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Improved matrix exponential for real matrices#746

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Improved matrix exponential for real matrices#746
BaronNashville wants to merge 1 commit intoJuliaIntervals:masterfrom
BaronNashville:master

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@BaronNashville BaronNashville commented Mar 12, 2026

The exponential of some real interval matrices outputted complex intervals. Added a check to rule that case out.

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Benchmark Results (Julia v1)

Time benchmarks
master 5fe89c0... master / 5fe89c0...
BigFloat MPFI/basics/* 25.3 ± 4 μs 24.8 ± 4 μs 1.02 ± 0.23
BigFloat MPFI/basics/+ 13.1 ± 4.1 μs 12.6 ± 4.1 μs 1.04 ± 0.47
BigFloat MPFI/basics/- 17 ± 3.9 μs 17.5 ± 4 μs 0.972 ± 0.31
BigFloat MPFI/basics// 19.3 ± 4 μs 19 ± 4.1 μs 1.02 ± 0.31
BigFloat MPFI/basics/abs 10.3 ± 3.8 μs 11.1 ± 4 μs 0.934 ± 0.48
BigFloat MPFI/basics/acos 0.67 ± 0.0089 ms 0.671 ± 0.0084 ms 0.998 ± 0.018
BigFloat MPFI/basics/asin 0.66 ± 0.0094 ms 0.659 ± 0.012 ms 1 ± 0.023
BigFloat MPFI/basics/atan 2.07 ± 0.01 ms 2.07 ± 0.0076 ms 1 ± 0.0061
BigFloat MPFI/basics/cos 0.355 ± 0.0094 ms 0.356 ± 0.0093 ms 0.997 ± 0.037
BigFloat MPFI/basics/cosh 0.426 ± 0.012 ms 0.426 ± 0.012 ms 1 ± 0.038
BigFloat MPFI/basics/exp 0.499 ± 0.01 ms 0.498 ± 0.011 ms 1 ± 0.03
BigFloat MPFI/basics/inv 18.7 ± 3.9 μs 19.3 ± 4 μs 0.97 ± 0.28
BigFloat MPFI/basics/log 0.468 ± 0.011 ms 0.468 ± 0.0089 ms 1 ± 0.03
BigFloat MPFI/basics/sin 0.458 ± 0.01 ms 0.458 ± 0.01 ms 1 ± 0.031
BigFloat MPFI/basics/sinh 0.576 ± 0.0099 ms 0.576 ± 0.0098 ms 1 ± 0.024
BigFloat MPFI/basics/sqrt 28.8 ± 7.9 μs 29.1 ± 7.9 μs 0.99 ± 0.38
BigFloat MPFI/basics/tan 0.38 ± 0.0098 ms 0.381 ± 0.01 ms 0.997 ± 0.037
BigFloat MPFI/basics/tanh 0.58 ± 0.01 ms 0.579 ± 0.01 ms 1 ± 0.025
BigFloat bareinterval/basics/* 0.0446 ± 0.0026 ms 0.043 ± 0.0025 ms 1.04 ± 0.086
BigFloat bareinterval/basics/+ 23.8 ± 3.7 μs 24.4 ± 3.7 μs 0.973 ± 0.21
BigFloat bareinterval/basics/- 23.6 ± 3.7 μs 24 ± 3.8 μs 0.981 ± 0.22
BigFloat bareinterval/basics// 20.7 ± 5.8 μs 20.9 ± 5.7 μs 0.99 ± 0.39
BigFloat bareinterval/basics/abs 16.8 ± 3.5 μs 16.7 ± 3.6 μs 1.01 ± 0.3
BigFloat bareinterval/basics/acos 0.708 ± 0.02 ms 0.709 ± 0.028 ms 0.999 ± 0.049
BigFloat bareinterval/basics/asin 0.689 ± 0.023 ms 0.695 ± 0.026 ms 0.991 ± 0.049
BigFloat bareinterval/basics/atan 2.09 ± 0.0091 ms 2.1 ± 0.0072 ms 0.992 ± 0.0055
BigFloat bareinterval/basics/cos 0.337 ± 0.098 ms 0.339 ± 0.099 ms 0.993 ± 0.41
