BigInteger Class
Basic dart BigInteger class. Implementation works across dart and dart2js.
Constructors
Code new BigInteger([a, b, c]) #
Constructor of BigInteger
Constructor can be called in mutiple ways
1) Passing byte array List
var x = new BigInteger(0x5
);
x.toString() == "5";
2) Passing int
int i = 5;
var x = new BigInteger(i);
x.toString() == "5";
3) Passing num
num i = 5;
var x = new BigInteger(i);
x.toString() == "5";
4) Passing double
double i = 5.0;
var x = new BigInteger(i);
x.toString() == "5";
5) Passing String
with optional base int
String s = "5";
var x = new BigInteger(s);
x.toString() == "5";
String s = "beef"; var x = new BigInteger(s); x.toString() == "beef";
BigInteger([a,b,c]) { // TODO: create mutiple constructors, instead of constructing based on the dynamimc type _lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509]; BI_RC = new Map(); _j_lm = ((canary&0xffffff)==0xefcafe); // Setup all the global scope js code here _setupDigitConversions(); _lplim = (1<<26)~/_lowprimes[_lowprimes.length-1]; _setupEngine(_am3, 28); this.array = new Map(); if (a != null) { if (a is int) { // this.fromNumber(a,b,c); // NOTE: the fromNumber implementation trys to exploit js numbers this.fromString(a.toString(), 10); } else if (a is double || a is num) { this.fromString(a.toInt().toString(), 10); } else if (b == null && a is! String) { this.fromString(a,256); } else { this.fromString(a,b); } } }
Static Methods
Code BigInteger get ONE() #
static BigInteger get ONE => nbv(1);
Code BigInteger get ZERO() #
static BigInteger get ZERO => nbv(0);
Code BigInteger nbi() #
Create a new BigInteger
static BigInteger nbi() { return new BigInteger(null, null, null); }
Code BigInteger nbv(int i) #
return BigInteger initialized to i
static BigInteger nbv(int i) { var r = nbi(); r.fromInt(i); return r; }
Static Fields
Code int BI_DB #
static int BI_DB;
Code int BI_DM #
static int BI_DM;
Code int BI_DV #
static int BI_DV;
Code int BI_F1 #
static int BI_F1;
Code int BI_F2 #
static int BI_F2;
Code int BI_FP #
static int BI_FP;
Code int BI_FV #
static int BI_FV;
Code int dbits #
Bits per digit
static int dbits;
Methods
Code BigInteger abs() #
|this|
BigInteger abs() { return (this.s<0)?this.negate_op():this; }
Code BigInteger add(a) #
this + a
BigInteger add(a) { var r = nbi(); this.addTo(a,r); return r; }
Code addTo(a, r) #
r = this + a
addTo(a,r) { var this_array = this.array; var a_array = a.array; var r_array = r.array; var i = 0, c = 0, m = Mathx.min(a.t,this.t); while(i < m) { c += this_array[i]+a_array[i]; r_array[i++] = c&BI_DM; c >>= BI_DB; } if(a.t < this.t) { c += a.s; while(i < this.t) { c += this_array[i]; r_array[i++] = c&BI_DM; c >>= BI_DB; } c += this.s; } else { c += this.s; while(i < a.t) { c += a_array[i]; r_array[i++] = c&BI_DM; c >>= BI_DB; } c += a.s; } r.s = (c<0)?-1:0; if(c > 0) r_array[i++] = c; else if(c < -1) r_array[i++] = BI_DV+c; r.t = i; r.clamp(); }
Code and(a) #
and(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
Code andNot(a) #
andNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
Code bitCount() #
return number of set bits
bitCount() { var this_array = this.array; var r = 0, x = this.s&BI_DM; for(var i = 0; i < this.t; ++i) r += cbit(this_array[i]^x); return r; }
Code int bitLength() #
return the number of bits in this
int bitLength() { var this_array = this.array; if(this.t <= 0) return 0; return BI_DB*(this.t-1)+nbits(this_array[this.t-1]^(this.s&BI_DM)); }
Code void bitwiseTo(BigInteger a, Function op, BigInteger r) #
r = this op a (bitwise)
