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Support ForwardDiff duals over BareInterval - #778

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timholy wants to merge 3 commits into
JuliaIntervals:masterfrom
timholy:teh/fd-bare
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Support ForwardDiff duals over BareInterval#778
timholy wants to merge 3 commits into
JuliaIntervals:masterfrom
timholy:teh/fd-bare

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@timholy

@timholy timholy commented Sep 5, 2026

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This has two commits; the second depends on the first, but arguably they should be merged without squashing. I can also split into two separate (sequential) PRs if you prefer.

The main goal here is to support differentiation and arithmetic for bare intervals in nested duals. At present I think this is the last performance work I need to make it possible to adopt IA.

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Benchmark Results (Julia v1)

Time benchmarks
master f64c50b... master / f64c50b...
BigFloat MPFI/basics/* 26.3 ± 3.6 μs 26.6 ± 3.6 μs 0.991 ± 0.19
BigFloat MPFI/basics/+ 13.4 ± 3.4 μs 13.9 ± 3.5 μs 0.965 ± 0.34
BigFloat MPFI/basics/- 19.2 ± 3.7 μs 19.1 ± 3.5 μs 1.01 ± 0.27
BigFloat MPFI/basics// 25.7 ± 7.2 μs 26.2 ± 6.8 μs 0.98 ± 0.38
BigFloat MPFI/basics/abs 11.3 ± 3.4 μs 11 ± 3.4 μs 1.03 ± 0.45
BigFloat MPFI/basics/acos 0.698 ± 0.0091 ms 0.681 ± 0.0089 ms 1.02 ± 0.019
BigFloat MPFI/basics/asin 0.679 ± 0.011 ms 0.666 ± 0.011 ms 1.02 ± 0.024
BigFloat MPFI/basics/atan 2.11 ± 0.0073 ms 2.1 ± 0.008 ms 1 ± 0.0051
BigFloat MPFI/basics/cos 0.359 ± 0.01 ms 0.36 ± 0.01 ms 0.999 ± 0.039
BigFloat MPFI/basics/cosh 0.431 ± 0.012 ms 0.432 ± 0.012 ms 1 ± 0.04
BigFloat MPFI/basics/exp 0.502 ± 0.01 ms 0.501 ± 0.0098 ms 1 ± 0.028
BigFloat MPFI/basics/inv 19.4 ± 3.6 μs 19.5 ± 3.6 μs 0.993 ± 0.26
BigFloat MPFI/basics/log 0.469 ± 0.011 ms 0.465 ± 0.01 ms 1.01 ± 0.032
BigFloat MPFI/basics/sin 0.468 ± 0.011 ms 0.466 ± 0.011 ms 1 ± 0.034
BigFloat MPFI/basics/sinh 0.572 ± 0.01 ms 0.573 ± 0.0099 ms 0.997 ± 0.025
BigFloat MPFI/basics/sqrt 22.8 ± 3.5 μs 21.9 ± 3.7 μs 1.04 ± 0.24
BigFloat MPFI/basics/tan 0.386 ± 0.01 ms 0.385 ± 0.01 ms 1 ± 0.037
BigFloat MPFI/basics/tanh 0.586 ± 0.01 ms 0.589 ± 0.01 ms 0.996 ± 0.024
BigFloat bareinterval/basics/* 0.04 ± 0.0025 ms 0.0405 ± 0.0025 ms 0.988 ± 0.087
BigFloat bareinterval/basics/+ 22.9 ± 3.3 μs 23.1 ± 3.4 μs 0.992 ± 0.2
BigFloat bareinterval/basics/- 23.3 ± 3.3 μs 24.4 ± 3.5 μs 0.956 ± 0.19
BigFloat bareinterval/basics// 20 ± 5 μs 20.8 ± 5 μs 0.962 ± 0.33
BigFloat bareinterval/basics/abs 15 ± 3.2 μs 15.3 ± 3.3 μs 0.98 ± 0.3
BigFloat bareinterval/basics/acos 0.714 ± 0.014 ms 0.715 ± 0.013 ms 0.999 ± 0.027
BigFloat bareinterval/basics/asin 0.726 ± 0.014 ms 0.708 ± 0.013 ms 1.03 ± 0.027
