// BigInt, a suite of routines for performing multiple-precision arithmetic in
// JavaScript.
//
// Copyright 1998-2005 David Shapiro.
//
// You may use, re-use, abuse,
// copy, and modify this code to your liking, but please keep this header.
// Thanks!
//
// Dave Shapiro
// dave@ohdave.com

// IMPORTANT THING: Be sure to set maxDigits according to your precision
// needs. Use the setMaxDigits() function to do this. See comments below.
//
// Tweaked by Ian Bunning
// Alterations:
// Fix bug in function biFromHex(s) to allow
// parsing of strings of length != 0 (mod 4)

// Changes made by Dave Shapiro as of 12/30/2004:
//
// The BigInt() constructor doesn't take a string anymore. If you want to
// create a BigInt from a string, use biFromDecimal() for base-10
// representations, biFromHex() for base-16 representations, or
// biFromString() for base-2-to-36 representations.
//
// biFromArray() has been removed. Use biCopy() instead, passing a BigInt
// instead of an array.
//
// The BigInt() constructor now only constructs a zeroed-out array.
// Alternatively, if you pass <true>, it won't construct any array. See the
// biCopy() method for an example of this.
//
// Be sure to set maxDigits depending on your precision needs. The default
// zeroed-out array ZERO_ARRAY is constructed inside the setMaxDigits()
// function. So use this function to set the variable. DON'T JUST SET THE
// VALUE. USE THE FUNCTION.
//
// ZERO_ARRAY exists to hopefully speed up construction of BigInts(). By
// precalculating the zero array, we can just use slice(0) to make copies of
// it. Presumably this calls faster native code, as opposed to setting the
// elements one at a time. I have not done any timing tests to verify this
// claim.

// Max number = 10^16 - 2 = 9999999999999998;
//               2^53     = 9007199254740992;

var biRadixBase = 2;
var biRadixBits = 16;
var bitsPerDigit = biRadixBits;
var biRadix = 1 << 16;
// = 2^16 = 65536
var biHalfRadix = biRadix >>> 1;
var biRadixSquared = biRadix * biRadix;
var maxDigitVal = biRadix - 1;
var maxInteger = 9999999999999998;

// maxDigits:
// Change this to accommodate your largest number size. Use setMaxDigits()
// to change it!
//
// In general, if you're working with numbers of size N bits, you'll need 2*N
// bits of storage. Each digit holds 16 bits. So, a 1024-bit key will need
//
// 1024 * 2 / 16 = 128 digits of storage.
//

var maxDigits;
var ZERO_ARRAY;
var bigZero, bigOne;

function setMaxDigits(value) {
    maxDigits = value;
    ZERO_ARRAY = new Array(maxDigits);
    for (var iza = 0; iza < ZERO_ARRAY.length; iza++)
        ZERO_ARRAY[iza] = 0;
    bigZero = new BigInt();
    bigOne = new BigInt();
    bigOne.digits[0] = 1;
}

setMaxDigits(20);

// The maximum number of digits in base 10 you can convert to an
// integer without JavaScript throwing up on you.
var dpl10 = 15;
// lr10 = 10 ^ dpl10
var lr10 = biFromNumber(1000000000000000);

function BigInt(flag) {
    if (typeof flag == "boolean" && flag == true) {
        this.digits = null;
    } else {
        this.digits = ZERO_ARRAY.slice(0);
    }
    this.isNeg = false;
}

function biFromDecimal(s) {
    var isNeg = s.charAt(0) == '-';
    var i = isNeg ? 1 : 0;
    var result;
    // Skip leading zeros.
    while (i < s.length && s.charAt(i) == '0')
        ++i;
    if (i == s.length) {
        result = new BigInt();
    } else {
        var digitCount = s.length - i;
        var fgl = digitCount % dpl10;
        if (fgl == 0)
            fgl = dpl10;
        result = biFromNumber(Number(s.substr(i, fgl)));
        i += fgl;
        while (i < s.length) {
            result = biAdd(biMultiply(result, lr10), biFromNumber(Number(s.substr(i, dpl10))));
            i += dpl10;
        }
        result.isNeg = isNeg;
    }
    return result;
}