void bitwiseTo(BigInteger a, Function op, BigInteger r) { var this_array = this.array; var a_array = a.array; var r_array = r.array; var i, f, m = Mathx.min(a.t,this.t); for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]); if(a.t < this.t) { f = a.s&BI_DM; for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f); r.t = this.t; } else { f = this.s&BI_DM; for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]); r.t = a.t; } r.s = op(this.s,a.s); r.clamp(); }
Code byteValue() #
return value as byte
byteValue() { var this_array = this.array; return (this.t==0)?this.s:(this_array[0]<<24)>>24; }
Code cbit(x) #
return number of 1 bits in x
cbit(x) { var r = 0; while(x != 0) { x &= x-1; ++r; } return r; }
Code changeBit(n, op) #
this op (1<<n)
changeBit(n,op) { var r = BigInteger.ONE.shiftLeft(n); this.bitwiseTo(r,op,r); return r; }
Code int chunkSize(r) #
return x s.t. r^x < DV
int chunkSize(r) { return (Mathx.LN2*BI_DB/Mathx.log(r)).floor().toInt(); }
Code void clamp() #
clamp off excess high words
void clamp() { var this_array = this.array; var c = this.s&BI_DM; while(this.t > 0 && this_array[this.t-1] == c) { --this.t; } }
Code clearBit(n) #
this & ~(1<<n)
clearBit(n) { return this.changeBit(n,op_andnot); }
Code clone() #
clone
clone() { var r = nbi(); this.copyTo(r); return r; }
Code int compareTo(a) #
return + if this
>
a, - if this
<
a, 0 if equal *
int compareTo(a) { var this_array = this.array; var a_array = a.array; var r = this.s-a.s; if(r != 0) return r; var i = this.t; r = i-a.t; if(r != 0) return r; while(--i >= 0) if((r=this_array[i]-a_array[i]) != 0) return r; return 0; }
Code void copyTo(BigInteger r) #
copy this
to
r
void copyTo(BigInteger r) { var this_array = this.array; var r_array = r.array; for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i]; r.t = this.t; r.s = this.s; }
Code dAddOffset(n, w) #
this += n << w words, this >= 0
dAddOffset(n,w) { var this_array = this.array; while(this.t <= w) this_array[this.t++] = 0; this_array[w] += n; while(this_array[w] >= BI_DV) { this_array[w] -= BI_DV; if(++w >= this.t) this_array[this.t++] = 0; ++this_array[w]; } }
Code dMultiply(n) #
this *= n, this >= 0, 1 < n < BI_DV
dMultiply(n) { var this_array = this.array; this_array[this.t] = this.am(0,n-1,this,0,0,this.t); ++this.t; this.clamp(); }
Code divRemTo(BigInteger m, q, BigInteger r) #
divide this by m, quotient and remainder to q, r (HAC 14.20) r != q, this != m. q or r may be null.
divRemTo(BigInteger m,q,BigInteger r) { var pm = m.abs(); if(pm.t <= 0) return; var pt = this.abs(); if(pt.t < pm.t) { if(q != null) q.fromInt(0); if(r != null) this.copyTo(r); return; } if(r == null) r = nbi(); var y = nbi(), ts = this.s, ms = m.s; var pm_array = pm.array; var nsh = BI_DB-nbits(pm_array[pm.t-1]); // normalize modulus if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); } else { pm.copyTo(y); pt.copyTo(r); } var ys = y.t; var y_array = y.array; var y0 = y_array[ys-1]; if(y0 == 0) return; var yt = y0*(1<<BI_F1)+((ys>1)?y_array[ys-2]>>BI_F2:0); var d1 = BI_FV/yt, d2 = (1<<BI_F1)/yt, e = 1<<BI_F2; var i = r.t, j = i-ys; BigInteger t = (q==null) ?nbi() : q; y.dlShiftTo(j,t); var r_array = r.array; if(r.compareTo(t) >= 0) { r_array[r.t++] = 1; r.subTo(t,r); } BigInteger.ONE.dlShiftTo(ys,t); t.subTo(y,y); // "negative" y so we can replace sub with am later while(y.t < ys) y_array[y.t++] = 0; while(--j >= 0) { // Estimate quotient digit var qd = (r_array[--i]==y0)?BI_DM:(r_array[i]*d1+(r_array[i-1]+e)*d2).floor(); if((r_array[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out y.dlShiftTo(j,t); r.subTo(t,r); while(r_array[i] < --qd) r.subTo(t,r); } } if(q != null) { r.drShiftTo(ys,q); if(ts != ms) BigInteger.ZERO.subTo(q,q); } r.t = ys; r.clamp(); if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder if(ts < 0) BigInteger.ZERO.subTo(r,r); }
