Repair roundoff-error problem for stddev/variance results near zero,

per complaint from Kemin Zhou.
Fix lack of precision in numeric stddev/variance.

diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 7d2018d..0f30fc6 100644 (file)
--- 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 1b955d5..321e673 100644 (file)
--- 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);