function biCopy(bi) {
    var result = new BigInt(true);
    result.digits = bi.digits.slice(0);
    result.isNeg = bi.isNeg;
    return result;
}

function biFromNumber(i) {
    var result = new BigInt();
    result.isNeg = i < 0;
    i = Math.abs(i);
    var j = 0;
    while (i > 0) {
        result.digits[j++] = i & maxDigitVal;
        i >>= biRadixBits;
    }
    return result;
}

function reverseStr(s) {
    var result = "";
    for (var i = s.length - 1; i > -1; --i) {
        result += s.charAt(i);
    }
    return result;
}

var hexatrigesimalToChar = new Array('0','1','2','3','4','5','6','7','8','9','a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z');

function biToString(x, radix) // 2 <= radix <= 36
{
    var b = new BigInt();
    b.digits[0] = radix;
    var qr = biDivideModulo(x, b);
    var result = hexatrigesimalToChar[qr[1].digits[0]];
    while (biCompare(qr[0], bigZero) == 1) {
        qr = biDivideModulo(qr[0], b);
        digit = qr[1].digits[0];
        result += hexatrigesimalToChar[qr[1].digits[0]];
    }
    return (x.isNeg ? "-" : "") + reverseStr(result);
}

function biToDecimal(x) {
    var b = new BigInt();
    b.digits[0] = 10;
    var qr = biDivideModulo(x, b);
    var result = String(qr[1].digits[0]);
    while (biCompare(qr[0], bigZero) == 1) {
        qr = biDivideModulo(qr[0], b);
        result += String(qr[1].digits[0]);
    }
    return (x.isNeg ? "-" : "") + reverseStr(result);
}

var hexToChar = new Array('0','1','2','3','4','5','6','7','8','9','a','b','c','d','e','f');

function digitToHex(n) {
    var mask = 0xf;
    var result = "";
    for (i = 0; i < 4; ++i) {
        result += hexToChar[n & mask];
        n >>>= 4;
    }
    return reverseStr(result);
}

function biToHex(x) {
    var result = "";
    var n = biHighIndex(x);
    for (var i = biHighIndex(x); i > -1; --i) {
        result += digitToHex(x.digits[i]);
    }
    return result;
}

function charToHex(c) {
    var ZERO = 48;
    var NINE = ZERO + 9;
    var littleA = 97;
    var littleZ = littleA + 25;
    var bigA = 65;
    var bigZ = 65 + 25;
    var result;

    if (c >= ZERO && c <= NINE) {
        result = c - ZERO;
    } else if (c >= bigA && c <= bigZ) {
        result = 10 + c - bigA;
    } else if (c >= littleA && c <= littleZ) {
        result = 10 + c - littleA;
    } else {
        result = 0;
    }
    return result;
}

function hexToDigit(s) {
    var result = 0;
    var sl = Math.min(s.length, 4);
    for (var i = 0; i < sl; ++i) {
        result <<= 4;
        result |= charToHex(s.charCodeAt(i))
    }
    return result;
}

function biFromHex(s) {
    var result = new BigInt();
    var sl = s.length;
    for (var i = sl, j = 0; i > 0; i -= 4,
    ++j) {
        result.digits[j] = hexToDigit(s.substr(Math.max(i - 4, 0), Math.min(i, 4)));
    }
    return result;
}

function biFromString(s, radix) {
    var isNeg = s.charAt(0) == '-';
    var istop = isNeg ? 1 : 0;
    var result = new BigInt();
    var place = new BigInt();
    place.digits[0] = 1;
    // radix^0
    for (var i = s.length - 1; i >= istop; i--) {
        var c = s.charCodeAt(i);
        var digit = charToHex(c);
        var biDigit = biMultiplyDigit(place, digit);
        result = biAdd(result, biDigit);
        place = biMultiplyDigit(place, radix);
    }
    result.isNeg = isNeg;
    return result;
}