Code BigInteger divide(a) #
this / a
BigInteger divide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
Code Map<int, BigInteger> divideAndRemainder(a) #
this/a, this%a
returns Map<BigInteger>
0
= this/a
1
= this%a
Map<int, BigInteger> divideAndRemainder(a) { var q = nbi(), r = nbi(); this.divRemTo(a,q,r); //return new Array(q,r); Map ret_m = new Map(); ret_m[0] = q; ret_m[1] = r; return ret_m; }
Code void dlShiftTo(n, r) #
r = this << n*DB
void dlShiftTo(n,r) { var this_array = this.array; var r_array = r.array; var i; for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i]; for(i = n-1; i >= 0; --i) r_array[i] = 0; r.t = this.t+n; r.s = this.s; }
Code void drShiftTo(n, r) #
r = this >> n*DB
void drShiftTo(n,r) { var this_array = this.array; var r_array = r.array; for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i]; r.t = Mathx.max(this.t-n,0); r.s = this.s; }
Code bool equals(BigInteger a) #
bool equals(BigInteger a) { return this.compareTo(a)==0 ? true : false; }
Code BigInteger exp(int e, z) #
this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
BigInteger exp(int e, z) { // TODO: z is one of the reduction algorithms, pass interface class if(e > 0xffffffff || e < 1) return BigInteger.ONE; BigInteger r = nbi(); BigInteger r2 = nbi(); BigInteger g = z.convert(this); int i = nbits(e)-1; g.copyTo(r); while(--i >= 0) { z.sqrTo(r,r2); if((e&(1<<i)) > 0) z.mulTo(r2,g,r); else { var t = r; r = r2; r2 = t; } } return z.revert(r); }
Code flipBit(n) #
this ^ (1<<n)
flipBit(n) { return this.changeBit(n,op_xor); }
Code void fromInt(int x) #
Code void fromRadix(s, b) #
convert from radix string
void fromRadix(s,b) { this.fromInt(0); if(b == null) b = 10; var cs = this.chunkSize(b); num d = Mathx.pow(b,cs); bool mi = false; int j = 0, w = 0; for(var i = 0; i < s.length; ++i) { var x = _intAt(s,i); if(x < 0) { if (s is String) { if(s[0] == "-" && this.signum() == 0) { mi = true; } } continue; } w = b*w+x; if(++j >= cs) { this.dMultiply(d); this.dAddOffset(w,0); j = 0; w = 0; } } if(j > 0) { this.dMultiply(Mathx.pow(b,j)); // w is zero there should not add offset if (w != 0) { this.dAddOffset(w,0); } } if(mi) { BigInteger.ZERO.subTo(this,this); } }
Code void fromString(s, int b) #
set from string s and radix b
void fromString(s, int b) { var this_array = this.array; var k; if(b == 16) k = 4; else if(b == 8) k = 3; else if(b == 256) k = 8; // byte array else if(b == 2) k = 1; else if(b == 32) k = 5; else if(b == 4) k = 2; else { this.fromRadix(s,b); return; } this.t = 0; this.s = 0; var i = s.length, mi = false, sh = 0; while(--i >= 0) { var x = (k==8) ? s[i] & 0xff : _intAt(s,i); // if k==8 its a byte array if(x < 0) { //if(s.charAt(i) == "-") mi = true; if(s[i] == "-") mi = true; continue; } mi = false; if(sh == 0) this_array[this.t++] = x; else if(sh+k > BI_DB) { this_array[this.t-1] |= (x&((1<<(BI_DB-sh))-1))<<sh; this_array[this.t++] = (x>>(BI_DB-sh)); } else this_array[this.t-1] |= x<<sh; sh += k; if(sh >= BI_DB) sh -= BI_DB; } if(k == 8 && (s[0]&0x80) != 0) { this.s = -1; if(sh > 0) this_array[this.t-1] |= ((1<<(BI_DB-sh))-1)<<sh; } this.clamp(); if(mi) BigInteger.ZERO.subTo(this,this); }
Code gcd(a) #
gcd(this,a) (HAC 14.54)
gcd(a) { var x = (this.s<0)?this.negate_op():this.clone(); var y = (a.s<0)?a.negate_op():a.clone(); if(x.compareTo(y) < 0) { var t = x; x = y; y = t; } var i = x.getLowestSetBit(), g = y.getLowestSetBit(); if(g < 0) return x; if(i < g) g = i; if(g > 0) { x.rShiftTo(g,x); y.rShiftTo(g,y); } while(x.signum() > 0) { if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x); if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y); if(x.compareTo(y) >= 0) { x.subTo(y,x); x.rShiftTo(1,x); } else { y.subTo(x,y); y.rShiftTo(1,y); } } if(g > 0) y.lShiftTo(g,y); return y; }
