On Tue, Jan 31, 2023, at 20:25, Dean Rasheed wrote: > That seems a bit wordy, given the context of this comment. I think > it's sufficient to just give the formula, and note that it simplifies > when DEC_DIGITS is even (not just 4): > > /* > * Assume the input was normalized, so arg.weight is accurate. The result > * then has at least sweight = floor(arg.weight * DEC_DIGITS / 2 + 1) > * digits before the decimal point. When DEC_DIGITS is even, we can save > * a few cycles, since the division is exact and there is no need to > * round down. > */ > #if DEC_DIGITS == ((DEC_DIGITS / 2) * 2) > sweight = arg.weight * DEC_DIGITS / 2 + 1; > #else > if (arg.weight >= 0) > sweight = arg.weight * DEC_DIGITS / 2 + 1; > else > sweight = 1 - (1 - arg.weight * DEC_DIGITS) / 2; > #endif
Nice, you managed to simplify it even further. I think the comment and the code now are crystal clear together. I've tested it successfully, test report attached. In summary: DEC_DIGITS=1 now produce 16 sig. figs. in the range sqrt(2e-31) .. sqrt(2e+32), which before had a mix of 17 and 18 sig. figs in the result. DEC_DIGTIS=2 now produce 16 sig. figs. in the range sqrt(2e-31) .. sqrt(2e+31), which before always had 17 sig. figs in the result. DEC_DIGITS=4 is unchanged. Exact tested patch attached, code copy/pasted verbatim from your email. Test
fix-sweight-v4.patch
Description: Binary data
--
-- Comparison of sig_figs(sqrt(n)) for HEAD vs fix-sweight-v4
-- when DEC_DIGITS == 1
--
DEC_DIGITS | n | HEAD | fix-sweight-v4 | diff
------------+--------------+------+----------------+------
1 | 2e-100 | 51 | 51 | 0
1 | 2e-99 | 50 | 50 | 0
1 | 2e-98 | 50 | 50 | 0
1 | 2e-97 | 49 | 49 | 0
1 | 2e-96 | 49 | 49 | 0
1 | 2e-95 | 48 | 48 | 0
1 | 2e-94 | 48 | 48 | 0
1 | 2e-93 | 47 | 47 | 0
1 | 2e-92 | 47 | 47 | 0
1 | 2e-91 | 46 | 46 | 0
1 | 2e-90 | 46 | 46 | 0
1 | 2e-89 | 45 | 45 | 0
1 | 2e-88 | 45 | 45 | 0
1 | 2e-87 | 44 | 44 | 0
1 | 2e-86 | 44 | 44 | 0
1 | 2e-85 | 43 | 43 | 0
1 | 2e-84 | 43 | 43 | 0
1 | 2e-83 | 42 | 42 | 0
1 | 2e-82 | 42 | 42 | 0
1 | 2e-81 | 41 | 41 | 0
1 | 2e-80 | 41 | 41 | 0
