Avoid gratuitous inaccuracy in numeric width_bucket().
Multiply before dividing, not the reverse, so that cases that should produce exact results do produce exact results. (width_bucket_float8 got this right already.) Even when the result is inexact, this avoids making it more inexact, since only the division step introduces any imprecision. While at it, fix compute_bucket() to not uselessly repeat the sign check already done by its caller, and avoid duplicating the multiply/divide steps by adjusting variable usage. Per complaint from Martin Visser. Although this seems like a bug fix, I'm hesitant to risk changing width_bucket()'s results in stable branches, so no back-patch. Discussion: https://postgr.es/m/6FA5117D-6AED-4656-8FEF-B74AC18FAD85@brytlyt.com
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@ -592,7 +592,8 @@ static void round_var(NumericVar *var, int rscale);
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static void trunc_var(NumericVar *var, int rscale);
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static void strip_var(NumericVar *var);
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static void compute_bucket(Numeric operand, Numeric bound1, Numeric bound2,
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const NumericVar *count_var, NumericVar *result_var);
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const NumericVar *count_var, bool reversed_bounds,
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NumericVar *result_var);
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static void accum_sum_add(NumericSumAccum *accum, const NumericVar *var1);
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static void accum_sum_rescale(NumericSumAccum *accum, const NumericVar *val);
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@ -1752,8 +1753,8 @@ width_bucket_numeric(PG_FUNCTION_ARGS)
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else if (cmp_numerics(operand, bound2) >= 0)
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add_var(&count_var, &const_one, &result_var);
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else
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compute_bucket(operand, bound1, bound2,
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&count_var, &result_var);
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compute_bucket(operand, bound1, bound2, &count_var, false,
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&result_var);
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break;
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/* bound1 > bound2 */
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@ -1763,8 +1764,8 @@ width_bucket_numeric(PG_FUNCTION_ARGS)
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else if (cmp_numerics(operand, bound2) <= 0)
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add_var(&count_var, &const_one, &result_var);
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else
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compute_bucket(operand, bound1, bound2,
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&count_var, &result_var);
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compute_bucket(operand, bound1, bound2, &count_var, true,
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&result_var);
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break;
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}
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@ -1783,11 +1784,13 @@ width_bucket_numeric(PG_FUNCTION_ARGS)
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/*
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* If 'operand' is not outside the bucket range, determine the correct
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* bucket for it to go. The calculations performed by this function
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* are derived directly from the SQL2003 spec.
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* are derived directly from the SQL2003 spec. Note however that we
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* multiply by count before dividing, to avoid unnecessary roundoff error.
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*/
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static void
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compute_bucket(Numeric operand, Numeric bound1, Numeric bound2,
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const NumericVar *count_var, NumericVar *result_var)
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const NumericVar *count_var, bool reversed_bounds,
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NumericVar *result_var)
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{
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NumericVar bound1_var;
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NumericVar bound2_var;
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@ -1797,23 +1800,21 @@ compute_bucket(Numeric operand, Numeric bound1, Numeric bound2,
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init_var_from_num(bound2, &bound2_var);
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init_var_from_num(operand, &operand_var);
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if (cmp_var(&bound1_var, &bound2_var) < 0)
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if (!reversed_bounds)
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{
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sub_var(&operand_var, &bound1_var, &operand_var);
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sub_var(&bound2_var, &bound1_var, &bound2_var);
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div_var(&operand_var, &bound2_var, result_var,
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select_div_scale(&operand_var, &bound2_var), true);
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}
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else
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{
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sub_var(&bound1_var, &operand_var, &operand_var);
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sub_var(&bound1_var, &bound2_var, &bound1_var);
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div_var(&operand_var, &bound1_var, result_var,
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select_div_scale(&operand_var, &bound1_var), true);
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sub_var(&bound1_var, &bound2_var, &bound2_var);
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}
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mul_var(result_var, count_var, result_var,
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result_var->dscale + count_var->dscale);
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mul_var(&operand_var, count_var, &operand_var,
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operand_var.dscale + count_var->dscale);
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div_var(&operand_var, &bound2_var, result_var,
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select_div_scale(&operand_var, &bound2_var), true);
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add_var(result_var, &const_one, result_var);
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floor_var(result_var, result_var);
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@ -1385,6 +1385,46 @@ SELECT width_bucket('Infinity'::float8, 1, 10, 10),
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(1 row)
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DROP TABLE width_bucket_test;
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-- Simple test for roundoff error when results should be exact
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SELECT x, width_bucket(x::float8, 10, 100, 9) as flt,
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width_bucket(x::numeric, 10, 100, 9) as num
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FROM generate_series(0, 110, 10) x;
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x | flt | num
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-----+-----+-----
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0 | 0 | 0
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10 | 1 | 1
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20 | 2 | 2
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30 | 3 | 3
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40 | 4 | 4
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50 | 5 | 5
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60 | 6 | 6
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70 | 7 | 7
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80 | 8 | 8
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90 | 9 | 9
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100 | 10 | 10
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110 | 10 | 10
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(12 rows)
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SELECT x, width_bucket(x::float8, 100, 10, 9) as flt,
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width_bucket(x::numeric, 100, 10, 9) as num
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FROM generate_series(0, 110, 10) x;
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x | flt | num
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-----+-----+-----
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0 | 10 | 10
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10 | 10 | 10
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20 | 9 | 9
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30 | 8 | 8
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40 | 7 | 7
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50 | 6 | 6
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60 | 5 | 5
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70 | 4 | 4
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80 | 3 | 3
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90 | 2 | 2
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100 | 1 | 1
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110 | 0 | 0
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(12 rows)
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--
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-- TO_CHAR()
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--
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SELECT '' AS to_char_1, to_char(val, '9G999G999G999G999G999')
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@ -888,6 +888,15 @@ SELECT width_bucket('Infinity'::float8, 1, 10, 10),
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DROP TABLE width_bucket_test;
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-- Simple test for roundoff error when results should be exact
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SELECT x, width_bucket(x::float8, 10, 100, 9) as flt,
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width_bucket(x::numeric, 10, 100, 9) as num
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FROM generate_series(0, 110, 10) x;
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SELECT x, width_bucket(x::float8, 100, 10, 9) as flt,
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width_bucket(x::numeric, 100, 10, 9) as num
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FROM generate_series(0, 110, 10) x;
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--
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-- TO_CHAR()
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--
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SELECT '' AS to_char_1, to_char(val, '9G999G999G999G999G999')
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