In coolbutuseless/lofi: Pack and Unpack Bits into Low Fidelity Representations

knitr::opts_chunk$set(
  collapse = FALSE,
  comment = "#>"
)

library(lofi)

Introduction

Double precision floating point values in R are stored in 64-bits - 1 bit sign, 11 for the exponent and 52 for the mantissa.

To convert to a low-fidelity representation, bits are dropped from the exponent and mantissa. This operation obviously results in a loss of precision in the number stored.

Note: lofi has no explicit detection or support for NA, NaN, Inf or denormalized numbers.

Double to 10-bit Lofi

Double precision floating point values are converted to low-fidelity representation by truncating the mantissa, and re-encoding the exponent. Low-fidelity floats have limited range, poorer precision, and will almost never give back the exact starting value when unpack()ed.

The following converts a double into a 10 bit float (with a sign bit, 2-bit exponent and 7-bit mantissa). The reconstructed double is close to the original value, but not an exact match.

(lofi <- dbl_to_lofi(-1.234, float_bits = c(1, 2, 7)))


recon <- lofi_to_dbl(lofi, float_bits = c(1, 2, 7))


png("man/figures/compact-float1.png", height = 260)
  exhibitionist::plot_compact_double(-1.234, base_size = 6)
dev.off()



png("man/figures/compact-float2.png", height = 260)
  exhibitionist::plot_float(lofi, float_bits = c(1, 2, 7), base_size = 8)
dev.off()


png("man/figures/compact-float3.png", height = 260)
  exhibitionist::plot_compact_double(recon, base_size = 6)
dev.off()

| Representation | Bits | Value | Bit layout | |-----------------------------|------| ---------|-----------------------------| | Double precision | 64 | -1.234 | | | Lofi double dbl_to_lofi(-1.234, float_bits = c(1, 2, 7)) | 10 | 669L | | | Reconstructed double lofi_to_dbl(669L, float_bits = c(1, 2, 7)) | 64 | -1.226562 | |

Double to 8-bit Lofi

A common 8-bit float (as described here) has 1-bit for the sign, 3-bits for the exponent and 4-bits for the mantissa.

This 8-bit float has a range of [-15.5, 15.5] and pretty terrible precision.

set.seed(1)

(original       <- round(runif(10, min = -15, max = 15), 3))
(lofi_values   <- dbl_to_lofi(original, float_bits = c(1, 3, 4)))
(reconstructed <- lofi_to_dbl(lofi_values, float_bits = c(1, 3, 4)))
abs(reconstructed - original)