1 | 2e-79 | 40 | 40 | 0
1 | 2e-78 | 40 | 40 | 0
1 | 2e-77 | 39 | 39 | 0
1 | 2e-76 | 39 | 39 | 0
1 | 2e-75 | 38 | 38 | 0
1 | 2e-74 | 38 | 38 | 0
1 | 2e-73 | 37 | 37 | 0
1 | 2e-72 | 37 | 37 | 0
1 | 2e-71 | 36 | 36 | 0
1 | 2e-70 | 36 | 36 | 0
1 | 2e-69 | 35 | 35 | 0
1 | 2e-68 | 35 | 35 | 0
1 | 2e-67 | 34 | 34 | 0
1 | 2e-66 | 34 | 34 | 0
1 | 2e-65 | 33 | 33 | 0
1 | 2e-64 | 33 | 33 | 0
1 | 2e-63 | 32 | 32 | 0
1 | 2e-62 | 32 | 32 | 0
1 | 2e-61 | 31 | 31 | 0
1 | 2e-60 | 31 | 31 | 0
1 | 2e-59 | 30 | 30 | 0
1 | 2e-58 | 30 | 30 | 0
1 | 2e-57 | 29 | 29 | 0
1 | 2e-56 | 29 | 29 | 0
1 | 2e-55 | 28 | 28 | 0
1 | 2e-54 | 28 | 28 | 0
1 | 2e-53 | 27 | 27 | 0
1 | 2e-52 | 27 | 27 | 0
1 | 2e-51 | 26 | 26 | 0
1 | 2e-50 | 26 | 26 | 0
1 | 2e-49 | 25 | 25 | 0
1 | 2e-48 | 25 | 25 | 0
1 | 2e-47 | 24 | 24 | 0
1 | 2e-46 | 24 | 24 | 0
1 | 2e-45 | 23 | 23 | 0
1 | 2e-44 | 23 | 23 | 0
1 | 2e-43 | 22 | 22 | 0
1 | 2e-42 | 22 | 22 | 0
1 | 2e-41 | 21 | 21 | 0
1 | 2e-40 | 21 | 21 | 0
1 | 2e-39 | 20 | 20 | 0
1 | 2e-38 | 20 | 20 | 0
1 | 2e-37 | 19 | 19 | 0
1 | 2e-36 | 19 | 19 | 0
1 | 2e-35 | 18 | 18 | 0
1 | 2e-34 | 18 | 18 | 0
1 | 2e-33 | 17 | 17 | 0
1 | 2e-32 | 17 | 17 | 0
1 | 2e-31 | 17 | 16 | -1
1 | 2e-30 | 17 | 16 | -1
1 | 2e-29 | 17 | 16 | -1
1 | 2e-28 | 17 | 16 | -1
1 | 2e-27 | 17 | 16 | -1
1 | 2e-26 | 17 | 16 | -1
1 | 2e-25 | 17 | 16 | -1
1 | 2e-24 | 17 | 16 | -1
1 | 2e-23 | 17 | 16 | -1
1 | 2e-22 | 17 | 16 | -1
1 | 2e-21 | 17 | 16 | -1
1 | 2e-20 | 17 | 16 | -1
1 | 2e-19 | 17 | 16 | -1
1 | 2e-18 | 17 | 16 | -1
1 | 2e-17 | 17 | 16 | -1
1 | 2e-16 | 17 | 16 | -1
1 | 2e-15 | 17 | 16 | -1
1 | 2e-14 | 17 | 16 | -1
1 | 2e-13 | 17 | 16 | -1
1 | 2e-12 | 17 | 16 | -1
1 | 2e-11 | 17 | 16 | -1
1 | 0.0000000002 | 17 | 16 | -1
1 | 0.000000002 | 17 | 16 | -1
1 | 0.00000002 | 17 | 16 | -1
1 | 0.0000002 | 17 | 16 | -1
1 | 0.000002 | 17 | 16 | -1
1 | 0.00002 | 17 | 16 | -1
1 | 0.0002 | 17 | 16 | -1
1 | 0.002 | 17 | 16 | -1
1 | 0.02 | 17 | 16 | -1
1 | 0.2 | 17 | 16 | -1
1 | 2 | 18 | 16 | -2
1 | 20 | 17 | 16 | -1
1 | 200 | 18 | 16 | -2
1 | 2000 | 17 | 16 | -1
1 | 20000 | 18 | 16 | -2
1 | 200000 | 17 | 16 | -1
