[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	152.500 μs	144.700 μs
N4f4	153.000 μs	134.000 μs
N3f5	152.000 μs	124.700 μs
N2f6	155.900 μs	134.000 μs
N1f7	157.100 μs	137.400 μs
N0f8	138.800 μs	137.400 μs

from	before (v0.9.3)	after
N14f2	155.700 μs	133.700 μs
N13f3	182.700 μs	170.000 μs
N12f4	174.100 μs	178.000 μs
N11f5	178.300 μs	142.200 μs
N10f6	182.800 μs	140.500 μs
N9f7	178.300 μs	135.200 μs
N8f8	455.800 μs	146.900 μs
N7f9	436.600 μs	149.300 μs
N6f10	436.400 μs	138.500 μs
N5f11	487.900 μs	135.300 μs
N4f12	462.500 μs	118.700 μs
N3f13	436.800 μs	113.000 μs
N2f14	435.800 μs	122.200 μs
N1f15	524.600 μs	103.900 μs
N0f16	228.400 μs	228.000 μs