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# Float­Precision

2015-06-17 00:15:11
source

## Multiple inexact-number precisions

Scheme (before R7RS) and Common Lisp require that implementations understand short-float, single-float, double-float and long-float syntax. These are written by replacing the e of exponential notation with an s, f, d, or l respectively. However, there is no requirement that any of these be distinct, only that they be consistent: short-floats cannot have more precision than long-floats, for example. Common Lisp requires that e notation be equivalent to f notation by default; Scheme has no such requirement.

I asked the usual Schemes and some Common Lisps to evaluate 3.1415926535897932385s0, 3.1415926535897932385f0, 3.1415926535897932385d0, and 3.1415926535897932385l0, where the numeric value is a 64-bit version of π. Common Lisps were asked about precision directly using the standard float-bits procedure. For Scheme, I inferred how many bits of precision were provided by the answers. Here are the results (note that IEEE doubles are 53-bit precision and IEEE singles are 24-bit precision):

All four numbers are the same and have 53-bit precision: Gauche, Gambit, Chicken (with or without the numbers egg)*, Guile*, Kawa, SISC, Chibi, SCM, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, STklos*, KSI†, S7†, UMB, VX*, SXM*, Spark, Dfsch†, Inlab*, Sagittarius

All four numbers are the same and have 18-digit precision (between 59 and 60 bits): Scheme 9

All four numbers are the same and have 20-bit precision: Shoe

The first two numbers have 24-bit precision, the last two have 53-bit precision (IEEE double): Racket, NexJ, Armed Bear CL, Allegro CL, Clozure CL, CMU CL, Embeddable CL, GNU CL, Steel Bank CL, Scieneer CL

The numbers have 19-bit, 24-bit, 53-bit, and 53-bit precision respectively: LispWorks

The numbers have 17-bit, 24-bit, 53-bit, and arbitrary (at least 64-bit) precision respectively: CLISP

The numbers have 24-bit, 24-bit, 53-bit, and arbitrary precision respectively: Kawa

No inexact numbers: SigScheme, Dream, Oaklisp, Owl Lisp

Report syntax errors or treat input as identifiers: Bigloo, Scheme48/scsh, TinyScheme, Dream, RScheme, BDC, XLisp, Rep, Schemik, Elk, Sizzle, FemtoLisp

Inputs are treated as as special lexical syntax, not as numbers: Llava

## Footnotes

*Output is truncated

†Output is printed incorrectly