BigFloat bareinterval/basics/cosh 0.468 ± 0.028 ms 0.468 ± 0.028 ms 1 ± 0.085
BigFloat bareinterval/basics/exp 0.508 ± 0.011 ms 0.507 ± 0.01 ms 1 ± 0.029
BigFloat bareinterval/basics/inv 26.5 ± 3.6 μs 27.1 ± 3.7 μs 0.978 ± 0.19
BigFloat bareinterval/basics/log 0.514 ± 0.034 ms 0.518 ± 0.034 ms 0.993 ± 0.092
BigFloat bareinterval/basics/sin 0.471 ± 0.1 ms 0.471 ± 0.1 ms 0.999 ± 0.3
BigFloat bareinterval/basics/sinh 0.584 ± 0.012 ms 0.583 ± 0.011 ms 1 ± 0.028
BigFloat bareinterval/basics/sqrt 0.0381 ± 0.003 ms 0.038 ± 0.0029 ms 1 ± 0.11
BigFloat bareinterval/basics/tan 0.332 ± 0.065 ms 0.332 ± 0.065 ms 0.999 ± 0.28
BigFloat bareinterval/basics/tanh 0.591 ± 0.012 ms 0.591 ± 0.011 ms 1 ± 0.027
BigFloat interval/basics/* 0.0484 ± 0.0023 ms 0.0464 ± 0.0021 ms 1.04 ± 0.069
BigFloat interval/basics/+ 26.7 ± 9.4 μs 27 ± 9.7 μs 0.988 ± 0.5
BigFloat interval/basics/- 27 ± 9.6 μs 26.7 ± 9.6 μs 1.01 ± 0.51
BigFloat interval/basics// 25.7 ± 5.6 μs 25.8 ± 5.6 μs 0.995 ± 0.3
BigFloat interval/basics/abs 16.1 ± 9.1 μs 16.1 ± 9.1 μs 0.996 ± 0.8
BigFloat interval/basics/acos 0.699 ± 0.051 ms 0.704 ± 0.052 ms 0.993 ± 0.1
BigFloat interval/basics/asin 0.681 ± 0.042 ms 0.683 ± 0.042 ms 0.997 ± 0.087
BigFloat interval/basics/atan 2.09 ± 0.008 ms 2.11 ± 0.006 ms 0.99 ± 0.0047
BigFloat interval/basics/cos 0.333 ± 0.015 ms 0.335 ± 0.013 ms 0.994 ± 0.059
BigFloat interval/basics/cosh 0.459 ± 0.027 ms 0.46 ± 0.026 ms 0.999 ± 0.082
BigFloat interval/basics/exp 0.514 ± 0.011 ms 0.514 ± 0.01 ms 1 ± 0.029
BigFloat interval/basics/inv 30.9 ± 8.2 μs 31.4 ± 8.6 μs 0.982 ± 0.37
BigFloat interval/basics/log 0.505 ± 0.051 ms 0.508 ± 0.05 ms 0.994 ± 0.14
BigFloat interval/basics/sin 0.479 ± 0.023 ms 0.478 ± 0.016 ms 1 ± 0.06
BigFloat interval/basics/sinh 0.59 ± 0.011 ms 0.59 ± 0.01 ms 1 ± 0.025
BigFloat interval/basics/sqrt 0.0432 ± 0.036 ms 0.0423 ± 0.036 ms 1.02 ± 1.2
BigFloat interval/basics/tan 0.278 ± 0.015 ms 0.279 ± 0.014 ms 0.997 ± 0.075
BigFloat interval/basics/tanh 0.598 ± 0.012 ms 0.598 ± 0.011 ms 1 ± 0.027
bareinterval/basics/* 1.95 ± 0.04 μs 1.99 ± 0.041 μs 0.98 ± 0.028
bareinterval/basics/+ 0.531 ± 0.01 μs 0.531 ± 0.02 μs 1 ± 0.042
bareinterval/basics/- 0.551 ± 0.01 μs 0.551 ± 0.011 μs 1 ± 0.027
bareinterval/basics// 1.22 ± 0.04 μs 1.23 ± 0.02 μs 0.992 ± 0.036
bareinterval/basics/abs 0.231 ± 0.01 μs 0.211 ± 0.02 μs 1.09 ± 0.11
bareinterval/basics/acos 2.93 ± 0.039 μs 2.89 ± 0.03 μs 1.01 ± 0.017
bareinterval/basics/asin 3.18 ± 0.03 μs 3.16 ± 0.021 μs 1.01 ± 0.012
bareinterval/basics/atan 13 ± 0.21 μs 13 ± 0.2 μs 0.999 ± 0.022
bareinterval/basics/cos 0.0492 ± 0.01 ms 0.0493 ± 0.011 ms 0.999 ± 0.3
