| /* |
| * Copyright (C) 2015 The Android Open Source Project |
| * |
| * Licensed under the Apache License, Version 2.0 (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.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| package com.android.calculator2; |
| |
| // We implement rational numbers of bounded size. |
| // If the length of the nuumerator plus the length of the denominator |
| // exceeds a maximum size, we simply return null, and rely on our caller |
| // do something else. |
| // We currently never return null for a pure integer. |
| // TODO: Reconsider that. With some care, large factorials might |
| // become much faster. |
| // |
| // We also implement a number of irrational functions. These return |
| // a non-null result only when the result is known to be rational. |
| |
| import java.math.BigInteger; |
| import com.hp.creals.CR; |
| |
| public class BoundedRational { |
| // TODO: Maybe eventually make this extend Number? |
| private static final int MAX_SIZE = 800; // total, in bits |
| |
| private final BigInteger mNum; |
| private final BigInteger mDen; |
| |
| public BoundedRational(BigInteger n, BigInteger d) { |
| mNum = n; |
| mDen = d; |
| } |
| |
| public BoundedRational(BigInteger n) { |
| mNum = n; |
| mDen = BigInteger.ONE; |
| } |
| |
| public BoundedRational(long n, long d) { |
| mNum = BigInteger.valueOf(n); |
| mDen = BigInteger.valueOf(d); |
| } |
| |
| public BoundedRational(long n) { |
| mNum = BigInteger.valueOf(n); |
| mDen = BigInteger.valueOf(1); |
| } |
| |
| // Debug or log messages only, not pretty. |
| public String toString() { |
| return mNum.toString() + "/" + mDen.toString(); |
| } |
| |
| // Output to user, more expensive, less useful for debugging |
| // Not internationalized. |
| public String toNiceString() { |
| BoundedRational nicer = reduce().positiveDen(); |
| String result = nicer.mNum.toString(); |
| if (!nicer.mDen.equals(BigInteger.ONE)) { |
| result += "/" + nicer.mDen; |
| } |
| return result; |
| } |
| |
| public static String toString(BoundedRational r) { |
| if (r == null) return "not a small rational"; |
| return r.toString(); |
| } |
| |
| // Primarily for debugging; clearly not exact |
| public double doubleValue() { |
| return mNum.doubleValue() / mDen.doubleValue(); |
| } |
| |
| public CR CRValue() { |
| return CR.valueOf(mNum).divide(CR.valueOf(mDen)); |
| } |
| |
| private boolean tooBig() { |
| if (mDen.equals(BigInteger.ONE)) return false; |
| return (mNum.bitLength() + mDen.bitLength() > MAX_SIZE); |
| } |
| |
| // return an equivalent fraction with a positive denominator. |
| private BoundedRational positiveDen() { |
| if (mDen.compareTo(BigInteger.ZERO) > 0) return this; |
| return new BoundedRational(mNum.negate(), mDen.negate()); |
| } |
| |
| // Return an equivalent fraction in lowest terms. |
| private BoundedRational reduce() { |
| if (mDen.equals(BigInteger.ONE)) return this; // Optimization only |
| BigInteger divisor = mNum.gcd(mDen); |
| return new BoundedRational(mNum.divide(divisor), mDen.divide(divisor)); |
| } |
| |
| // Return a possibly reduced version of this that's not tooBig. |
| // Return null if none exists. |
| private BoundedRational maybeReduce() { |
| if (!tooBig()) return this; |
| BoundedRational result = positiveDen(); |
| if (!result.tooBig()) return this; |
| result = result.reduce(); |
| if (!result.tooBig()) return this; |
| return null; |
| } |
| |
