org.apache.commons.math.dfp
public class Dfp extends java.lang.Object implements FieldElement<Dfp>
Another floating point class. This one is built using radix 10000 which is 104, so its almost decimal.
The design goals here are:
Trade offs:
Numbers are represented in the following form:
n = sign × mant × (radix)exp;where sign is ±1, mantissa represents a fractional number between zero and one. mant[0] is the least significant digit. exp is in the range of -32767 to 32768
IEEE 854-1987 Notes and differences
IEEE 854 requires the radix to be either 2 or 10. The radix here is 10000, so that requirement is not met, but it is possible that a subclassed can be made to make it behave as a radix 10 number. It is my opinion that if it looks and behaves as a radix 10 number then it is one and that requirement would be met.
The radix of 10000 was chosen because it should be faster to operate on 4 decimal digits at once instead of one at a time. Radix 10 behavior can be realized by add an additional rounding step to ensure that the number of decimal digits represented is constant.
The IEEE standard specifically leaves out internal data encoding, so it is reasonable to conclude that such a subclass of this radix 10000 system is merely an encoding of a radix 10 system.
IEEE 854 also specifies the existence of "sub-normal" numbers. This class does not contain any such entities. The most significant radix 10000 digit is always non-zero. Instead, we support "gradual underflow" by raising the underflow flag for numbers less with exponent less than expMin, but don't flush to zero until the exponent reaches MIN_EXP-digits. Thus the smallest number we can represent would be: 1E(-(MIN_EXP-digits-1)*4), eg, for digits=5, MIN_EXP=-32767, that would be 1e-131092.
IEEE 854 defines that the implied radix point lies just to the right of the most significant digit and to the left of the remaining digits. This implementation puts the implied radix point to the left of all digits including the most significant one. The most significant digit here is the one just to the right of the radix point. This is a fine detail and is really only a matter of definition. Any side effects of this can be rendered invisible by a subclass.
DfpField
Modifier and Type | Field and Description |
---|---|
private static java.lang.String |
ADD_TRAP
Name for traps triggered by addition.
|
private static java.lang.String |
ALIGN_TRAP
Name for traps triggered by alignment.
|
private static java.lang.String |
DIVIDE_TRAP
Name for traps triggered by division.
|
static int |
ERR_SCALE
The amount under/overflows are scaled by before going to trap handler
|
protected int |
exp
Exponent.
|
private DfpField |
field
Factory building similar Dfp's.
|
static byte |
FINITE
Indicator value for normal finite numbers.
|
private static java.lang.String |
GREATER_THAN_TRAP
Name for traps triggered by greaterThan.
|
static byte |
INFINITE
Indicator value for Infinity.
|
private static java.lang.String |
LESS_THAN_TRAP
Name for traps triggered by lessThan.
|
protected int[] |
mant
Mantissa.
|
static int |
MAX_EXP
The maximum exponent before overflow is signaled and results flushed
to infinity
|
static int |
MIN_EXP
The minimum exponent before underflow is signaled.
|
private static java.lang.String |
MULTIPLY_TRAP
Name for traps triggered by multiplication.
|
private static java.lang.String |
NAN_STRING
String for NaN representation.
|
protected byte |
nans
Indicator for non-finite / non-number values.
|
private static java.lang.String |
NEG_INFINITY_STRING
String for negative infinity representation.
|
private static java.lang.String |
NEW_INSTANCE_TRAP
Name for traps triggered by newInstance.
|
private static java.lang.String |
NEXT_AFTER_TRAP
Name for traps triggered by nextAfter.
|
private static java.lang.String |
POS_INFINITY_STRING
String for positive infinity representation.
|
static byte |
QNAN
Indicator value for quiet NaN.
|
static int |
RADIX
The radix, or base of this system.
|
protected byte |
sign
Sign bit: & for positive, -1 for negative.
|
static byte |
SNAN
Indicator value for signaling NaN.
|
private static java.lang.String |
SQRT_TRAP
Name for traps triggered by square root.
|
private static java.lang.String |
TRUNC_TRAP
Name for traps triggered by truncation.
|
Modifier | Constructor and Description |
---|---|
|
Dfp(Dfp d)
Copy constructor.
|
protected |
Dfp(DfpField field)
Makes an instance with a value of zero.
|
protected |
Dfp(DfpField field,
byte x)
Create an instance from a byte value.
|
protected |
Dfp(DfpField field,
byte sign,
byte nans)
Creates an instance with a non-finite value.
|
protected |
Dfp(DfpField field,
double x)
Create an instance from a double value.
|
protected |
Dfp(DfpField field,
int x)
Create an instance from an int value.
|
protected |
Dfp(DfpField field,
long x)
Create an instance from a long value.
|
protected |
Dfp(DfpField field,
java.lang.String s)
Create an instance from a String representation.
