public final class BigIntegerMath
extends java.lang.Object
BigInteger
.
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 int
and for long
can be found in IntMath
and
LongMath
respectively.
Modifier and Type | Class and Description |
---|---|
private static class |
BigIntegerMath.BigIntegerToDoubleRounder |
Modifier and Type | Field and Description |
---|---|
private static double |
LN_10 |
private static double |
LN_2 |
(package private) static int |
SQRT2_PRECOMPUTE_THRESHOLD |
(package private) static java.math.BigInteger |
SQRT2_PRECOMPUTED_BITS |
Modifier | Constructor and Description |
---|---|
private |
BigIntegerMath() |
Modifier and Type | Method and Description |
---|---|
static java.math.BigInteger |
binomial(int n,
int k)
Returns
n choose k , also known as the binomial coefficient of n and
k , that is, n! / (k! (n - k)!) . |
static java.math.BigInteger |
ceilingPowerOfTwo(java.math.BigInteger x)
Returns the smallest power of two greater than or equal to
x . |
static java.math.BigInteger |
divide(java.math.BigInteger p,
java.math.BigInteger q,
java.math.RoundingMode mode)
Returns the result of dividing
p by q , rounding using the specified RoundingMode . |
static java.math.BigInteger |
factorial(int n)
Returns
n! , that is, the product of the first n positive integers, or 1
if n == 0 . |
(package private) static boolean |
fitsInLong(java.math.BigInteger x) |
static java.math.BigInteger |
floorPowerOfTwo(java.math.BigInteger x)
Returns the largest power of two less than or equal to
x . |
static boolean |
isPowerOfTwo(java.math.BigInteger x)
Returns
true if x represents a power of two. |
(package private) static java.math.BigInteger |
listProduct(java.util.List<java.math.BigInteger> nums) |
(package private) static java.math.BigInteger |
listProduct(java.util.List<java.math.BigInteger> nums,
int start,
int end) |
static int |
log10(java.math.BigInteger x,
java.math.RoundingMode mode)
Returns the base-10 logarithm of
x , rounded according to the specified rounding mode. |
static int |
log2(java.math.BigInteger x,
java.math.RoundingMode mode)
Returns the base-2 logarithm of
x , rounded according to the specified rounding mode. |
static double |
roundToDouble(java.math.BigInteger x,
java.math.RoundingMode mode)
Returns
x , rounded to a double with the specified rounding mode. |
static java.math.BigInteger |
sqrt(java.math.BigInteger x,
java.math.RoundingMode mode)
Returns the square root of
x , rounded with the specified rounding mode. |
private static java.math.BigInteger |
sqrtApproxWithDoubles(java.math.BigInteger x) |
private static java.math.BigInteger |
sqrtFloor(java.math.BigInteger x) |
static final int SQRT2_PRECOMPUTE_THRESHOLD
static final java.math.BigInteger SQRT2_PRECOMPUTED_BITS
private static final double LN_10
private static final double LN_2
public static java.math.BigInteger ceilingPowerOfTwo(java.math.BigInteger x)
x
. This is equivalent to
BigInteger.valueOf(2).pow(log2(x, CEILING))
.java.lang.IllegalArgumentException
- if x <= 0
public static java.math.BigInteger floorPowerOfTwo(java.math.BigInteger x)
x
. This is equivalent to BigInteger.valueOf(2).pow(log2(x, FLOOR))
.java.lang.IllegalArgumentException
- if x <= 0
public static boolean isPowerOfTwo(java.math.BigInteger x)
true
if x
represents a power of two.public static int log2(java.math.BigInteger x, java.math.RoundingMode mode)
x
, rounded according to the specified rounding mode.java.lang.IllegalArgumentException
- if x <= 0
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not a power of twopublic static int log10(java.math.BigInteger x, java.math.RoundingMode mode)
x
, rounded according to the specified rounding mode.java.lang.IllegalArgumentException
- if x <= 0
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not a power of tenpublic static java.math.BigInteger sqrt(java.math.BigInteger x, java.math.RoundingMode mode)
x
, rounded with the specified rounding mode.java.lang.IllegalArgumentException
- if x < 0
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and sqrt(x)
is not an integerprivate static java.math.BigInteger sqrtFloor(java.math.BigInteger x)
private static java.math.BigInteger sqrtApproxWithDoubles(java.math.BigInteger x)
public static double roundToDouble(java.math.BigInteger x, java.math.RoundingMode mode)
x
, rounded to a double
with the specified rounding mode. If x
is precisely representable as a double
, its double
value will be returned;
otherwise, the rounding will choose between the two nearest representable values with mode
.
For the case of RoundingMode.HALF_DOWN
, HALF_UP
, and HALF_EVEN
,
infinite double
values are considered infinitely far away. For example, 2^2000 is not
representable as a double, but roundToDouble(BigInteger.valueOf(2).pow(2000), HALF_UP)
will return Double.MAX_VALUE
, not Double.POSITIVE_INFINITY
.
For the case of RoundingMode.HALF_EVEN
, this implementation uses the IEEE 754
default rounding mode: if the two nearest representable values are equally near, the one with
the least significant bit zero is chosen. (In such cases, both of the nearest representable
values are even integers; this method returns the one that is a multiple of a greater power of
two.)
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not precisely representable as a double
public static java.math.BigInteger divide(java.math.BigInteger p, java.math.BigInteger q, java.math.RoundingMode mode)
p
by q
, rounding using the specified RoundingMode
.java.lang.ArithmeticException
- if q == 0
, or if mode == UNNECESSARY
and a
is not an integer multiple of b
public static java.math.BigInteger factorial(int n)
n!
, that is, the product of the first n
positive integers, or 1
if n == 0
.
Warning: the result takes O(n log n) space, so use cautiously.
This uses an efficient binary recursive algorithm to compute the factorial with balanced multiplies. It also removes all the 2s from the intermediate products (shifting them back in at the end).
java.lang.IllegalArgumentException
- if n < 0
static java.math.BigInteger listProduct(java.util.List<java.math.BigInteger> nums)
static java.math.BigInteger listProduct(java.util.List<java.math.BigInteger> nums, int start, int end)
public static java.math.BigInteger binomial(int n, int k)
n
choose k
, also known as the binomial coefficient of n
and
k
, that is, n! / (k! (n - k)!)
.
Warning: the result can take as much as O(k log n) space.
java.lang.IllegalArgumentException
- if n < 0
, k < 0
, or k > n
static boolean fitsInLong(java.math.BigInteger x)