###: Hexadecimal Floating-Point Constants

by Peter McGoron

Submitted as SRFI 270

Status

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Abstract

Floating-point numbers are generally in radix 2, but are written by users in radix 10. This SRFI introduces C99's hexadecimal floating point constants into Scheme syntax.

Rationale

Computers generally use binary floating point to store numbers, while humans like decimals. To express binary floating point exactly, one can use hexadecimal floating point constants, which are written in base-16 instead of base-10. They represent binary floating point numbers precisely (as long as they can fit in the number).

Specification

Non-normative text is in small text.

Syntax

The formal syntax of Scheme is modified to have the following new productions:

⟨ureal R⟩

::= ⟨hex float body R⟩ ⟨hex float suffix⟩

⟨hex float body 16⟩

::= ⟨uinteger 16⟩

| . ⟨digit 16⟩⁺

| ⟨digit 16⟩⁺ . ⟨digit 16⟩^*

⟨hex float suffix⟩

::= p ⟨sign⟩^? ⟨digit 10⟩⁺

The exponential separator is p because it is ambiguous if e would be a decimal separator or a hex digit.

If a system has multiple precisions of floats, then the syntax could be extended such that ⟨exponent marker⟩ follows p.

A hexadecimal floating point number is interpreted such that

x_nx_n−1…x₀.x₋₁x₋₂…x_−mpd

where each x is a hexadecimal digit and d is a base-10 number, is equal to

(X_n×16ⁿ + X_n−1×16ⁿ⁻¹ + … + X₀ + X₋₁×16⁻¹ + X₋₂×16⁻² + … + X_−m×16^−m)×2^d

where X_i is the numerical value of the digit x_i.

Procedures

The procedure number->string must understand hexadecimal floats.

(read-hexadecimal-float [port])

Read a hexadecimal float from the current input stream. A hexadecimal may start with #x. The number is exact if it has #e in it, an inexact otherwise.

(write-hexadecimal-float x [port])

Write a floating point number in canonical format. This means:

• For a normal number, the integer part is 1.
• For a subnormal number, the integer part is 0.

Examples

This section is non-normative.

Implementation

MIT-Scheme natively supports this syntax. A parser for numbers that incoporates this is in TODO.

Acknowledgements

Taylor Campbell suggested it to me on #scheme.

Copyright

© 2026 Peter McGoron.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice (including the next paragraph) shall be included in all copies or substantial portions of the Software.

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