io.prestosql.hadoop.$internal.com.google.common.math.IntMath Maven / Gradle / Ivy
Show all versions of hadoop-apache Show documentation
/*
* Copyright (C) 2011 The Guava Authors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package io.prestosql.hadoop.$internal.com.google.common.math;
import static io.prestosql.hadoop.$internal.com.google.common.base.Preconditions.checkArgument;
import static io.prestosql.hadoop.$internal.com.google.common.base.Preconditions.checkNotNull;
import static io.prestosql.hadoop.$internal.com.google.common.math.MathPreconditions.checkNoOverflow;
import static io.prestosql.hadoop.$internal.com.google.common.math.MathPreconditions.checkNonNegative;
import static io.prestosql.hadoop.$internal.com.google.common.math.MathPreconditions.checkPositive;
import static io.prestosql.hadoop.$internal.com.google.common.math.MathPreconditions.checkRoundingUnnecessary;
import static java.lang.Math.abs;
import static java.math.RoundingMode.HALF_EVEN;
import static java.math.RoundingMode.HALF_UP;
import io.prestosql.hadoop.$internal.com.google.common.annotations.Beta;
import io.prestosql.hadoop.$internal.com.google.common.annotations.GwtCompatible;
import io.prestosql.hadoop.$internal.com.google.common.annotations.GwtIncompatible;
import io.prestosql.hadoop.$internal.com.google.common.annotations.VisibleForTesting;
import java.math.BigInteger;
import java.math.RoundingMode;
/**
* A class for arithmetic on values of type {@code int}. Where possible, methods are defined and
* named analogously to their {@code BigInteger} counterparts.
*
* The implementations of many methods in this class are based on material from Henry S. Warren,
* Jr.'s Hacker's Delight, (Addison Wesley, 2002).
*
*
Similar functionality for {@code long} and for {@link BigInteger} can be found in
* {@link LongMath} and {@link BigIntegerMath} respectively. For other common operations on
* {@code int} values, see {@link io.prestosql.hadoop.$internal.com.google.common.primitives.Ints}.
*
* @author Louis Wasserman
* @since 11.0
*/
@Beta
@GwtCompatible(emulated = true)
public final class IntMath {
// NOTE: Whenever both tests are cheap and functional, it's faster to use &, | instead of &&, ||
/**
* Returns {@code true} if {@code x} represents a power of two.
*
*
This differs from {@code Integer.bitCount(x) == 1}, because
* {@code Integer.bitCount(Integer.MIN_VALUE) == 1}, but {@link Integer#MIN_VALUE} is not a power
* of two.
*/
public static boolean isPowerOfTwo(int x) {
return x > 0 & (x & (x - 1)) == 0;
}
/**
* Returns the base-2 logarithm of {@code x}, rounded according to the specified rounding mode.
*
* @throws IllegalArgumentException if {@code x <= 0}
* @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}
* is not a power of two
*/
@GwtIncompatible("need BigIntegerMath to adequately test")
@SuppressWarnings("fallthrough")
public static int log2(int x, RoundingMode mode) {
checkPositive("x", x);
switch (mode) {
case UNNECESSARY:
checkRoundingUnnecessary(isPowerOfTwo(x));
// fall through
case DOWN:
case FLOOR:
return (Integer.SIZE - 1) - Integer.numberOfLeadingZeros(x);
case UP:
case CEILING:
return Integer.SIZE - Integer.numberOfLeadingZeros(x - 1);
case HALF_DOWN:
case HALF_UP:
case HALF_EVEN:
// Since sqrt(2) is irrational, log2(x) - logFloor cannot be exactly 0.5
int leadingZeros = Integer.numberOfLeadingZeros(x);
int cmp = MAX_POWER_OF_SQRT2_UNSIGNED >>> leadingZeros;
// floor(2^(logFloor + 0.5))
int logFloor = (Integer.SIZE - 1) - leadingZeros;
return (x <= cmp) ? logFloor : logFloor + 1;
default:
throw new AssertionError();
}
}
/** The biggest half power of two that can fit in an unsigned int. */
@VisibleForTesting static final int MAX_POWER_OF_SQRT2_UNSIGNED = 0xB504F333;
/**
* Returns the base-10 logarithm of {@code x}, rounded according to the specified rounding mode.
