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DecFP: IEEE Decimal Floating-point in Julia

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The DecFP package is a Julia wrapper around the Intel Decimal Floating-Point Math Library, providing a software implementation of the IEEE 754-2008 Decimal Floating-Point Arithmetic specification.

32-bit, 64-bit, and 128-bit decimal floating-point types Dec32, Dec64, and Dec128, respectively, are provided (corresponding to 7, 16, and 34 decimal digits of precision, respectively). This is very different from packages such as Decimals.jl, which provide arbitrary-precision decimal types analogous to BigFloat: arbitrary precision types are very flexible, but fixed-precision types such as those in DecFP are much faster (though still about 50x slower than the hardware binary floating-point types Float32 and Float64) and more memory-efficient (an array of Dec64 values has exactly the same memory footprint as an array of Float64 values).

The latest version of the DecFP package requires Julia 1.3 or later.

Usage

Dec64 and the other types mentioned above can be constructed from other Julia numeric types (binary floating-point or integers) via Dec64(3.5) or Dec(3), from strings by parse(Dec64, "3.2") or d64"3.2" (a Julia string macro); similarly for Dec32 and Dec128. The string macro d"3.2" constructs Dec64.

  • Note: A decimal floating-point constant like 1.1 in Julia refers to a Float64 (binary floating-point) value. So, for example, Dec128(1.999999999999999999) == 2.0 ≠ d128"1.999999999999999999", since Julia first rounds 1.999999999999999999 to the closest Float64 value (2.0) before converting to Dec128. If you need to specify an exact decimal constant, therefore, use one of the string-based constructors. If you use a string macro like d128"1.999999999999999999", then the string parsing occurs before compilation and incurs no runtime cost.

Once a decimal float is constructed, most Julia arithmetic and special functions should work without modification. For example, d"3.2" * d"4.5" produces the (exact) Dec64 result 14.4 All basic arithmetic functions are supported, and many special functions (sqrt, log, trigonometric functions, etc.). Mixed operations involving decimal and binary floating-point or integer types are supported (the result is promoted to decimal floating-point).

In general, you should be able to use the DecFP types in any context where you would have used binary floating-point types: arrays, complex arithmetic, and linear algebra should all work, for the most part.