi, num); + +BigInt.addInt_(bi, num); +BigInt.add_(bi, bi); +BigInt.copy_(bi, bi); +num = BigInt.copyInt_(bi, num); +BigInt.GCD_(bi, bi); +b = BigInt.inverseMod_(bi, bi); +BigInt.mod_(bi, bi); +BigInt.mult_(bi, bi); +BigInt.multMod_(bi, bi, bi); +BigInt.powMod_(bi, bi, bi); +BigInt.randBigInt_(bi, num, num); +BigInt.randTruePrime_(bi, num); +BigInt.sub_(bi, bi); +BigInt.addShift_(bi, bi, num); +BigInt.carry_(bi); +BigInt.divide_(bi, bi, bi, bi); +num = BigInt.divInt_(bi, num); +BigInt.eGCD_(bi, bi, bi, bi, bi); +BigInt.halve_(bi); +BigInt.leftShift_(bi, num); +BigInt.linComb_(bi, bi, num, num); +BigInt.linCombShift_(bi, bi, num, num); +BigInt.mont_(bi, bi, bi, num); +BigInt.multInt_(bi, num); +BigInt.rightShift_(bi, num); +BigInt.squareMod_(bi, bi); +BigInt.subShift_(bi, bi, num); + +function someRandomRealCode() { + bi = BigInt.int2bigInt(22, 5); + bi = BigInt.str2bigInt("FFFFFFFFFFFFFFFFC90FDAA2", 16); + str = BigInt.bigInt2str(bi, 16); +} diff --git a/bigint/bigint.d.ts b/bigint/bigint.d.ts new file mode 100644 index 0000000000..61543b1c60 --- /dev/null +++ b/bigint/bigint.d.ts @@ -0,0 +1,245 @@ +// Type definitions for BigInt v5.5.1 +// Project: https://github.com/Evgenus/BigInt +// Definitions by: Eugene Chernyshov +// Definitions: https://github.com/borisyankov/DefinitelyTyped + +declare module BigInt { + export interface BigInt extends Array { + } + + export interface IRandom { + (): number; + } + + export function setRandom(random: IRandom): void; + + // bigInt add(x,y) + // return (x+y) for bigInts x and y. + export function add(x: BigInt, y: BigInt): BigInt; + + // bigInt addInt(x,n) + // return (x+n) where x is a bigInt and n is an integer. + export function addInt(x: BigInt, n: number): BigInt; + + // string bigInt2str(x,base) + // return a string form of bigInt x in a given base, with 2 <= base <= 95 + export function bigInt2str(x: BigInt, base: number): string; + export function bigInt2str(x: BigInt, base: string): string; + + // int bitSize(x) + // return how many bits long the bigInt x is, not counting leading zeros + export function bitSize(x: BigInt): number; + + // bigInt dup(x) + // return a copy of bigInt x + export function dup(x: BigInt): BigInt; + + // boolean equals(x,y) + // is the bigInt x equal to the bigint y? + export function equals(x: BigInt, y: BigInt): boolean; + + // boolean equalsInt(x,y) + // is bigint x equal to integer y? + export function equalsInt(x: BigInt, y: number): boolean; + + // bigInt expand(x,n) + // return a copy of x with at least n elements, adding leading zeros if needed + export function expand(value: BigInt, n: number): BigInt; + + // Array findPrimes(n) + // return array of all primes less than integer n + export function findPrimes(n: number): number[]; + + // bigInt GCD(x,y) + // return greatest common divisor of bigInts x and y (each with same number of elements). + export function GCD(x: BigInt, y: BigInt): BigInt; + + // boolean greater(x,y) + // is x>y? (x and y are nonnegative bigInts) + export function greater(x: BigInt, y: BigInt): boolean; + + // boolean greaterShift(x,y,shift) + // is (x <<(shift*bpe)) > y? + export function greaterShift(x: BigInt, y: BigInt, shift: number): boolean; + + // bigInt int2bigInt(t,n,m) + // return a bigInt equal to integer t, with at least n bits and m array elements + export function int2bigInt(t: number, n?: number, m?: number): BigInt; + + // bigInt inverseMod(x,n) + // return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null + export function inverseMod(x: BigInt, n: BigInt): BigInt; + + // int inverseModInt(x,n) + // return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse + export function inverseModInt(x: number, n: number): BigInt; + + // boolean isZero(x) + // is the bigInt x equal to zero? + export function isZero(x: BigInt): boolean; + + // boolean millerRabin(x,b) + // does one round of