1 | 2000000 | 18 | 16 | -2
1 | 20000000 | 17 | 16 | -1
1 | 200000000 | 18 | 16 | -2
1 | 2000000000 | 17 | 16 | -1
1 | 20000000000 | 18 | 16 | -2
1 | 2e+11 | 17 | 16 | -1
1 | 2e+12 | 18 | 16 | -2
1 | 2e+13 | 17 | 16 | -1
1 | 2e+14 | 18 | 16 | -2
1 | 2e+15 | 17 | 16 | -1
1 | 2e+16 | 18 | 16 | -2
1 | 2e+17 | 17 | 16 | -1
1 | 2e+18 | 18 | 16 | -2
1 | 2e+19 | 17 | 16 | -1
1 | 2e+20 | 18 | 16 | -2
1 | 2e+21 | 17 | 16 | -1
1 | 2e+22 | 18 | 16 | -2
1 | 2e+23 | 17 | 16 | -1
1 | 2e+24 | 18 | 16 | -2
1 | 2e+25 | 17 | 16 | -1
1 | 2e+26 | 18 | 16 | -2
1 | 2e+27 | 17 | 16 | -1
1 | 2e+28 | 18 | 16 | -2
1 | 2e+29 | 17 | 16 | -1
1 | 2e+30 | 18 | 16 | -2
1 | 2e+31 | 17 | 16 | -1
1 | 2e+32 | 18 | 17 | -1
1 | 2e+33 | 17 | 17 | 0
1 | 2e+34 | 18 | 18 | 0
1 | 2e+35 | 18 | 18 | 0
1 | 2e+36 | 19 | 19 | 0
1 | 2e+37 | 19 | 19 | 0
1 | 2e+38 | 20 | 20 | 0
1 | 2e+39 | 20 | 20 | 0
1 | 2e+40 | 21 | 21 | 0
1 | 2e+41 | 21 | 21 | 0
1 | 2e+42 | 22 | 22 | 0
1 | 2e+43 | 22 | 22 | 0
1 | 2e+44 | 23 | 23 | 0
1 | 2e+45 | 23 | 23 | 0
1 | 2e+46 | 24 | 24 | 0
1 | 2e+47 | 24 | 24 | 0
1 | 2e+48 | 25 | 25 | 0
1 | 2e+49 | 25 | 25 | 0
1 | 2e+50 | 26 | 26 | 0
1 | 2e+51 | 26 | 26 | 0
1 | 2e+52 | 27 | 27 | 0
1 | 2e+53 | 27 | 27 | 0
1 | 2e+54 | 28 | 28 | 0
1 | 2e+55 | 28 | 28 | 0
1 | 2e+56 | 29 | 29 | 0
1 | 2e+57 | 29 | 29 | 0
1 | 2e+58 | 30 | 30 | 0
1 | 2e+59 | 30 | 30 | 0
1 | 2e+60 | 31 | 31 | 0
1 | 2e+61 | 31 | 31 | 0
1 | 2e+62 | 32 | 32 | 0
1 | 2e+63 | 32 | 32 | 0
1 | 2e+64 | 33 | 33 | 0
1 | 2e+65 | 33 | 33 | 0
1 | 2e+66 | 34 | 34 | 0
1 | 2e+67 | 34 | 34 | 0
1 | 2e+68 | 35 | 35 | 0
1 | 2e+69 | 35 | 35 | 0
1 | 2e+70 | 36 | 36 | 0
1 | 2e+71 | 36 | 36 | 0
1 | 2e+72 | 37 | 37 | 0
1 | 2e+73 | 37 | 37 | 0
1 | 2e+74 | 38 | 38 | 0
1 | 2e+75 | 38 | 38 | 0
1 | 2e+76 | 39 | 39 | 0
1 | 2e+77 | 39 | 39 | 0
1 | 2e+78 | 40 | 40 | 0
1 | 2e+79 | 40 | 40 | 0
1 | 2e+80 | 41 | 41 | 0
1 | 2e+81 | 41 | 41 | 0
1 | 2e+82 | 42 | 42 | 0
1 | 2e+83 | 42 | 42 | 0
1 | 2e+84 | 43 | 43 | 0
1 | 2e+85 | 43 | 43 | 0
1 | 2e+86 | 44 | 44 | 0
1 | 2e+87 | 44 | 44 | 0
1 | 2e+88 | 45 | 45 | 0
1 | 2e+89 | 45 | 45 | 0
1 | 2e+90 | 46 | 46 | 0
