diff --git a/dist/bigint-mod-arith-latest.browser.js b/dist/bigint-mod-arith-latest.browser.js new file mode 100644 index 0000000..51de4da --- /dev/null +++ b/dist/bigint-mod-arith-latest.browser.js @@ -0,0 +1,178 @@ +var bigintModArith = (function (exports) { + 'use strict'; + + const _ZERO = BigInt(0); + const _ONE = BigInt(1); + const _TWO = BigInt(2); + + /** + * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0 + * + * @param {number|bigint} a + * + * @returns {bigint} the absolute value of a + */ + function abs(a) { + a = BigInt(a); + return (a >= _ZERO) ? a : -a; + } + + /** + * @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b). + * @property {bigint} g + * @property {bigint} x + * @property {bigint} y + */ + /** + * An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm. + * Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b). + * + * @param {number|bigint} a + * @param {number|bigint} b + * + * @returns {egcdReturn} + */ + function eGcd(a, b) { + a = BigInt(a); + b = BigInt(b); + let x = _ZERO; + let y = _ONE; + let u = _ONE; + let v = _ZERO; + + while (a !== _ZERO) { + let q = b / a; + let r = b % a; + let m = x - (u * q); + let n = y - (v * q); + b = a; + a = r; + x = u; + y = v; + u = m; + v = n; + } + return { + b: b, + x: x, + y: y + }; + } + + /** + * Greatest-common divisor of two integers based on the iterative binary algorithm. + * + * @param {number|bigint} a + * @param {number|bigint} b + * + * @returns {bigint} The greatest common divisor of a and b + */ + function gcd(a, b) { + a = abs(a); + b = abs(b); + let shift = _ZERO; + while (!((a | b) & _ONE)) { + a >>= _ONE; + b >>= _ONE; + shift++; + } + while (!(a & _ONE)) a >>= _ONE; + do { + while (!(b & _ONE)) b >>= _ONE; + if (a > b) { + let x = a; + a = b; + b = x; + } + b -= a; + } while (b); + + // rescale + return a << shift; + } + + /** + * The least common multiple computed as abs(a*b)/gcd(a,b) + * @param {number|bigint} a + * @param {number|bigint} b + * + * @returns {bigint} The least common multiple of a and b + */ + function lcm(a, b) { + a = BigInt(a); + b = BigInt(b); + return abs(a * b) / gcd(a, b); + } + + /** + * Modular inverse. + * + * @param {number|bigint} a The number to find an inverse for + * @param {number|bigint} n The modulo + * + * @returns {bigint} the inverse modulo n + */ + function modInv(a, n) { + let egcd = eGcd(a, n); + if (egcd.b !== _ONE) { + return null; // modular inverse does not exist + } else { + return toZn(egcd.x, n); + } + } + + /** + * Modular exponentiation a**b mod n + * @param {number|bigint} a base + * @param {number|bigint} b exponent + * @param {number|bigint} n modulo + * + * @returns {bigint} a**b mod n + */ + function modPow(a, b, n) { + // See Knuth, volume 2, section 4.6.3. + n = BigInt(n); + a = toZn(a, n); + b = BigInt(b); + if (b < _ZERO) { + return modInv(modPow(a, abs(b), n), n); + } + let result = _ONE; + let x = a; + while (b > 0) { + var leastSignificantBit = b % _TWO; + b = b / _TWO; + if (leastSignificantBit == _ONE) { + result = result * x; + result = result % n; + } + x = x * x; + x = x % n; + } + return result; + } + + /** + * Finds the smallest positive element that is congruent to a in modulo n + * @param {number|bigint} a An integer + * @param {number|bigint} n The modulo + * + * @returns {bigint} The smallest positive representation of a in modulo n + */ + function toZn(a, n) { + n = BigInt(n); + a = BigInt(a) % n; + return (a < 0) ? a + n : a; + } + + exports.abs = abs; + exports.eGcd = eGcd; + exports.gcd = gcd; + exports.lcm = lcm; + exports.modInv = modInv; + exports.modPow = modPow; + exports.toZn = toZn; + + return exports; + +}({})); diff --git a/dist/bigint-mod-arith-latest.browser.min.js b/dist/bigint-mod-arith-latest.browser.min.js new file mode 100644 index 0000000..31c795d --- /dev/null +++ b/dist/bigint-mod-arith-latest.browser.min.js @@ -0,0 +1 @@ +var bigintModArith=function(a){'use strict';function c(b){return b=BigInt(b),b>=i?b:-b}function d(c,d){c=BigInt(c),d=BigInt(d);let e=i,f=j,g=j,h=i;for(;c!==i;){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}}function e(d,e){d=c(d),e=c(e);let f=i;for(;!((d|e)&j);)d>>=j,e>>=j,f++;for(;!(d&j);)d>>=j;do{for(;!(e&j);)e>>=j;if(d>e){let a=d;d=e,e=a}e-=d}while(e);return d<b?b+c:b}const i=BigInt(0),j=BigInt(1),k=BigInt(2);return a.abs=c,a.eGcd=d,a.gcd=e,a.lcm=function(d,f){return d=BigInt(d),f=BigInt(f),c(d*f)/e(d,f)},a.modInv=f,a.modPow=g,a.toZn=h,a}({});