Miller-Rabin base integer b say that bigInt x is possibly prime? (b is bigInt, 1=1). If s=1, then the most significant of those n bits is set to 1. + export function randBigInt(n: number, s: number): BigInt; + + // bigInt randTruePrime(k) + // return a new, random, k-bit, true prime bigInt using Maurer's algorithm. + export function randTruePrime(k: number): BigInt; + + // bigInt randProbPrime(k) + // return a new, random, k-bit, probable prime bigInt (probability it's composite less than 2^-80). + export function randProbPrime(k: number): BigInt; + + // 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 + export function str2bigInt(s: string, b: number, n?: number, m?: number): BigInt; + export function str2bigInt(s: string, b: string, n?: number, m?: number): BigInt; + + // bigInt sub(x,y) + // return (x-y) for bigInts x and y. Negative answers will be 2s complement + export function sub(x: BigInt, y: BigInt): BigInt; + + // bigInt trim(x,k) + // return a copy of x with exactly k leading zero elements + export function trim(x: BigInt, k: number): BigInt; + + // void addInt_(x,n) + // do x=x+n where x is a bigInt and n is an integer + export function addInt_(x: BigInt, n: number): void; + + // void add_(x,y) + // do x=x+y for bigInts x and y + export function add_(x: BigInt, y: BigInt): void; + + // void copy_(x,y) + // do x=y on bigInts x and y + export function copy_(x: BigInt, y: BigInt): void; + + // void copyInt_(x,n) + // do x=n on bigInt x and integer n + export function copyInt_(x: BigInt, n: number): number; + + // void GCD_(x,y) + // set x to the greatest common divisor of bigInts x and y, (y is destroyed). (This never overflows its array). + export function GCD_(x: BigInt, y: BigInt): void; + + // boolean inverseMod_(x,n) + // do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist + export function inverseMod_(x: BigInt, n: BigInt): boolean; + + // void mod_(x,n) + // do x=x mod n for bigInts x and n. (This never overflows its array). + export function mod_(x: BigInt, n: BigInt): void; + + // void mult_(x,y) + // do x=x*y for bigInts x and y. + export function mult_(x: BigInt, y: BigInt): void; + + // void multMod_(x,y,n) + // do x=x*y mod n for bigInts x,y,n. + export function multMod_(x: BigInt, y: BigInt, n: BigInt): void; + + // 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. + export function powMod_(x: BigInt, y: BigInt, n: BigInt): void; + + // 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. + export function randBigInt_(b: BigInt, n: number, s: number): void; + + // void randTruePrime_(ans,k) + // do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb. + export function randTruePrime_(ans: BigInt, k: number): void; + + // void sub_(x,y) + // do x=x-y for bigInts x and y. Negative answers will be 2s complement. + export function sub_(x: BigInt, y: BigInt): void; + + // void addShift_(x,y,ys) + // do x=x+(y<<(ys*bpe)) + export function addShift_(x: BigInt, y: BigInt, ys: number): void; + + // void carry_(x) + // do carries and borrows so each element of the bigInt x fits in bpe bits. + export function carry_(x: BigInt): void; + + // void divide_(x,y,q,r) + // divide x by y giving quotient q and remainder r + export function divide_(x: BigInt, y: BigInt, q: BigInt, r: BigInt): void; + + // int divInt_(x,n) + // do x=floor(x/n) for bigInt x and integer n, and return the remainder. (This never overflows its array). + export function divInt_(x: BigInt, n: number): number; + + // void eGCD_(x,y,d,a,b) + // sets a,b,d to positive bigInts such that d = GCD_(x,y) = a*x-b*y + export function eGCD_(x: BigInt, y: BigInt, d: BigInt, a: BigInt, b: BigInt): void; + + // void halve_(x) + // do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement. (This never overflows its array). + export function halve_(x: BigInt): void; + + // void leftShift_(x,n) + // left shift bigInt x by n bits. n