/***** BEGIN LICENSE BLOCK *****

* Version: EPL 1.0/GPL 2.0/LGPL 2.1

*

* The contents of this file are subject to the Eclipse Public

* License Version 1.0 (the "License"); you may not use this file

* except in compliance with the License. You may obtain a copy of

* the License at http://www.eclipse.org/legal/epl-v10.html

*

* Software distributed under the License is distributed on an "AS

* IS" basis, WITHOUT WARRANTY OF ANY KIND, either express or

* implied. See the License for the specific language governing

* rights and limitations under the License.

*

* Copyright (C) 2006 Charles O Nutter <headius@headius.com>

*

* Alternatively, the contents of this file may be used under the terms of

* either of the GNU General Public License Version 2 or later (the "GPL"),

* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),

* in which case the provisions of the GPL or the LGPL are applicable instead

* of those above. If you wish to allow use of your version of this file only

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* decision by deleting the provisions above and replace them with the notice

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* the provisions above, a recipient may use your version of this file under

* the terms of any one of the EPL, the GPL or the LGPL.

***** END LICENSE BLOCK *****/

package org.jruby.util;

import java.math.BigInteger;

import org.joni.Regex;

import org.jcodings.specific.ASCIIEncoding;

import org.jruby.Ruby;

import org.jruby.RubyBignum;

import org.jruby.RubyFixnum;

import org.jruby.RubyFloat;

import org.jruby.RubyInteger;

import org.jruby.runtime.ThreadContext;

import org.jruby.runtime.builtin.IRubyObject;

import static org.jruby.javasupport.util.RuntimeHelpers.invokedynamic;

import static org.jruby.runtime.invokedynamic.MethodNames.OP_CMP;

public class Numeric {

public static final boolean CANON = true;

/** f_add

*

*/

public static IRubyObject f_add(ThreadContext context, IRubyObject x, IRubyObject y) {

if (y instanceof RubyFixnum && ((RubyFixnum)y).getLongValue() == 0) return x;

if (x instanceof RubyFixnum && ((RubyFixnum)x).getLongValue() == 0) return y;

return x.callMethod(context, "+", y);

}

/** f_cmp

*

*/

public static IRubyObject f_cmp(ThreadContext context, IRubyObject x, IRubyObject y) {

if (x instanceof RubyFixnum && y instanceof RubyFixnum) {

long c = ((RubyFixnum)x).getLongValue() - ((RubyFixnum)y).getLongValue();

if (c > 0) {

return RubyFixnum.one(context.runtime);

} else if (c < 0) {

return RubyFixnum.minus_one(context.runtime);

}

return RubyFixnum.zero(context.runtime);

}

return invokedynamic(context, x, OP_CMP, y);

}

/** f_div

*

*/

public static IRubyObject f_div(ThreadContext context, IRubyObject x, IRubyObject y) {

if (y instanceof RubyFixnum && ((RubyFixnum)y).getLongValue() == 1) return x;

return x.callMethod(context, "/", y);

}

/** f_gt_p

*

*/

public static IRubyObject f_gt_p(ThreadContext context, IRubyObject x, IRubyObject y) {

if (x instanceof RubyFixnum && y instanceof RubyFixnum) {

return ((RubyFixnum)x).getLongValue() > ((RubyFixnum)y).getLongValue() ? context.runtime.getTrue() : context.runtime.getFalse();

}

return x.callMethod(context, ">", y);

}

/** f_lt_p

*

*/

public static IRubyObject f_lt_p(ThreadContext context, IRubyObject x, IRubyObject y) {

if (x instanceof RubyFixnum && y instanceof RubyFixnum) {

return ((RubyFixnum)x).getLongValue() < ((RubyFixnum)y).getLongValue() ? context.runtime.getTrue() : context.runtime.getFalse();

}

return x.callMethod(context, "<", y);

}

/** f_mod

*

*/

public static IRubyObject f_mod(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "%", y);

}

/** f_mul

*

*/

public static IRubyObject f_mul(ThreadContext context, IRubyObject x, IRubyObject y) {

