rossi.dfp
Class dfpmath

java.lang.Object
  |
  +--rossi.dfp.dfpmath

All Implemented Interfaces:

dfpconstants

public class dfpmath

extends java.lang.Object

implements dfpconstants

Mathematical routines and constants for use with dfp. Constants are defined with in dfpconstants.java

Field Summary

static dfp	E E
static dfp[]	E_SPLIT E_SPLIT The number e split in two pieces
static dfp	LN10 ln(10)
static dfp	LN2 ln(2)
static dfp[]	LN2_SPLIT LN2_SPLIT The number e split in two pieces
static dfp	LN5 ln(5)
static dfp[]	LN5_SPLIT LN5_SPLIT The number e split in two pieces
static dfp	PI PI
static dfp[]	PI_SPLIT PI_SPLIT in 2 pieces
static dfp	SQR2 sqrt(2)
static dfp	SQR2_2 sqrt(2)/2
static dfp[]	SQR2_SPLIT sqrt(2) in 2 pieces
static dfp	SQR3 sqrt(3)
static dfp	SQR3_3 sqrt(3)/3

Fields inherited from interface rossi.dfp.dfpconstants

STR_E, STR_LN10, STR_LN2, STR_LN5, STR_PI, STR_SQR2, STR_SQR2_2, STR_SQR3, STR_SQR3_3

Constructor Summary

dfpmath()

Method Summary

static dfp	acos(dfp a)
static dfp	asin(dfp a)
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
protected static dfp	atanInternal(dfp a)
static dfp	cos(dfp a) computes the cosine of the argument
protected static dfp	cosInternal(dfp[] a) Computes cos(a) Used when 0 < a < pi/4.
static dfp	exp(dfp a) Computes e to the given power.
protected static dfp	expInternal(dfp a) Computes e to the given power.
static dfp	ln(dfp a) Returns the natural logarithm of a.
protected static dfp[]	lnInternal(dfp[] a) Computes the natural log of a number between 0 and 2
static dfp	pow(dfp x, dfp y) Computes x to the y power.
static dfp	pow(dfp base, int a) Raises base to the power a by successive squaring
static dfp	sin(dfp a) computes the sine of the argument
protected static dfp	sinInternal(dfp[] a) Computes sin(a) Used when 0 < a < pi/4.
protected static dfp[]	split(dfp a) Splits a dfp into 2 dfp's such that their sum is equal to the input dfp
protected static dfp[]	split(java.lang.String a) Breaks a string representation up into two dfp's such that the sum of them is equivilent to the input string, but has higher precision than using a single dfp.
protected static dfp[]	splitDiv(dfp[] a, dfp[] b) Divide two numbers that are split in to two pices that are meant to be added together.
protected static dfp[]	splitMult(dfp[] a, dfp[] b) Multiply two numbers that are split in to two pices that are meant to be added together.
protected static dfp	splitPow(dfp[] base, int a) Raise a split base to the a power.
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

Field Detail

SQR2

public static final dfp SQR2

sqrt(2)

SQR2_SPLIT

public static final dfp[] SQR2_SPLIT

sqrt(2) in 2 pieces

SQR2_2

public static final dfp SQR2_2

sqrt(2)/2

SQR3

public static final dfp SQR3

sqrt(3)

SQR3_3

public static final dfp SQR3_3

sqrt(3)/3

PI

public static final dfp PI

PI

PI_SPLIT

public static final dfp[] PI_SPLIT

PI_SPLIT in 2 pieces

E

public static final dfp E

E

E_SPLIT

public static final dfp[] E_SPLIT

E_SPLIT The number e split in two pieces

LN2

public static final dfp LN2

ln(2)

LN2_SPLIT

public static final dfp[] LN2_SPLIT

LN2_SPLIT The number e split in two pieces

LN5

public static final dfp LN5

ln(5)

LN5_SPLIT

public static final dfp[] LN5_SPLIT

LN5_SPLIT The number e split in two pieces

LN10

public static final dfp LN10

ln(10)

Constructor Detail

dfpmath

public dfpmath()

Method Detail

split

protected static dfp[] split(java.lang.String a)

Breaks a string representation up into two dfp's such that the sum of them is equivilent to the input string, but has higher precision than using a single dfp. Useful for improving accuracy of exponentination and critical multplies

split

protected static dfp[] split(dfp a)

Splits a dfp into 2 dfp's such that their sum is equal to the input dfp

splitMult

protected static dfp[] splitMult(dfp[] a,
                                 dfp[] b)

Multiply two numbers that are split in to two pices that are meant to be added together. Use binomail multiplication so ab = a0 b0 + a0 b1 + a1 b0 + a1 b1 Store the first term in result0, the rest in result1

splitDiv

protected static dfp[] splitDiv(dfp[] a,
                                dfp[] b)

Divide two numbers that are split in to two pices that are meant to be added together. Inverse of split mult above: (a+b) / (c+d) = (a/c) + ( (bc-ad)/(c**2+cd) )

splitPow

protected static dfp splitPow(dfp[] base,
                              int a)

Raise a split base to the a power. return a combined result

pow

public static dfp pow(dfp base,
                      int a)

Raises base to the power a by successive squaring

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 e**n and a taylor series to compute e**m. We return (e**n)(e**m)

expInternal

protected static dfp expInternal(dfp a)

Computes e to the given power. Where -1 < a < 1. Use the classic Taylor series. 1 + x**2/2! + x**3/3! + x**4/4! ...

ln

public static dfp ln(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.

lnInternal

protected static dfp[] lnInternal(dfp[] a)

Computes the natural log of a number between 0 and 2

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

sinInternal

protected static dfp sinInternal(dfp[] a)

Computes sin(a) Used when 0 < a < pi/4. Uses the classic Taylor series. x - x**3/3! + x**5/5! ...

cosInternal

protected static dfp cosInternal(dfp[] a)

Computes cos(a) Used when 0 < a < pi/4. Uses the classic Taylor series for cosine. 1 - x**2/2! + x**4/4! ...

sin

public static dfp sin(dfp a)

computes the sine of the argument

cos

public static dfp cos(dfp a)

computes the cosine of the argument

tan

public static dfp tan(dfp a)

computes the tangent of the argument

atanInternal

protected static dfp atanInternal(dfp 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

asin

public static dfp asin(dfp a)

acos

public static dfp acos(dfp a)