Code getLowestSetBit() #
returns index of lowest 1-bit (or -1 if none)
getLowestSetBit() { var this_array = this.array; for(var i = 0; i < this.t; ++i) if(this_array[i] != 0) return i*BI_DB+lbit(this_array[i]); if(this.s < 0) return this.t*BI_DB; return -1; }
Code intValue() #
return value as integer
intValue() { var this_array = this.array; if(this.s < 0) { if(this.t == 1) return this_array[0]-BI_DV; else if(this.t == 0) return -1; } else if(this.t == 1) return this_array[0]; else if(this.t == 0) return 0; // assumes 16 < DB < 32 return ((this_array[1]&((1<<(32-BI_DB))-1))<<BI_DB)|this_array[0]; }
Code invDigit() #
return "-1/this % 2^DB"; useful for Mont. reduction justification:
xy == 1 (mod m)
xy = 1+km
xy(2-xy) = (1+km)(1-km)
xy(2-xy)
= 1-k^2m^2
xy(2-xy)
== 1 (mod m^2)
if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
JS multiply "overflows" differently from C/C++, so care is needed here.
invDigit() { var this_array = this.array; if(this.t < 1) return 0; var x = this_array[0]; if((x&1) == 0) return 0; var y = x&3; // y == 1/x mod 2^2 y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4 y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8 y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16 // last step - calculate inverse mod DV directly; // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints y = (y*(2-x*y%BI_DV))%BI_DV; // y == 1/x mod 2^dbits // we really want the negative inverse, and -DV < y < DV return (y>0)?BI_DV-y:-y; }
Code isEven() #
true iff this
is even
isEven() { var this_array = this.array; return ((this.t>0)?(this_array[0]&1):this.s) == 0; }
Code bool isProbablePrime(int t) #
test primality with certainty >= 1-.5^t
bool isProbablePrime(int t) { var i, x = this.abs(); var x_array = x.array; if(x.t == 1 && x_array[0] <= _lowprimes[_lowprimes.length-1]) { for(i = 0; i < _lowprimes.length; ++i) if(x_array[0] == _lowprimes[i]) return true; return false; } if(x.isEven()) return false; i = 1; while(i < _lowprimes.length) { var m = _lowprimes[i], j = i+1; while(j < _lowprimes.length && m < _lplim) m *= _lowprimes[j++]; m = x.modInt(m); while(i < j) if(m%_lowprimes[i++] == 0) return false; } return x.millerRabin(t); }
Code void lShiftTo(n, r) #
r = this << n
void lShiftTo(n,r) { var this_array = this.array; var r_array = r.array; var bs = n%BI_DB; var cbs = BI_DB-bs; var bm = (1<<cbs)-1; int ds = n~/BI_DB; var c = (this.s<<bs)&BI_DM; var i; for(i = this.t-1; i >= 0; --i) { r_array[i+ds+1] = (this_array[i]>>cbs)|c; c = (this_array[i]&bm)<<bs; } for(i = ds-1; i >= 0; --i) r_array[i] = 0; r_array[ds] = c; r.t = this.t+ds+1; r.s = this.s; r.clamp(); }
Code lbit(x) #
return index of lowest 1-bit in x, x < 2^31
lbit(x) { if(x == 0) return -1; var r = 0; if((x&0xffff) == 0) { x >>= 16; r += 16; } if((x&0xff) == 0) { x >>= 8; r += 8; } if((x&0xf) == 0) { x >>= 4; r += 4; } if((x&3) == 0) { x >>= 2; r += 2; } if((x&1) == 0) ++r; return r; }
Code BigInteger max(BigInteger a) #
BigInteger max(BigInteger a) { return(this.compareTo(a)>0)?this:a; }
Code bool millerRabin(t) #
true if probably prime (HAC 4.24, Miller-Rabin)