*
* @throws IllegalArgumentException if {@code x <= 0}
* @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}
* is not a power of ten
*/
@GwtIncompatible("need BigIntegerMath to adequately test")
@SuppressWarnings("fallthrough")
public static int log10(int x, RoundingMode mode) {
checkPositive("x", x);
int logFloor = log10Floor(x);
int floorPow = POWERS_OF_10[logFloor];
switch (mode) {
case UNNECESSARY:
checkRoundingUnnecessary(x == floorPow);
// fall through
case FLOOR:
case DOWN:
return logFloor;
case CEILING:
case UP:
return (x == floorPow) ? logFloor : logFloor + 1;
case HALF_DOWN:
case HALF_UP:
case HALF_EVEN:
// sqrt(10) is irrational, so log10(x) - logFloor is never exactly 0.5
return (x <= HALF_POWERS_OF_10[logFloor]) ? logFloor : logFloor + 1;
default:
throw new AssertionError();
}
}
private static int log10Floor(int x) {
for (int i = 1; i < POWERS_OF_10.length; i++) {
if (x < POWERS_OF_10[i]) {
return i - 1;
}
}
return POWERS_OF_10.length - 1;
}
@VisibleForTesting static final int[] POWERS_OF_10 =
{1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
// HALF_POWERS_OF_10[i] = largest int less than 10^(i + 0.5)
@VisibleForTesting static final int[] HALF_POWERS_OF_10 =
{3, 31, 316, 3162, 31622, 316227, 3162277, 31622776, 316227766, Integer.MAX_VALUE};
/**
* Returns {@code b} to the {@code k}th power. Even if the result overflows, it will be equal to
* {@code BigInteger.valueOf(b).pow(k).intValue()}. This implementation runs in {@code O(log k)}
* time.
*
*
Compare {@link #checkedPow}, which throws an {@link ArithmeticException} upon overflow.
*
* @throws IllegalArgumentException if {@code k < 0}
*/
@GwtIncompatible("failing tests")
public static int pow(int b, int k) {
checkNonNegative("exponent", k);
switch (b) {
case 0:
return (k == 0) ? 1 : 0;
case 1:
return 1;
case (-1):
return ((k & 1) == 0) ? 1 : -1;
case 2:
return (k < Integer.SIZE) ? (1 << k) : 0;
case (-2):
if (k < Integer.SIZE) {
return ((k & 1) == 0) ? (1 << k) : -(1 << k);
} else {
return 0;
}
}
for (int accum = 1;; k >>= 1) {
switch (k) {
case 0:
return accum;
case 1:
return b * accum;
default:
accum *= ((k & 1) == 0) ? 1 : b;
b *= b;
}
}
}
/**
* Returns the square root of {@code x}, rounded with the specified rounding mode.
*
* @throws IllegalArgumentException if {@code x < 0}
* @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and
* {@code sqrt(x)} is not an integer
*/
@GwtIncompatible("need BigIntegerMath to adequately test")
@SuppressWarnings("fallthrough")
public static int sqrt(int x, RoundingMode mode) {
checkNonNegative("x", x);
int sqrtFloor = sqrtFloor(x);
switch (mode) {
case UNNECESSARY:
checkRoundingUnnecessary(sqrtFloor * sqrtFloor == x); // fall through
case FLOOR:
case DOWN:
return sqrtFloor;
case CEILING:
case UP:
return (sqrtFloor * sqrtFloor == x) ? sqrtFloor : sqrtFloor + 1;
case HALF_DOWN:
case HALF_UP:
case HALF_EVEN:
int halfSquare = sqrtFloor * sqrtFloor + sqrtFloor;
/*
* We wish to test whether or not x <= (sqrtFloor + 0.5)^2 = halfSquare + 0.25.
* Since both x and halfSquare are integers, this is equivalent to testing whether or not
* x <= halfSquare. (We have to deal with overflow, though.)