1 | 2e+91 | 46 | 46 | 0
1 | 2e+92 | 47 | 47 | 0
1 | 2e+93 | 47 | 47 | 0
1 | 2e+94 | 48 | 48 | 0
1 | 2e+95 | 48 | 48 | 0
1 | 2e+96 | 49 | 49 | 0
1 | 2e+97 | 49 | 49 | 0
1 | 2e+98 | 50 | 50 | 0
1 | 2e+99 | 50 | 50 | 0
1 | 2e+100 | 51 | 51 | 0
(201 rows)
--
-- Comparison of sig_figs(sqrt(n)) for HEAD vs fix-sweight-v4
-- when DEC_DIGITS == 2
--
DEC_DIGITS | n | HEAD | fix-sweight-v4 | diff
------------+--------------+------+----------------+------
2 | 2e-100 | 51 | 51 | 0
2 | 2e-99 | 50 | 50 | 0
2 | 2e-98 | 50 | 50 | 0
2 | 2e-97 | 49 | 49 | 0
2 | 2e-96 | 49 | 49 | 0
2 | 2e-95 | 48 | 48 | 0
2 | 2e-94 | 48 | 48 | 0
2 | 2e-93 | 47 | 47 | 0
2 | 2e-92 | 47 | 47 | 0
2 | 2e-91 | 46 | 46 | 0
2 | 2e-90 | 46 | 46 | 0
2 | 2e-89 | 45 | 45 | 0
2 | 2e-88 | 45 | 45 | 0
2 | 2e-87 | 44 | 44 | 0
2 | 2e-86 | 44 | 44 | 0
2 | 2e-85 | 43 | 43 | 0
2 | 2e-84 | 43 | 43 | 0
2 | 2e-83 | 42 | 42 | 0
2 | 2e-82 | 42 | 42 | 0
2 | 2e-81 | 41 | 41 | 0
2 | 2e-80 | 41 | 41 | 0
2 | 2e-79 | 40 | 40 | 0
2 | 2e-78 | 40 | 40 | 0
2 | 2e-77 | 39 | 39 | 0
2 | 2e-76 | 39 | 39 | 0
2 | 2e-75 | 38 | 38 | 0
2 | 2e-74 | 38 | 38 | 0
2 | 2e-73 | 37 | 37 | 0
2 | 2e-72 | 37 | 37 | 0
2 | 2e-71 | 36 | 36 | 0
2 | 2e-70 | 36 | 36 | 0
2 | 2e-69 | 35 | 35 | 0
2 | 2e-68 | 35 | 35 | 0
2 | 2e-67 | 34 | 34 | 0
2 | 2e-66 | 34 | 34 | 0
2 | 2e-65 | 33 | 33 | 0
2 | 2e-64 | 33 | 33 | 0
2 | 2e-63 | 32 | 32 | 0
2 | 2e-62 | 32 | 32 | 0
2 | 2e-61 | 31 | 31 | 0
2 | 2e-60 | 31 | 31 | 0
2 | 2e-59 | 30 | 30 | 0
2 | 2e-58 | 30 | 30 | 0
2 | 2e-57 | 29 | 29 | 0
2 | 2e-56 | 29 | 29 | 0
2 | 2e-55 | 28 | 28 | 0
2 | 2e-54 | 28 | 28 | 0
2 | 2e-53 | 27 | 27 | 0
2 | 2e-52 | 27 | 27 | 0
2 | 2e-51 | 26 | 26 | 0
2 | 2e-50 | 26 | 26 | 0
2 | 2e-49 | 25 | 25 | 0
2 | 2e-48 | 25 | 25 | 0
2 | 2e-47 | 24 | 24 | 0
2 | 2e-46 | 24 | 24 | 0
2 | 2e-45 | 23 | 23 | 0
2 | 2e-44 | 23 | 23 | 0
2 | 2e-43 | 22 | 22 | 0
2 | 2e-42 | 22 | 22 | 0
2 | 2e-41 | 21 | 21 | 0
2 | 2e-40 | 21 | 21 | 0
2 | 2e-39 | 20 | 20 | 0
2 | 2e-38 | 20 | 20 | 0
2 | 2e-37 | 19 | 19 | 0
2 | 2e-36 | 19 | 19 | 0
2 | 2e-35 | 18 | 18 | 0
2 | 2e-34 | 18 | 18 | 0
2 | 2e-33 | 17 | 17 | 0
2 | 2e-32 | 17 | 17 | 0