|
Modifier and Type | Method and Description |
---|---|
Dfp |
add(Dfp x)
Add x to this.
|
protected int |
align(int e)
Make our exp equal to the supplied one, this may cause rounding.
|
Dfp |
ceil()
Round to an integer using the round ceil mode.
|
int |
classify()
Returns the type - one of FINITE, INFINITE, SNAN, QNAN.
|
private static int |
compare(Dfp a,
Dfp b)
Compare two instances.
|
protected int |
complement(int extra)
Negate the mantissa of this by computing the complement.
|
static Dfp |
copysign(Dfp x,
Dfp y)
Creates an instance that is the same as x except that it has the sign of y.
|
protected java.lang.String |
dfp2sci()
Convert an instance to a string using scientific notation.
|
protected java.lang.String |
dfp2string()
Convert an instance to a string using normal notation.
|
Dfp |
divide(Dfp divisor)
Divide this by divisor.
|
Dfp |
divide(int divisor)
Divide by a single digit less than radix.
|
Dfp |
dotrap(int type,
java.lang.String what,
Dfp oper,
Dfp result)
Raises a trap.
|
boolean |
equals(java.lang.Object other)
Check if instance is equal to x.
|
Dfp |
floor()
Round to an integer using the round floor mode.
|
DfpField |
getField()
|
Dfp |
getOne()
Get the constant 1.
|
int |
getRadixDigits()
Get the number of radix digits of the instance.
|
Dfp |
getTwo()
Get the constant 2.
|
Dfp |
getZero()
Get the constant 0.
|
boolean |
greaterThan(Dfp x)
Check if instance is greater than x.
|
int |
hashCode()
Gets a hashCode for the instance.
|
int |
intValue()
Convert this to an integer.
|
boolean |
isInfinite()
Check if instance is infinite.
|
boolean |
isNaN()
Check if instance is not a number.
|
boolean |
lessThan(Dfp x)
Check if instance is less than x.
|
int |
log10()
Get the exponent of the greatest power of 10 that is less than or equal to abs(this).
|
int |
log10K()
Get the exponent of the greatest power of 10000 that is
less than or equal to the absolute value of this.
|
Dfp |
multiply(Dfp x)
Multiply this by x.
|
Dfp |
multiply(int x)
Multiply this by a single digit 0<=x<radix.
|
Dfp |
negate()
Returns a number that is this number with the sign bit reversed.
|
Dfp |
newInstance()
Create an instance with a value of 0.
|
Dfp |
newInstance(byte x)
Create an instance from a byte value.
|
Dfp |
newInstance(byte sig,
byte code)
Creates an instance with a non-finite value.
|
Dfp |
newInstance(Dfp d)
Create an instance by copying an existing one.
|
Dfp |
newInstance(double x)
Create an instance from a double value.
|
Dfp |
newInstance(int x)
Create an instance from an int value.
|
Dfp |
newInstance(long x)
Create an instance from a long value.
|
Dfp |
newInstance(java.lang.String s)
Create an instance from a String representation.
|
Dfp |
nextAfter(Dfp x)
Returns the next number greater than this one in the direction of x.
|
Dfp |
power10(int e)
Return the specified power of 10.
|
Dfp |
power10K(int e)
Get the specified power of 10000.
|
Dfp |
remainder(Dfp d)
Returns the IEEE remainder.
|
Dfp |
rint()
Round to nearest integer using the round-half-even method.
|
protected int |
round(int n)
Round this given the next digit n using the current rounding mode.
|
protected void |
shiftLeft()
Shift the mantissa left, and adjust the exponent to compensate.
|
protected void |
shiftRight()
Shift the mantissa right, and adjust the exponent to compensate.
|
Dfp |
sqrt()
Compute the square root.
|
Dfp |
subtract(Dfp x)
Subtract x from this.
|
double |
toDouble()
Convert the instance into a double.
|
double[] |
toSplitDouble()
Convert the instance into a split double.
|
java.lang.String |
toString()
Get a string representation of the instance.
|
protected Dfp |
trap(int type,
java.lang.String what,
Dfp oper,
Dfp def,
Dfp result)
Trap handler.
|
protected Dfp |
trunc(DfpField.RoundingMode rmode)
Does the integer conversions with the specified rounding.
|
boolean |
unequal(Dfp x)
Check if instance is not equal to x.
