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Add :ulp rounding mode based on prevfloat and nextfloat#744

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OlivierHnt merged 3 commits intoJuliaIntervals:masterfrom
OlivierHnt:core-math
Mar 30, 2026
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Add :ulp rounding mode based on prevfloat and nextfloat#744
OlivierHnt merged 3 commits intoJuliaIntervals:masterfrom
OlivierHnt:core-math

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@OlivierHnt OlivierHnt commented Feb 20, 2026 •
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This PR introduces the :ulp rounding mode, which uses the CORE-MATH functions as much as possible (fallback on MPFR as for the :correct rounding mode).

The motivation is to be able to opt for a faster rounding mode (at the cost of accuracy), and to be GPU compatible.

@OlivierHnt OlivierHnt marked this pull request as draft February 20, 2026 11:38
@OlivierHnt OlivierHnt marked this pull request as ready for review February 20, 2026 18:59
@OlivierHnt OlivierHnt linked an issue Mar 1, 2026 that may be closed by this pull request
Replacing CRlibm with CORE-MATH #592
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@Kolaru Kolaru closed this Mar 3, 2026
@Kolaru Kolaru reopened this Mar 3, 2026
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github-actions Bot commented Mar 3, 2026 •
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Benchmark Results (Julia v1)

Time benchmarks
master 42bb7df... master / 42bb7df...
BigFloat MPFI/basics/* 25.6 ± 3.6 μs 25.4 ± 3.7 μs 1.01 ± 0.21
BigFloat MPFI/basics/+ 12.8 ± 3.5 μs 12.7 ± 3.5 μs 1.01 ± 0.39
BigFloat MPFI/basics/- 17.7 ± 3.6 μs 17.9 ± 3.5 μs 0.99 ± 0.28
BigFloat MPFI/basics// 19.4 ± 3.8 μs 19.5 ± 3.6 μs 0.994 ± 0.26
BigFloat MPFI/basics/abs 10.4 ± 3.5 μs 10.5 ± 3.4 μs 0.996 ± 0.47
BigFloat MPFI/basics/acos 0.681 ± 0.01 ms 0.679 ± 0.01 ms 1 ± 0.021
BigFloat MPFI/basics/asin 0.66 ± 0.012 ms 0.664 ± 0.012 ms 0.994 ± 0.025
BigFloat MPFI/basics/atan 2.1 ± 0.0097 ms 2.1 ± 0.0086 ms 1 ± 0.0062
BigFloat MPFI/basics/cos 0.364 ± 0.011 ms 0.362 ± 0.011 ms 1.01 ± 0.044
BigFloat MPFI/basics/cosh 0.431 ± 0.013 ms 0.431 ± 0.012 ms 1 ± 0.04
BigFloat MPFI/basics/exp 0.501 ± 0.012 ms 0.503 ± 0.012 ms 0.996 ± 0.033
BigFloat MPFI/basics/inv 20 ± 3.5 μs 19.8 ± 3.6 μs 1.01 ± 0.26
BigFloat MPFI/basics/log 0.471 ± 0.011 ms 0.472 ± 0.012 ms 0.998 ± 0.035
BigFloat MPFI/basics/sin 0.469 ± 0.013 ms 0.472 ± 0.013 ms 0.993 ± 0.038