BigFloat bareinterval/basics/atan 2.12 ± 0.0082 ms 2.1 ± 0.0074 ms 1.01 ± 0.0052
BigFloat bareinterval/basics/cos 0.415 ± 0.084 ms 0.416 ± 0.086 ms 0.998 ± 0.29
BigFloat bareinterval/basics/cosh 0.479 ± 0.012 ms 0.478 ± 0.011 ms 1 ± 0.034
BigFloat bareinterval/basics/exp 0.512 ± 0.011 ms 0.512 ± 0.011 ms 1 ± 0.029
BigFloat bareinterval/basics/inv 26.2 ± 3.2 μs 27 ± 3.4 μs 0.97 ± 0.17
BigFloat bareinterval/basics/log 0.502 ± 0.011 ms 0.5 ± 0.011 ms 1 ± 0.032
BigFloat bareinterval/basics/sin 0.553 ± 0.083 ms 0.554 ± 0.082 ms 0.999 ± 0.21
BigFloat bareinterval/basics/sinh 0.582 ± 0.011 ms 0.582 ± 0.011 ms 0.999 ± 0.026
BigFloat bareinterval/basics/sqrt 31.2 ± 2.4 μs 0.0317 ± 0.0027 ms 0.987 ± 0.12
BigFloat bareinterval/basics/tan 0.322 ± 0.056 ms 0.325 ± 0.056 ms 0.991 ± 0.24
BigFloat bareinterval/basics/tanh 0.596 ± 0.01 ms 0.596 ± 0.011 ms 1 ± 0.025
BigFloat interval/basics/* 0.043 ± 0.012 ms 0.0445 ± 0.012 ms 0.965 ± 0.36
BigFloat interval/basics/+ 17.9 ± 0.69 μs 19.3 ± 0.53 μs 0.929 ± 0.044
BigFloat interval/basics/- 18.5 ± 0.35 μs 18.1 ± 0.27 μs 1.02 ± 0.025
BigFloat interval/basics// 20.9 ± 0.25 μs 22 ± 0.21 μs 0.951 ± 0.015
BigFloat interval/basics/abs 14.7 ± 8.1 μs 15 ± 7.8 μs 0.979 ± 0.74
BigFloat interval/basics/acos 0.707 ± 0.038 ms 0.708 ± 0.034 ms 0.999 ± 0.072
BigFloat interval/basics/asin 0.695 ± 0.0099 ms 0.69 ± 0.011 ms 1.01 ± 0.021
BigFloat interval/basics/atan 2.12 ± 0.0089 ms 2.11 ± 0.0055 ms 1.01 ± 0.005
BigFloat interval/basics/cos 0.335 ± 0.013 ms 0.336 ± 0.013 ms 0.996 ± 0.054
BigFloat interval/basics/cosh 0.468 ± 0.011 ms 0.47 ± 0.011 ms 0.997 ± 0.034
BigFloat interval/basics/exp 0.522 ± 0.0093 ms 0.521 ± 0.0095 ms 1 ± 0.026
BigFloat interval/basics/inv 22.2 ± 0.27 μs 23.3 ± 0.25 μs 0.954 ± 0.016
BigFloat interval/basics/log 0.502 ± 0.013 ms 0.499 ± 0.013 ms 1.01 ± 0.036
BigFloat interval/basics/sin 0.483 ± 0.013 ms 0.484 ± 0.013 ms 0.997 ± 0.039
BigFloat interval/basics/sinh 0.59 ± 0.01 ms 0.591 ± 0.01 ms 0.998 ± 0.024
BigFloat interval/basics/sqrt 0.0392 ± 0.0012 ms 0.0392 ± 0.0011 ms 1 ± 0.04
BigFloat interval/basics/tan 0.281 ± 0.012 ms 0.281 ± 0.012 ms 1 ± 0.061
BigFloat interval/basics/tanh 0.605 ± 0.0097 ms 0.605 ± 0.0095 ms 1 ± 0.023
bareinterval/basics/* 1.82 ± 0.049 μs 1.82 ± 0.05 μs 1 ± 0.038
bareinterval/basics/+ 0.491 ± 0.01 μs 0.481 ± 0.01 μs 1.02 ± 0.03
bareinterval/basics/- 0.501 ± 0.01 μs 0.501 ± 0.01 μs 1 ± 0.028
bareinterval/basics// 1.17 ± 0.04 μs 1.17 ± 0.031 μs 1 ± 0.043
bareinterval/basics/abs 0.16 ± 0.011 μs 0.16 ± 0.011 μs 1 ± 0.097
bareinterval/basics/acos 2.69 ± 0.011 μs 2.71 ± 0.01 μs 0.989 ± 0.0054
bareinterval/basics/asin 2.98 ± 0.03 μs 2.99 ± 0.031 μs 0.997 ± 0.014
bareinterval/basics/atan 13 ± 0.25 μs 13.2 ± 0.16 μs 0.981 ± 0.022
bareinterval/basics/cos 0.0684 ± 0.021 ms 0.0682 ± 0.02 ms 1 ± 0.42
