Class ExtendedPrecision

java.lang.Object

org.apache.commons.numbers.core.ExtendedPrecision

final class ExtendedPrecision
extends Object

Computes extended precision floating-point operations.

Extended precision computation is delegated to the DD class. The methods here are extensions to prevent overflow or underflow in intermediate computations.

Field Summary

Fields

Modifier and Type	Field	Description
private static final double	DOWN_SCALE	The scale to use when down-scaling during a split into a high part.
private static final double	DOWN_SCALE2	The downscale factor squared.
private static final double	SAFE_LOWER	The lower limit for a product x * y below which the round-off component may be sub-normal.
private static final double	SAFE_UPPER	The upper limit above which a number may overflow during the split into a high part.
private static final double	UP_SCALE	The scale to use when up-scaling during a split into a high part.
private static final double	UP_SCALE2	The upscale factor squared.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	ExtendedPrecision()	Private constructor.

Method Summary

Modifier and Type	Method	Description
(package private) static double	productLow(double x, double y, double xy)	Compute the low part of the double length number (z,zz) for the exact product of x and y.

Methods inherited from class Object

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

Field Details

SAFE_UPPER

private static final double SAFE_UPPER

The upper limit above which a number may overflow during the split into a high part. Assuming the multiplier is above 2^27 and the maximum exponent is 1023 then a safe limit is a value with an exponent of (1023 - 27) = 2^996. 996 is the value obtained from Math.getExponent(Double.MAX_VALUE / MULTIPLIER).

See Also:

• Constant Field Values

SAFE_LOWER

private static final double SAFE_LOWER

The lower limit for a product x * y below which the round-off component may be sub-normal. This is set as 2^-1022 * 2^54.

See Also:

• Constant Field Values

DOWN_SCALE

private static final double DOWN_SCALE

The scale to use when down-scaling during a split into a high part. This must be smaller than the inverse of the multiplier and a power of 2 for exact scaling.

See Also:

• Constant Field Values

UP_SCALE

private static final double UP_SCALE

The scale to use when up-scaling during a split into a high part. This is the inverse of DOWN_SCALE.

See Also:

• Constant Field Values

UP_SCALE2

private static final double UP_SCALE2

The upscale factor squared.

See Also:

• Constant Field Values

DOWN_SCALE2

private static final double DOWN_SCALE2

The downscale factor squared.

See Also:

• Constant Field Values

Constructor Details

ExtendedPrecision

private ExtendedPrecision()

Private constructor.

Method Details

productLow

static double productLow(double x,
 double y,
 double xy)

Compute the low part of the double length number (z,zz) for the exact product of x and y. This is equivalent to computing a double containing the magnitude of the rounding error when converting the exact 106-bit significand of the multiplication result to a 53-bit significand.

The method is written to be functionally similar to using a fused multiply add (FMA) operation to compute the low part, for example JDK 9's Math.fma function (note the sign change in the input argument for the product):

 double x = ...;
 double y = ...;
 double xy = x * y;
 double low1 = Math.fma(x, y, -xy);
 double low2 = productLow(x, y, xy);

Special cases:

• If x * y is sub-normal or zero then the result is 0.0.
• If x * y is infinite or NaN then the result is NaN.

This method delegates to DD.twoProductLow(double, double, double) but uses scaling to avoid intermediate overflow.

Parameters:

x - First factor.

y - Second factor.

xy - Product of the factors (x * y).

Returns:

the low part of the product double length number

See Also:

• DD.twoProductLow(double, double, double)