bool millerRabin(t) { var n1 = this.subtract(BigInteger.ONE); var k = n1.getLowestSetBit(); if(k <= 0) return false; var r = n1.shiftRight(k); t = (t+1)>>1; if(t > _lowprimes.length) t = _lowprimes.length; var a = nbi(); for(var i = 0; i < t; ++i) { a.fromInt(_lowprimes[i]); var y = a.modPow(r,this); if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) { var j = 1; while(j++ < k && y.compareTo(n1) != 0) { y = y.modPowInt(2,this); if(y.compareTo(BigInteger.ONE) == 0) return false; } if(y.compareTo(n1) != 0) return false; } } return true; }
Code BigInteger min(BigInteger a) #
BigInteger min(BigInteger a) { return(this.compareTo(a)<0)?this:a; }
Code mod(a) #
this mod a
mod(a) { var r = nbi(); this.abs().divRemTo(a,null,r); if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r); return r; }
Code int modInt(int n) #
this % n, n < 2^26
int modInt(int n) { var this_array = this.array; if(n <= 0) return 0; var d = BI_DV%n, r = (this.s<0)?n-1:0; if(this.t > 0) if(d == 0) r = this_array[0]%n; else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n; return r; }
Code BigInteger modInverse(BigInteger m) #
1/this % m (HAC 14.61)
BigInteger modInverse(BigInteger m) { var ac = m.isEven(); if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO; var u = m.clone(), v = this.clone(); var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1); while(u.signum() != 0) { while(u.isEven()) { u.rShiftTo(1,u); if(ac) { if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); } a.rShiftTo(1,a); } else if(!b.isEven()) b.subTo(m,b); b.rShiftTo(1,b); } while(v.isEven()) { v.rShiftTo(1,v); if(ac) { if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); } c.rShiftTo(1,c); } else if(!d.isEven()) d.subTo(m,d); d.rShiftTo(1,d); } if(u.compareTo(v) >= 0) { u.subTo(v,u); if(ac) a.subTo(c,a); b.subTo(d,b); } else { v.subTo(u,v); if(ac) c.subTo(a,c); d.subTo(b,d); } } if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO; if(d.compareTo(m) >= 0) return d.subtract(m); if(d.signum() < 0) d.addTo(m,d); else return d; if(d.signum() < 0) return d.add(m); else return d; }
Code modPow(BigInteger e, BigInteger m) #
this^e % m (HAC 14.85)
modPow(BigInteger e, BigInteger m) { // TODO: need to create interface for the reduction algorithms var e_array = e.array; var i = e.bitLength(), k, r = nbv(1), z; if(i <= 0) return r; else if(i < 18) k = 1; else if(i < 48) k = 3; else if(i < 144) k = 4; else if(i < 768) k = 5; else k = 6; if(i < 8) z = new Classic(m); else if(m.isEven()) z = new Barrett(m); else z = new Montgomery(m); // precomputation var g = new Map(), n = 3, k1 = k-1, km = (1<<k)-1; g[1] = z.convert(this); if(k > 1) { var g2 = nbi(); z.sqrTo(g[1],g2); while(n <= km) { g[n] = nbi(); z.mulTo(g2,g[n-2],g[n]); n += 2; } } var j = e.t-1, w, is1 = true, r2 = nbi(), t; i = nbits(e_array[j])-1; while(j >= 0) { if(i >= k1) w = (e_array[j]>>(i-k1))&km; else { w = (e_array[j]&((1<<(i+1))-1))<<(k1-i); if(j > 0) w |= e_array[j-1]>>(BI_DB+i-k1); } n = k; while((w&1) == 0) { w >>= 1; --n; } if((i -= n) < 0) { i += BI_DB; --j; } if(is1) { // ret == 1, don't bother squaring or multiplying it g[w].copyTo(r); is1 = false; } else { while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; } if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; } z.mulTo(r2,g[w],r); } while(j >= 0 && (e_array[j]&(1<<i)) == 0) { z.sqrTo(r,r2); t = r; r = r2; r2 = t; if(--i < 0) { i = BI_DB-1; --j; } } } return z.revert(r); }
Code BigInteger modPowInt(int e, BigInteger m) #
this^e % m, 0 <= e < 2^32
BigInteger modPowInt(int e, BigInteger m) { var z; if(e < 256 || m.isEven()) { z = new Classic(m); } else { z = new Montgomery(m); } return this.exp(e,z); }
Code BigInteger multiply(a) #
this * a
BigInteger multiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
Code multiplyLowerTo(a, n, r) #
r = lower n words of "this * a", a.t <= n "this" should be the larger one if appropriate.