bareinterval/basics/cosh 7.17 ± 0.031 μs 7.16 ± 0.031 μs 1 ± 0.0061
bareinterval/basics/exp 4.28 ± 0.05 μs 4.27 ± 0.05 μs 1 ± 0.017
bareinterval/basics/inv 0.902 ± 0.021 μs 0.902 ± 0.04 μs 1 ± 0.05
bareinterval/basics/log 6.4 ± 0.031 μs 6.28 ± 0.04 μs 1.02 ± 0.0082
bareinterval/basics/sin 0.0671 ± 0.02 ms 0.0669 ± 0.02 ms 1 ± 0.42
bareinterval/basics/sinh 10.1 ± 0.06 μs 10.1 ± 0.061 μs 0.999 ± 0.0085
bareinterval/basics/sqrt 1.1 ± 0.02 μs 1.09 ± 0.02 μs 1.01 ± 0.026
bareinterval/basics/tan 0.0383 ± 0.0024 ms 0.0386 ± 0.0025 ms 0.991 ± 0.091
bareinterval/basics/tanh 0.306 ± 0.0096 ms 0.306 ± 0.0096 ms 0.998 ± 0.044
interval/basics/* 2.77 ± 0.06 μs 2.98 ± 0.071 μs 0.929 ± 0.03
interval/basics/+ 1.34 ± 0.031 μs 1.53 ± 0.049 μs 0.875 ± 0.035
interval/basics/- 1.36 ± 0.031 μs 1.56 ± 0.04 μs 0.871 ± 0.03
interval/basics// 1.83 ± 0.2 μs 2.04 ± 0.25 μs 0.898 ± 0.15
interval/basics/abs 0.351 ± 0.05 μs 0.351 ± 0.07 μs 1 ± 0.25
interval/basics/acos 3.28 ± 0.06 μs 3.28 ± 0.05 μs 1 ± 0.024
interval/basics/asin 3.56 ± 0.041 μs 3.56 ± 0.049 μs 1 ± 0.018
interval/basics/atan 13.3 ± 0.21 μs 13.2 ± 0.22 μs 1 ± 0.023
interval/basics/cos 0.0519 ± 0.018 ms 0.0524 ± 0.019 ms 0.991 ± 0.5
interval/basics/cosh 8.91 ± 0.08 μs 8.92 ± 0.071 μs 0.999 ± 0.012
interval/basics/exp 4.77 ± 0.06 μs 4.79 ± 0.051 μs 0.996 ± 0.016
interval/basics/inv 1.35 ± 0.029 μs 1.39 ± 0.039 μs 0.971 ± 0.034
interval/basics/log 2.52 ± 0.051 μs 2.5 ± 0.06 μs 1 ± 0.032
interval/basics/sin 0.0672 ± 0.0033 ms 0.0675 ± 0.0034 ms 0.996 ± 0.07
interval/basics/sinh 10.5 ± 0.071 μs 10.5 ± 0.081 μs 0.996 ± 0.01
interval/basics/sqrt 1.53 ± 0.05 μs 1.55 ± 0.05 μs 0.988 ± 0.045
interval/basics/tan 0.0387 ± 0.0019 ms 0.0388 ± 0.002 ms 0.998 ± 0.069
interval/basics/tanh 0.306 ± 0.012 ms 0.307 ± 0.013 ms 0.998 ± 0.059
time_to_load 0.107 ± 0.00074 s 0.108 ± 0.0023 s 0.994 ± 0.022
Memory benchmarks
master f64c50b... master / f64c50b...
BigFloat MPFI/basics/* 0.424 k allocs: 21.3 kB 0.424 k allocs: 21.3 kB 1
BigFloat MPFI/basics/+ 0.302 k allocs: 16.5 kB 0.302 k allocs: 16.5 kB 1
BigFloat MPFI/basics/- 0.402 k allocs: 20.4 kB 0.402 k allocs: 20.4 kB 1
BigFloat MPFI/basics// 0.345 k allocs: 18.2 kB 0.345 k allocs: 18.2 kB 1
BigFloat MPFI/basics/abs 0.324 k allocs: 17.4 kB 0.324 k allocs: 17.4 kB 1
BigFloat MPFI/basics/acos 1.24 k allocs: 0.0445 MB 1.24 k allocs: 0.0445 MB 1
BigFloat MPFI/basics/asin 1.08 k allocs: 0.0417 MB 1.08 k allocs: 0.0417 MB 1
BigFloat MPFI/basics/atan 2.14 k allocs: 0.0543 MB 2.14 k allocs: 0.0543 MB 1
BigFloat MPFI/basics/cos 2.9 k allocs: 0.0975 MB 2.9 k allocs: 0.0975 MB 1
BigFloat MPFI/basics/cosh 0.781 k allocs: 0.0322 MB 0.781 k allocs: 0.0322 MB 1
BigFloat MPFI/basics/exp 0.902 k allocs: 0.036 MB 0.902 k allocs: 0.036 MB 1
BigFloat MPFI/basics/inv 0.351 k allocs: 18.4 kB 0.351 k allocs: 18.4 kB 1