Ruby runtime = context.runtime;

if (y instanceof RubyFixnum) {

long iy = ((RubyFixnum)y).getLongValue();

if (iy == 0) {

if (x instanceof RubyFixnum || x instanceof RubyBignum) return RubyFixnum.zero(runtime);

} else if (iy == 1) {

return x;

}

} else if (x instanceof RubyFixnum) {

long ix = ((RubyFixnum)x).getLongValue();

if (ix == 0) {

if (y instanceof RubyFixnum || y instanceof RubyBignum) return RubyFixnum.zero(runtime);

} else if (ix == 1) {

return y;

}

}

return x.callMethod(context, "*", y);

}

/** f_sub

*

*/

public static IRubyObject f_sub(ThreadContext context, IRubyObject x, IRubyObject y) {

if (y instanceof RubyFixnum && ((RubyFixnum)y).getLongValue() == 0) return x;

return x.callMethod(context, "-", y);

}

/** f_xor

*

*/

public static IRubyObject f_xor(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "^", y);

}

/** f_abs

*

*/

public static IRubyObject f_abs(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "abs");

}

/** f_abs2

*

*/

public static IRubyObject f_abs2(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "abs2");

}

/** f_arg

*

*/

public static IRubyObject f_arg(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "arg");

}

/** f_conjugate

*

*/

public static IRubyObject f_conjugate(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "conjugate");

}

/** f_denominator

*

*/

public static IRubyObject f_denominator(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "denominator");

}

/** f_exact_p

*

*/

public static IRubyObject f_exact_p(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "exact?");

}

/** f_numerator

*

*/

public static IRubyObject f_numerator(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "numerator");

}

/** f_polar

*

*/

public static IRubyObject f_polar(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "polar");

}

/** f_real_p

*

*/

public static IRubyObject f_real_p(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "real?");

}

/** f_integer_p

*

*/

public static IRubyObject f_integer_p(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "integer?");

}

/** f_divmod

*

*/

public static IRubyObject f_divmod(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "divmod", y);

}

/** f_floor

*

*/

public static IRubyObject f_floor(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "floor");

}

/** f_inspect

*

*/

public static IRubyObject f_inspect(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "inspect");

}

/** f_negate

*

*/

public static IRubyObject f_negate(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "-@");

}

/** f_to_f

*

*/

public static IRubyObject f_to_f(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "to_f");

}

/** f_to_i

*

*/

public static IRubyObject f_to_i(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "to_i");

}

/** f_to_r

*

*/

public static IRubyObject f_to_r(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "to_r");

}

/** f_to_s

*

*/

public static IRubyObject f_to_s(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "to_s");

}

/** f_truncate

*

*/

public static IRubyObject f_truncate(ThreadContext context, IRubyObject x) {

return x.callMethod(context, "truncate");

}

/** f_equal

*

* Note: This may not return a value which is a boolean. other.== can

* return non-boolean (which unless it is nil it will be isTrue()).

*

*/

public static IRubyObject f_equal(ThreadContext context, IRubyObject x, IRubyObject y) {

if (x instanceof RubyFixnum && y instanceof RubyFixnum) {

return context.runtime.newBoolean(((RubyFixnum) x).getLongValue() == ((RubyFixnum) y).getLongValue());

}

return x.callMethod(context, "==", y);

}

/** f_expt

*

*/

public static IRubyObject f_expt(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "**", y);

}

/** f_idiv

*

*/

public static IRubyObject f_idiv(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "div", y);

}

/** f_quo

*

*/

public static IRubyObject f_quo(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "quo", y);

}

/** f_rshift

*

*/

public static IRubyObject f_rshift(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, ">>", y);

}

/** f_lshift

*

*/

public static IRubyObject f_lshift(ThreadContext context, IRubyObject x, IRubyObject y) {

return x.callMethod(context, "<<", y);

}

/** f_negative_p

*

*/

public static boolean f_negative_p(ThreadContext context, IRubyObject x) {

if (x instanceof RubyFixnum) return ((RubyFixnum)x).getLongValue() < 0;

return x.callMethod(context, "<", RubyFixnum.zero(context.runtime)).isTrue();