multiplyLowerTo(a,n,r) { var r_array = r.array; var a_array = a.array; var i = Mathx.min(this.t+a.t,n); r.s = 0; // assumes a,this >= 0 r.t = i; while(i > 0) r_array[--i] = 0; var j; for(j = r.t-this.t; i < j; ++i) r_array[i+this.t] = this.am(0,a_array[i],r,i,0,this.t); for(j = Mathx.min(a.t,n); i < j; ++i) this.am(0,a_array[i],r,i,0,n-i); r.clamp(); }
Code void multiplyTo(a, r) #
r = this * a, r != this,a (HAC 14.12)
this
should be the larger one if appropriate.
void multiplyTo(a,r) { var this_array = this.array; var r_array = r.array; BigInteger x = this.abs(); BigInteger y = a.abs(); var y_array = y.array; var i = x.t; r.t = i+y.t; while(--i >= 0) r_array[i] = 0; for(i = 0; i < y.t; ++i) r_array[i+x.t] = x.am(0,y_array[i],r,i,0,x.t); r.s = 0; r.clamp(); if(this.s != a.s) { BigInteger.ZERO.subTo(r,r); } }
Code multiplyUpperTo(a, n, r) #
r = "this * a" without lower n words, n > 0 "this" should be the larger one if appropriate.
multiplyUpperTo(a,n,r) { var r_array = r.array; var a_array = a.array; --n; var i = r.t = this.t+a.t-n; r.s = 0; // assumes a,this >= 0 while(--i >= 0) r_array[i] = 0; for(i = Mathx.max(n-this.t,0); i < a.t; ++i) r_array[this.t+i-n] = this.am(n-i,a_array[i],r,0,0,this.t+i-n); r.clamp(); r.drShiftTo(1,r); }
Code int nbits(x) #
returns bit length of the integer x
int nbits(x) { var r = 1, t; if (x is double) x = x.toInt(); if((t=x>>16) != 0) { x = t; r += 16; } if((t=x>>8) != 0) { x = t; r += 8; } if((t=x>>4) != 0) { x = t; r += 4; } if((t=x>>2) != 0) { x = t; r += 2; } if((t=x>>1) != 0) { x = t; r += 1; } return r; }
Code negate_op() #
-this
negate_op() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
Code not() #
~this
not() { var this_array = this.array; var r = nbi(); var r_array = r.array; for(var i = 0; i < this.t; ++i) { r_array[i] = BI_DM & ~this_array[i]; } r.t = this.t; r.s = ~this.s; return r; }
Code op_and(x, y) #
this & a
op_and(x,y) { return x&y; }
Code op_andnot(x, y) #
this & ~a
op_andnot(x,y) { return x&~y; }
Code op_or(x, y) #
this | a
op_or(x,y) { return x|y; }
Code op_xor(x, y) #
this ^ a
op_xor(x,y) { return x^y; }
Code BigInteger operator *(BigInteger other) #
BigInteger operator *(BigInteger other) => multiply(other);
Code BigInteger operator -(BigInteger other) #
BigInteger operator -(BigInteger other) => subtract(other);
Code BigInteger operator &(BigInteger other) #
BigInteger operator &(BigInteger other) => and(other);
Code bool operator >=(BigInteger other) #
bool operator >=(BigInteger other) => compareTo(other) >= 0 ? true : false;
Code BigInteger operator <<(int shiftAmount) #
BigInteger operator <<(int shiftAmount) => shiftLeft(shiftAmount);
Code bool operator <(BigInteger other) #
bool operator <(BigInteger other) => compareTo(other) < 0 ? true : false;
Code BigInteger operator negate() #
BigInteger operator -() => this.negate_op();
Code BigInteger operator ~/(BigInteger other) #
BigInteger operator ~/(BigInteger other) { throw "Not Implemented"; }
Code bool operator >(BigInteger other) #
bool operator >(BigInteger other) => compareTo(other) > 0 ? true : false;
Code BigInteger operator ~() #
BigInteger operator ~() => not();
Code BigInteger operator /(BigInteger other) #
BigInteger operator /(BigInteger other) => divide(other);
Code BigInteger operator ^(BigInteger other) #
