fr.cnes.sirius.patrius.math.dfp

Class DfpMath

java.lang.Object

fr.cnes.sirius.patrius.math.dfp.DfpMath

public final class DfpMath
extends Object

Mathematical routines for use with Dfp. The constants are defined in DfpField

Since:

2.2

Version:

$Id: DfpMath.java 18108 2017-10-04 06:45:27Z bignon $

Method Summary

Modifier and Type	Method and Description
static Dfp	acos(Dfp aIn) 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 x, Dfp y) Computes x to the y power.
static Dfp	pow(Dfp base, int aIn) Raises base to the power a by successive squaring.
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

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

Method Detail

pow

public static Dfp pow(Dfp base,
                      int aIn)

Raises base to the power a by successive squaring.

Parameters:

base - number to raise

aIn - power

Returns:

base^a

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 e^m. We return e*ⁿ × e^m

Parameters:

a - power at which e should be raised

Returns:

e^a

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. x^y = x^u * 2^b * e^c

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:

x^y

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 aIn)

computes the arc-cosine of the argument.

Parameters:

aIn - number from which arc-cosine is desired

Returns:

acos(a)