Floating-point numbers in Stak Scheme

@raviqqe

September 1, 2024

Contents

• Stak Scheme
• Numeric tower in R7RS
• Implementation in Stak Scheme
• Future work

Stak Scheme

• A bytecode compiler and virtual machine (VM) for Scheme
  • The compiler is written in Scheme.
  • The VM is written in Rust.
• It aims to support R7RS-small.

Progress

• Floating-point number

Numeric tower in R7RS

• R7RS defines a numeric tower.
  • number?
  • complex?
  • real?
  • rational?
  • integer?

> 1+2i
1+2i
> 3.14
3.14
> 1/3
1/3
> 42
42

Numeric tower in R7RS

• exact and inexact conversion

> (inexact 1/3)
0.3333333333333333
> (exact 3.14)
7070651414971679/2251799813685248

Implementation in Stak Scheme

• Stak Scheme supports numbers represented by 63-bit integers or 64-bit floating-point numbers internally.
• They are switched by Rust's feature system.
• The bytecode compiler compiles floating-point numbers in source codes into integer components.
  • Signs, mantissae, and exponents
  • Smaller mantissae and exponents take less space in bytecodes.
  • Generated bytecodes re-calculate floating-point numbers on initialization.

Implementation in Stak Scheme

Problems

Degraded precision in bytecodes

• Floating-point numbers' integer components are calculated by normal exp and log procedures.
  • We can't calculate accurate mantissae and exponents.

Demo

Future work

• Optimize bytecode decoding

Summary

• Building floating-point numbers is fun!