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Commit e54a758

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deanrasheeddeanrasheed
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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
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‎src/backend/utils/adt/numeric.c

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+5-1Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -10266,9 +10266,13 @@ power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result)
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*/
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ln_dweight = estimate_ln_dweight(base);
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/*
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* Set the scale for the low-precision calculation, computing ln(base) to
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* around 8 significant digits. Note that ln_dweight may be as small as
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* -SHRT_MAX, so the scale may exceed NUMERIC_MAX_DISPLAY_SCALE here.
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*/
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local_rscale = 8 - ln_dweight;
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local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE);
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local_rscale = Min(local_rscale, NUMERIC_MAX_DISPLAY_SCALE);
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ln_var(base, &ln_base, local_rscale);
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‎src/test/regress/expected/numeric.out

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+6Lines changed: 6 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -2483,6 +2483,12 @@ select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero;
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0
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(1 row)
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select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000);
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round
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----------------------------------------------------------
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25218976308958387188077465658068501556514992509509282366
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(1 row)
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-- cases that used to error out
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select 0.12 ^ (-25);
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?column?

‎src/test/regress/sql/numeric.sql

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+1Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -1148,6 +1148,7 @@ select 1.2 ^ 345;
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select 0.12 ^ (-20);
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select 1.000000000123 ^ (-2147483648);
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select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero;
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select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000);
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-- cases that used to error out
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select 0.12 ^ (-25);

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