BigFloat MPFI/basics/sinh 0.574 ± 0.011 ms 0.575 ± 0.011 ms 0.999 ± 0.027
BigFloat MPFI/basics/sqrt 27.8 ± 6.4 μs 27.7 ± 6.8 μs 1.01 ± 0.34
BigFloat MPFI/basics/tan 0.389 ± 0.012 ms 0.388 ± 0.012 ms 1 ± 0.042
BigFloat MPFI/basics/tanh 0.584 ± 0.012 ms 0.585 ± 0.012 ms 0.999 ± 0.028
BigFloat bareinterval/basics/* 0.0433 ± 0.0023 ms 0.0425 ± 0.0026 ms 1.02 ± 0.082
BigFloat bareinterval/basics/+ 23.4 ± 3.4 μs 22.9 ± 3.4 μs 1.02 ± 0.21
BigFloat bareinterval/basics/- 23.9 ± 3.3 μs 23.8 ± 3.5 μs 1 ± 0.2
BigFloat bareinterval/basics// 20.4 ± 5 μs 20.6 ± 5 μs 0.99 ± 0.34
BigFloat bareinterval/basics/abs 15.5 ± 3.3 μs 15.6 ± 3.3 μs 0.993 ± 0.29
BigFloat bareinterval/basics/acos 0.718 ± 0.023 ms 0.717 ± 0.024 ms 1 ± 0.046
BigFloat bareinterval/basics/asin 0.698 ± 0.023 ms 0.698 ± 0.023 ms 1 ± 0.047
BigFloat bareinterval/basics/atan 2.11 ± 0.0088 ms 2.12 ± 0.0095 ms 0.998 ± 0.0061
BigFloat bareinterval/basics/cos 0.344 ± 0.085 ms 0.347 ± 0.086 ms 0.991 ± 0.35
BigFloat bareinterval/basics/cosh 0.47 ± 0.025 ms 0.473 ± 0.025 ms 0.995 ± 0.074
BigFloat bareinterval/basics/exp 0.507 ± 0.011 ms 0.518 ± 0.013 ms 0.978 ± 0.033
BigFloat bareinterval/basics/inv 24.9 ± 3.2 μs 27.1 ± 3.3 μs 0.918 ± 0.16
BigFloat bareinterval/basics/log 0.515 ± 0.03 ms 0.517 ± 0.03 ms 0.996 ± 0.081
BigFloat bareinterval/basics/sin 0.48 ± 0.091 ms 0.482 ± 0.092 ms 0.998 ± 0.27
BigFloat bareinterval/basics/sinh 0.579 ± 0.012 ms 0.583 ± 0.012 ms 0.994 ± 0.028
BigFloat bareinterval/basics/sqrt 0.0369 ± 0.003 ms 0.0359 ± 0.003 ms 1.03 ± 0.12
BigFloat bareinterval/basics/tan 0.328 ± 0.057 ms 0.329 ± 0.057 ms 0.997 ± 0.24
BigFloat bareinterval/basics/tanh 0.595 ± 0.011 ms 0.595 ± 0.012 ms 1 ± 0.027
BigFloat interval/basics/* 0.0468 ± 0.002 ms 0.0472 ± 0.002 ms 0.992 ± 0.059
BigFloat interval/basics/+ 25.9 ± 8.3 μs 26 ± 8.2 μs 0.995 ± 0.45
BigFloat interval/basics/- 26.6 ± 8.8 μs 26.2 ± 8.4 μs 1.02 ± 0.47
BigFloat interval/basics// 25.3 ± 4.9 μs 25.2 ± 4.8 μs 1 ± 0.27
BigFloat interval/basics/abs 15 ± 7.8 μs 14.9 ± 7.8 μs 1 ± 0.74
BigFloat interval/basics/acos 0.711 ± 0.047 ms 0.711 ± 0.044 ms 0.999 ± 0.091
BigFloat interval/basics/asin 0.692 ± 0.038 ms 0.693 ± 0.038 ms 0.999 ± 0.077
BigFloat interval/basics/atan 2.11 ± 0.0067 ms 2.12 ± 0.0083 ms 0.996 ± 0.005
BigFloat interval/basics/cos 0.339 ± 0.018 ms 0.341 ± 0.016 ms 0.993 ± 0.069
BigFloat interval/basics/cosh 0.466 ± 0.023 ms 0.47 ± 0.023 ms 0.992 ± 0.069
BigFloat interval/basics/exp 0.518 ± 0.011 ms 0.521 ± 0.011 ms 0.995 ± 0.03
