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Round at up to 38 decimal places instead of 18 - #35
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October 8, 2026 10:53
Every rounding path refused a place outside -18 to 18, the largest power of ten in a 64-bit integer. Rational has held Int128 since 0.4.0, and from_decimal and _r span 10^-38 to 10^38, so checked_round with SignificantDigits failed for every value below 10^(n - 19): 15 significant digits of anything below 1e-4. MaximumDecimalPlaces, 38, is now the one limit checked_round (both forms), round_wide_ratio, and with it rounded_in_unit and decide_rounding, and rounded_square_root refuse past. An intermediate that does not fit is still Overflow, never a wrong or clamped value: 2/3 at 38 places, an irrational square root past 19 places. checked_decimal_text keeps refusing fewer than -18 places on its own, which it used to inherit from checked_round. rational_from_double's documented limits are recomputed and pinned on both sides: a double below 2^53 rounds at every place up to 22, a fraction over at least 2^N up to 31. Refs #34 Signed-off-by: Christian Parpart <c.parpart@lastrada.net>
rounded_ln, rounded_log10 and rounded_exp now take places from -38 to 38, as checked_round does. decide_rounding scales an end by up to 10^38, so the transcendental kernel widens from 384 to 448 bits: e^-80 to whole 10^38s scales the denominator 2^(192+116) past 2^384. The exponential's shortcut below -43 assumed e^x was below a quarter of the last kept unit at any place accepted, which holds only up to 18 places: at 22 places e^-50 is 2e-22, not 0. The shortcut now starts below -89, the argument whose exponential is below a quarter of 10^-38, and the kernel's reduction takes arguments down to -89 (m up to 129); the error bound and the width bounds in the kernel's comment are restated for it. A logarithm's enclosure is at least 1.6e-37 wide, so a logarithm rounded at 37 or 38 places is Overflow, never a guess; up to 30 places the reference table decides every row. The documented constant-evaluation costs are re-measured: 10 to 15 percent more per enclosure. Refs #34 Signed-off-by: Christian Parpart <c.parpart@lastrada.net>
Text output keeps refusing more than 18 decimal places either way: fixed 64-bit digit buffers, long division and the compile-time format-spec checks. Its comments said that limit was checked_round's, or the -18 to 18 DecimalPlaces spans; rounding now reaches 38, so they state it as the text layer's own. format.hpp's two bare 18s name ExactDecimalPlaces. No behaviour changes. Refs #34 Signed-off-by: Christian Parpart <c.parpart@lastrada.net>
The numbers guide states the new rounding limit and recomputes the limits rational_from_double meets; the expressions guide gives the rounded logarithms' and exponential's places, the logarithms' 36-place ceiling and the exponential's threshold at -89, and the exact log10 range of 10^-38 to 10^38 the code has. The display guide and the numeric-headroom page keep 18 places as text output's own limit. The changelog records both, and MaximumDecimalPlaces. Refs #34 Signed-off-by: Christian Parpart <c.parpart@lastrada.net>
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October 8, 2026 10:30
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Rounding refused any place outside -18 to 18, a limit left over from the 64-bit
Rational. SinceRationalholdsInt128andfrom_decimalspans 10^-38 to 10^38, that limit madechecked_round(v, SignificantDigits { 15 }, mode)fail for every value below 1e-4. Rounding now reaches 38 places in each direction; text output keeps its own 18-place limit.Fixes #34
Changes
MaximumDecimalPlaces(38) is the bound forchecked_round(both overloads),round_wide_ratio(and sorounded_in_unit,decide_rounding,rounded_output),rounded_sqrtand the rounded logarithms and exponential. An intermediate that does not fit is stillOverflow, never a clamped value: an irrational square root stops at 19 places, a logarithm the kernel computes at 36, 2/3 at 38 places does not fit.decide_roundingscales by up to 10^38. Constant-evaluation cost per enclosure rises 10 to 15 percent; every compile-time test still fits the default budgets of cl, clang-cl, g++-14 and clang++.rounded_expcorrectness at more than 18 places. Its shortcut for very negative arguments (answer 0 or one unit) started below -43, which is only right up to 18 places; at 22 places e^-50 read 0 instead of 2e-22. The shortcut now starts below -89 and the kernel covers -89 up, with the error bound restated. Tests pin the threshold from both sides.decimal_text,number_text, traces,render()andstd::formatbehave as before, guarded by their own checks rather than bychecked_roundrefusing.rational_from_double's documented limits recomputed and pinned on both sides; theround_wide_ratioagreement test extended to -38..38; the guides and the changelog updated.