function biToBytes(x) // Returns a string containing raw bytes.
{
    var result = "";
    for (var i = biHighIndex(x); i > -1; --i) {
        result += digitToBytes(x.digits[i]);
    }
    return result;
}

function digitToBytes(n) // Convert two-byte digit to string containing both bytes.
{
    var c1 = String.fromCharCode(n & 0xff);
    n >>>= 8;
    var c2 = String.fromCharCode(n & 0xff);
    return c2 + c1;
}

function biDump(b) {
    return (b.isNeg ? "-" : "") + b.digits.join(" ");
}

function biAdd(x, y) {
    var result;

    if (x.isNeg != y.isNeg) {
        y.isNeg = !y.isNeg;
        result = biSubtract(x, y);
        y.isNeg = !y.isNeg;
    } else {
        result = new BigInt();
        var c = 0;
        var n;
        for (var i = 0; i < x.digits.length; ++i) {
            n = x.digits[i] + y.digits[i] + c;
            result.digits[i] = n & 0xffff;
            c = Number(n >= biRadix);
        }
        result.isNeg = x.isNeg;
    }
    return result;
}

function biSubtract(x, y) {
    var result;
    if (x.isNeg != y.isNeg) {
        y.isNeg = !y.isNeg;
        result = biAdd(x, y);
        y.isNeg = !y.isNeg;
    } else {
        result = new BigInt();
        var n, c;
        c = 0;
        for (var i = 0; i < x.digits.length; ++i) {
            n = x.digits[i] - y.digits[i] + c;
            result.digits[i] = n & 0xffff;
            // Stupid non-conforming modulus operation.
            if (result.digits[i] < 0)
                result.digits[i] += biRadix;
            c = 0 - Number(n < 0);
        }
        // Fix up the negative sign, if any.
        if (c == -1) {
            c = 0;
            for (var i = 0; i < x.digits.length; ++i) {
                n = 0 - result.digits[i] + c;
                result.digits[i] = n & 0xffff;
                // Stupid non-conforming modulus operation.
                if (result.digits[i] < 0)
                    result.digits[i] += biRadix;
                c = 0 - Number(n < 0);
            }
            // Result is opposite sign of arguments.
            result.isNeg = !x.isNeg;
        } else {
            // Result is same sign.
            result.isNeg = x.isNeg;
        }
    }
    return result;
}

function biHighIndex(x) {
    var result = x.digits.length - 1;
    while (result > 0 && x.digits[result] == 0)
        --result;
    return result;
}

function biNumBits(x) {
    var n = biHighIndex(x);
    var d = x.digits[n];
    var m = (n + 1) * bitsPerDigit;
    var result;
    for (result = m; result > m - bitsPerDigit; --result) {
        if ((d & 0x8000) != 0)
            break;
        d <<= 1;
    }
    return result;
}

function biMultiply(x, y) {
    var result = new BigInt();
    var c;
    var n = biHighIndex(x);
    var t = biHighIndex(y);
    var u, uv, k;

    for (var i = 0; i <= t; ++i) {
        c = 0;
        k = i;
        for (j = 0; j <= n; ++j,
        ++k) {
            uv = result.digits[k] + x.digits[j] * y.digits[i] + c;
            result.digits[k] = uv & maxDigitVal;
            c = uv >>> biRadixBits;
        }
        result.digits[i + n + 1] = c;
    }
    // Someone give me a logical xor, please.
    result.isNeg = x.isNeg != y.isNeg;
    return result;
}

function biMultiplyDigit(x, y) {
    var n, c, uv;

    result = new BigInt();
    n = biHighIndex(x);
    c = 0;
    for (var j = 0; j <= n; ++j) {
        uv = result.digits[j] + x.digits[j] * y + c;
        result.digits[j] = uv & maxDigitVal;
        c = uv >>> biRadixBits;
    }
    result.digits[1 + n] = c;
    return result;
}