| public int compareTo(BoundedRational r) { |
| // Compare by multiplying both sides by denominators, |
| // invert result if denominator product was negative. |
| return mNum.multiply(r.mDen).compareTo(r.mNum.multiply(mDen)) |
| * mDen.signum() * r.mDen.signum(); |
| } |
| |
| public int signum() { |
| return mNum.signum() * mDen.signum(); |
| } |
| |
| public boolean equals(BoundedRational r) { |
| return compareTo(r) == 0; |
| } |
| |
| // We use static methods for arithmetic, so that we can |
| // easily handle the null case. |
| // We try to catch domain errors whenever possible, sometimes even when |
| // one of the arguments is null, but not relevant. |
| |
| // Returns equivalent BigInteger result if it exists, null if not. |
| public static BigInteger asBigInteger(BoundedRational r) { |
| if (r == null) return null; |
| if (!r.mDen.equals(BigInteger.ONE)) r = r.reduce(); |
| if (!r.mDen.equals(BigInteger.ONE)) return null; |
| return r.mNum; |
| } |
| public static BoundedRational add(BoundedRational r1, BoundedRational r2) { |
| if (r1 == null || r2 == null) return null; |
| final BigInteger den = r1.mDen.multiply(r2.mDen); |
| final BigInteger num = r1.mNum.multiply(r2.mDen) |
| .add(r2.mNum.multiply(r1.mDen)); |
| return new BoundedRational(num,den).maybeReduce(); |
| } |
| |
| public static BoundedRational negate(BoundedRational r) { |
| if (r == null) return null; |
| return new BoundedRational(r.mNum.negate(), r.mDen); |
| } |
| |
| static BoundedRational subtract(BoundedRational r1, BoundedRational r2) { |
| return add(r1, negate(r2)); |
| } |
| |
| static BoundedRational multiply(BoundedRational r1, BoundedRational r2) { |
| // It's tempting but marginally unsound to reduce 0 * null to zero. |
| // The null could represent an infinite value, for which we |
| // failed to throw an exception because it was too big. |
| if (r1 == null || r2 == null) return null; |
| final BigInteger num = r1.mNum.multiply(r2.mNum); |
| final BigInteger den = r1.mDen.multiply(r2.mDen); |
| return new BoundedRational(num,den).maybeReduce(); |
| } |
| |
| public static class ZeroDivisionException extends ArithmeticException { |
| public ZeroDivisionException() { |
| super("Division by zero"); |
| } |
| } |
| |
| static BoundedRational inverse(BoundedRational r) { |
| if (r == null) return null; |
| if (r.mNum.equals(BigInteger.ZERO)) { |
| throw new ZeroDivisionException(); |
| } |
| return new BoundedRational(r.mDen, r.mNum); |
| } |
| |
| static BoundedRational divide(BoundedRational r1, BoundedRational r2) { |
| return multiply(r1, inverse(r2)); |
| } |
| |
| static BoundedRational sqrt(BoundedRational r) { |
| // Return non-null if numerator and denominator are small perfect |
| // squares. |
| if (r == null) return null; |
| r = r.positiveDen().reduce(); |
| if (r.mNum.compareTo(BigInteger.ZERO) < 0) { |
| throw new ArithmeticException("sqrt(negative)"); |
| } |
| final BigInteger num_sqrt = BigInteger.valueOf(Math.round(Math.sqrt( |
| r.mNum.doubleValue()))); |
| if (!num_sqrt.multiply(num_sqrt).equals(r.mNum)) return null; |
| final BigInteger den_sqrt = BigInteger.valueOf(Math.round(Math.sqrt( |
| r.mDen.doubleValue()))); |
| if (!den_sqrt.multiply(den_sqrt).equals(r.mDen)) return null; |
| return new BoundedRational(num_sqrt, den_sqrt); |
| } |
| |
| public final static BoundedRational ZERO = new BoundedRational(0); |
| public final static BoundedRational HALF = new BoundedRational(1,2); |