*/
return (x <= halfSquare | halfSquare < 0) ? sqrtFloor : sqrtFloor + 1;
default:
throw new AssertionError();
}
}
private static int sqrtFloor(int x) {
// There is no loss of precision in converting an int to a double, according to
// http://java.sun.com/docs/books/jls/third_edition/html/conversions.html#5.1.2
return (int) Math.sqrt(x);
}
/**
* Returns the result of dividing {@code p} by {@code q}, rounding using the specified
* {@code RoundingMode}.
*
* @throws ArithmeticException if {@code q == 0}, or if {@code mode == UNNECESSARY} and {@code a}
* is not an integer multiple of {@code b}
*/
@GwtIncompatible("failing tests")
@SuppressWarnings("fallthrough")
public static int divide(int p, int q, RoundingMode mode) {
checkNotNull(mode);
if (q == 0) {
throw new ArithmeticException("/ by zero"); // for GWT
}
int div = p / q;
int rem = p - q * div; // equal to p % q
if (rem == 0) {
return div;
}
/*
* Normal Java division rounds towards 0, consistently with RoundingMode.DOWN. We just have to
* deal with the cases where rounding towards 0 is wrong, which typically depends on the sign of
* p / q.
*
* signum is 1 if p and q are both nonnegative or both negative, and -1 otherwise.
*/
int signum = 1 | ((p ^ q) >> (Integer.SIZE - 1));
boolean increment;
switch (mode) {
case UNNECESSARY:
checkRoundingUnnecessary(rem == 0);
// fall through
case DOWN:
increment = false;
break;
case UP:
increment = true;
break;
case CEILING:
increment = signum > 0;
break;
case FLOOR:
increment = signum < 0;
break;
case HALF_EVEN:
case HALF_DOWN:
case HALF_UP:
int absRem = abs(rem);
int cmpRemToHalfDivisor = absRem - (abs(q) - absRem);
// subtracting two nonnegative ints can't overflow
// cmpRemToHalfDivisor has the same sign as compare(abs(rem), abs(q) / 2).
if (cmpRemToHalfDivisor == 0) { // exactly on the half mark
increment = (mode == HALF_UP || (mode == HALF_EVEN & (div & 1) != 0));
} else {
increment = cmpRemToHalfDivisor > 0; // closer to the UP value
}
break;
default:
throw new AssertionError();
}
return increment ? div + signum : div;
}
/**
* Returns {@code x mod m}. This differs from {@code x % m} in that it always returns a
* non-negative result.
*
*
For example:
{@code
*
* mod(7, 4) == 3
* mod(-7, 4) == 1
* mod(-1, 4) == 3
* mod(-8, 4) == 0
* mod(8, 4) == 0}
*
* @throws ArithmeticException if {@code m <= 0}
*/
public static int mod(int x, int m) {
if (m <= 0) {
throw new ArithmeticException("Modulus " + m + " must be > 0");
}
int result = x % m;
return (result >= 0) ? result : result + m;
}
/**
* Returns the greatest common divisor of {@code a, b}. Returns {@code 0} if
* {@code a == 0 && b == 0}.
*
* @throws IllegalArgumentException if {@code a < 0} or {@code b < 0}
*/
public static int gcd(int a, int b) {
/*
* The reason we require both arguments to be >= 0 is because otherwise, what do you return on
* gcd(0, Integer.MIN_VALUE)? BigInteger.gcd would return positive 2^31, but positive 2^31
* isn't an int.
*/
checkNonNegative("a", a);
checkNonNegative("b", b);
// The simple Euclidean algorithm is the fastest for ints, and is easily the most readable.
while (b != 0) {
int t = b;
b = a % b;
a = t;
}
return a;
}
/**
* Returns the sum of {@code a} and {@code b}, provided it does not overflow.
*
* @throws ArithmeticException if {@code a + b} overflows in signed {@code int} arithmetic
*/
public static int checkedAdd(int a, int b) {
long result = (long) a + b;
checkNoOverflow(result == (int) result);
return (int) result;
}
/**
* Returns the difference of {@code a} and {@code b}, provided it does not overflow.
