Class DfpMath

• public class DfpMath
extends Object
Mathematical routines for use with Dfp. The constants are defined in DfpField
Since:
2.2
• Method Summary

All Methods
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.
• Method Detail

• 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 < k <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| < 1.0 and y is -Infinity then result is +Infinity
• if |x| > 1.0 and y is -Infinity then result is +0
• if |x| < 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 < 0 then result is +0
• if x = +0 and y < 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 < 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 < 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 < 0 and y > 0, finite, and odd integer then result is -(|x|y)
• if x < 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)