Add :ulp rounding mode based on prevfloat and nextfloat

[OlivierHnt]

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.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	2aa7e54...	master / 2aa7e54...
BigFloat MPFI/basics/*	25.3 ± 3.9 μs	25.4 ± 4 μs	0.997 ± 0.22
BigFloat MPFI/basics/+	12.5 ± 4 μs	12.6 ± 3.9 μs	0.987 ± 0.44
BigFloat MPFI/basics/-	17.2 ± 4.9 μs	17.5 ± 4.1 μs	0.982 ± 0.36
BigFloat MPFI/basics//	19.6 ± 3.9 μs	20.1 ± 4.3 μs	0.973 ± 0.29
BigFloat MPFI/basics/abs	10.6 ± 3.9 μs	10.3 ± 3.9 μs	1.02 ± 0.54
BigFloat MPFI/basics/acos	0.667 ± 0.0095 ms	0.666 ± 0.0087 ms	1 ± 0.019
BigFloat MPFI/basics/asin	0.647 ± 0.0098 ms	0.662 ± 0.0089 ms	0.977 ± 0.02
BigFloat MPFI/basics/atan	2.07 ± 0.022 ms	2.08 ± 0.014 ms	0.997 ± 0.013
BigFloat MPFI/basics/cos	0.354 ± 0.0091 ms	0.353 ± 0.0091 ms	1 ± 0.036
BigFloat MPFI/basics/cosh	0.423 ± 0.011 ms	0.425 ± 0.012 ms	0.996 ± 0.038
BigFloat MPFI/basics/exp	0.497 ± 0.01 ms	0.496 ± 0.011 ms	1 ± 0.03
BigFloat MPFI/basics/inv	19.1 ± 3.9 μs	18.9 ± 4 μs	1.01 ± 0.29
BigFloat MPFI/basics/log	0.469 ± 0.0088 ms	0.465 ± 0.0088 ms	1.01 ± 0.027
BigFloat MPFI/basics/sin	0.457 ± 0.01 ms	0.456 ± 0.01 ms	1 ± 0.031
BigFloat MPFI/basics/sinh	0.564 ± 0.0095 ms	0.565 ± 0.0098 ms	0.999 ± 0.024
BigFloat MPFI/basics/sqrt	28.2 ± 7.5 μs	28.2 ± 7.4 μs	0.999 ± 0.37
BigFloat MPFI/basics/tan	0.38 ± 0.0095 ms	0.379 ± 0.0094 ms	1 ± 0.035
BigFloat MPFI/basics/tanh	0.576 ± 0.01 ms	0.576 ± 0.011 ms	0.999 ± 0.026
BigFloat bareinterval/basics/*	0.0437 ± 0.0033 ms	0.149 ± 0.085 ms	0.292 ± 0.17
BigFloat bareinterval/basics/+	24.5 ± 3.9 μs	0.0707 ± 0.04 ms	0.347 ± 0.2
BigFloat bareinterval/basics/-	25.6 ± 4 μs	0.0706 ± 0.0068 ms	0.362 ± 0.066
BigFloat bareinterval/basics//	21.2 ± 6 μs	0.085 ± 0.039 ms	0.249 ± 0.13
BigFloat bareinterval/basics/abs	17.6 ± 3.9 μs	0.0855 ± 0.042 ms	0.206 ± 0.11
BigFloat bareinterval/basics/acos	0.712 ± 0.026 ms	0.775 ± 0.075 ms	0.919 ± 0.095
BigFloat bareinterval/basics/asin	0.691 ± 0.024 ms	0.762 ± 0.075 ms	0.906 ± 0.094
BigFloat bareinterval/basics/atan	2.08 ± 0.023 ms	2.13 ± 0.039 ms	0.978 ± 0.021
BigFloat bareinterval/basics/cos	0.336 ± 0.097 ms	0.38 ± 0.097 ms	0.885 ± 0.34
BigFloat bareinterval/basics/cosh	0.465 ± 0.027 ms	0.484 ± 0.069 ms	0.962 ± 0.15
