root/trunk/etc/longrational.d

/*
Copyright (c) 2004 Daniel Horn
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.
3. The name of the author may not be used to endorse or promote products
   derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
module etc.longrational;
/*
version (Long) {
}else {
  import bigint.bigint;
  alias bigint.bigint.Int Int;
}
*/

/*
version (Long) {
}else {
  template TypeCreate(T:Int) {
    Int make (int i) {
      return new Int(i);
    }
    real retrieve (Int k) {
      return std.string.atof(k.toString());
    }
    long retrieveLong (Int k) {
      return k.toLong();
    }
    Int make (char[] i) {
      return new Int (i);
    }
  }
  template ToString (T:Int) {
    char[] toString(T a) {
      return a.toString();
    }
  }
  alias TypeCreate!(Int).make makeType;
}
version (Long) {
}else {
template Zero(T:Int) {
  Int zero() {
    static Int z = new Int(0);
    return z;
  }
  Int one () {
    static Int o = new Int(1);
    return o;
  }
}
*/

struct BigRational(T, int rat, Allocator) {
  private import std.string;
  private import std.math;

  static BigRational ZERO() {
    static BigRational z = BigRational();
    return z;
  }
  static BigRational ONE() {
    static BigRational o=BigRational.create(Allocator.one,
                        Allocator.one);
    return o;
  }
  static BigRational MINUS_ONE() {
    static BigRational o=BigRational.create(-Allocator.one,
                        Allocator.one);
    return o;
  }
  static BigRational TWO() {
    static BigRational o=BigRational.create(Allocator.one+Allocator.one,
                        Allocator.one);
    return o;
  }
 private:
  T n;
  T d;
  static T int_pow (T a, T b) {
    if (b==Allocator.zero) return Allocator.one;
    if (b==Allocator.one) return a;
    static T two =Allocator.one+Allocator.one; 
    T half_b = b/two;
    T tmp=int_pow(a,half_b);
    if (a%tmp!=Allocator.zero) {
    return a*tmp*tmp;
    }else {
      return tmp*tmp;
    }
  }
  static T int_gcd_recurse (T less, T more) {
    T zero = Allocator.zero;
    if (less==zero)
      return more;
    T amb = more%less;
    if (amb==zero) {
      return less;
    }
    return int_gcd_recurse(amb,less);
  }
  static T int_abs (T a) {
    T zero = Allocator.zero;
    return a<zero?-a:a;
  }
  static T int_gcd (T aa,  T bb) {
    T a = int_abs(aa);
    T b = int_abs(bb);
    return int_gcd_recurse(a<b?a:b,a<b?b:a);
  }
  static T int_modshr(T a) {
    static T zero = Allocator.zero;
    static T one = Allocator.one;
    static T two = one+one;
    if (a%two!=zero&&a!=one)
      return a/two+one;
    return a/two;
  }
  static T int_sqrt(T a) {
    if (a==Allocator.one) {
      return Allocator.one;
    }
    if (a==Allocator.zero)
      return Allocator.zero;
    T guess = int_modshr(a);
    T mag = int_modshr(guess);
    while (mag>Allocator.zero) {
      T sqrguess = guess*guess;
      if (sqrguess==a)
    return guess;
      if (sqrguess<a) {
    guess=guess+mag;
      }else {
    guess=guess-mag;
      }      
      mag=int_modshr(mag);
    }
    assert (guess*guess==a);
    return guess;
  }
  BigRational InternalRationalize() {
    if (d<Allocator.zero) {
      n=-n;
      d=-d;
    }
    if (rat!=0)
      return Rationalize();
    return *this;
  }
 public:
  int wholeNumber() {
    Rationalize();
    return d==Allocator.one;
  }
  BigRational sqrt () {
    Rationalize();
    return create(int_sqrt(n),int_sqrt(d));
  }
  real toReal() {
    Rationalize();
    return Allocator.retrieve(n/d)+Allocator.retrieve(n%d)/Allocator.retrieve(d);
  }
  static BigRational opCall (BigRational r) {
    return create(r.n,r.d);
  }
  BigRational abs() {
    if ((*this)>=BigRational.ZERO)
      return *this;
    return -*this;
  }
  long toLong() {
    Rationalize();
    return Allocator.retrieveLong(n/d);
  }  
  static BigRational create (T nn) {
    BigRational r;
    r.n=nn;
    r.d=Allocator.one;
    return r;
  }

