Class BigIntegerMath
- java.lang.Object
-
- com.google.common.math.BigIntegerMath
-
public final class BigIntegerMath extends java.lang.Object
A class for arithmetic on values of typeBigInteger
.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 forlong
can be found inIntMath
andLongMath
respectively.- Since:
- 11.0
-
-
Nested Class Summary
Nested Classes Modifier and Type Class Description private static class
BigIntegerMath.BigIntegerToDoubleRounder
-
Field Summary
Fields Modifier and Type Field 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
-
Constructor Summary
Constructors Modifier Constructor Description private
BigIntegerMath()
-
Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static java.math.BigInteger
binomial(int n, int k)
Returnsn
choosek
, also known as the binomial coefficient ofn
andk
, 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 tox
.static java.math.BigInteger
divide(java.math.BigInteger p, java.math.BigInteger q, java.math.RoundingMode mode)
Returns the result of dividingp
byq
, rounding using the specifiedRoundingMode
.static java.math.BigInteger
factorial(int n)
Returnsn!
, that is, the product of the firstn
positive integers, or1
ifn == 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 tox
.static boolean
isPowerOfTwo(java.math.BigInteger x)
Returnstrue
ifx
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 ofx
, rounded according to the specified rounding mode.static int
log2(java.math.BigInteger x, java.math.RoundingMode mode)
Returns the base-2 logarithm ofx
, rounded according to the specified rounding mode.static double
roundToDouble(java.math.BigInteger x, java.math.RoundingMode mode)
Returnsx
, rounded to adouble
with the specified rounding mode.static java.math.BigInteger
sqrt(java.math.BigInteger x, java.math.RoundingMode mode)
Returns the square root ofx
, 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)
-
-
-
Field Detail
-
SQRT2_PRECOMPUTE_THRESHOLD
static final int SQRT2_PRECOMPUTE_THRESHOLD
- See Also:
- Constant Field Values
-
SQRT2_PRECOMPUTED_BITS
static final java.math.BigInteger SQRT2_PRECOMPUTED_BITS
-
LN_10
private static final double LN_10
-
LN_2
private static final double LN_2
-
-
Method Detail
-
ceilingPowerOfTwo
public static java.math.BigInteger ceilingPowerOfTwo(java.math.BigInteger x)
Returns the smallest power of two greater than or equal tox
. This is equivalent toBigInteger.valueOf(2).pow(log2(x, CEILING))
.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
- Since:
- 20.0
-
floorPowerOfTwo
public static java.math.BigInteger floorPowerOfTwo(java.math.BigInteger x)
Returns the largest power of two less than or equal tox
. This is equivalent toBigInteger.valueOf(2).pow(log2(x, FLOOR))
.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
- Since:
- 20.0
-
isPowerOfTwo
public static boolean isPowerOfTwo(java.math.BigInteger x)
Returnstrue
ifx
represents a power of two.
-
log2
public static int log2(java.math.BigInteger x, java.math.RoundingMode mode)
Returns the base-2 logarithm ofx
, rounded according to the specified rounding mode.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not a power of two
-
log10
public static int log10(java.math.BigInteger x, java.math.RoundingMode mode)
Returns the base-10 logarithm ofx
, rounded according to the specified rounding mode.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not a power of ten
-
sqrt
public static java.math.BigInteger sqrt(java.math.BigInteger x, java.math.RoundingMode mode)
Returns the square root ofx
, rounded with the specified rounding mode.- Throws:
java.lang.IllegalArgumentException
- ifx < 0
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andsqrt(x)
is not an integer
-
sqrtFloor
private static java.math.BigInteger sqrtFloor(java.math.BigInteger x)
-
sqrtApproxWithDoubles
private static java.math.BigInteger sqrtApproxWithDoubles(java.math.BigInteger x)
-
roundToDouble
public static double roundToDouble(java.math.BigInteger x, java.math.RoundingMode mode)
Returnsx
, rounded to adouble
with the specified rounding mode. Ifx
is precisely representable as adouble
, itsdouble
value will be returned; otherwise, the rounding will choose between the two nearest representable values withmode
.For the case of
RoundingMode.HALF_DOWN
,HALF_UP
, andHALF_EVEN
, infinitedouble
values are considered infinitely far away. For example, 2^2000 is not representable as a double, butroundToDouble(BigInteger.valueOf(2).pow(2000), HALF_UP)
will returnDouble.MAX_VALUE
, notDouble.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.)- Throws:
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not precisely representable as adouble
- Since:
- 30.0
-
divide
public static java.math.BigInteger divide(java.math.BigInteger p, java.math.BigInteger q, java.math.RoundingMode mode)
Returns the result of dividingp
byq
, rounding using the specifiedRoundingMode
.- Throws:
java.lang.ArithmeticException
- ifq == 0
, or ifmode == UNNECESSARY
anda
is not an integer multiple ofb
-
factorial
public static java.math.BigInteger factorial(int n)
Returnsn!
, that is, the product of the firstn
positive integers, or1
ifn == 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).
- Throws:
java.lang.IllegalArgumentException
- ifn < 0
-
listProduct
static java.math.BigInteger listProduct(java.util.List<java.math.BigInteger> nums)
-
listProduct
static java.math.BigInteger listProduct(java.util.List<java.math.BigInteger> nums, int start, int end)
-
binomial
public static java.math.BigInteger binomial(int n, int k)
Returnsn
choosek
, also known as the binomial coefficient ofn
andk
, that is,n! / (k! (n - k)!)
.Warning: the result can take as much as O(k log n) space.
- Throws:
java.lang.IllegalArgumentException
- ifn < 0
,k < 0
, ork > n
-
fitsInLong
static boolean fitsInLong(java.math.BigInteger x)
-
-