Package org.apache.commons.math.dfp

Class DfpMath

java.lang.Object
org.apache.commons.math.dfp.DfpMath
public class DfpMath extends Object
Mathematical routines for use with Dfp. The constants are defined in DfpField
Since:
2.2

  • Method Summary

    Modifier and Type
    Method
    Description
    static Dfp
    acos(Dfp a)
    computes the arc-cosine of the argument.
    static Dfp
    asin(Dfp a)
    computes the arc-sine of the argument.
    static Dfp
    atan(Dfp a)
    computes the arc tangent of the argument Uses the typical taylor series but may reduce arguments using the following identity tan(x+y) = (tan(x) + tan(y)) / (1 - tan(x)*tan(y)) since tan(PI/8) = sqrt(2)-1, atan(x) = atan( (x - sqrt(2) + 1) / (1+x*sqrt(2) - x) + PI/8.0
    static Dfp
    cos(Dfp a)
    computes the cosine of the argument.
    static Dfp
    exp(Dfp a)
    Computes e to the given power.
    static Dfp
    log(Dfp a)
    Returns the natural logarithm of a.
    static Dfp
    pow(Dfp base, int a)
    Raises base to the power a by successive squaring.
    static Dfp
    pow(Dfp x, Dfp y)
    Computes x to the y power.
    static Dfp
    sin(Dfp a)
    computes the sine of the argument.
    static Dfp
    tan(Dfp a)
    computes the tangent of the argument.

    Methods inherited from class java.lang.Object

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

  • Method Details

    • pow

      public static Dfp pow(Dfp base, int a)
      Raises base to the power a by successive squaring.
      Parameters:
      base - number to raise
      a - power
      Returns:
      basea

    • exp

      public static Dfp exp(Dfp a)
      Computes e to the given power. a is broken into two parts, such that a = n+m where n is an integer. We use pow() to compute en and a Taylor series to compute em. We return e*n × em
      Parameters:
      a - power at which e should be raised
      Returns:
      ea

    • log

      public static Dfp log(Dfp a)
      Returns the natural logarithm of a. a is first split into three parts such that a = (10000^h)(2^j)k. ln(a) is computed by ln(a) = ln(5)*h + ln(2)*(h+j) + ln(k) k is in the range 2/3 invalid input: '<' k invalid input: '<'4/3 and is passed on to a series expansion.
      Parameters:
      a - number from which logarithm is requested
      Returns:
      log(a)

    • pow

      public static Dfp pow(Dfp x, Dfp y)
      Computes x to the y power.

      Uses the following method:

      1. Set u = rint(y), v = y-u
      2. Compute a = v * ln(x)
      3. Compute b = rint( a/ln(2) )
      4. Compute c = a - b*ln(2)
      5. xy = xu * 2b * ec
      if |y| > 1e8, then we compute by exp(y*ln(x))

      Special Cases

      • if y is 0.0 or -0.0 then result is 1.0
      • if y is 1.0 then result is x
      • if y is NaN then result is NaN
      • if x is NaN and y is not zero then result is NaN
      • if |x| > 1.0 and y is +Infinity then result is +Infinity
      • if |x| invalid input: '<' 1.0 and y is -Infinity then result is +Infinity
      • if |x| > 1.0 and y is -Infinity then result is +0
      • if |x| invalid input: '<' 1.0 and y is +Infinity then result is +0
      • if |x| = 1.0 and y is +/-Infinity then result is NaN
      • if x = +0 and y > 0 then result is +0
      • if x = +Inf and y invalid input: '<' 0 then result is +0
      • if x = +0 and y invalid input: '<' 0 then result is +Inf
      • if x = +Inf and y > 0 then result is +Inf
      • if x = -0 and y > 0, finite, not odd integer then result is +0
      • if x = -0 and y invalid input: '<' 0, finite, and odd integer then result is -Inf
      • if x = -Inf and y > 0, finite, and odd integer then result is -Inf
      • if x = -0 and y invalid input: '<' 0, not finite odd integer then result is +Inf
      • if x = -Inf and y > 0, not finite odd integer then result is +Inf
      • if x invalid input: '<' 0 and y > 0, finite, and odd integer then result is -(|x|y)
      • if x invalid input: '<' 0 and y > 0, finite, and not integer then result is NaN
      Parameters:
      x - base to be raised
      y - power to which base should be raised
      Returns:
      xy

    • sin

      public static Dfp sin(Dfp a)
      computes the sine of the argument.
      Parameters:
      a - number from which sine is desired
      Returns:
      sin(a)

    • cos

      public static Dfp cos(Dfp a)
      computes the cosine of the argument.
      Parameters:
      a - number from which cosine is desired
      Returns:
      cos(a)

    • tan

      public static Dfp tan(Dfp a)
      computes the tangent of the argument.
      Parameters:
      a - number from which tangent is desired
      Returns:
      tan(a)

    • atan

      public static Dfp atan(Dfp a)
      computes the arc tangent of the argument Uses the typical taylor series but may reduce arguments using the following identity tan(x+y) = (tan(x) + tan(y)) / (1 - tan(x)*tan(y)) since tan(PI/8) = sqrt(2)-1, atan(x) = atan( (x - sqrt(2) + 1) / (1+x*sqrt(2) - x) + PI/8.0
      Parameters:
      a - number from which arc-tangent is desired
      Returns:
      atan(a)

    • asin

      public static Dfp asin(Dfp a)
      computes the arc-sine of the argument.
      Parameters:
      a - number from which arc-sine is desired
      Returns:
      asin(a)

    • acos

      public static Dfp acos(Dfp a)
      computes the arc-cosine of the argument.
      Parameters:
      a - number from which arc-cosine is desired
      Returns:
      acos(a)