| public final static BoundedRational MINUS_HALF = new BoundedRational(-1,2); |
| public final static BoundedRational ONE = new BoundedRational(1); |
| public final static BoundedRational MINUS_ONE = new BoundedRational(-1); |
| public final static BoundedRational TWO = new BoundedRational(2); |
| public final static BoundedRational MINUS_TWO = new BoundedRational(-2); |
| public final static BoundedRational THIRTY = new BoundedRational(30); |
| public final static BoundedRational MINUS_THIRTY = new BoundedRational(-30); |
| public final static BoundedRational FORTY_FIVE = new BoundedRational(45); |
| public final static BoundedRational MINUS_FORTY_FIVE = |
| new BoundedRational(-45); |
| public final static BoundedRational NINETY = new BoundedRational(90); |
| public final static BoundedRational MINUS_NINETY = new BoundedRational(-90); |
| |
| private static BoundedRational map0to0(BoundedRational r) { |
| if (r == null) return null; |
| if (r.mNum.equals(BigInteger.ZERO)) { |
| return ZERO; |
| } |
| return null; |
| } |
| |
| private static BoundedRational map0to1(BoundedRational r) { |
| if (r == null) return null; |
| if (r.mNum.equals(BigInteger.ZERO)) { |
| return ONE; |
| } |
| return null; |
| } |
| |
| private static BoundedRational map1to0(BoundedRational r) { |
| if (r == null) return null; |
| if (r.mNum.equals(r.mDen)) { |
| return ZERO; |
| } |
| return null; |
| } |
| |
| // Throw an exception if the argument is definitely out of bounds for asin |
| // or acos. |
| private static void checkAsinDomain(BoundedRational r) { |
| if (r == null) return; |
| if (r.mNum.abs().compareTo(r.mDen.abs()) > 0) { |
| throw new ArithmeticException("inverse trig argument out of range"); |
| } |
| } |
| |
| public static BoundedRational sin(BoundedRational r) { |
| return map0to0(r); |
| } |
| |
| private final static BigInteger BIG360 = BigInteger.valueOf(360); |
| |
| public static BoundedRational degreeSin(BoundedRational r) { |
| final BigInteger r_BI = asBigInteger(r); |
| if (r_BI == null) return null; |
| final int r_int = r_BI.mod(BIG360).intValue(); |
| if (r_int % 30 != 0) return null; |
| switch (r_int / 10) { |
| case 0: |
| return ZERO; |
| case 3: // 30 degrees |
| return HALF; |
| case 9: |
| return ONE; |
| case 15: |
| return HALF; |
| case 18: // 180 degrees |
| return ZERO; |
| case 21: |
| return MINUS_HALF; |
| case 27: |
| return MINUS_ONE; |
| case 33: |
| return MINUS_HALF; |
| default: |
| return null; |
| } |
| } |
| |
| public static BoundedRational asin(BoundedRational r) { |
| checkAsinDomain(r); |
| return map0to0(r); |
| } |
| |
| public static BoundedRational degreeAsin(BoundedRational r) { |
| checkAsinDomain(r); |
| final BigInteger r2_BI = asBigInteger(multiply(r, TWO)); |
| if (r2_BI == null) return null; |
| final int r2_int = r2_BI.intValue(); |
| // Somewhat surprisingly, it seems to be the case that the following |
| // covers all rational cases: |
| switch (r2_int) { |
| case -2: // Corresponding to -1 argument |
| return MINUS_NINETY; |
| case -1: // Corresponding to -1/2 argument |
| return MINUS_THIRTY; |
| case 0: |
| return ZERO; |
| case 1: |
| return THIRTY; |
| case 2: |
| return NINETY; |
| default: |
| throw new AssertionError("Impossible asin arg"); |
| } |
| } |
| |
| public static BoundedRational tan(BoundedRational r) { |
| // Unlike the degree case, we cannot check for the singularity, |
