More accurate calculation of variance and standard deviation for large number of…

More accurate calculation of variance and standard deviation for large number of samples with low variance (now using Welford's method).

h2/src/test/org/h2/test/test-1.3.txt

@@ -7509,6 +7509,12 @@ select stddev_pop(x) s_px, stddev_samp(x) s_sx, var_pop(x) v_px, var_samp(x) v_s
 stddev_pop(y) s_py, stddev_samp(y) s_sy, var_pop(y) v_py, var_samp(y) v_sy from t;
 > ok
 
+select var(100000000.1) z from system_range(1, 1000000);
+> Z
+> ---
+> 0.0
+> rows: 1
+
 select * from s;
 > S_PX S_SX V_PX V_SX S_PY S_SY V_PY V_SY
 > ---- ---- ---- ---- ---- ---- ---- ----
@@ -7561,9 +7567,9 @@ insert into t values(1000000016, 16);
 > update count: 1
 
 select * from s;
-> S_PX              S_SX              V_PX               V_SX S_PY              S_SY              V_PY               V_SY
-> ----------------- ----------------- ------------------ ---- ----------------- ----------------- ------------------ ----
-> 4.874423042781576 5.449770637375485 23.759999999999998 29.7 4.874423042781576 5.449770637375485 23.759999999999998 29.7
+> S_PX              S_SX              V_PX              V_SX               S_PY              S_SY              V_PY  V_SY
+> ----------------- ----------------- ----------------- ------------------ ----------------- ----------------- ----- ------------------
+> 4.874423036912116 5.449770630813229 23.75999994277954 29.699999928474426 4.874423042781577 5.449770637375485 23.76 29.700000000000003
 > rows: 1
 
 select stddev_pop(distinct x) s_px, stddev_samp(distinct x) s_sx, var_pop(distinct x) v_px, var_samp(distinct x) v_sx,