[kimikage]

This fixes the double-rounding issue in N2f14, N1f15, and N0f16. (Fixes #364)

julia> Float16(reinterpret(N2f14, 0x4007))
Float16(1.0)   # before
Float16(1.001) # after

julia> Float16(reinterpret(N1f15, 0x800f))
Float16(1.0)   # before
Float16(1.001) # after

julia> Float16(reinterpret(N0f16, 0xffaf))
Float16(0.999)) # before
Float16(0.9985) # after

julia> Float16(reinterpret(N0f16, 0xffef))
Float16(1.0)     # before
Float16(0.9995)) # after

This also make the tests more robust regarding issue #246.

This improves performance for Normed(UInt16, f) where f in 8:15. Performance improvements for other types are minor.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.78%. Comparing base (c4a4edd) to head (714a854).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #372      +/-   ##
==========================================
+ Coverage   96.73%   96.78%   +0.05%     
==========================================
  Files           7        7              
  Lines         827      840      +13     
==========================================
+ Hits          800      813      +13     
  Misses         27       27              

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[kimikage]

Benchmark

using FixedPointNumbers, BenchmarkTools

f16s = zeros(Float16, 1000, 1000);
for f in 2:8
    N = Normed{UInt8, f}
    ns = rand(N, 1000, 1000);
    println(N)
    @btime $f16s .= Float16.($ns)
end
for f in 2:16
    N = Normed{UInt16, f}
    ns = rand(N, 1000, 1000);
    println(N)
    @btime $f16s .= Float16.($ns)
end

Julia v1.13.3

julia> versioninfo()
Julia Version 1.13.3
Commit 67ac47b9cd (2026-10-25 15:28 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz
  WORD_SIZE: 64
  LLVM: libLLVM-20.1.8 (ORCJIT, tigerlake)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 8 virtual cores)

from	before (v0.9.3)	after
N6f2	72.500 μs	63.800 μs
N5f3	77.000 μs	63.400 μs
N4f4	74.600 μs	62.200 μs
N3f5	70.500 μs	64.300 μs
N2f6	70.600 μs	61.900 μs
N1f7	76.900 μs	65.600 μs
N0f8	71.300 μs	69.100 μs

from	before (v0.9.3)	after
N14f2	88.200 μs	81.800 μs
N13f3	85.900 μs	84.500 μs
N12f4	88.300 μs	85.900 μs
N11f5	85.900 μs	81.700 μs
N10f6	85.900 μs	79.500 μs
N9f7	93.300 μs	79.200 μs
N8f8	501.200 μs	81.800 μs
N7f9	435.800 μs	79.200 μs
N6f10	501.200 μs	86.400 μs
N5f11	501.200 μs	76.400 μs
N4f12	477.300 μs	102.900 μs
N3f13	541.800 μs	87.000 μs
N2f14	541.800 μs	95.400 μs
N1f15	541.800 μs	101.100 μs
N0f16	116.600 μs	79.500 μs

[kimikage]

Julia v1.10.12

julia> versioninfo()
Julia Version 1.10.12
Commit d93beab124 (2026-08-15 10:29 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)

from	before (v0.9.3)	after
N6f2	136.800 μs	114.000 μs
N5f3	135.900 μs	114.400 μs
N4f4	136.600 μs	114.000 μs
N3f5	135.700 μs	116.500 μs
N2f6	136.000 μs	114.100 μs
N1f7	136.600 μs	114.000 μs
N0f8	135.800 μs	114.400 μs

from	before (v0.9.3)	after
N14f2	155.600 μs	115.800 μs
N13f3	155.600 μs	155.400 μs
N12f4	155.700 μs	155.300 μs
N11f5	155.500 μs	115.300 μs
N10f6	155.800 μs	117.600 μs
N9f7	155.800 μs	115.500 μs
N8f8	436.400 μs	115.700 μs
N7f9	436.600 μs	115.400 μs
N6f10	436.400 μs	117.600 μs
N5f11	477.100 μs	117.900 μs
N4f12	462.500 μs	118.700 μs
N3f13	436.800 μs	113.000 μs
N2f14	435.800 μs	122.200 μs
N1f15	466.200 μs	103.900 μs
N0f16	197.600 μs	194.100 μs

[kimikage]

I think there's still room for improvement, but since there are no obvious regressions, we'll move forward.