function arrayCopy(src, srcStart, dest, destStart, n) {
    var m = Math.min(srcStart + n, src.length);
    for (var i = srcStart, j = destStart; i < m; ++i,
    ++j) {
        dest[j] = src[i];
    }
}

var highBitMasks = new Array(0x0000,0x8000,0xC000,0xE000,0xF000,0xF800,0xFC00,0xFE00,0xFF00,0xFF80,0xFFC0,0xFFE0,0xFFF0,0xFFF8,0xFFFC,0xFFFE,0xFFFF);

function biShiftLeft(x, n) {
    var digitCount = Math.floor(n / bitsPerDigit);
    var result = new BigInt();
    arrayCopy(x.digits, 0, result.digits, digitCount, result.digits.length - digitCount);
    var bits = n % bitsPerDigit;
    var rightBits = bitsPerDigit - bits;
    for (var i = result.digits.length - 1, i1 = i - 1; i > 0; --i,
    --i1) {
        result.digits[i] = ((result.digits[i] << bits) & maxDigitVal) | ((result.digits[i1] & highBitMasks[bits]) >>> (rightBits));
    }
    result.digits[0] = ((result.digits[i] << bits) & maxDigitVal);
    result.isNeg = x.isNeg;
    return result;
}

var lowBitMasks = new Array(0x0000,0x0001,0x0003,0x0007,0x000F,0x001F,0x003F,0x007F,0x00FF,0x01FF,0x03FF,0x07FF,0x0FFF,0x1FFF,0x3FFF,0x7FFF,0xFFFF);

function biShiftRight(x, n) {
    var digitCount = Math.floor(n / bitsPerDigit);
    var result = new BigInt();
    arrayCopy(x.digits, digitCount, result.digits, 0, x.digits.length - digitCount);
    var bits = n % bitsPerDigit;
    var leftBits = bitsPerDigit - bits;
    for (var i = 0, i1 = i + 1; i < result.digits.length - 1; ++i,
    ++i1) {
        result.digits[i] = (result.digits[i] >>> bits) | ((result.digits[i1] & lowBitMasks[bits]) << leftBits);
    }
    result.digits[result.digits.length - 1] >>>= bits;
    result.isNeg = x.isNeg;
    return result;
}

function biMultiplyByRadixPower(x, n) {
    var result = new BigInt();
    arrayCopy(x.digits, 0, result.digits, n, result.digits.length - n);
    return result;
}

function biDivideByRadixPower(x, n) {
    var result = new BigInt();
    arrayCopy(x.digits, n, result.digits, 0, result.digits.length - n);
    return result;
}

function biModuloByRadixPower(x, n) {
    var result = new BigInt();
    arrayCopy(x.digits, 0, result.digits, 0, n);
    return result;
}

function biCompare(x, y) {
    if (x.isNeg != y.isNeg) {
        return 1 - 2 * Number(x.isNeg);
    }
    for (var i = x.digits.length - 1; i >= 0; --i) {
        if (x.digits[i] != y.digits[i]) {
            if (x.isNeg) {
                return 1 - 2 * Number(x.digits[i] > y.digits[i]);
            } else {
                return 1 - 2 * Number(x.digits[i] < y.digits[i]);
            }
        }
    }
    return 0;
}

function biDivideModulo(x, y) {
    var nb = biNumBits(x);
    var tb = biNumBits(y);
    var origYIsNeg = y.isNeg;
    var q, r;
    if (nb < tb) {
        // |x| < |y|
        if (x.isNeg) {
            q = biCopy(bigOne);
            q.isNeg = !y.isNeg;
            x.isNeg = false;
            y.isNeg = false;
            r = biSubtract(y, x);
            // Restore signs, 'cause they're references.
            x.isNeg = true;
            y.isNeg = origYIsNeg;
        } else {
            q = new BigInt();
            r = biCopy(x);
        }
        return new Array(q,r);
    }

    q = new BigInt();
    r = x;

