Fix corner-case loss of precision in numeric pow() calculation
Commit 7d9a4737c268f61fb8800957631f12d3f13be218 greatly improved the
accuracy of the numeric transcendental functions, however it failed to
consider the case where the result from pow() is close to the overflow
threshold, for example 0.12 ^ -2345.6. For such inputs, where the
result has more than 2000 digits before the decimal point, the decimal
result weight estimate was being clamped to 2000, leading to a loss of
precision in the final calculation.
Fix this by replacing the clamping code with an overflow test that
aborts the calculation early if the final result is sure to overflow,
based on the overflow limit in exp_var(). This provides the same
protection against integer overflow in the subsequent result scale
computation as the original clamping code, but it also ensures that
precision is never lost and saves compute cycles in cases that are
sure to overflow.
The new early overflow test works with the initial low-precision
result (expected to be accurate to around 8 significant digits) and
includes a small fuzz factor to ensure that it doesn't kick in for
values that would not overflow exp_var(), so the overall overflow
threshold of pow() is unchanged and consistent for all inputs with
non-integer exponents.
Author: Dean Rasheed
Reviewed-by: Tom Lane
Discussion: http://www.postgresql.org/message-id/CAEZATCUj3U-cQj0jjoia=qgs0SjE3auroxh8swvNKvZWUqegrg@mail.gmail.com
See-also: http://www.postgresql.org/message-id/CAEZATCV7w+8iB=07dJ8Q0zihXQT1semcQuTeK+4_rogC_zq5Hw@mail.gmail.com
Branch
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master
Details
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http://git.postgresql.org/pg/commitdiff/18a02ad2a506e4425c6dd2ea235039cd5659467d
Modified Files
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src/backend/utils/adt/numeric.c | 20 ++++++++++++++++----
src/test/regress/expected/numeric_big.out | 14 ++++++++++++++
src/test/regress/sql/numeric_big.sql | 10 ++++++++++
3 files changed, 40 insertions(+), 4 deletions(-)