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Commit d6136e69 authored by Hans Boehm's avatar Hans Boehm Committed by Android Git Automerger
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am ca9a5ad0: am 114e08db: Merge "BoundedRational.java cleanup" into mnc-dr-dev 

* commit 'ca9a5ad0':
  BoundedRational.java cleanup
parents 1a78db27 ca9a5ad0
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src/com/android/calculator2/BoundedRational.java
View file @ d6136e69
......@@ -16,22 +16,25 @@
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;
/**
* Rational numbers that may turn to null if they get too big.
* For many operations, 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 or for a BoundedRational that has just been
* constructed.
*
* We also implement a number of irrational functions. These return a non-null result only when
* the result is known to be rational.
*/
public class BoundedRational {
// TODO: Consider returning null for integers. With some care, large factorials might become
// much faster.
// TODO: Maybe eventually make this extend Number?
private static final int MAX_SIZE = 800; // total, in bits
private final BigInteger mNum;
......@@ -57,13 +60,19 @@ public class BoundedRational {
mDen = BigInteger.valueOf(1);
}
// Debug or log messages only, not pretty.
/**
* Convert to String reflecting raw representation.
* 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.
/**
* Convert to readable String.
* Intended for output output to user. More expensive, less useful for debugging than
* toString(). Not internationalized.
*/
public String toNiceString() {
BoundedRational nicer = reduce().positiveDen();
String result = nicer.mNum.toString();
......@@ -74,11 +83,16 @@ public class BoundedRational {
}
public static String toString(BoundedRational r) {
if (r == null) return "not a small rational";
if (r == null) {
return "not a small rational";
}
return r.toString();
}
// Primarily for debugging; clearly not exact
/**
* Return a double approximation.
* Primarily for debugging.
*/
public double doubleValue() {
return mNum.doubleValue() / mDen.doubleValue();
}
......@@ -93,39 +107,55 @@ public class BoundedRational {
}
private boolean tooBig() {
if (mDen.equals(BigInteger.ONE)) return false;
if (mDen.equals(BigInteger.ONE)) {
return false;
}
return (mNum.bitLength() + mDen.bitLength() > MAX_SIZE);
}
// return an equivalent fraction with a positive denominator.
/**
* Return an equivalent fraction with a positive denominator.
*/
private BoundedRational positiveDen() {
if (mDen.compareTo(BigInteger.ZERO) > 0) return this;
if (mDen.signum() > 0) {
return this;
}
return new BoundedRational(mNum.negate(), mDen.negate());
}
// Return an equivalent fraction in lowest terms.
/**
* Return an equivalent fraction in lowest terms.
* Denominator sign may remain negative.
*/
private BoundedRational reduce() {
if (mDen.equals(BigInteger.ONE)) return this; // Optimization only
BigInteger divisor = mNum.gcd(mDen);
if (mDen.equals(BigInteger.ONE)) {
return this; // Optimization only
}
final 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.
/**
* Return a possibly reduced version of this that's not tooBig().
* Return null if none exists.
*/
private BoundedRational maybeReduce() {
if (!tooBig()) return this;
if (!tooBig()) {
return this;
}
BoundedRational result = positiveDen();
if (!result.tooBig()) return this;
result = result.reduce();
if (!result.tooBig()) return this;
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();
// 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() {
......@@ -136,28 +166,37 @@ public class BoundedRational {
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.
// 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.
/**
* 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;
if (r == null) {
return null;
}
final BigInteger[] quotAndRem = r.mNum.divideAndRemainder(r.mDen);
if (quotAndRem[1].signum() == 0) {
return quotAndRem[0];
} else {
return null;
}
}
public static BoundedRational add(BoundedRational r1, BoundedRational r2) {
if (r1 == null || r2 == null) return null;
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));
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;
if (r == null) {
return null;
}
return new BoundedRational(r.mNum.negate(), r.mDen);
}
......@@ -166,10 +205,11 @@ public class BoundedRational {
}
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;
// It's tempting but marginally unsound to reduce 0 * null to 0. 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();
......@@ -181,9 +221,14 @@ public class BoundedRational {
}
}
/**
* Return the reciprocal of r (or null).