  static BigRational create (T nn, T dd) {
    BigRational r;
    r.n=nn;
    r.d=dd;
    return r;
  }
  static BigRational opCall (real r) {
    if (r<0) return -opCall(-r);
    if (r==0) return opCall();
    T d=Allocator.one;
    while (r!=std.math.floor(r)) {
      r*=2;
      d=d+d;
    }
    return create(Allocator.make(std.string.toString(r)),d);
  }
  static BigRational opCall (double r) {
    return opCall(cast(real)r);
  }
  static BigRational opCall (float r) {
    return opCall(cast(real)r);
  }
  static BigRational opCall (long nn, ulong dd) {
    BigRational r;
    r.n=Allocator.make(nn);
    r.d=Allocator.make(dd);
    return r;
  }
  static BigRational opCall (long nn) {
    BigRational r;
    r.n=Allocator.make(nn);
    r.d=Allocator.one;
    return r;
  }
  static BigRational opCall (int nn) {
    return opCall(cast(long)nn);
  }
  static BigRational opCall (uint nn) {
    return opCall(cast(long)nn);
  }
  static BigRational opCall (ulong nn) {
    return opCall(cast(long)nn);
  }

  static BigRational opCall (char[] nn, char[] dd) {
    BigRational r;
    r.n=Allocator.make(nn);
    r.d=Allocator.make(dd);
    return r;
  }
  static BigRational opCall (char[] nn) {
    BigRational r;
    r.n=Allocator.make(nn);
    r.d=Allocator.one;
    return r;
  }
  static BigRational opCall () {
    BigRational r;
    r.n = Allocator.zero;
    r.d = Allocator.one;
    //char* tmp = std.string.toStringz(ToString!(T).toString();
    return r;
  }
  BigRational Rationalize() {
    T k = int_gcd(n,d);
    n=n/k;
    d=d/k;
    return *this;
  }
  void swap(inout BigRational b) {
    T bn=b.n;
    T bd=b.d;
    b.n=n;
    b.d=d;
    n=bn;
    d=bd;
  }
  BigRational opNeg() {
    return create(-n,d).InternalRationalize();
  }
  T IntegerPart() {
    return n/d;
  }
  T Floor() {
    T k = n/d;
    if (n<Allocator.zero&&k*d!=n)
      k=k-Allocator.one;
    return k;
  }
  BigRational floor() {
    return BigRational.create(Floor());
  }
  T Ceil() {
    T k = n/d;
    if (k>Allocator.zero&&k*d!=n)
      k=k+Allocator.one;
    return k;
  }
  BigRational ceil() {
    return BigRational.create(Ceil());
  }
  BigRational pow(T b) {
    return create(int_pow(n,b),int_pow(d,b));
  }
  BigRational Fraction() {
    BigRational ret = *this-create(Floor(),Allocator.one);
    //    if (ret<BigRational())
    //      ret+=BigRational(Allocator.one,Allocator.one);
    return ret;
  }
  int isFloat() {
    static T zero = Allocator.zero;
    static T one = Allocator.one;
    static T two = one+one;
    T g = int_gcd(n,d);
    g= d/g;
    T cur = one;
    while (cur<=g) {
      if (cur==g)
    return 1;
      cur=cur*two;
    }
    return 0;
  }
  T FractionalFloat(uint term) {
    static T zero = Allocator.zero;
    static T one = Allocator.one;
    static T two = one+one;
    assert (isFloat());
    BigRational frac = Fraction();
    T cur=one;
    T ret=zero;
    uint i=0;
    while (frac!=ZERO&&(term==0||i++<term)) {
      frac*=TWO;
      if (frac>=ONE) {
    ret=ret+cur;
    frac=frac-ONE;
      }
      cur=cur*two;
    }
    return ret;
  }

