This module provides a general-purpose Number type supporting decimal arithmetic for both limited precision floating-point (IEEE 754-2008) and for arbitrary precision floating-point (following the same principles as IEEE 754 and IEEE 854-1987) as described in the General Decimal Arithmetic Specification by Mike Cowlishaw. In addition to floating-point arithmetic, integer and unrounded floating-point arithmetic are included as subsets.

Unlike the binary floating-point types Float and Double, the Number type can represent and perform arithmetic with decimal numbers exactly. Internally, a Number is represented with an integral coefficient and base-10 exponent.

The Number type supports lossless conversion to and from a string representation via the Show and Read instances. Note that there may be multiple representations of values that are numerically equal (e.g. 1 and 1.00) which are preserved by this conversion.

It is recommended to create an alias for the type of numbers you wish to support in your application. For example:

 type Decimal = BasicDecimal

This is a basic number type with 9 decimal digits of precision that rounds half up.

 type Decimal = ExtendedDecimal P15

This is a number type with 15 decimal digits of precision that rounds half even. There are a range of ready-made precisions available, including P1 through P50 on up to P2000. Alternatively, an arbitrary precision can be constructed through type application of PPlus1 and/or PTimes2 to any existing precision.

 type Decimal = GeneralDecimal

This is a number type with infinite precision. Note that not all operations support numbers with infinite precision.

 type Decimal = Number P34 RoundDown

This is a custom number type with 34 decimal digits of precision that rounds down (truncates). Several Rounding algorithms are available to choose from.

A decimal number type may be used in a default declaration, possibly replacing Double or Integer. For example:

 default (Integer, Decimal)