BigFloat MPFI/basics/log 0.407 k allocs: 20.6 kB 0.407 k allocs: 20.6 kB 1
BigFloat MPFI/basics/sin 3.18 k allocs: 0.106 MB 3.18 k allocs: 0.106 MB 1
BigFloat MPFI/basics/sinh 0.915 k allocs: 0.0369 MB 0.915 k allocs: 0.0369 MB 1
BigFloat MPFI/basics/sqrt 0.302 k allocs: 16.5 kB 0.302 k allocs: 16.5 kB 1
BigFloat MPFI/basics/tan 2.8 k allocs: 0.098 MB 2.8 k allocs: 0.098 MB 1
BigFloat MPFI/basics/tanh 0.908 k allocs: 0.0362 MB 0.908 k allocs: 0.0362 MB 1
BigFloat bareinterval/basics/* 0.262 k allocs: 26 kB 0.262 k allocs: 26 kB 1
BigFloat bareinterval/basics/+ 0.202 k allocs: 20.4 kB 0.202 k allocs: 20.4 kB 1
BigFloat bareinterval/basics/- 0.202 k allocs: 20.4 kB 0.202 k allocs: 20.4 kB 1
BigFloat bareinterval/basics// 0.1 k allocs: 10.8 kB 0.1 k allocs: 10.8 kB 1
BigFloat bareinterval/basics/abs 0.199 k allocs: 20.1 kB 0.199 k allocs: 20.1 kB 1
BigFloat bareinterval/basics/acos 1.27 k allocs: 0.0692 MB 1.27 k allocs: 0.0692 MB 1
BigFloat bareinterval/basics/asin 1.17 k allocs: 0.0659 MB 1.17 k allocs: 0.0659 MB 1
BigFloat bareinterval/basics/atan 2.04 k allocs: 0.058 MB 2.04 k allocs: 0.058 MB 1
BigFloat bareinterval/basics/cos 2.45 k allocs: 0.185 MB 2.45 k allocs: 0.185 MB 1
BigFloat bareinterval/basics/cosh 1.01 k allocs: 0.0671 MB 1.01 k allocs: 0.0671 MB 1
BigFloat bareinterval/basics/exp 0.802 k allocs: 0.0397 MB 0.802 k allocs: 0.0397 MB 1
BigFloat bareinterval/basics/inv 0.198 k allocs: 20 kB 0.198 k allocs: 20 kB 1
BigFloat bareinterval/basics/log 0.616 k allocs: 0.0522 MB 0.616 k allocs: 0.0522 MB 1
BigFloat bareinterval/basics/sin 2.9 k allocs: 0.197 MB 2.9 k allocs: 0.197 MB 1
BigFloat bareinterval/basics/sinh 0.815 k allocs: 0.0407 MB 0.815 k allocs: 0.0407 MB 1
BigFloat bareinterval/basics/sqrt 0.26 k allocs: 25.8 kB 0.26 k allocs: 25.8 kB 1
BigFloat bareinterval/basics/tan 1.67 k allocs: 0.124 MB 1.67 k allocs: 0.124 MB 1
BigFloat bareinterval/basics/tanh 0.808 k allocs: 0.0399 MB 0.808 k allocs: 0.0399 MB 1
BigFloat interval/basics/* 0.263 k allocs: 26.8 kB 0.263 k allocs: 26.8 kB 1
BigFloat interval/basics/+ 0.203 k allocs: 21.2 kB 0.203 k allocs: 21.2 kB 1
BigFloat interval/basics/- 0.203 k allocs: 21.2 kB 0.203 k allocs: 21.2 kB 1
BigFloat interval/basics// 0.101 k allocs: 11.6 kB 0.101 k allocs: 11.6 kB 1
BigFloat interval/basics/abs 0.2 k allocs: 20.9 kB 0.2 k allocs: 20.9 kB 1
BigFloat interval/basics/acos 1.71 k allocs: 0.11 MB 1.71 k allocs: 0.11 MB 0.998
BigFloat interval/basics/asin 1.47 k allocs: 0.0944 MB 1.47 k allocs: 0.0946 MB 0.998
BigFloat interval/basics/atan 2.04 k allocs: 0.0595 MB 2.04 k allocs: 0.0593 MB 1
BigFloat interval/basics/cos 2.45 k allocs: 0.186 MB 2.45 k allocs: 0.186 MB 1
BigFloat interval/basics/cosh 1.01 k allocs: 0.068 MB 1.01 k allocs: 0.068 MB 1
BigFloat interval/basics/exp 0.803 k allocs: 0.0407 MB 0.803 k allocs: 0.0407 MB 0.999