BigFloat interval/basics/inv 29.9 ± 7.6 μs 0.0318 ± 0.0078 ms 0.942 ± 0.33
BigFloat interval/basics/log 0.511 ± 0.045 ms 0.515 ± 0.044 ms 0.993 ± 0.12
BigFloat interval/basics/sin 0.488 ± 0.024 ms 0.489 ± 0.023 ms 0.997 ± 0.067
BigFloat interval/basics/sinh 0.589 ± 0.011 ms 0.591 ± 0.012 ms 0.997 ± 0.027
BigFloat interval/basics/sqrt 0.0428 ± 0.031 ms 0.0428 ± 0.031 ms 1 ± 1
BigFloat interval/basics/tan 0.284 ± 0.018 ms 0.284 ± 0.018 ms 0.997 ± 0.089
BigFloat interval/basics/tanh 0.604 ± 0.011 ms 0.603 ± 0.012 ms 1 ± 0.027
bareinterval/basics/* 2.01 ± 0.05 μs 1.97 ± 0.04 μs 1.02 ± 0.033
bareinterval/basics/+ 0.541 ± 0.01 μs 0.541 ± 0.01 μs 1 ± 0.026
bareinterval/basics/- 0.561 ± 0.001 μs 0.551 ± 0.011 μs 1.02 ± 0.02
bareinterval/basics// 1.24 ± 0.02 μs 1.23 ± 0.029 μs 1.01 ± 0.029
bareinterval/basics/abs 0.22 ± 0.01 μs 0.22 ± 0.001 μs 1 ± 0.046
bareinterval/basics/acos 2.89 ± 0.031 μs 2.89 ± 0.031 μs 1 ± 0.015
bareinterval/basics/asin 3.15 ± 0.03 μs 3.18 ± 0.031 μs 0.991 ± 0.014
bareinterval/basics/atan 12.9 ± 0.2 μs 13 ± 0.21 μs 0.991 ± 0.022
bareinterval/basics/cos 0.0502 ± 0.0027 ms 0.0512 ± 0.0069 ms 0.981 ± 0.14
bareinterval/basics/cosh 7.26 ± 0.04 μs 7.26 ± 0.04 μs 1 ± 0.0078
bareinterval/basics/exp 4.3 ± 0.04 μs 4.29 ± 0.05 μs 1 ± 0.015
bareinterval/basics/inv 1.06 ± 0.02 μs 1.07 ± 0.03 μs 0.991 ± 0.033
bareinterval/basics/log 2.11 ± 0.06 μs 2.11 ± 0.02 μs 1 ± 0.03
bareinterval/basics/sin 0.0492 ± 0.019 ms 0.0503 ± 0.018 ms 0.978 ± 0.51
bareinterval/basics/sinh 9.97 ± 0.06 μs 9.99 ± 0.06 μs 0.998 ± 0.0085
bareinterval/basics/sqrt 1.18 ± 0.02 μs 1.18 ± 0.02 μs 1 ± 0.024
bareinterval/basics/tan 29.1 ± 0.33 μs 29.2 ± 0.37 μs 0.995 ± 0.017
bareinterval/basics/tanh 0.295 ± 0.0093 ms 0.295 ± 0.01 ms 1 ± 0.047
interval/basics/* 3.42 ± 0.079 μs 3.2 ± 0.07 μs 1.07 ± 0.034
interval/basics/+ 1.65 ± 0.07 μs 1.49 ± 0.081 μs 1.11 ± 0.076
interval/basics/- 1.68 ± 0.071 μs 1.53 ± 0.08 μs 1.1 ± 0.074
interval/basics// 2.65 ± 0.06 μs 2.48 ± 0.07 μs 1.07 ± 0.039
interval/basics/abs 0.942 ± 0.14 μs 0.952 ± 0.15 μs 0.989 ± 0.21
interval/basics/acos 5.21 ± 0.079 μs 5.01 ± 0.08 μs 1.04 ± 0.023
interval/basics/asin 5.3 ± 0.07 μs 5.17 ± 0.069 μs 1.02 ± 0.019
interval/basics/atan 14.7 ± 0.19 μs 14.6 ± 0.19 μs 1.01 ± 0.019
interval/basics/cos 0.0679 ± 0.019 ms 0.07 ± 0.019 ms 0.971 ± 0.39
interval/basics/cosh 10.3 ± 0.079 μs 10.3 ± 0.071 μs 1 ± 0.01
interval/basics/exp 6.64 ± 0.091 μs 6.83 ± 0.11 μs 0.972 ± 0.021
interval/basics/inv 2.04 ± 0.06 μs 2.07 ± 0.09 μs 0.986 ± 0.052