    // Normalize Y.
    var t = Math.ceil(tb / bitsPerDigit) - 1;
    var lambda = 0;
    while (y.digits[t] < biHalfRadix) {
        y = biShiftLeft(y, 1);
        ++lambda;
        ++tb;
        t = Math.ceil(tb / bitsPerDigit) - 1;
    }
    // Shift r over to keep the quotient constant. We'll shift the
    // remainder back at the end.
    r = biShiftLeft(r, lambda);
    nb += lambda;
    // Update the bit count for x.
    var n = Math.ceil(nb / bitsPerDigit) - 1;

    var b = biMultiplyByRadixPower(y, n - t);
    while (biCompare(r, b) != -1) {
        ++q.digits[n - t];
        r = biSubtract(r, b);
    }
    for (var i = n; i > t; --i) {
        var ri = (i >= r.digits.length) ? 0 : r.digits[i];
        var ri1 = (i - 1 >= r.digits.length) ? 0 : r.digits[i - 1];
        var ri2 = (i - 2 >= r.digits.length) ? 0 : r.digits[i - 2];
        var yt = (t >= y.digits.length) ? 0 : y.digits[t];
        var yt1 = (t - 1 >= y.digits.length) ? 0 : y.digits[t - 1];
        if (ri == yt) {
            q.digits[i - t - 1] = maxDigitVal;
        } else {
            q.digits[i - t - 1] = Math.floor((ri * biRadix + ri1) / yt);
        }

        var c1 = q.digits[i - t - 1] * ((yt * biRadix) + yt1);
        var c2 = (ri * biRadixSquared) + ((ri1 * biRadix) + ri2);
        while (c1 > c2) {
            --q.digits[i - t - 1];
            c1 = q.digits[i - t - 1] * ((yt * biRadix) | yt1);
            c2 = (ri * biRadix * biRadix) + ((ri1 * biRadix) + ri2);
        }

        b = biMultiplyByRadixPower(y, i - t - 1);
        r = biSubtract(r, biMultiplyDigit(b, q.digits[i - t - 1]));
        if (r.isNeg) {
            r = biAdd(r, b);
            --q.digits[i - t - 1];
        }
    }
    r = biShiftRight(r, lambda);
    // Fiddle with the signs and stuff to make sure that 0 <= r < y.
    q.isNeg = x.isNeg != origYIsNeg;
    if (x.isNeg) {
        if (origYIsNeg) {
            q = biAdd(q, bigOne);
        } else {
            q = biSubtract(q, bigOne);
        }
        y = biShiftRight(y, lambda);
        r = biSubtract(y, r);
    }
    // Check for the unbelievably stupid degenerate case of r == -0.
    if (r.digits[0] == 0 && biHighIndex(r) == 0)
        r.isNeg = false;

    return new Array(q,r);
}

function biDivide(x, y) {
    return biDivideModulo(x, y)[0];
}

function biModulo(x, y) {
    return biDivideModulo(x, y)[1];
}

function biMultiplyMod(x, y, m) {
    return biModulo(biMultiply(x, y), m);
}

function biPow(x, y) {
    var result = bigOne;
    var a = x;
    while (true) {
        if ((y & 1) != 0)
            result = biMultiply(result, a);
        y >>= 1;
        if (y == 0)
            break;
        a = biMultiply(a, a);
    }
    return result;
}

function biPowMod(x, y, m) {
    var result = bigOne;
    var a = x;
    var k = y;
    while (true) {
        if ((k.digits[0] & 1) != 0)
            result = biMultiplyMod(result, a, m);
        k = biShiftRight(k, 1);
        if (k.digits[0] == 0 && biHighIndex(k) == 0)
            break;
        a = biMultiplyMod(a, a, m);
    }
    return result;
}

module.exports.biFromHex = biFromHex
module.exports.bigInt = BigInt
module.exports.biHighIndex = biHighIndex
module.exports.biCopy = biCopy
module.exports.biHighIndex = biHighIndex
module.exports.biDivide = biDivide