}

/** f_zero_p

*

*/

public static boolean f_zero_p(ThreadContext context, IRubyObject x) {

if (x instanceof RubyFixnum) return ((RubyFixnum)x).getLongValue() == 0;

return x.callMethod(context, "==", RubyFixnum.zero(context.runtime)).isTrue();

}

/** f_one_p

*

*/

public static boolean f_one_p(ThreadContext context, IRubyObject x) {

if (x instanceof RubyFixnum) return ((RubyFixnum)x).getLongValue() == 1;

return x.callMethod(context, "==", RubyFixnum.one(context.runtime)).isTrue();

}

/** i_gcd

*

*/

public static long i_gcd(long x, long y) {

if (x < 0) x = -x;

if (y < 0) y = -y;

if (x == 0) return y;

if (y == 0) return x;

while (x > 0) {

long t = x;

x = y % x;

y = t;

}

return y;

}

/** f_gcd

*

*/

public static IRubyObject f_gcd(ThreadContext context, IRubyObject x, IRubyObject y) {

if (x instanceof RubyFixnum && y instanceof RubyFixnum) {

return RubyFixnum.newFixnum(context.runtime, i_gcd(((RubyFixnum)x).getLongValue(), ((RubyFixnum)y).getLongValue()));

}

if (f_negative_p(context, x)) x = f_negate(context, x);

if (f_negative_p(context, y)) y = f_negate(context, y);

if (f_zero_p(context, x)) return y;

if (f_zero_p(context, y)) return x;

for (;;) {

if (x instanceof RubyFixnum) {

if (((RubyFixnum)x).getLongValue() == 0) return y;

if (y instanceof RubyFixnum) {

return RubyFixnum.newFixnum(context.runtime, i_gcd(((RubyFixnum)x).getLongValue(), ((RubyFixnum)y).getLongValue()));

}

}

IRubyObject z = x;

x = f_mod(context, y, x);

y = z;

}

}

/** f_lcm

*

*/

public static IRubyObject f_lcm(ThreadContext context, IRubyObject x, IRubyObject y) {

if (f_zero_p(context, x) || f_zero_p(context, y)) {

return RubyFixnum.zero(context.runtime);

}

return f_abs(context, f_mul(context, f_div(context, x, f_gcd(context, x, y)), y));

}

public static long i_ilog2(ThreadContext context, IRubyObject x) {

long q = (x.callMethod(context, "size").convertToInteger().getLongValue() - 8) * 8 + 1;

if (q > 0) {

x = f_rshift(context, x, RubyFixnum.newFixnum(context.runtime, q));

}

long fx = x.convertToInteger().getLongValue();

long r = -1;

while (fx != 0) {

fx >>= 1;

r += 1;

}

return q + r;

}

public static double ldexp(double f, long e) {

return f * Math.pow(2.0, e);

}

public static double frexp(double mantissa, long[]e) {

short sign = 1;

long exponent = 0;

if (Double.isInfinite(mantissa) || Double.isNaN(mantissa)) {

return mantissa;

}

if (mantissa != 0.0) {

if (mantissa < 0) {

mantissa = -mantissa;

sign = -1;

}

for (; mantissa < 0.5; mantissa *= 2.0, exponent -=1) { }

for (; mantissa >= 1.0; mantissa *= 0.5, exponent +=1) { }

}

e[0] = exponent;

return sign * mantissa;

}

private static long SQRT_LONG_MAX = ((long)1) << ((8 * 8 - 1) / 2);

static boolean fitSqrtLong(long n) {

return n < SQRT_LONG_MAX && n >= -SQRT_LONG_MAX;

}

public static IRubyObject int_pow(ThreadContext context, long x, long y) {

boolean neg = x < 0;

long z = 1;

if (neg) x = -x;

if ((y & 1) != 0) {

z = x;

} else {

neg = false;

}

y &= ~1;