BigFloat bareinterval/basics/exp	0.503 ± 0.01 ms	0.54 ± 0.028 ms	0.931 ± 0.051
BigFloat bareinterval/basics/inv	27.5 ± 4.1 μs	0.0738 ± 0.0045 ms	0.372 ± 0.06
BigFloat bareinterval/basics/log	0.518 ± 0.032 ms	0.562 ± 0.066 ms	0.922 ± 0.12
BigFloat bareinterval/basics/sin	0.469 ± 0.11 ms	0.514 ± 0.19 ms	0.912 ± 0.39
BigFloat bareinterval/basics/sinh	0.571 ± 0.011 ms	0.61 ± 0.03 ms	0.937 ± 0.049
BigFloat bareinterval/basics/sqrt	0.0383 ± 0.0033 ms	0.113 ± 0.0066 ms	0.338 ± 0.035
BigFloat bareinterval/basics/tan	0.331 ± 0.065 ms	0.314 ± 0.12 ms	1.05 ± 0.46
BigFloat bareinterval/basics/tanh	0.586 ± 0.011 ms	0.623 ± 0.03 ms	0.941 ± 0.049
BigFloat interval/basics/*	0.0483 ± 0.003 ms	0.0826 ± 0.1 ms	0.585 ± 0.71
BigFloat interval/basics/+	27.5 ± 10 μs	0.091 ± 0.055 ms	0.303 ± 0.22
BigFloat interval/basics/-	28 ± 10 μs	0.0529 ± 0.055 ms	0.53 ± 0.58
BigFloat interval/basics//	25.8 ± 5.6 μs	0.0573 ± 0.062 ms	0.449 ± 0.49
BigFloat interval/basics/abs	16.6 ± 9.5 μs	0.0819 ± 0.049 ms	0.202 ± 0.17
BigFloat interval/basics/acos	0.708 ± 0.055 ms	0.741 ± 0.13 ms	0.955 ± 0.18
BigFloat interval/basics/asin	0.683 ± 0.044 ms	0.72 ± 0.051 ms	0.949 ± 0.091
BigFloat interval/basics/atan	2.08 ± 0.0049 ms	2.11 ± 0.049 ms	0.982 ± 0.023
BigFloat interval/basics/cos	0.335 ± 0.015 ms	0.392 ± 0.014 ms	0.854 ± 0.048
BigFloat interval/basics/cosh	0.457 ± 0.026 ms	0.49 ± 0.017 ms	0.933 ± 0.062
BigFloat interval/basics/exp	0.51 ± 0.0099 ms	0.542 ± 0.047 ms	0.942 ± 0.084
BigFloat interval/basics/inv	31.5 ± 5.7 μs	0.107 ± 0.0071 ms	0.295 ± 0.057
BigFloat interval/basics/log	0.506 ± 0.048 ms	0.536 ± 0.1 ms	0.945 ± 0.2
BigFloat interval/basics/sin	0.478 ± 0.026 ms	0.535 ± 0.035 ms	0.893 ± 0.075
BigFloat interval/basics/sinh	0.577 ± 0.01 ms	0.608 ± 0.044 ms	0.949 ± 0.07
BigFloat interval/basics/sqrt	0.0426 ± 0.037 ms	0.0726 ± 0.0035 ms	0.587 ± 0.51
BigFloat interval/basics/tan	0.279 ± 0.015 ms	0.325 ± 0.014 ms	0.857 ± 0.058
BigFloat interval/basics/tanh	0.593 ± 0.013 ms	0.622 ± 0.043 ms	0.953 ± 0.069
bareinterval/basics/*	2.4 ± 0.03 μs	1.96 ± 0.04 μs	1.22 ± 0.029
bareinterval/basics/+	0.822 ± 0.011 μs	0.531 ± 0.01 μs	1.55 ± 0.036
bareinterval/basics/-	0.752 ± 0.011 μs	0.552 ± 0.01 μs	1.36 ± 0.032
bareinterval/basics//	1.54 ± 0.02 μs	1.22 ± 0.02 μs	1.26 ± 0.026
