From 07009651ce4b2cc866171aed32bb67c8c65137ce Mon Sep 17 00:00:00 2001
From: Tom Lane <tgl@sss.pgh.pa.us>
Date: Tue, 11 Dec 2001 02:02:12 +0000
Subject: [PATCH] Repair roundoff-error problem for stddev/variance results
near zero, per complaint from Kemin Zhou. Fix lack of precision in numeric
stddev/variance.
---
src/backend/utils/adt/float.c | 24 +++++--
src/backend/utils/adt/numeric.c | 115 ++++++++++++++++++++++----------
2 files changed, 98 insertions(+), 41 deletions(-)
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 7d2018d7470..0f30fc63efb 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -8,7 +8,7 @@
*
*
* IDENTIFICATION
- * $Header: /cvsroot/pgsql/src/backend/utils/adt/float.c,v 1.77 2001/11/05 17:46:29 momjian Exp $
+ * $Header: /cvsroot/pgsql/src/backend/utils/adt/float.c,v 1.78 2001/12/11 02:02:12 tgl Exp $
*
*-------------------------------------------------------------------------
*/
@@ -1580,7 +1580,8 @@ float8_variance(PG_FUNCTION_ARGS)
float8 *transvalues;
float8 N,
sumX,
- sumX2;
+ sumX2,
+ numerator;
transvalues = check_float8_array(transarray, "float8_variance");
N = transvalues[0];
@@ -1594,7 +1595,13 @@ float8_variance(PG_FUNCTION_ARGS)
if (N <= 1.0)
PG_RETURN_FLOAT8(0.0);
- PG_RETURN_FLOAT8((N * sumX2 - sumX * sumX) / (N * (N - 1.0)));
+ numerator = N * sumX2 - sumX * sumX;
+
+ /* Watch out for roundoff error producing a negative numerator */
+ if (numerator <= 0.0)
+ PG_RETURN_FLOAT8(0.0);
+
+ PG_RETURN_FLOAT8(numerator / (N * (N - 1.0)));
}
Datum
@@ -1604,7 +1611,8 @@ float8_stddev(PG_FUNCTION_ARGS)
float8 *transvalues;
float8 N,
sumX,
- sumX2;
+ sumX2,
+ numerator;
transvalues = check_float8_array(transarray, "float8_stddev");
N = transvalues[0];
@@ -1618,7 +1626,13 @@ float8_stddev(PG_FUNCTION_ARGS)
if (N <= 1.0)
PG_RETURN_FLOAT8(0.0);
- PG_RETURN_FLOAT8(sqrt((N * sumX2 - sumX * sumX) / (N * (N - 1.0))));
+ numerator = N * sumX2 - sumX * sumX;
+
+ /* Watch out for roundoff error producing a negative numerator */
+ if (numerator <= 0.0)
+ PG_RETURN_FLOAT8(0.0);
+
+ PG_RETURN_FLOAT8(sqrt(numerator / (N * (N - 1.0))));
}
diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index 1b955d5e6c6..321e673aab3 100644
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -5,7 +5,7 @@
*
* 1998 Jan Wieck
*
- * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.48 2001/11/05 17:46:29 momjian Exp $
+ * $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.49 2001/12/11 02:02:12 tgl Exp $
*
* ----------
*/
@@ -159,6 +159,7 @@ static void add_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void div_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
+static int select_div_scale(NumericVar *var1, NumericVar *var2);
static void mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void ceil_var(NumericVar *var, NumericVar *result);
static void floor_var(NumericVar *var, NumericVar *result);
@@ -999,28 +1000,7 @@ numeric_div(PG_FUNCTION_ARGS)
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
- /* ----------
- * The result scale of a division isn't specified in any
- * SQL standard. For Postgres it is the following (where
- * SR, DR are the result- and display-scales of the returned
- * value, S1, D1, S2 and D2 are the scales of the two arguments,
- * The minimum and maximum scales are compile time options from
- * numeric.h):
- *
- * DR = MIN(MAX(D1 + D2, MIN_DISPLAY_SCALE), MAX_DISPLAY_SCALE)
- * SR = MIN(MAX(MAX(S1 + S2, MIN_RESULT_SCALE), DR + 4), MAX_RESULT_SCALE)
- *
- * By default, any result is computed with a minimum of 34 digits
- * after the decimal point or at least with 4 digits more than
- * displayed.