interval/basics/log 5.05 ± 0.06 μs 4.94 ± 0.06 μs 1.02 ± 0.017
interval/basics/sin 0.0677 ± 0.02 ms 0.0679 ± 0.02 ms 0.997 ± 0.41
interval/basics/sinh 13.3 ± 0.08 μs 13.2 ± 0.079 μs 1.01 ± 0.0086
interval/basics/sqrt 2.13 ± 0.081 μs 3.4 ± 1.2 μs 0.628 ± 0.22
interval/basics/tan 0.0391 ± 0.0019 ms 0.0394 ± 0.0019 ms 0.992 ± 0.067
interval/basics/tanh 0.306 ± 0.0069 ms 0.309 ± 0.0069 ms 0.993 ± 0.032
time_to_load 0.107 ± 0.00074 s 0.109 ± 0.002 s 0.982 ± 0.019
Memory benchmarks
master 42bb7df... master / 42bb7df...
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: 0.0355 MB 1.08 k allocs: 0.0355 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 1.33 k allocs: 0.0741 MB 1.33 k allocs: 0.0741 MB 1
BigFloat bareinterval/basics/asin 1.23 k allocs: 0.0647 MB 1.23 k allocs: 0.0647 MB 1
BigFloat bareinterval/basics/atan 2.04 k allocs: 0.08 MB 2.04 k allocs: 0.08 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 0.804 k allocs: 0.0694 MB 0.804 k allocs: 0.0694 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 0.304 k allocs: 29.9 kB 0.304 k allocs: 29.9 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 1.77 k allocs: 0.115 MB 1.77 k allocs: 0.115 MB 1
BigFloat interval/basics/asin 1.53 k allocs: 0.0932 MB 1.53 k allocs: 0.0932 MB 1
BigFloat interval/basics/atan 2.04 k allocs: 0.0812 MB 2.04 k allocs: 0.0812 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: 0.0682 MB 1.01 k allocs: 0.0681 MB 1
BigFloat interval/basics/exp 0.803 k allocs: 0.0409 MB 0.803 k allocs: 0.041 MB 0.997
BigFloat interval/basics/inv 0.199 k allocs: 20.8 kB 0.199 k allocs: 20.8 kB 1
BigFloat interval/basics/log 1.1 k allocs: 0.0977 MB 1.1 k allocs: 0.0977 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: 0.042 MB 0.816 k allocs: 0.0418 MB 1
BigFloat interval/basics/sqrt 0.758 k allocs: 0.0715 MB 0.758 k allocs: 0.0715 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: 0.0411 MB 0.809 k allocs: 0.041 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 kB 0.29 k allocs: 23 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: 24.4 kB 0.291 k allocs: 24.4 kB 1
interval/basics/tanh 1.03 k allocs: 0.0367 MB 1.03 k allocs: 0.0367 MB 1
time_to_load 0.145 k allocs: 11 kB 0.154 k allocs: 11.4 kB 0.963

@OlivierHnt OlivierHnt merged commit bbb8340 into JuliaIntervals:master Mar 30, 2026
22 checks passed
@OlivierHnt OlivierHnt deleted the core-math branch March 30, 2026 01:52
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Replacing CRlibm with CORE-MATH

2 participants

@OlivierHnt @Kolaru