2 | 2e-31 | 17 | 16 | -1
2 | 2e-30 | 17 | 16 | -1
2 | 2e-29 | 17 | 16 | -1
2 | 2e-28 | 17 | 16 | -1
2 | 2e-27 | 17 | 16 | -1
2 | 2e-26 | 17 | 16 | -1
2 | 2e-25 | 17 | 16 | -1
2 | 2e-24 | 17 | 16 | -1
2 | 2e-23 | 17 | 16 | -1
2 | 2e-22 | 17 | 16 | -1
2 | 2e-21 | 17 | 16 | -1
2 | 2e-20 | 17 | 16 | -1
2 | 2e-19 | 17 | 16 | -1
2 | 2e-18 | 17 | 16 | -1
2 | 2e-17 | 17 | 16 | -1
2 | 2e-16 | 17 | 16 | -1
2 | 2e-15 | 17 | 16 | -1
2 | 2e-14 | 17 | 16 | -1
2 | 2e-13 | 17 | 16 | -1
2 | 2e-12 | 17 | 16 | -1
2 | 2e-11 | 17 | 16 | -1
2 | 0.0000000002 | 17 | 16 | -1
2 | 0.000000002 | 17 | 16 | -1
2 | 0.00000002 | 17 | 16 | -1
2 | 0.0000002 | 17 | 16 | -1
2 | 0.000002 | 17 | 16 | -1
2 | 0.00002 | 17 | 16 | -1
2 | 0.0002 | 17 | 16 | -1
2 | 0.002 | 17 | 16 | -1
2 | 0.02 | 17 | 16 | -1
2 | 0.2 | 17 | 16 | -1
2 | 2 | 17 | 16 | -1
2 | 20 | 17 | 16 | -1
2 | 200 | 17 | 16 | -1
2 | 2000 | 17 | 16 | -1
2 | 20000 | 17 | 16 | -1
2 | 200000 | 17 | 16 | -1
2 | 2000000 | 17 | 16 | -1
2 | 20000000 | 17 | 16 | -1
2 | 200000000 | 17 | 16 | -1
2 | 2000000000 | 17 | 16 | -1
2 | 20000000000 | 17 | 16 | -1
2 | 2e+11 | 17 | 16 | -1
2 | 2e+12 | 17 | 16 | -1
2 | 2e+13 | 17 | 16 | -1
2 | 2e+14 | 17 | 16 | -1
2 | 2e+15 | 17 | 16 | -1
2 | 2e+16 | 17 | 16 | -1
2 | 2e+17 | 17 | 16 | -1
2 | 2e+18 | 17 | 16 | -1
2 | 2e+19 | 17 | 16 | -1
2 | 2e+20 | 17 | 16 | -1
2 | 2e+21 | 17 | 16 | -1
2 | 2e+22 | 17 | 16 | -1
2 | 2e+23 | 17 | 16 | -1
2 | 2e+24 | 17 | 16 | -1
2 | 2e+25 | 17 | 16 | -1
2 | 2e+26 | 17 | 16 | -1
2 | 2e+27 | 17 | 16 | -1
2 | 2e+28 | 17 | 16 | -1
2 | 2e+29 | 17 | 16 | -1
2 | 2e+30 | 17 | 16 | -1
2 | 2e+31 | 17 | 16 | -1
2 | 2e+32 | 17 | 17 | 0
2 | 2e+33 | 17 | 17 | 0
2 | 2e+34 | 18 | 18 | 0
2 | 2e+35 | 18 | 18 | 0
2 | 2e+36 | 19 | 19 | 0
2 | 2e+37 | 19 | 19 | 0
2 | 2e+38 | 20 | 20 | 0
2 | 2e+39 | 20 | 20 | 0
2 | 2e+40 | 21 | 21 | 0
2 | 2e+41 | 21 | 21 | 0
2 | 2e+42 | 22 | 22 | 0
2 | 2e+43 | 22 | 22 | 0
2 | 2e+44 | 23 | 23 | 0
2 | 2e+45 | 23 | 23 | 0
2 | 2e+46 | 24 | 24 | 0
2 | 2e+47 | 24 | 24 | 0
2 | 2e+48 | 25 | 25 | 0
2 | 2e+49 | 25 | 25 | 0
2 | 2e+50 | 26 | 26 | 0
2 | 2e+51 | 26 | 26 | 0