*
* @throws ArithmeticException if {@code a - b} overflows in signed {@code int} arithmetic
*/
public static int checkedSubtract(int a, int b) {
long result = (long) a - b;
checkNoOverflow(result == (int) result);
return (int) result;
}
/**
* Returns the product of {@code a} and {@code b}, provided it does not overflow.
*
* @throws ArithmeticException if {@code a * b} overflows in signed {@code int} arithmetic
*/
public static int checkedMultiply(int a, int b) {
long result = (long) a * b;
checkNoOverflow(result == (int) result);
return (int) result;
}
/**
* Returns the {@code b} to the {@code k}th power, provided it does not overflow.
*
* {@link #pow} may be faster, but does not check for overflow.
*
* @throws ArithmeticException if {@code b} to the {@code k}th power overflows in signed
* {@code int} arithmetic
*/
@GwtIncompatible("failing tests")
public static int checkedPow(int b, int k) {
checkNonNegative("exponent", k);
switch (b) {
case 0:
return (k == 0) ? 1 : 0;
case 1:
return 1;
case (-1):
return ((k & 1) == 0) ? 1 : -1;
case 2:
checkNoOverflow(k < Integer.SIZE - 1);
return 1 << k;
case (-2):
checkNoOverflow(k < Integer.SIZE);
return ((k & 1) == 0) ? 1 << k : -1 << k;
}
int accum = 1;
while (true) {
switch (k) {
case 0:
return accum;
case 1:
return checkedMultiply(accum, b);
default:
if ((k & 1) != 0) {
accum = checkedMultiply(accum, b);
}
k >>= 1;
if (k > 0) {
checkNoOverflow(-FLOOR_SQRT_MAX_INT <= b & b <= FLOOR_SQRT_MAX_INT);
b *= b;
}
}
}
}
@VisibleForTesting static final int FLOOR_SQRT_MAX_INT = 46340;
/**
* Returns {@code n!}, that is, the product of the first {@code n} positive
* integers, {@code 1} if {@code n == 0}, or {@link Integer#MAX_VALUE} if the
* result does not fit in a {@code int}.
*
* @throws IllegalArgumentException if {@code n < 0}
*/
@GwtIncompatible("need BigIntegerMath to adequately test")
public static int factorial(int n) {
checkNonNegative("n", n);
return (n < FACTORIALS.length) ? FACTORIALS[n] : Integer.MAX_VALUE;
}
static final int[] FACTORIALS = {
1,
1,
1 * 2,
1 * 2 * 3,
1 * 2 * 3 * 4,
1 * 2 * 3 * 4 * 5,
1 * 2 * 3 * 4 * 5 * 6,
1 * 2 * 3 * 4 * 5 * 6 * 7,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11,
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12};
/**
* Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
* {@code k}, or {@link Integer#MAX_VALUE} if the result does not fit in an {@code int}.
*
* @throws IllegalArgumentException if {@code n < 0}, {@code k < 0} or {@code k > n}
*/
@GwtIncompatible("need BigIntegerMath to adequately test")
public static int binomial(int n, int k) {
checkNonNegative("n", n);
checkNonNegative("k", k);
checkArgument(k <= n, "k (%s) > n (%s)", k, n);
if (k > (n >> 1)) {
k = n - k;
}
if (k >= BIGGEST_BINOMIALS.length || n > BIGGEST_BINOMIALS[k]) {
return Integer.MAX_VALUE;
}
switch (k) {
case 0:
return 1;
case 1:
return n;
default:
long result = 1;
for (int i = 0; i < k; i++) {
result *= n - i;
result /= i + 1;
}
return (int) result;
}
}
// binomial(BIGGEST_BINOMIALS[k], k) fits in an int, but not binomial(BIGGEST_BINOMIALS[k]+1,k).
@VisibleForTesting static int[] BIGGEST_BINOMIALS = {
Integer.MAX_VALUE,
Integer.MAX_VALUE,
65536,
2345,
477,
193,
110,
75,
58,
49,
43,
39,
37,
35,
34,
34,
33
};
private IntMath() {}
}