| // since it occurs at an irrational argument. |
| return map0to0(r); |
| } |
| |
| public static BoundedRational degreeTan(BoundedRational r) { |
| final BoundedRational degree_sin = degreeSin(r); |
| final BoundedRational degree_cos = degreeCos(r); |
| if (degree_cos != null && degree_cos.mNum.equals(BigInteger.ZERO)) { |
| throw new ArithmeticException("Tangent undefined"); |
| } |
| return divide(degree_sin, degree_cos); |
| } |
| |
| public static BoundedRational atan(BoundedRational r) { |
| return map0to0(r); |
| } |
| |
| public static BoundedRational degreeAtan(BoundedRational r) { |
| final BigInteger r_BI = asBigInteger(r); |
| if (r_BI == null) return null; |
| if (r_BI.abs().compareTo(BigInteger.ONE) > 0) return null; |
| final int r_int = r_BI.intValue(); |
| // Again, these seem to be all rational cases: |
| switch (r_int) { |
| case -1: |
| return MINUS_FORTY_FIVE; |
| case 0: |
| return ZERO; |
| case 1: |
| return FORTY_FIVE; |
| default: |
| throw new AssertionError("Impossible atan arg"); |
| } |
| } |
| |
| public static BoundedRational cos(BoundedRational r) { |
| return map0to1(r); |
| } |
| |
| public static BoundedRational degreeCos(BoundedRational r) { |
| return degreeSin(add(r, NINETY)); |
| } |
| |
| public static BoundedRational acos(BoundedRational r) { |
| checkAsinDomain(r); |
| return map1to0(r); |
| } |
| |
| public static BoundedRational degreeAcos(BoundedRational r) { |
| final BoundedRational asin_r = degreeAsin(r); |
| return subtract(NINETY, asin_r); |
| } |
| |
| private static final BigInteger BIG_TWO = BigInteger.valueOf(2); |
| |
| // Compute an integral power of this |
| private BoundedRational pow(BigInteger exp) { |
| if (exp.compareTo(BigInteger.ZERO) < 0) { |
| return inverse(pow(exp.negate())); |
| } |
| if (exp.equals(BigInteger.ONE)) return this; |
| if (exp.and(BigInteger.ONE).intValue() == 1) { |
| return multiply(pow(exp.subtract(BigInteger.ONE)), this); |
| } |
| if (exp.equals(BigInteger.ZERO)) { |
| return ONE; |
| } |
| BoundedRational tmp = pow(exp.shiftRight(1)); |
| if (Thread.interrupted()) { |
| throw new CR.AbortedException(); |
| } |
| return multiply(tmp, tmp); |
| } |
| |
| public static BoundedRational pow(BoundedRational base, BoundedRational exp) { |
| if (exp == null) return null; |
| if (exp.mNum.equals(BigInteger.ZERO)) { |
| return new BoundedRational(1); |
| } |
| if (base == null) return null; |
| exp = exp.reduce().positiveDen(); |
| if (!exp.mDen.equals(BigInteger.ONE)) return null; |
| return base.pow(exp.mNum); |
| } |
| |
| public static BoundedRational ln(BoundedRational r) { |
| if (r != null && r.signum() <= 0) { |
| throw new ArithmeticException("log(non-positive)"); |
| } |
| return map1to0(r); |
| } |
| |
| public static BoundedRational exp(BoundedRational r) { |
| return map0to1(r); |
| } |
| |
| // Return the base 10 log of n, if n is a power of 10, -1 otherwise. |
| // n must be positive. |
| private static long b10Log(BigInteger n) { |
| // This algorithm is very naive, but we doubt it matters. |
| long count = 0; |
| while (n.mod(BigInteger.TEN).equals(BigInteger.ZERO)) { |
| n = n.divide(BigInteger.TEN); |
| ++count; |
| } |
| if (n.equals(BigInteger.ONE)) { |
| return count; |
| } |
| return -1; |
| } |
| |
| public static BoundedRational log(BoundedRational r) { |
| if (r == null) return null; |
| if (r.signum() <= 0) { |
| throw new ArithmeticException("log(non-positive)"); |
| } |