2 | 2e+52 | 27 | 27 | 0
2 | 2e+53 | 27 | 27 | 0
2 | 2e+54 | 28 | 28 | 0
2 | 2e+55 | 28 | 28 | 0
2 | 2e+56 | 29 | 29 | 0
2 | 2e+57 | 29 | 29 | 0
2 | 2e+58 | 30 | 30 | 0
2 | 2e+59 | 30 | 30 | 0
2 | 2e+60 | 31 | 31 | 0
2 | 2e+61 | 31 | 31 | 0
2 | 2e+62 | 32 | 32 | 0
2 | 2e+63 | 32 | 32 | 0
2 | 2e+64 | 33 | 33 | 0
2 | 2e+65 | 33 | 33 | 0
2 | 2e+66 | 34 | 34 | 0
2 | 2e+67 | 34 | 34 | 0
2 | 2e+68 | 35 | 35 | 0
2 | 2e+69 | 35 | 35 | 0
2 | 2e+70 | 36 | 36 | 0
2 | 2e+71 | 36 | 36 | 0
2 | 2e+72 | 37 | 37 | 0
2 | 2e+73 | 37 | 37 | 0
2 | 2e+74 | 38 | 38 | 0
2 | 2e+75 | 38 | 38 | 0
2 | 2e+76 | 39 | 39 | 0
2 | 2e+77 | 39 | 39 | 0
2 | 2e+78 | 40 | 40 | 0
2 | 2e+79 | 40 | 40 | 0
2 | 2e+80 | 41 | 41 | 0
2 | 2e+81 | 41 | 41 | 0
2 | 2e+82 | 42 | 42 | 0
2 | 2e+83 | 42 | 42 | 0
2 | 2e+84 | 43 | 43 | 0
2 | 2e+85 | 43 | 43 | 0
2 | 2e+86 | 44 | 44 | 0
2 | 2e+87 | 44 | 44 | 0
2 | 2e+88 | 45 | 45 | 0
2 | 2e+89 | 45 | 45 | 0
2 | 2e+90 | 46 | 46 | 0
2 | 2e+91 | 46 | 46 | 0
2 | 2e+92 | 47 | 47 | 0
2 | 2e+93 | 47 | 47 | 0
2 | 2e+94 | 48 | 48 | 0
2 | 2e+95 | 48 | 48 | 0
2 | 2e+96 | 49 | 49 | 0
2 | 2e+97 | 49 | 49 | 0
2 | 2e+98 | 50 | 50 | 0
2 | 2e+99 | 50 | 50 | 0
2 | 2e+100 | 51 | 51 | 0
(201 rows)
--
-- Comparison of sig_figs(sqrt(n)) for HEAD vs fix-sweight-v4
-- when DEC_DIGITS == 4
--
DEC_DIGITS | n | HEAD | fix-sweight-v4 | diff
------------+--------------+------+----------------+------
4 | 2e-100 | 51 | 51 | 0
4 | 2e-99 | 50 | 50 | 0
4 | 2e-98 | 50 | 50 | 0
4 | 2e-97 | 49 | 49 | 0
4 | 2e-96 | 49 | 49 | 0
4 | 2e-95 | 48 | 48 | 0
4 | 2e-94 | 48 | 48 | 0
4 | 2e-93 | 47 | 47 | 0
4 | 2e-92 | 47 | 47 | 0
4 | 2e-91 | 46 | 46 | 0
4 | 2e-90 | 46 | 46 | 0
4 | 2e-89 | 45 | 45 | 0
4 | 2e-88 | 45 | 45 | 0
4 | 2e-87 | 44 | 44 | 0
4 | 2e-86 | 44 | 44 | 0
4 | 2e-85 | 43 | 43 | 0
4 | 2e-84 | 43 | 43 | 0
4 | 2e-83 | 42 | 42 | 0
4 | 2e-82 | 42 | 42 | 0
4 | 2e-81 | 41 | 41 | 0
4 | 2e-80 | 41 | 41 | 0
4 | 2e-79 | 40 | 40 | 0
4 | 2e-78 | 40 | 40 | 0
4 | 2e-77 | 39 | 39 | 0
4 | 2e-76 | 39 | 39 | 0
4 | 2e-75 | 38 | 38 | 0
4 | 2e-74 | 38 | 38 | 0
4 | 2e-73 | 37 | 37 | 0
4 | 2e-72 | 37 | 37 | 0