bareinterval/basics/abs	0.301 ± 0.021 μs	0.29 ± 0.01 μs	1.04 ± 0.081
bareinterval/basics/acos	2.98 ± 0.031 μs	2.93 ± 0.039 μs	1.02 ± 0.017
bareinterval/basics/asin	3.17 ± 0.02 μs	3.15 ± 0.03 μs	1.01 ± 0.012
bareinterval/basics/atan	13.1 ± 0.18 μs	13.3 ± 0.21 μs	0.983 ± 0.021
bareinterval/basics/cos	0.05 ± 0.017 ms	0.0654 ± 0.0015 ms	0.764 ± 0.26
bareinterval/basics/cosh	7.88 ± 0.04 μs	7.26 ± 0.04 μs	1.08 ± 0.0081
bareinterval/basics/exp	4.44 ± 0.039 μs	4.32 ± 0.05 μs	1.03 ± 0.015
bareinterval/basics/inv	1.24 ± 0.04 μs	1.05 ± 0.022 μs	1.18 ± 0.045
bareinterval/basics/log	2.14 ± 0.02 μs	2.17 ± 4.1 μs	0.986 ± 1.9
bareinterval/basics/sin	0.0491 ± 0.021 ms	0.0653 ± 0.054 ms	0.752 ± 0.7
bareinterval/basics/sinh	10.1 ± 0.061 μs	9.99 ± 0.06 μs	1.01 ± 0.0086
bareinterval/basics/sqrt	1.12 ± 0.021 μs	1.35 ± 0.02 μs	0.829 ± 0.02
bareinterval/basics/tan	28.8 ± 0.55 μs	0.0374 ± 0.00071 ms	0.769 ± 0.021
bareinterval/basics/tanh	0.288 ± 0.0084 ms	0.288 ± 0.0084 ms	1 ± 0.041
interval/basics/*	3.86 ± 0.091 μs	3.22 ± 0.08 μs	1.2 ± 0.041
interval/basics/+	1.84 ± 0.1 μs	1.49 ± 0.091 μs	1.24 ± 0.1
interval/basics/-	1.79 ± 0.12 μs	1.52 ± 0.09 μs	1.18 ± 0.11
interval/basics//	2.83 ± 0.09 μs	2.46 ± 0.079 μs	1.15 ± 0.052
interval/basics/abs	0.932 ± 0.15 μs	0.882 ± 0.11 μs	1.06 ± 0.22
interval/basics/acos	5.06 ± 0.09 μs	5.02 ± 0.061 μs	1.01 ± 0.022
interval/basics/asin	5.16 ± 0.08 μs	5.15 ± 0.07 μs	1 ± 0.021
interval/basics/atan	13 ± 0.23 μs	16.3 ± 1.9 μs	0.795 ± 0.093
interval/basics/cos	0.0708 ± 0.022 ms	0.119 ± 0.054 ms	0.595 ± 0.33
interval/basics/cosh	10.8 ± 0.1 μs	10.3 ± 0.079 μs	1.05 ± 0.013
interval/basics/exp	5.5 ± 0.1 μs	6.66 ± 0.09 μs	0.826 ± 0.019
interval/basics/inv	2.35 ± 0.32 μs	2.04 ± 0.08 μs	1.15 ± 0.16
interval/basics/log	5 ± 0.08 μs	4.94 ± 0.06 μs	1.01 ± 0.02
interval/basics/sin	0.0702 ± 0.022 ms	0.119 ± 0.053 ms	0.591 ± 0.32
interval/basics/sinh	11.4 ± 0.11 μs	13.2 ± 0.08 μs	0.868 ± 0.0099
interval/basics/sqrt	2.14 ± 0.09 μs	2.32 ± 0.11 μs	0.923 ± 0.058
interval/basics/tan	0.0405 ± 0.002 ms	0.0663 ± 0.0039 ms	0.611 ± 0.047
interval/basics/tanh	0.302 ± 0.0078 ms	0.303 ± 0.01 ms	0.997 ± 0.043
time_to_load	0.106 ± 0.0029 s	0.108 ± 0.0026 s	0.985 ± 0.036

Memory benchmarks

	master	2aa7e54...	master / 2aa7e54...