| r = r.reduce().positiveDen(); |
| if (r == null) return null; |
| if (r.mDen.equals(BigInteger.ONE)) { |
| long log = b10Log(r.mNum); |
| if (log != -1) return new BoundedRational(log); |
| } else if (r.mNum.equals(BigInteger.ONE)) { |
| long log = b10Log(r.mDen); |
| if (log != -1) return new BoundedRational(-log); |
| } |
| return null; |
| } |
| |
| // Generalized factorial. |
| // Compute n * (n - step) * (n - 2 * step) * ... |
| // This can be used to compute factorial a bit faster, especially |
| // if BigInteger uses sub-quadratic multiplication. |
| private static BigInteger genFactorial(long n, long step) { |
| if (n > 4 * step) { |
| BigInteger prod1 = genFactorial(n, 2 * step); |
| if (Thread.interrupted()) { |
| throw new CR.AbortedException(); |
| } |
| BigInteger prod2 = genFactorial(n - step, 2 * step); |
| if (Thread.interrupted()) { |
| throw new CR.AbortedException(); |
| } |
| return prod1.multiply(prod2); |
| } else { |
| BigInteger res = BigInteger.valueOf(n); |
| for (long i = n - step; i > 1; i -= step) { |
| res = res.multiply(BigInteger.valueOf(i)); |
| } |
| return res; |
| } |
| } |
| |
| // Factorial; |
| // always produces non-null (or exception) when called on non-null r. |
| public static BoundedRational fact(BoundedRational r) { |
| if (r == null) return null; // Caller should probably preclude this case. |
| final BigInteger r_BI = asBigInteger(r); |
| if (r_BI == null) { |
| throw new ArithmeticException("Non-integral factorial argument"); |
| } |
| if (r_BI.signum() < 0) { |
| throw new ArithmeticException("Negative factorial argument"); |
| } |
| if (r_BI.bitLength() > 30) { |
| // Will fail. LongValue() may not work. Punt now. |
| throw new ArithmeticException("Factorial argument too big"); |
| } |
| return new BoundedRational(genFactorial(r_BI.longValue(), 1)); |
| } |
| |
| private static final BigInteger BIG_FIVE = BigInteger.valueOf(5); |
| private static final BigInteger BIG_MINUS_ONE = BigInteger.valueOf(-1); |
| |
| // Return the number of decimal digits to the right of the |
| // decimal point required to represent the argument exactly, |
| // or Integer.MAX_VALUE if it's not possible. |
| // Never returns a value les than zero, even if r is |
| // a power of ten. |
| static int digitsRequired(BoundedRational r) { |
| if (r == null) return Integer.MAX_VALUE; |
| int powers_of_two = 0; // Max power of 2 that divides denominator |
| int powers_of_five = 0; // Max power of 5 that divides denominator |
| // Try the easy case first to speed things up. |
| if (r.mDen.equals(BigInteger.ONE)) return 0; |
| r = r.reduce(); |
| BigInteger den = r.mDen; |
| while (!den.testBit(0)) { |
| ++powers_of_two; |
| den = den.shiftRight(1); |
| } |
| while (den.mod(BIG_FIVE).equals(BigInteger.ZERO)) { |
| ++powers_of_five; |
| den = den.divide(BIG_FIVE); |
| } |
| // If the denominator has a factor of other than 2 or 5 |
| // (the divisors of 10), the decimal expansion does not |
| // terminate. Multiplying the fraction by any number of |
| // powers of 10 will not cancel the demoniator. |
| // (Recall the fraction was in lowest terms to start with.) |
| // Otherwise the powers of 10 we need to cancel the denominator |
| // is the larger of powers_of_two and powers_of_five. |
| if (!den.equals(BigInteger.ONE) && !den.equals(BIG_MINUS_ONE)) { |
| return Integer.MAX_VALUE; |
| } |
| return Math.max(powers_of_two, powers_of_five); |
| } |
| } |