jsat.math

Class FastMath

java.lang.Object

jsat.math.FastMath

public class FastMath
extends Object

This class contains fast implementations of many of the methods located in Math and SpecialMath. This speed comes at the cost of correctness, and in general the methods in this class attempt to have a relative error no worse than 10^-3 for most inputs.

Implementation details - and therfore accuracy / speed - may change over time. 10^-3 is not a hard guarantee, but a goal. The accuracy near asymptotes and extreme values will never be guaranteed. The handling of special values will never be guaranteed.

Author:

Edward Raff

Constructor Summary

Constructors

Constructor and Description
FastMath()

Method Summary

Modifier and Type	Method and Description
static double	digamma(double x) Computes the digamma function of the input
static double	exp(double x) Exponentiates the given input value
static double	log(double x) Computes the natural logarithm of the input
static double	log2_2pd1(double x) Computes log2(x) using a Pade approximation.
static double	log2_c11(double x) Computes log2(x) using a cache of 211 values, consuming approximately 17 kilobytes of memory. The results are generally accurate to an absolute and relative error of 10-4
static double	log2(double x) Computes log2(x)
static double	pow(double a, double b) Computes ab.
static double	pow2(double x) Computes 2x. The results are generally accurate to an relative error of 10-4, but can be as accurate as 10-10
static double	pow2(int x) Computes 2x exactly be exploiting the IEEE format

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FastMath

public FastMath()

Method Detail

log

public static double log(double x)

Computes the natural logarithm of the input

Parameters:

x - the input

Returns:

log_e(x)

log2

public static double log2(double x)

Computes log₂(x)

Parameters:

x - the input

Returns:

the log base 2 of x

log2_2pd1

public static double log2_2pd1(double x)

Computes log₂(x) using a Pade approximation. It is slower than log2_c11(double) but dose not use any extra memory.
The results are generally accurate to an absolute and relative error of 10^-4, but relative error can get as high as 10^-10

Parameters:

x - the input

Returns:

the log base 2 of x

log2_c11

public static double log2_c11(double x)

Computes log₂(x) using a cache of 2¹¹ values, consuming approximately 17 kilobytes of memory.
The results are generally accurate to an absolute and relative error of 10^-4

Parameters:

x - the input

Returns:

the log base 2 of x

pow2

public static double pow2(int x)

Computes 2^x exactly be exploiting the IEEE format

Parameters:

x - the integer power to raise 2 too

Returns:

2^x

pow2

public static double pow2(double x)

Computes 2^x.
The results are generally accurate to an relative error of 10^-4, but can be as accurate as 10^-10

Parameters:

x - the power to raise to

Returns:

pow

public static double pow(double a,
                         double b)

Computes a^b.

Parameters:

a - the base

b - the power

Returns:

a^b

exp

public static double exp(double x)

Exponentiates the given input value

Parameters:

x - the input

Returns:

e^x

digamma

public static double digamma(double x)

Computes the digamma function of the input

Parameters:

x - the input value

Returns:

ψ(x)