*/
static BoundedRational inverse(BoundedRational r) {
if (r == null) return null;
if (r.mNum.equals(BigInteger.ZERO)) {
if (r == null) {
return null;
}
if (r.mNum.signum() == 0) {
throw new ZeroDivisionException();
}
return new BoundedRational(r.mDen, r.mNum);
......@@ -194,19 +239,22 @@ public class BoundedRational {
}
static BoundedRational sqrt(BoundedRational r) {
// Return non-null if numerator and denominator are small perfect
// squares.
if (r == null) return null;
// 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) {
if (r.mNum.signum() < 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;
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);
}
......@@ -220,39 +268,45 @@ public class BoundedRational {
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 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)) {
if (r == null) {
return null;
}
if (r.mNum.signum() == 0) {
return ZERO;
}
return null;
}
private static BoundedRational map0to1(BoundedRational r) {
if (r == null) return null;
if (r.mNum.equals(BigInteger.ZERO)) {
if (r == null) {
return null;
}
if (r.mNum.signum() == 0) {
return ONE;
}
return null;
}
private static BoundedRational map1to0(BoundedRational r) {
if (r == null) return null;
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.
// 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 == null) {
return;
}
if (r.mNum.abs().compareTo(r.mDen.abs()) > 0) {
throw new ArithmeticException("inverse trig argument out of range");
}
......@@ -266,9 +320,13 @@ public class BoundedRational {
public static BoundedRational degreeSin(BoundedRational r) {
final BigInteger r_BI = asBigInteger(r);
if (r_BI == null) return null;
if (r_BI == null) {
return null;
}
final int r_int = r_BI.mod(BIG360).intValue();
if (r_int % 30 != 0) return null;
if (r_int % 30 != 0) {
return null;
}
switch (r_int / 10) {
case 0:
return ZERO;
......@@ -299,10 +357,12 @@ public class BoundedRational {
public static BoundedRational degreeAsin(BoundedRational r) {
checkAsinDomain(r);
final BigInteger r2_BI = asBigInteger(multiply(r, TWO));
if (r2_BI == null) return null;
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:
// 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;
......@@ -320,18 +380,18 @@ public class BoundedRational {
}
public static BoundedRational tan(BoundedRational r) {
// Unlike the degree case, we cannot check for the singularity,
// since it occurs at an irrational argument.
// 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)) {
final BoundedRational degSin = degreeSin(r);
final BoundedRational degCos = degreeCos(r);
if (degCos != null && degCos.mNum.signum() == 0) {
throw new ArithmeticException("Tangent undefined");
}
return divide(degree_sin, degree_cos);
return divide(degSin, degCos);
}
public static BoundedRational atan(BoundedRational r) {
......@@ -340,8 +400,12 @@ public class BoundedRational {
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;
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) {
......@@ -376,16 +440,20 @@ public class BoundedRational {
private static final BigInteger BIG_TWO = BigInteger.valueOf(2);
// Compute an integral power of this
/**
* Compute an integral power of this.
*/
private BoundedRational pow(BigInteger exp) {
if (exp.compareTo(BigInteger.ZERO) < 0) {
if (exp.signum() < 0) {
return inverse(pow(exp.negate()));
}
if (exp.equals(BigInteger.ONE)) return this;
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)) {
if (exp.signum() == 0) {
return ONE;
}
BoundedRational tmp = pow(exp.shiftRight(1));
......@@ -396,13 +464,21 @@ public class BoundedRational {
}
public static BoundedRational pow(BoundedRational base, BoundedRational exp) {
if (exp == null) return null;
if (exp.mNum.equals(BigInteger.ZERO)) {
if (exp == null) {
return null;
}
if (exp.mNum.signum() == 0) {
// Questionable if base has undefined value. Java.lang.Math.pow() returns 1 anyway,
// so we do the same.
return new BoundedRational(1);
}
if (base == null) return null;
if (base == null) {
return null;
}
exp = exp.reduce().positiveDen();
if (!exp.mDen.equals(BigInteger.ONE)) return null;
if (!exp.mDen.equals(BigInteger.ONE)) {
return null;
}
return base.pow(exp.mNum);
}
......@@ -417,12 +493,14 @@ public class BoundedRational {
return map0to1(r);
}
// Return the base 10 log of n, if n is a power of 10, -1 otherwise.