Ruby runtime = context.runtime;

do {

while (y % 2 == 0) {

if (!fitSqrtLong(x)) {

IRubyObject v = RubyBignum.newBignum(runtime, RubyBignum.fix2big(RubyFixnum.newFixnum(runtime, x))).op_pow(context, RubyFixnum.newFixnum(runtime, y));

if (z != 1) v = RubyBignum.newBignum(runtime, RubyBignum.fix2big(RubyFixnum.newFixnum(runtime, neg ? -z : z))).op_mul19(context, v);

return v;

}

x *= x;

y >>= 1;

}

BigInteger bigX = BigInteger.valueOf(x);

BigInteger bigXZ = bigX.multiply(bigX);

if (bigXZ.divide(bigX).longValue() != z) {

IRubyObject v = RubyBignum.newBignum(runtime, RubyBignum.fix2big(RubyFixnum.newFixnum(runtime, x))).op_pow(context, RubyFixnum.newFixnum(runtime, y));

if (z != 1) v = RubyBignum.newBignum(runtime, RubyBignum.fix2big(RubyFixnum.newFixnum(runtime, neg ? -z : z))).op_mul19(context, v);

return v;

}

z = bigXZ.longValue();

} while(--y != 0);

if (neg) z = -z;

return RubyFixnum.newFixnum(runtime, z);

}

public static boolean k_exact_p(IRubyObject x) {

return !(x instanceof RubyFloat);

}

public static boolean k_inexact_p(IRubyObject x) {

return x instanceof RubyFloat;

}

public static final class ComplexPatterns {

public static final Regex comp_pat0, comp_pat1, comp_pat2, underscores_pat;

static {

String WS = "\\s*";

String DIGITS = "(?:\\d(?:_\\d|\\d)*)";

String NUMERATOR = "(?:" + DIGITS + "?\\.)?" + DIGITS + "(?:[eE][-+]?" + DIGITS + ")?";

String DENOMINATOR = DIGITS;

String NUMBER = "[-+]?" + NUMERATOR + "(?:\\/" + DENOMINATOR + ")?";

String NUMBERNOS = NUMERATOR + "(?:\\/" + DENOMINATOR + ")?";

String PATTERN0 = "\\A" + WS + "(" + NUMBER + ")@(" + NUMBER + ")" + WS;

String PATTERN1 = "\\A" + WS + "([-+])?(" + NUMBER + ")?[iIjJ]" + WS;

String PATTERN2 = "\\A" + WS + "(" + NUMBER + ")(([-+])(" + NUMBERNOS + ")?[iIjJ])?" + WS;

comp_pat0 = new Regex(PATTERN0.getBytes(), 0, PATTERN0.length(), 0, ASCIIEncoding.INSTANCE);

comp_pat1 = new Regex(PATTERN1.getBytes(), 0, PATTERN1.length(), 0, ASCIIEncoding.INSTANCE);

comp_pat2 = new Regex(PATTERN2.getBytes(), 0, PATTERN2.length(), 0, ASCIIEncoding.INSTANCE);

underscores_pat = new Regex("_+".getBytes(), 0, 2, 0, ASCIIEncoding.INSTANCE);

}

}

public static final class RationalPatterns {

public static final Regex rat_pat, an_e_pat, a_dot_pat;

static {

String WS = "\\s*";

String DIGITS = "(?:\\d(?:_\\d|\\d)*)";

String NUMERATOR = "(?:" + DIGITS + "?\\.)?" + DIGITS + "(?:[eE][-+]?" + DIGITS + ")?";

String DENOMINATOR = DIGITS;

String PATTERN = "\\A" + WS + "([-+])?(" + NUMERATOR + ")(?:\\/(" + DENOMINATOR + "))?" + WS;

rat_pat = new Regex(PATTERN.getBytes(), 0, PATTERN.length(), 0, ASCIIEncoding.INSTANCE);

an_e_pat = new Regex("[Ee]".getBytes(), 0, 4, 0, ASCIIEncoding.INSTANCE);

a_dot_pat = new Regex("\\.".getBytes(), 0, 2, 0, ASCIIEncoding.INSTANCE);

}

}

/*

The algorithm here is the method described in CLISP. Bruno Haible has

graciously given permission to use this algorithm. He says, "You can use

it, if you present the following explanation of the algorithm."

