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

diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index 9f16f09c11000882cffd2f0e127baed3e0f9c018..885d50f5fc3e7e455cd4e4e85548386ef07fee8d 100644 (file)
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -9245,9 +9245,13 @@ 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 5c54d7bc48d2fb786fa726f2dfc313ca3646f818..4ca9fd640885f7e278749d75fbe1e7c6cbaefd8f 100644 (file)
--- a/src/test/regress/expected/numeric.out
+++ b/src/test/regress/expected/numeric.out
@@ -1774,6 +1774,12 @@ 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 c0388691e5699e05ec08fd17d7cddc71c6654e5a..34f96d1aab345d7f233ab374d2d0fe6695977ae1 100644 (file)
--- a/src/test/regress/sql/numeric.sql
+++ b/src/test/regress/sql/numeric.sql
@@ -935,6 +935,7 @@ 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);