  bit[] FractionalBits(uint term) {
    assert (isFloat());
    BigRational frac = Fraction();
    bit[] ret;
    uint i=0;
    while (frac!=ZERO&&(term==0||i++<term)) {
      frac*=TWO;
      ret.length=ret.length+1;
      if (frac>=ONE) {
    ret[ret.length-1]=1;
    frac-=ONE;
      }else{
    ret[ret.length-1]=0;
      }
    }
    return ret;
  }
  BigRational opMulAssign(BigRational b) {
    n=n*b.n;
    d=d*b.d;
    InternalRationalize();
    return *this;
  }
  BigRational opMul(BigRational b) {
    return create(n*b.n,d*b.d).InternalRationalize();
  }
  BigRational opAddAssign(BigRational b) {
    n=n*b.d+b.n*d;
    d=d*b.d;
    return InternalRationalize();
  }
  BigRational opAdd(BigRational b) {
    return create(n*b.d+d*b.n,d*b.d).InternalRationalize();
  }
  BigRational opAdd(long b) {
    return *this+create(Allocator.make(b),Allocator.one);
  }
  BigRational opSubAssign(BigRational b) {
    n=n*b.d-b.n*d;
    d=d*b.d;
    return InternalRationalize();
  }
  BigRational opSub(BigRational b) {
    return create(n*b.d-d*b.n,d*b.d).InternalRationalize();
  }
  /*  BigRational opSub_r(BigRational b) {
    return create(d*b.n-n*b.d,d*b.d).InternalRationalize();
    }*/
  BigRational opDivAssign(BigRational b) {
    n=n*b.d;
    d=d*b.n;
    InternalRationalize();
    return *this;
  }
  BigRational opDiv(BigRational b) {
    return create(n*b.d,d*b.n).InternalRationalize();
  }
  /*
  BigRational opDiv_r(BigRational b) {
    return create(d*b.n,n*b.d).InternalRationalize();
  }
  */
  BigRational opModAssign(BigRational b) {
    n = (n*b.d) % (b.n*d);
    d = b.d*d;
    InternalRationalize();
    return *this;
  }
  BigRational opMod(BigRational b) {
    return create((n*b.d) % (b.n*d),b.d*d).InternalRationalize();
  }
  /*
  BigRational opMod_r(BigRational b) {
    return create((b.n*d)%(n*b.d), b.d*d).InternalRationalize();
  }
  */
  int opEquals (BigRational r) {
    //char * tmp = std.string.toStringz(std.string.toString(n));
    //char * tmp1 = std.string.toStringz(std.string.toString(d));
    //printf ("M %s %s\t",tmp,tmp1);

    return (n*r.d==d*r.n)?1:0;
  }
  int opCmp (BigRational rr) {    
    T thus = n*rr.d;
    T r  = rr.n*d;
    if (thus<r) return -1;
    if (thus>r) return 1;
    return 0;
  }
  char[] toString(){
    BigRational r=*this;
    r.Rationalize();
    return Allocator.toString(r.n)~"/"~Allocator.toString(r.d);
  }
  BigRational print () {
    //printf ("%d/%d=",cast(int)n,cast(int)d);

    BigRational r=*this;
    r.Rationalize();
    char * num=std.string.toStringz(Allocator.toString(r.n));
    char * den=std.string.toStringz(Allocator.toString(r.d));
    printf ("%s/%s",num,den);
    //printf ("=%d/%d",cast(int)n,cast(int)d);
    return *this;
  }
}
/*
version (Long){
  alias BigRational!(long,1) Rational;
}else {
  alias BigRational!(Int,1) Rational;
}
alias Rational rational;
*/
import etc.typecreate.intrinsiccreate;
alias etc.typecreate.intrinsiccreate.TypeCreate!(long) TC;
alias BigRational!(long, 1, TC ) rational;