https://github.com/jeffreysarnoff/lowlevelfloatfunctions.jl
Manipulate sign, exponent, significand of Float64, Float32, Float16 values.
https://github.com/jeffreysarnoff/lowlevelfloatfunctions.jl
exponent exponent-bias floating-point julia significand
Last synced: 3 months ago
JSON representation
Manipulate sign, exponent, significand of Float64, Float32, Float16 values.
- Host: GitHub
- URL: https://github.com/jeffreysarnoff/lowlevelfloatfunctions.jl
- Owner: JeffreySarnoff
- License: mit
- Created: 2017-12-12T04:08:22.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2018-11-19T13:34:44.000Z (over 6 years ago)
- Last Synced: 2025-01-20T19:55:00.183Z (4 months ago)
- Topics: exponent, exponent-bias, floating-point, julia, significand
- Language: Julia
- Size: 99.6 KB
- Stars: 2
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# LowLevelFloatFunctions.jl
### Manipulate sign, exponent, significand of Float64, Float32, Float16 values.
> These functions allow you to alter each floating point field individually
(get, modify, replace) while the rest of the floating point value’s bits
are unmodified. As the system floats are immutable, replacing a subfield
actually generates a new float with the bit logic as above.
#### Copyright © 2017 by Jeffrey Sarnoff. Released under The MIT License.
[](https://travis-ci.org/JeffreySarnoff/LowLevelFloatFunctions.jl)
-------
**This is for you.**
*It would be helpful to know what use is made -- Issue 1 is to let me know.*
-----
## Exports
#### value extraction
sign, exponent, significand
#### field getting and setting
sign_field, exponent_field, signficand_field,
unbiased_exponent_field, biased_exponent_field,
sign_and_exponent_fields, exponent_and_significand_fields
#### characterization
sign_bits, exponent_bits, significand_bits,
exponent_max, exponent_min, exponent_field_max,
exponent_bias
#### utilitiarian
bitwidth, hexstring
## Use
These values are used below.
```julia
julia> sqrt2₆₄, sqrt17₆₄ = sqrt(Float64(2)), sqrt(Float64(17))
#> (1.4142_1356_2373_0951, 4.1231_0562_5617_6610#> )
julia> sqrt2₃₂, sqrt17₃₂ = sqrt(Float32(2)), sqrt(Float32(17))
#> (1.4142_135f0, 4.1231_055f0)
julia> sqrt2₁₆, sqrt17₁₆ = sqrt(Float16(2)), sqrt(Float16(17))
#> (Float16(1.414), Float16(4.125))
```
#### value extraction
```julia
julia> significand(-sqrt17₆₄),
significand( sqrt17₃₂),
significand(-sqrt17₁₆)
#> (-1.0307764064044151, 1.0307764f0, Float16(-1.031))
julia> exponent(-sqrt17₆₄),
exponent( sqrt17₃₂),
exponent(-sqrt17₁₆)
#> (2, 2, 2)
julia> biased_exponent(-sqrt17₆₄),
biased_exponent( sqrt17₃₂),
biased_exponent(-sqrt17₁₆)
#> (1025, 129, 17)
julia> sign(-sqrt17₆₄),
sign( sqrt17₃₂),
sign(-sqrt17₁₆)
#> (-1.0, 1.0f0, Float16(-1.0))
```
#### field getting
```julia
julia> significand_field(sqrt2₆₄),
significand_field(sqrt2₃₂),
significand_field(sqrt2₁₆)
#> (0x0006a09e667f3bcd, 0x003504f3, 0x01a8)
julia> biased_exponent_field(-sqrt17₆₄),
biased_exponent_field(sqrt17₃₂),
biased_exponent_field(-sqrt17₁₆)
#> (0x0000000000000401, 0x00000081, 0x0011)
julia> unbiased_exponent_field(-sqrt17₆₄),
unbiased_exponent_field( sqrt17₃₂),
unbiased_exponent_field(-sqrt17₁₆)
#> (0x0000000000000002, 0x00000002, 0x0002)
julia> sign_field(-sqrt17₆₄),
sign_field( sqrt17₃₂),
sign_field(-sqrt17₁₆)
#> (0x0000000000000001, 0x00000000, 0x0001)
```
#### field setting
```julia
julia> sign_field(-sqrt2₆₄, 0%UInt64)
#> 1.4142135623730951
julia> exponent_field(sqrt2₆₄, exponent_field(sqrt2₆₄)+one(UInt64))
#> 2.8284271247461903
julia> ans/2
#> 1.4142135623730951
julia> significand_field(sqrt2₃₂, significand_field(sqrt2₃₂) - one(UInt32)),
significand_field(sqrt2₃₂, significand_field(sqrt2₃₂)),
significand_field(sqrt2₃₂, significand_field(sqrt2₃₂) + one(UInt32))
#> (1.4142134f0, 1.4142135f0, 1.4142137f0)
julia> prevfloat(sqrt2₃₂), sqrt2₃₂, nextfloat(sqrt2₃₂)
#> (1.4142134f0, 1.4142135f0, 1.4142137f0)
```
#### characterization
```julia
julia> sign_bits(Float64),
exponent_bits(Float32),
significand_bits(Float16)
#> (1, 8, 10)
julia> exponent_min(Float64),
exponent_max(Float64),
exponent_field_max(Float64)
#> #> (-1022, 1023, 0x0000000000000400)
julia> exponent_bias(Float32)
#> 1023
```
#### utilitiarian
```julia
julia> bitwidth(Float64), bitwidth(Float32)
#> (64, 32)
julia> hexstring(sqrt2₆₄), hexstring(sqrt2₃₂)
#> ("3ff6a09e667f3bcd", "3fb504f3")
```