BigInteger operator ^(BigInteger other) => xor(other);
Code BigInteger operator %(BigInteger other) #
BigInteger operator %(BigInteger other) => remainder(other);
Code BigInteger operator |(BigInteger other) #
BigInteger operator |(BigInteger other) => or(other);
Code bool operator ==(BigInteger other) #
bool operator ==(BigInteger other) => compareTo(other) == 0 ? true : false;
Code BigInteger operator >>(int shiftAmount) #
BigInteger operator >>(int shiftAmount) => shiftRight(shiftAmount);
Code BigInteger operator +(BigInteger other) #
BigInteger operator +(BigInteger other) => add(other);
Code bool operator <=(BigInteger other) #
bool operator <=(BigInteger other) => compareTo(other) <= 0 ? true : false;
Code or(a) #
or(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
Code BigInteger pow(int e) #
this^e
BigInteger pow(int e) { return this.exp(e,new NullExp()); }
Code void rShiftTo(n, r) #
r = this >> n
void rShiftTo(n,r) { var this_array = this.array; var r_array = r.array; r.s = this.s; var ds = n~/BI_DB; if(ds >= this.t) { r.t = 0; return; } var bs = n%BI_DB; var cbs = BI_DB-bs; var bm = (1<<bs)-1; r_array[0] = this_array[ds]>>bs; for(var i = ds+1; i < this.t; ++i) { r_array[i-ds-1] |= (this_array[i]&bm)<<cbs; r_array[i-ds] = this_array[i]>>bs; } if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs; r.t = this.t-ds; r.clamp(); }
Code BigInteger remainder(BigInteger a) #
this % a
BigInteger remainder(BigInteger a) { BigInteger r = nbi(); this.divRemTo(a,null,r); return r; }
Code setBit(n) #
this | (1<<n)
setBit(n) { return this.changeBit(n,op_or); }
Code shiftLeft(n) #
this << n
shiftLeft(n) { var r = nbi(); if(n < 0) { this.rShiftTo(-n,r); } else { this.lShiftTo(n,r); } return r; }
Code shiftRight(n) #
this >> n
shiftRight(n) { var r = nbi(); if(n < 0) { this.lShiftTo(-n,r); } else { this.rShiftTo(n,r); } return r; }
Code shortValue() #
return value as short (assumes DB>=16)
shortValue() { var this_array = this.array; return (this.t==0)?this.s:(this_array[0]<<16)>>16; }
Code int signum() #
0 if this == 0, 1 if this > 0
int signum() { var this_array = this.array; if(this.s < 0) { return -1; } else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) { return 0; } else { return 1; } }
Code void squareTo(r) #
r = this^2, r != this (HAC 14.16)
void squareTo(r) { var x = this.abs(); var x_array = x.array; var r_array = r.array; var i = r.t = 2*x.t; while(--i >= 0) r_array[i] = 0; for(i = 0; i < x.t-1; ++i) { var c = x.am(i,x_array[i],r,2*i,0,1); if((r_array[i+x.t]+=x.am(i+1,2*x_array[i],r,2*i+1,c,x.t-i-1)) >= BI_DV) { r_array[i+x.t] -= BI_DV; r_array[i+x.t+1] = 1; } } if(r.t > 0) r_array[r.t-1] += x.am(i,x_array[i],r,2*i,0,1); r.s = 0; r.clamp(); }
Code void subTo(a, r) #
r = this - a
void subTo(a,r) { var this_array = this.array; var r_array = r.array; var a_array = a.array; int i = 0; int c = 0; int m = Mathx.min(a.t, this.t); while(i < m) { c += (this_array[i].toInt() - a_array[i].toInt()).toInt(); r_array[i++] = c&BI_DM; c >>= BI_DB; // NOTE: this is to bypass a dart2js bug if (c == 4294967295) { c = -1; } } if(a.t < this.t) { c -= a.s; while(i < this.t) { c += this_array[i]; r_array[i++] = c&BI_DM; c >>= BI_DB; // NOTE: this is to bypass a dart2js bug if (c == 4294967295) { c = -1; } } c += this.s; } else { c += this.s; while(i < a.t) { c -= a_array[i]; r_array[i++] = c&BI_DM; c >>= BI_DB; if (c == 4294967295) { c = -1; } } c -= a.s; } r.s = (c<0) ? -1 : 0; if(c < -1) { r_array[i++] = BI_DV+c; } else if(c > 0) { r_array[i++] = c; } r.t = i; r.clamp(); }
