Keep the digits of log, log10 and log2 near 1 - #1468
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- Above 1, log took log10(x) * ln10, and the reduction of log10 subtracts terms near 1. Below 1, both took the value of 1/x, which rounds. Near 1 the two lose most digits, and log(0.9999999_DF) gives -0. - log2 calls log, so it lost the same digits. - For x in [0.5, 1.5], x - 1 is exact, and log1p takes its series branch there, which does not call log. log and log10 now take log1p(x - 1) in this range. - log keeps x equal to 1 out of the new branch, so the downward mode still gives +0. - github_issue_1110 expected the old log10 value 4.4e-33, and now expects the correctly rounded value.
- log10 divided the rounded log1p by ln10, and log2 divided the rounded log by ln2. Near 1 these two more roundings gave up to 4 units in the last digit. - log1p_parts gives the two parts of the series of log1p before its last rounding, and log1p itself uses it as before. - log10 and log2 now scale the two parts with 2/ln(10) and 2/ln(2) in two parts each, and round only once. - The series of log1p used all terms of its table for each argument, thus log, log10 and log2 near 1 became slower than the old path. log1p_series_sum now uses only the terms which can change the result. It gets their number from the exponent and the leading digit of w^2, and each term that it drops is less than 0.01 of the last digit. Fixes boostorg#1467
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Looks reasonable to me. Will merge once green. Thanks
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## develop #1468 +/- ##
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+ Coverage 98.6% 98.6% +0.1%
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Files 306 307 +1
Lines 25620 25705 +85
Branches 2202 2203 +1
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+ Hits 25256 25340 +84
- Misses 364 365 +1
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log,log10andlog2lost most of their digits. Above 1,logtooklog10(x) * ln10, and the reduction oflog10subtracts terms near 1. Below 1, thefunctions took the value of
1/x, which rounds.xin[0.5, 1.5],x - 1is exact.lognow takeslog1p(x - 1)there.log10andlog2scale the two parts of thelog1pseries with2/ln(10)and2/ln(2), each held in two parts. The result rounds only once.log1pseries uses only the terms that can change the result. Each term that itdrops is less than 0.01 of the last digit.
github_issue_1110expected the old value4.4e-33. It now expects the correctlyrounded value.
github_issue_1467.cppcompares the three functions with MPFR values forthe six types.
Near 1 the three functions are inside 0.5 units in the last digit, and they need 16 to
51 percent less time than before. Over a wide range the time changes by less than 5
percent. Issue #1467 gives the values, the MPFR sweep and the full benchmark.
Fixes #1467