|
public static final int RADIX
public static final int MIN_EXP
public static final int MAX_EXP
public static final int ERR_SCALE
public static final byte FINITE
public static final byte INFINITE
public static final byte SNAN
public static final byte QNAN
private static final java.lang.String NAN_STRING
private static final java.lang.String POS_INFINITY_STRING
private static final java.lang.String NEG_INFINITY_STRING
private static final java.lang.String ADD_TRAP
private static final java.lang.String MULTIPLY_TRAP
private static final java.lang.String DIVIDE_TRAP
private static final java.lang.String SQRT_TRAP
private static final java.lang.String ALIGN_TRAP
private static final java.lang.String TRUNC_TRAP
private static final java.lang.String NEXT_AFTER_TRAP
private static final java.lang.String LESS_THAN_TRAP
private static final java.lang.String GREATER_THAN_TRAP
private static final java.lang.String NEW_INSTANCE_TRAP
protected int[] mant
protected byte sign
protected int exp
protected byte nans
private final DfpField field
protected Dfp(DfpField field)
field
- field to which this instance belongsprotected Dfp(DfpField field, byte x)
field
- field to which this instance belongsx
- value to convert to an instanceprotected Dfp(DfpField field, int x)
field
- field to which this instance belongsx
- value to convert to an instanceprotected Dfp(DfpField field, long x)
field
- field to which this instance belongsx
- value to convert to an instanceprotected Dfp(DfpField field, double x)
field
- field to which this instance belongsx
- value to convert to an instancepublic Dfp(Dfp d)
d
- instance to copyprotected Dfp(DfpField field, java.lang.String s)
field
- field to which this instance belongss
- string representation of the instancepublic Dfp newInstance()
public Dfp newInstance(byte x)
x
- value to convert to an instancepublic Dfp newInstance(int x)
x
- value to convert to an instancepublic Dfp newInstance(long x)
x
- value to convert to an instancepublic Dfp newInstance(double x)
x
- value to convert to an instancepublic Dfp newInstance(Dfp d)
d
- instance to copypublic Dfp newInstance(java.lang.String s)
s
- string representation of the instancepublic Dfp newInstance(byte sig, byte code)
public DfpField getField()
Field
(really a DfpField
) to which the instance belongs.
The field is linked to the number of digits and acts as a factory
for Dfp
instances.
getField
in interface FieldElement<Dfp>
Field
(really a DfpField
) to which the instance belongspublic int getRadixDigits()
public Dfp getZero()
public Dfp getOne()
public Dfp getTwo()
protected void shiftLeft()
protected void shiftRight()
protected int align(int e)
e
- desired exponentpublic boolean lessThan(Dfp x)
x
- number to check instance againstpublic boolean greaterThan(Dfp x)
x
- number to check instance againstpublic boolean isInfinite()
public boolean isNaN()
public boolean equals(java.lang.Object other)
equals
in class java.lang.Object
other
- object to check instance againstpublic int hashCode()
hashCode
in class java.lang.Object
public boolean unequal(Dfp x)
x
- number to check instance againstprivate static int compare(Dfp a, Dfp b)
a
- first instance in comparisonb
- second instance in comparisonpublic Dfp rint()
public Dfp floor()
public Dfp ceil()
public Dfp remainder(Dfp d)
d
- divisorprotected Dfp trunc(DfpField.RoundingMode rmode)
rmode
- rounding mode to usepublic int intValue()
public int log10K()
public Dfp power10K(int e)
e
- desired powerpublic int log10()
public Dfp power10(int e)
e
- desired powerprotected int complement(int extra)
extra
- ???public Dfp add(Dfp x)
add
in interface FieldElement<Dfp>
x
- number to addpublic Dfp negate()
public Dfp subtract(Dfp x)
subtract
in interface FieldElement<Dfp>
x
- number to subtractprotected int round(int n)
n
- ???public Dfp multiply(Dfp x)
multiply
in interface FieldElement<Dfp>
x
- multiplicandpublic Dfp multiply(int x)
x
- multiplicandpublic Dfp divide(Dfp divisor)
divide
in interface FieldElement<Dfp>
divisor
- divisorpublic Dfp divide(int divisor)
divisor
- divisorpublic Dfp sqrt()
public java.lang.String toString()
toString
in class java.lang.Object
protected java.lang.String dfp2sci()
protected java.lang.String dfp2string()
public Dfp dotrap(int type, java.lang.String what, Dfp oper, Dfp result)
type
- the trap typewhat
- - name of routine trap occurred inoper
- - input operator to functionresult
- - the result computed prior to the trapprotected Dfp trap(int type, java.lang.String what, Dfp oper, Dfp def, Dfp result)
type
- The exception type - e.g. FLAG_OVERFLOWwhat
- The name of the routine we were in e.g. divide()oper
- An operand to this function if anydef
- The default return value if trap not enabledresult
- The result that is specified to be delivered per
IEEE 854, if anypublic int classify()
public static Dfp copysign(Dfp x, Dfp y)
x
- number to get the value fromy
- number to get the sign frompublic Dfp nextAfter(Dfp x)
x
- direction where to look atpublic double toDouble()
toSplitDouble()
public double[] toSplitDouble()
toDouble()
Copyright (c) 2003-2013 Apache Software Foundation