4 | 2e-71 | 36 | 36 | 0
4 | 2e-70 | 36 | 36 | 0
4 | 2e-69 | 35 | 35 | 0
4 | 2e-68 | 35 | 35 | 0
4 | 2e-67 | 34 | 34 | 0
4 | 2e-66 | 34 | 34 | 0
4 | 2e-65 | 33 | 33 | 0
4 | 2e-64 | 33 | 33 | 0
4 | 2e-63 | 32 | 32 | 0
4 | 2e-62 | 32 | 32 | 0
4 | 2e-61 | 31 | 31 | 0
4 | 2e-60 | 31 | 31 | 0
4 | 2e-59 | 30 | 30 | 0
4 | 2e-58 | 30 | 30 | 0
4 | 2e-57 | 29 | 29 | 0
4 | 2e-56 | 29 | 29 | 0
4 | 2e-55 | 28 | 28 | 0
4 | 2e-54 | 28 | 28 | 0
4 | 2e-53 | 27 | 27 | 0
4 | 2e-52 | 27 | 27 | 0
4 | 2e-51 | 26 | 26 | 0
4 | 2e-50 | 26 | 26 | 0
4 | 2e-49 | 25 | 25 | 0
4 | 2e-48 | 25 | 25 | 0
4 | 2e-47 | 24 | 24 | 0
4 | 2e-46 | 24 | 24 | 0
4 | 2e-45 | 23 | 23 | 0
4 | 2e-44 | 23 | 23 | 0
4 | 2e-43 | 22 | 22 | 0
4 | 2e-42 | 22 | 22 | 0
4 | 2e-41 | 21 | 21 | 0
4 | 2e-40 | 21 | 21 | 0
4 | 2e-39 | 20 | 20 | 0
4 | 2e-38 | 20 | 20 | 0
4 | 2e-37 | 19 | 19 | 0
4 | 2e-36 | 19 | 19 | 0
4 | 2e-35 | 18 | 18 | 0
4 | 2e-34 | 18 | 18 | 0
4 | 2e-33 | 17 | 17 | 0
4 | 2e-32 | 17 | 17 | 0
4 | 2e-31 | 16 | 16 | 0
4 | 2e-30 | 17 | 17 | 0
4 | 2e-29 | 17 | 17 | 0
4 | 2e-28 | 16 | 16 | 0
4 | 2e-27 | 16 | 16 | 0
4 | 2e-26 | 17 | 17 | 0
4 | 2e-25 | 17 | 17 | 0
4 | 2e-24 | 16 | 16 | 0
4 | 2e-23 | 16 | 16 | 0
4 | 2e-22 | 17 | 17 | 0
4 | 2e-21 | 17 | 17 | 0
4 | 2e-20 | 16 | 16 | 0
4 | 2e-19 | 16 | 16 | 0
4 | 2e-18 | 17 | 17 | 0
4 | 2e-17 | 17 | 17 | 0
4 | 2e-16 | 16 | 16 | 0
4 | 2e-15 | 16 | 16 | 0
4 | 2e-14 | 17 | 17 | 0
4 | 2e-13 | 17 | 17 | 0
4 | 2e-12 | 16 | 16 | 0
4 | 2e-11 | 16 | 16 | 0
4 | 0.0000000002 | 17 | 17 | 0
4 | 0.000000002 | 17 | 17 | 0
4 | 0.00000002 | 16 | 16 | 0
4 | 0.0000002 | 16 | 16 | 0
4 | 0.000002 | 17 | 17 | 0
4 | 0.00002 | 17 | 17 | 0
4 | 0.0002 | 16 | 16 | 0
4 | 0.002 | 16 | 16 | 0
4 | 0.02 | 17 | 17 | 0
4 | 0.2 | 17 | 17 | 0
4 | 2 | 16 | 16 | 0
4 | 20 | 16 | 16 | 0
4 | 200 | 17 | 17 | 0
4 | 2000 | 17 | 17 | 0
4 | 20000 | 16 | 16 | 0
4 | 200000 | 16 | 16 | 0
4 | 2000000 | 17 | 17 | 0
4 | 20000000 | 17 | 17 | 0
4 | 200000000 | 16 | 16 | 0
4 | 2000000000 | 16 | 16 | 0
4 | 20000000000 | 17 | 17 | 0
4 | 2e+11 | 17 | 17 | 0
4 | 2e+12 | 16 | 16 | 0
4 | 2e+13 | 16 | 16 | 0