bareinterval/basics/cosh 7.28 ± 0.07 μs 7.26 ± 0.031 μs 1 ± 0.011
bareinterval/basics/exp 4.33 ± 0.059 μs 4.31 ± 0.05 μs 1 ± 0.018
bareinterval/basics/inv 1.1 ± 0.04 μs 1.07 ± 0.02 μs 1.03 ± 0.042
bareinterval/basics/log 6.48 ± 0.03 μs 2.11 ± 0.01 μs 3.07 ± 0.02
bareinterval/basics/sin 0.0484 ± 0.021 ms 0.0485 ± 0.021 ms 0.998 ± 0.61
bareinterval/basics/sinh 9.99 ± 0.059 μs 9.99 ± 0.069 μs 1 ± 0.0091
bareinterval/basics/sqrt 1.2 ± 0.03 μs 1.18 ± 0.021 μs 1.02 ± 0.031
bareinterval/basics/tan 28.5 ± 0.29 μs 28.4 ± 0.25 μs 1 ± 0.014
bareinterval/basics/tanh 0.292 ± 0.0086 ms 0.288 ± 0.0084 ms 1.02 ± 0.042
interval/basics/* 3.24 ± 0.071 μs 3.22 ± 0.07 μs 1.01 ± 0.031
interval/basics/+ 1.52 ± 0.09 μs 1.49 ± 0.061 μs 1.02 ± 0.073
interval/basics/- 1.53 ± 0.1 μs 1.53 ± 0.061 μs 1 ± 0.076
interval/basics// 2.48 ± 0.08 μs 2.46 ± 0.061 μs 1.01 ± 0.041
interval/basics/abs 0.971 ± 0.13 μs 0.941 ± 0.12 μs 1.03 ± 0.19
interval/basics/acos 5.02 ± 0.06 μs 4.99 ± 0.06 μs 1.01 ± 0.017
interval/basics/asin 5.16 ± 0.06 μs 5.16 ± 0.051 μs 1 ± 0.015
interval/basics/atan 14.8 ± 0.21 μs 14.9 ± 0.2 μs 0.989 ± 0.019
interval/basics/cos 0.07 ± 0.022 ms 0.0696 ± 0.022 ms 1.01 ± 0.45
interval/basics/cosh 10.3 ± 0.08 μs 10.3 ± 0.08 μs 1 ± 0.011
interval/basics/exp 6.68 ± 0.1 μs 6.65 ± 0.1 μs 1 ± 0.021
interval/basics/inv 2.05 ± 0.09 μs 2.05 ± 0.06 μs 1 ± 0.053
interval/basics/log 4.96 ± 0.069 μs 4.93 ± 0.05 μs 1.01 ± 0.017
interval/basics/sin 0.0691 ± 0.023 ms 0.0694 ± 0.023 ms 0.995 ± 0.46
interval/basics/sinh 13.2 ± 0.071 μs 13.2 ± 0.079 μs 0.999 ± 0.0081
interval/basics/sqrt 2.12 ± 0.06 μs 2.12 ± 0.051 μs 1 ± 0.037
interval/basics/tan 0.0398 ± 0.0021 ms 0.0398 ± 0.0021 ms 1 ± 0.074
interval/basics/tanh 0.305 ± 0.0081 ms 0.302 ± 0.0086 ms 1.01 ± 0.039
time_to_load 0.105 ± 0.0023 s 0.106 ± 0.00043 s 0.995 ± 0.022
Memory benchmarks
master 5fe89c0... master / 5fe89c0...
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: 0.0933 MB 1.53 k allocs: 0.0929 MB 1
BigFloat interval/basics/atan 2.04 k allocs: 0.0812 MB 2.04 k allocs: 0.0811 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: 0.0681 MB 1.01 k allocs: 0.068 MB 1
BigFloat interval/basics/exp 0.803 k allocs: 0.0408 MB 0.803 k allocs: 0.0408 MB 1
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: 0.0417 MB 0.816 k allocs: 0.0418 MB 0.999
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: 0.0409 MB 0.809 k allocs: 0.0409 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 0.145 k allocs: 11 kB 1

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@BaronNashville