- * ----------
- */
- res_dscale = MAX(arg1.dscale + arg2.dscale, NUMERIC_MIN_DISPLAY_SCALE);
- res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
- global_rscale = MAX(arg1.rscale + arg2.rscale,
- NUMERIC_MIN_RESULT_SCALE);
- global_rscale = MAX(global_rscale, res_dscale + 4);
- global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
+ res_dscale = select_div_scale(&arg1, &arg2);
/*
* Do the divide, set the display scale and return the result
@@ -1884,6 +1864,7 @@ numeric_variance(PG_FUNCTION_ARGS)
vsumX,
vsumX2,
vNminus1;
+ int div_dscale;
/* We assume the input is array of numeric */
deconstruct_array(transarray,
@@ -1924,10 +1905,21 @@ numeric_variance(PG_FUNCTION_ARGS)
mul_var(&vsumX, &vsumX, &vsumX); /* now vsumX contains sumX * sumX */
mul_var(&vN, &vsumX2, &vsumX2); /* now vsumX2 contains N * sumX2 */
sub_var(&vsumX2, &vsumX, &vsumX2); /* N * sumX2 - sumX * sumX */
- mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
- div_var(&vsumX2, &vNminus1, &vsumX); /* variance */
- res = make_result(&vsumX);
+ if (cmp_var(&vsumX2, &const_zero) <= 0)
+ {
+ /* Watch out for roundoff error producing a negative numerator */
+ res = make_result(&const_zero);
+ }
+ else
+ {
+ mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
+ div_dscale = select_div_scale(&vsumX2, &vNminus1);
+ div_var(&vsumX2, &vNminus1, &vsumX); /* variance */
+ vsumX.dscale = div_dscale;
+
+ res = make_result(&vsumX);
+ }
free_var(&vN);
free_var(&vNminus1);
@@ -1951,6 +1943,7 @@ numeric_stddev(PG_FUNCTION_ARGS)
vsumX,
vsumX2,
vNminus1;
+ int div_dscale;
/* We assume the input is array of numeric */
deconstruct_array(transarray,
@@ -1991,11 +1984,22 @@ numeric_stddev(PG_FUNCTION_ARGS)
mul_var(&vsumX, &vsumX, &vsumX); /* now vsumX contains sumX * sumX */
mul_var(&vN, &vsumX2, &vsumX2); /* now vsumX2 contains N * sumX2 */
sub_var(&vsumX2, &vsumX, &vsumX2); /* N * sumX2 - sumX * sumX */
- mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
- div_var(&vsumX2, &vNminus1, &vsumX); /* variance */
- sqrt_var(&vsumX, &vsumX); /* stddev */
- res = make_result(&vsumX);
+ if (cmp_var(&vsumX2, &const_zero) <= 0)
+ {
+ /* Watch out for roundoff error producing a negative numerator */
+ res = make_result(&const_zero);
+ }
+ else
+ {
+ mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
+ div_dscale = select_div_scale(&vsumX2, &vNminus1);
+ div_var(&vsumX2, &vNminus1, &vsumX); /* variance */
+ vsumX.dscale = div_dscale;
+ sqrt_var(&vsumX, &vsumX); /* stddev */
+
+ res = make_result(&vsumX);
+ }
free_var(&vN);
free_var(&vNminus1);
@@ -3318,6 +3322,50 @@ div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
}
+/*
+ * Default scale selection for division
+ *
+ * Returns the appropriate display scale for the division result,
+ * and sets global_rscale to the result scale to use during div_var.
+ *
+ * Note that this must be called before div_var.
+ */
+static int
+select_div_scale(NumericVar *var1, NumericVar *var2)
+{
+ int res_dscale;
+ int res_rscale;
+
+ /* ----------
+ * The result scale of a division isn't specified in any
+ * SQL standard. For Postgres it is the following (where
+ * SR, DR are the result- and display-scales of the returned
+ * value, S1, D1, S2 and D2 are the scales of the two arguments,
+ * The minimum and maximum scales are compile time options from
+ * numeric.h):
+ *
+ * DR = MIN(MAX(D1 + D2, MIN_DISPLAY_SCALE), MAX_DISPLAY_SCALE)
+ * SR = MIN(MAX(MAX(S1 + S2, DR + 4), MIN_RESULT_SCALE), MAX_RESULT_SCALE)
+ *
+ * By default, any result is computed with a minimum of 34 digits
+ * after the decimal point or at least with 4 digits more than
+ * displayed.
+ * ----------
+ */
+ res_dscale = var1->dscale + var2->dscale;
+ res_dscale = MAX(res_dscale, NUMERIC_MIN_DISPLAY_SCALE);
+ res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
+
+ res_rscale = var1->rscale + var2->rscale;
+ res_rscale = MAX(res_rscale, res_dscale + 4);
+ res_rscale = MAX(res_rscale, NUMERIC_MIN_RESULT_SCALE);
+ res_rscale = MIN(res_rscale, NUMERIC_MAX_RESULT_SCALE);
+ global_rscale = res_rscale;
+
+ return res_dscale;
+}
+
+
/* ----------
* mod_var() -
*
@@ -3343,12 +3391,7 @@ mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
*/
save_global_rscale = global_rscale;
- div_dscale = MAX(var1->dscale + var2->dscale, NUMERIC_MIN_DISPLAY_SCALE);
- div_dscale = MIN(div_dscale, NUMERIC_MAX_DISPLAY_SCALE);
- global_rscale = MAX(var1->rscale + var2->rscale,
- NUMERIC_MIN_RESULT_SCALE);
- global_rscale = MAX(global_rscale, div_dscale + 4);
- global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
+ div_dscale = select_div_scale(var1, var2);
div_var(var1, var2, &tmp);
--
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