4 | 2e+14 | 17 | 17 | 0
4 | 2e+15 | 17 | 17 | 0
4 | 2e+16 | 16 | 16 | 0
4 | 2e+17 | 16 | 16 | 0
4 | 2e+18 | 17 | 17 | 0
4 | 2e+19 | 17 | 17 | 0
4 | 2e+20 | 16 | 16 | 0
4 | 2e+21 | 16 | 16 | 0
4 | 2e+22 | 17 | 17 | 0
4 | 2e+23 | 17 | 17 | 0
4 | 2e+24 | 16 | 16 | 0
4 | 2e+25 | 16 | 16 | 0
4 | 2e+26 | 17 | 17 | 0
4 | 2e+27 | 17 | 17 | 0
4 | 2e+28 | 16 | 16 | 0
4 | 2e+29 | 16 | 16 | 0
4 | 2e+30 | 17 | 17 | 0
4 | 2e+31 | 17 | 17 | 0
4 | 2e+32 | 17 | 17 | 0
4 | 2e+33 | 17 | 17 | 0
4 | 2e+34 | 18 | 18 | 0
4 | 2e+35 | 18 | 18 | 0
4 | 2e+36 | 19 | 19 | 0
4 | 2e+37 | 19 | 19 | 0
4 | 2e+38 | 20 | 20 | 0
4 | 2e+39 | 20 | 20 | 0
4 | 2e+40 | 21 | 21 | 0
4 | 2e+41 | 21 | 21 | 0
4 | 2e+42 | 22 | 22 | 0
4 | 2e+43 | 22 | 22 | 0
4 | 2e+44 | 23 | 23 | 0
4 | 2e+45 | 23 | 23 | 0
4 | 2e+46 | 24 | 24 | 0
4 | 2e+47 | 24 | 24 | 0
4 | 2e+48 | 25 | 25 | 0
4 | 2e+49 | 25 | 25 | 0
4 | 2e+50 | 26 | 26 | 0
4 | 2e+51 | 26 | 26 | 0
4 | 2e+52 | 27 | 27 | 0
4 | 2e+53 | 27 | 27 | 0
4 | 2e+54 | 28 | 28 | 0
4 | 2e+55 | 28 | 28 | 0
4 | 2e+56 | 29 | 29 | 0
4 | 2e+57 | 29 | 29 | 0
4 | 2e+58 | 30 | 30 | 0
4 | 2e+59 | 30 | 30 | 0
4 | 2e+60 | 31 | 31 | 0
4 | 2e+61 | 31 | 31 | 0
4 | 2e+62 | 32 | 32 | 0
4 | 2e+63 | 32 | 32 | 0
4 | 2e+64 | 33 | 33 | 0
4 | 2e+65 | 33 | 33 | 0
4 | 2e+66 | 34 | 34 | 0
4 | 2e+67 | 34 | 34 | 0
4 | 2e+68 | 35 | 35 | 0
4 | 2e+69 | 35 | 35 | 0
4 | 2e+70 | 36 | 36 | 0
4 | 2e+71 | 36 | 36 | 0
4 | 2e+72 | 37 | 37 | 0
4 | 2e+73 | 37 | 37 | 0
4 | 2e+74 | 38 | 38 | 0
4 | 2e+75 | 38 | 38 | 0
4 | 2e+76 | 39 | 39 | 0
4 | 2e+77 | 39 | 39 | 0
4 | 2e+78 | 40 | 40 | 0
4 | 2e+79 | 40 | 40 | 0
4 | 2e+80 | 41 | 41 | 0
4 | 2e+81 | 41 | 41 | 0
4 | 2e+82 | 42 | 42 | 0
4 | 2e+83 | 42 | 42 | 0
4 | 2e+84 | 43 | 43 | 0
4 | 2e+85 | 43 | 43 | 0
4 | 2e+86 | 44 | 44 | 0
4 | 2e+87 | 44 | 44 | 0
4 | 2e+88 | 45 | 45 | 0
4 | 2e+89 | 45 | 45 | 0
4 | 2e+90 | 46 | 46 | 0
4 | 2e+91 | 46 | 46 | 0
4 | 2e+92 | 47 | 47 | 0
4 | 2e+93 | 47 | 47 | 0
4 | 2e+94 | 48 | 48 | 0
4 | 2e+95 | 48 | 48 | 0
4 | 2e+96 | 49 | 49 | 0
4 | 2e+97 | 49 | 49 | 0
4 | 2e+98 | 50 | 50 | 0
4 | 2e+99 | 50 | 50 | 0
4 | 2e+100 | 51 | 51 | 0
(201 rows)
