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.

This is for you.

It would be helpful to know what use is made -- Issue 1 is to let me know.

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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> 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> 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> 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> 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> 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> bitwidth(Float64), bitwidth(Float32)
#> (64, 32)

julia> hexstring(sqrt2₆₄), hexstring(sqrt2₃₂)
#> ("3ff6a09e667f3bcd", "3fb504f3")