BigFloat interval/basics/inv 0.199 k allocs: 20.8 kB 0.199 k allocs: 20.8 kB 1
BigFloat interval/basics/log 0.917 k allocs: 0.0805 MB 0.917 k allocs: 0.0805 MB 1
BigFloat interval/basics/sin 2.9 k allocs: 0.198 MB 2.9 k allocs: 0.198 MB 1
BigFloat interval/basics/sinh 0.816 k allocs: 0.0416 MB 0.816 k allocs: 0.0416 MB 0.999
BigFloat interval/basics/sqrt 0.714 k allocs: 0.0675 MB 0.714 k allocs: 0.0675 MB 1
BigFloat interval/basics/tan 1.67 k allocs: 0.125 MB 1.67 k allocs: 0.125 MB 1
BigFloat interval/basics/tanh 0.809 k allocs: 0.0409 MB 0.809 k allocs: 0.0408 MB 1
bareinterval/basics/* 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/+ 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/- 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics// 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/abs 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/acos 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/asin 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/atan 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/cos 0.56 k allocs: 0.0423 MB 0.56 k allocs: 0.0423 MB 1
bareinterval/basics/cosh 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/exp 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/inv 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/log 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/sin 0.56 k allocs: 0.0423 MB 0.56 k allocs: 0.0423 MB 1
bareinterval/basics/sinh 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/sqrt 2 allocs: 1.62 kB 2 allocs: 1.62 kB 1
bareinterval/basics/tan 0.29 k allocs: 23.1 kB 0.29 k allocs: 23.1 kB 1
bareinterval/basics/tanh 1.03 k allocs: 0.0359 MB 1.03 k allocs: 0.0359 MB 1
interval/basics/* 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/+ 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/- 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics// 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/abs 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/acos 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/asin 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/atan 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/cos 0.561 k allocs: 0.0431 MB 0.561 k allocs: 0.0431 MB 1
interval/basics/cosh 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/exp 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/inv 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/log 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/sin 0.561 k allocs: 0.0431 MB 0.561 k allocs: 0.0431 MB 1
interval/basics/sinh 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/sqrt 3 allocs: 2.45 kB 3 allocs: 2.45 kB 1
interval/basics/tan 0.291 k allocs: 24 kB 0.291 k allocs: 24 kB 1
interval/basics/tanh 1.03 k allocs: 0.0367 MB 1.03 k allocs: 0.0367 MB 1
time_to_load 0.201 k allocs: 11.8 kB 0.201 k allocs: 11.8 kB 1