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	1.71 k allocs: 0.158 MB	0.161
BigFloat bareinterval/basics/+	0.202 k allocs: 20.4 kB	0.802 k allocs: 0.0748 MB	0.266
BigFloat bareinterval/basics/-	0.202 k allocs: 20.4 kB	0.802 k allocs: 0.0748 MB	0.266
BigFloat bareinterval/basics//	0.1 k allocs: 10.8 kB	0.954 k allocs: 0.0887 MB	0.119
BigFloat bareinterval/basics/abs	0.199 k allocs: 20.1 kB	1.1 k allocs: 0.102 MB	0.192
BigFloat bareinterval/basics/acos	1.33 k allocs: 0.0741 MB	2.2 k allocs: 0.154 MB	0.481
BigFloat bareinterval/basics/asin	1.23 k allocs: 0.0647 MB	2.14 k allocs: 0.149 MB	0.435
BigFloat bareinterval/basics/atan	2.04 k allocs: 0.08 MB	2.44 k allocs: 0.117 MB	0.686
BigFloat bareinterval/basics/cos	2.45 k allocs: 0.185 MB	4.11 k allocs: 0.336 MB	0.55
BigFloat bareinterval/basics/cosh	1.01 k allocs: 0.0671 MB	1.76 k allocs: 0.136 MB	0.494
BigFloat bareinterval/basics/exp	0.802 k allocs: 0.0397 MB	1.2 k allocs: 0.0764 MB	0.52
BigFloat bareinterval/basics/inv	0.198 k allocs: 20 kB	0.8 k allocs: 0.0746 MB	0.262
BigFloat bareinterval/basics/log	0.804 k allocs: 0.0694 MB	1.43 k allocs: 0.127 MB	0.548
BigFloat bareinterval/basics/sin	2.9 k allocs: 0.197 MB	4.55 k allocs: 0.349 MB	0.566
BigFloat bareinterval/basics/sinh	0.815 k allocs: 0.0407 MB	1.22 k allocs: 0.0773 MB	0.526
BigFloat bareinterval/basics/sqrt	0.304 k allocs: 29.9 kB	1.24 k allocs: 0.115 MB	0.255
BigFloat bareinterval/basics/tan	1.67 k allocs: 0.124 MB	2.92 k allocs: 0.238 MB	0.519
BigFloat bareinterval/basics/tanh	0.808 k allocs: 0.0399 MB	1.21 k allocs: 0.0766 MB	0.522
BigFloat interval/basics/*	0.263 k allocs: 26.8 kB	2.01 k allocs: 0.186 MB	0.141
BigFloat interval/basics/+	0.203 k allocs: 21.2 kB	1.1 k allocs: 0.103 MB	0.201
BigFloat interval/basics/-	0.203 k allocs: 21.2 kB	1.1 k allocs: 0.103 MB	0.201
BigFloat interval/basics//	0.101 k allocs: 11.6 kB	1.35 k allocs: 0.126 MB	0.09
BigFloat interval/basics/abs	0.2 k allocs: 20.9 kB	1.1 k allocs: 0.103 MB	0.198
BigFloat interval/basics/acos	1.77 k allocs: 0.115 MB	3.15 k allocs: 0.241 MB	0.477
BigFloat interval/basics/asin	1.53 k allocs: 0.0933 MB	3.09 k allocs: 0.236 MB	0.395
BigFloat interval/basics/atan	2.04 k allocs: 0.0811 MB	2.74 k allocs: 0.145 MB	0.558
BigFloat interval/basics/cos	2.45 k allocs: 0.186 MB	4.41 k allocs: 0.365 MB	0.51
BigFloat interval/basics/cosh	1.01 k allocs: 0.0683 MB	2.06 k allocs: 0.164 MB	0.416
BigFloat interval/basics/exp	0.803 k allocs: 0.041 MB	1.5 k allocs: 0.105 MB	0.391
BigFloat interval/basics/inv	0.199 k allocs: 20.8 kB	1.2 k allocs: 0.112 MB	0.181
BigFloat interval/basics/log	1.1 k allocs: 0.0977 MB	2.19 k allocs: 0.197 MB	0.497
BigFloat interval/basics/sin	2.9 k allocs: 0.198 MB	4.85 k allocs: 0.377 MB	0.526
BigFloat interval/basics/sinh	0.816 k allocs: 0.0419 MB	1.52 k allocs: 0.106 MB	0.397
BigFloat interval/basics/sqrt	0.758 k allocs: 0.0715 MB	1.99 k allocs: 0.185 MB	0.387
BigFloat interval/basics/tan	1.67 k allocs: 0.125 MB	3.42 k allocs: 0.285 MB	0.437
BigFloat interval/basics/tanh	0.809 k allocs: 0.0413 MB	1.51 k allocs: 0.105 MB	0.392
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	1.22 k allocs: 0.102 MB	0.413
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	1.22 k allocs: 0.102 MB	0.413
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	0.626 k allocs: 0.0532 MB	0.422
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	1.22 k allocs: 0.103 MB	0.418
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	1.22 k allocs: 0.103 MB	0.418
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	0.627 k allocs: 0.0546 MB	0.437
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