From b2a0f1673371fd0156685b44b06a818609ed7c95 Mon Sep 17 00:00:00 2001 From: Dean Rasheed Date: Wed, 6 Oct 2021 13:22:33 +0100 Subject: [PATCH] Fix corner-case loss of precision in numeric_power(). This fixes a loss of precision that occurs when the first input is very close to 1, so that its logarithm is very small. Formerly, during the initial low-precision calculation to estimate the result weight, the logarithm was computed to a local rscale that was capped to NUMERIC_MAX_DISPLAY_SCALE (1000). However, the base may be as close as 1e-16383 to 1, hence its logarithm may be as small as 1e-16383, and so the local rscale needs to be allowed to exceed 16383, otherwise all precision is lost, leading to a poor choice of rscale for the full-precision calculation. Fix this by removing the cap on the local rscale during the initial low-precision calculation, as we already do in the full-precision calculation. This doesn't change the fact that the initial calculation is a low-precision approximation, computing the logarithm to around 8 significant digits, which is very fast, especially when the base is very close to 1. Patch by me, reviewed by Alvaro Herrera. Discussion: https://postgr.es/m/CAEZATCV-Ceu%2BHpRMf416yUe4KKFv%3DtdgXQAe5-7S9tD%3D5E-T1g%40mail.gmail.com --- src/backend/utils/adt/numeric.c | 6 +++++- src/test/regress/expected/numeric.out | 6 ++++++ src/test/regress/sql/numeric.sql | 1 + 3 files changed, 12 insertions(+), 1 deletion(-) diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c index 8318616796..2ef0be6df1 100644 --- a/src/backend/utils/adt/numeric.c +++ b/src/backend/utils/adt/numeric.c @@ -8302,9 +8302,13 @@ power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result) */ ln_dweight = estimate_ln_dweight(base); + /* + * Set the scale for the low-precision calculation, computing ln(base) to + * around 8 significant digits. Note that ln_dweight may be as small as + * -SHRT_MAX, so the scale may exceed NUMERIC_MAX_DISPLAY_SCALE here. + */ local_rscale = 8 - ln_dweight; local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE); - local_rscale = Min(local_rscale, NUMERIC_MAX_DISPLAY_SCALE); ln_var(base, &ln_base, local_rscale); diff --git a/src/test/regress/expected/numeric.out b/src/test/regress/expected/numeric.out index 4ec5c7d979..ced7980709 100644 --- a/src/test/regress/expected/numeric.out +++ b/src/test/regress/expected/numeric.out @@ -1723,6 +1723,12 @@ select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero; 0 (1 row) +select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000); + round +---------------------------------------------------------- + 25218976308958387188077465658068501556514992509509282366 +(1 row) + -- cases that used to error out select 0.12 ^ (-25); ?column? diff --git a/src/test/regress/sql/numeric.sql b/src/test/regress/sql/numeric.sql index 75ffb0044a..e5ff2b5902 100644 --- a/src/test/regress/sql/numeric.sql +++ b/src/test/regress/sql/numeric.sql @@ -922,6 +922,7 @@ select 1.2 ^ 345; select 0.12 ^ (-20); select 1.000000000123 ^ (-2147483648); select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero; +select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000); -- cases that used to error out select 0.12 ^ (-25);