// n must be positive.
/**
* 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)) {
while (n.mod(BigInteger.TEN).signum() == 0) {
if (Thread.interrupted()) {
throw new CR.AbortedException();
}
......@@ -436,26 +514,35 @@ public class BoundedRational {
}
public static BoundedRational log(BoundedRational r) {
if (r == null) return null;
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 == null) {
return null;
}
if (r.mDen.equals(BigInteger.ONE)) {
long log = b10Log(r.mNum);
if (log != -1) return new BoundedRational(log);
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);
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.
/**
* Generalized factorial.
* Compute n * (n - step) * (n - 2 * step) * etc. 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);
......@@ -476,61 +563,68 @@ public class BoundedRational {
}
}
// Factorial;
// always produces non-null (or exception) when called on non-null r.
/**
* Factorial function.
* 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) {
if (r == null) {
return null;
}
final BigInteger rAsInt = asBigInteger(r);
if (rAsInt == null) {
throw new ArithmeticException("Non-integral factorial argument");
}
if (r_BI.signum() < 0) {
if (rAsInt.signum() < 0) {
throw new ArithmeticException("Negative factorial argument");
}
if (r_BI.bitLength() > 30) {
if (rAsInt.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));
return new BoundedRational(genFactorial(rAsInt.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.
/**
* Return the number of decimal digits to the right of the decimal point required to represent
* the argument exactly.
* Return Integer.MAX_VALUE if that's not possible. Never returns a value less 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
if (r == null) {
return Integer.MAX_VALUE;
}
int powersOfTwo = 0; // Max power of 2 that divides denominator
int powersOfFive = 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;
if (r.mDen.equals(BigInteger.ONE)) {
return 0;
}
r = r.reduce();
BigInteger den = r.mDen;
if (den.bitLength() > MAX_SIZE) {
return Integer.MAX_VALUE;
}
while (!den.testBit(0)) {
++powers_of_two;
++powersOfTwo;
den = den.shiftRight(1);
}
while (den.mod(BIG_FIVE).equals(BigInteger.ZERO)) {
++powers_of_five;
while (den.mod(BIG_FIVE).signum() == 0) {
++powersOfFive;
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 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
// powersOfTwo and powersOfFive.
if (!den.equals(BigInteger.ONE) && !den.equals(BIG_MINUS_ONE)) {
return Integer.MAX_VALUE;
}
return Math.max(powers_of_two, powers_of_five);
return Math.max(powersOfTwo, powersOfFive);
}
}
tests/src/com/android/calculator2/BRTest.java
View file @ d6136e69
......@@ -139,6 +139,12 @@ public class BRTest extends TestCase {
check(BR_0.signum() == 0, "signum(0)");
check(BR_M1.signum() == -1, "signum(-1)");
check(BR_2.signum() == 1, "signum(2)");
check(BoundedRational.asBigInteger(BR_390).intValue() == 390, "390.asBigInteger()");
check(BoundedRational.asBigInteger(BoundedRational.HALF) == null, "1/2.asBigInteger()");
check(BoundedRational.asBigInteger(BoundedRational.MINUS_HALF) == null,
"-1/2.asBigInteger()");
check(BoundedRational.asBigInteger(new BoundedRational(15, -5)).intValue() == -3,
"-15/5.asBigInteger()");
check(BoundedRational.digitsRequired(BoundedRational.ZERO) == 0, "digitsRequired(0)");
check(BoundedRational.digitsRequired(BoundedRational.HALF) == 1, "digitsRequired(1/2)");
check(BoundedRational.digitsRequired(BoundedRational.MINUS_HALF) == 1,
......
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