@OlivierHnt

OlivierHnt commented Sep 6, 2026

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Looks good to me. I wonder whether we just never got around implementing ForwardDiff for BareInterval, or if there was a deeper reason?
@Kolaru can you have a look?

Kolaru
Kolaru reviewed Sep 8, 2026
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@Kolaru Kolaru left a comment

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Thanks a lot for the PR!

As I mention in comment, to me it looks like that this PR introduce a design that is not guaranteed. And (unfortunately T_T), I think we need to figure that out before we can move forward.

Comment thread ext/IntervalArithmeticForwardDiffExt.jl Outdated
Comment thread ext/IntervalArithmeticForwardDiffExt.jl Outdated
Comment thread ext/IntervalArithmeticForwardDiffExt.jl Outdated
@timholy
Support integer and rational BareInterval powers
28fbdb2 
Add integer and rational exponents, including literal integer powers.

Assisted-by: Claude Opus 5 <noreply@anthropic.com>
@timholy
Support ForwardDiff duals over BareInterval
18ecfa1 
Add differentiation and arithmetic for bare intervals in nested duals.
Use thin-zero checks for interval partials in power rules and, when
supported by ForwardDiff, its zero-partial checks.

Treat real constants and derivative coefficients as exact. Callers who
need to track this assumption through `isguaranteed` should use decorated
intervals.

Assisted-by: Claude Fable 5 (claude-fable-5) <noreply@anthropic.com>
@timholy

timholy commented Sep 19, 2026

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I've rebased on current master and hopefully addressed @Kolaru's concerns.

@timholy
Vendor FD code to support BareInterval
f64c50b 
This allows FD support without defining operations against inexact quantities

Assisted-by: Claude Fable 5.1 <noreply@anthropic.com>
@timholy

timholy commented Sep 19, 2026

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If you do want to merge this as two commits, LMK and I can squash everything after the first commit together, leaving the first distinct.

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@timholy @OlivierHnt @Kolaru