Algorithm (recursively presented):

If x is a rational number, return x.

If x = 0.0, return 0.

If x < 0.0, return (- (rationalize (- x))).

If x > 0.0:

Call (integer-decode-float x). It returns a m,e,s=1 (mantissa,

exponent, sign).

If m = 0 or e >= 0: return x = m*2^e.

Search a rational number between a = (m-1/2)*2^e and b = (m+1/2)*2^e

with smallest possible numerator and denominator.

Note 1: If m is a power of 2, we ought to take a = (m-1/4)*2^e.

But in this case the result will be x itself anyway, regardless of

the choice of a. Therefore we can simply ignore this case.

Note 2: At first, we need to consider the closed interval [a,b].

but since a and b have the denominator 2^(|e|+1) whereas x itself

has a denominator <= 2^|e|, we can restrict the search to the open

interval (a,b).

So, for given a and b (0 < a < b) we are searching a rational number

y with a <= y <= b.

Recursive algorithm fraction_between(a,b):

c := (ceiling a)

if c < b

then return c ; because a <= c < b, c integer

else

; a is not integer (otherwise we would have had c = a < b)

k := c-1 ; k = floor(a), k < a < b <= k+1

return y = k + 1/fraction_between(1/(b-k), 1/(a-k))

; note 1 <= 1/(b-k) < 1/(a-k)

You can see that we are actually computing a continued fraction expansion.

Algorithm (iterative):

If x is rational, return x.

Call (integer-decode-float x). It returns a m,e,s (mantissa,

exponent, sign).

If m = 0 or e >= 0, return m*2^e*s. (This includes the case x = 0.0.)

Create rational numbers a := (2*m-1)*2^(e-1) and b := (2*m+1)*2^(e-1)

(positive and already in lowest terms because the denominator is a

power of two and the numerator is odd).

Start a continued fraction expansion

p[-1] := 0, p[0] := 1, q[-1] := 1, q[0] := 0, i := 0.

Loop

c := (ceiling a)

if c >= b

then k := c-1, partial_quotient(k), (a,b) := (1/(b-k),1/(a-k)),

goto Loop

finally partial_quotient(c).

Here partial_quotient(c) denotes the iteration

i := i+1, p[i] := c*p[i-1]+p[i-2], q[i] := c*q[i-1]+q[i-2].

At the end, return s * (p[i]/q[i]).

This rational number is already in lowest terms because

p[i]*q[i-1]-p[i-1]*q[i] = (-1)^i.

*/

public static IRubyObject[] nurat_rationalize_internal(ThreadContext context, IRubyObject[] ary) {

IRubyObject a, b, p, q;

a = ary[0];

b = ary[1];

IRubyObject c, k, t, p0, p1, p2, q0, q1, q2;

RubyFixnum zero = RubyFixnum.zero(context.runtime);

RubyFixnum one = RubyFixnum.one(context.runtime);

p0 = q1 = zero;

p1 = q0 = one;

while (true) {

c = a.callMethod(context, "ceil");

if (f_lt_p(context, c, b).isTrue()) {

break;

}

k = f_sub(context, c, one);

p2 = f_add(context, f_mul(context, k, p1), p0);

q2 = f_add(context, f_mul(context, k, q1), q0);

t = f_quo(context, one, f_sub(context, b, k));

b = f_quo(context, one, f_sub(context, a, k));

a = t;

p0 = p1;

q0 = q1;

p1 = p2;

q1 = q2;

}

p = f_add(context, f_mul(context, c, p1), p0);

q = f_add(context, f_mul(context, c, q1), q0);

IRubyObject[] v = new IRubyObject[]{p, q};

return v;

}

public static void checkInteger(ThreadContext context, IRubyObject obj) {

if (!(obj instanceof RubyInteger)) {

throw context.runtime.newTypeError("not an integer");

}

}

}