Code BigInteger subtract(a) #
this - a
BigInteger subtract(a) { var r = nbi(); this.subTo(a,r); return r; }
Code testBit(n) #
true iff nth bit is set
testBit(n) { var this_array = this.array; var j = (n/BI_DB).floor(); if(j >= this.t) return(this.s!=0); return((this_array[j]&(1<<(n%BI_DB)))!=0); }
Code Map toByteArray() #
convert to bigendian byte array Map
Map toByteArray() { var this_array = this.array; var i = this.t, r = new Map(); r[0] = this.s; var p = BI_DB-(i*BI_DB)%8, d, k = 0; if(i-- > 0) { if(p < BI_DB && (d = this_array[i]>>p) != (this.s&BI_DM)>>p) r[k++] = d|(this.s<<(BI_DB-p)); while(i >= 0) { if(p < 8) { d = (this_array[i]&((1<<p)-1))<<(8-p); d |= this_array[--i]>>(p+=BI_DB-8); } else { d = (this_array[i]>>(p-=8))&0xff; if(p <= 0) { p += BI_DB; --i; } } if((d&0x80) != 0) d |= -256; if(k == 0 && (this.s&0x80) != (d&0x80)) ++k; if(k > 0 || d != this.s) r[k++] = d; } } return r; }
Code String toRadix([int b = 10]) #
convert to radix string , http://dartbug.com/461 num only supports up to radix 16
String toRadix([int b=10]) { if(b == null) b = 10; if(this.signum() == 0 || b < 2 || b > 36) return "0"; var cs = this.chunkSize(b); var a = Mathx.pow(b,cs); var d = nbv(a), y = nbi(), z = nbi(), r = ""; this.divRemTo(d,y,z); while(y.signum() > 0) { r = "${(a+z.intValue()).toRadixString(b).substring(1)}${r}"; y.divRemTo(d,y,z); } return "${z.intValue().toRadixString(b)}${r}"; }
Code String toString([int b]) #
return string representation in given radix b
String toString([int b]) { // NOTE: overriding toString like this is probably bad. var this_array = this.array; if(this.s < 0) { return "-${this.negate_op().toString(b)}"; //return "-"+this.negate().toString(b); } var k; if(b == 16) k = 4; else if(b == 8) k = 3; else if(b == 2) k = 1; else if(b == 32) k = 5; else if(b == 4) k = 2; else return this.toRadix(b); var km = (1<<k)-1, d, m = false, r = "", i = this.t; var p = BI_DB-(i*BI_DB)%k; if(i-- > 0) { if(p < BI_DB && (d = this_array[i]>>p) > 0) { m = true; r = _int2char(d); } while(i >= 0) { if(p < k) { d = (this_array[i]&((1<<p)-1))<<(k-p); d |= this_array[--i]>>(p+=BI_DB-k); } else { d = (this_array[i].toInt()>>(p-=k.toInt()).toInt())&km.toInt(); if(p <= 0) { p += BI_DB; --i; } } if(d > 0) m = true; if(m) r = "${r}${_int2char(d)}"; //r += int2char(d); // NOTE: Might not be best use of string } } return m ? r : "0"; }
Code xor(a) #
xor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
Fields
Code Map BI_RC #
Map BI_RC;
Code var BI_RM #
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
Code Function am #
Function am;
Code Map array #
Internal data structure of BigInteger implementation.
Holds the bits in a Map
that is keyed by its integer values
that represent its location in an Array type structure. While
This is not the most optimal implementation, it was done to
support a rapid implementation. This will be replaced at a later
time for a List
data structure.
Map array;
Code int canary #
JavaScript engine analysis
int canary = 0xdeadbeefcafe;
Code var s #
var s;
Code int t #
int t;