improve calc function CRITBINOM

CRITBINOM could not handle large sample quantities, e.g.
CRITBINOM(1080,0.5,0.1).
This patch fixes that and also improves the efficiency of
the function by always iterating from the end nearest to
the cumulative binomial distribution.

Change-Id: I35f965acc83e26141fb2cf5a7e3303ec0791f04a
Reviewed-on: https://gerrit.libreoffice.org/6559Reviewed-by: Eike Rathke <erack@redhat.com>
Tested-by: Eike Rathke <erack@redhat.com>

sc/source/core/tool/interpr3.cxx

@@ -1383,14 +1383,49 @@ void ScInterpreter::ScCritBinom()
             PushIllegalArgument();
         else
         {
+            double fFactor;
             double q = (0.5 - p) + 0.5;           // get one bit more for p near 1.0
-            double fFactor = pow(q,n);
-            if (fFactor <= ::std::numeric_limits<double>::min())
+            if ( q > p )                          // work from the side where the cumulative curve is
             {
-                fFactor = pow(p, n);
-                if (fFactor <= ::std::numeric_limits<double>::min())
-                    PushNoValue();
+                // work from 0 upwards
+                fFactor = pow(q,n);
+                if (fFactor > ::std::numeric_limits<double>::min())
+                {
+                    double fSum = fFactor;
+                    sal_uInt32 max = static_cast<sal_uInt32> (n), i;
+                    for (i = 0; i < max && fSum < alpha; i++)
+                    {
+                        fFactor *= (n-i)/(i+1)*p/q;
+                        fSum += fFactor;
+                    }
+                    PushDouble(i);
+                }
                 else
+                {
+                    // accumulate BinomDist until accumulated BinomDist reaches alpha
+                    double fSum = 0.0, x;
+                    sal_uInt32 max = static_cast<sal_uInt32> (n), i;
+                    for (i = 0; i < max && fSum < alpha; i++)
+                    {
+                        x = GetBetaDistPDF( p, ( i + 1 ), ( n - i + 1 ) )/( n + 1 );
+                        if ( !nGlobalError )
+                        {
+                            fSum += x;
+                        }
+                        else
+                        {
+                            PushNoValue();
+                            return;
+                        }
+                    }
+                    PushDouble( i - 1 );
+                }
+            }
+            else
+            {
+                // work from n backwards
+                fFactor = pow(p, n);
+                if (fFactor > ::std::numeric_limits<double>::min())
                 {
                     double fSum = 1.0 - fFactor;
                     sal_uInt32 max = static_cast<sal_uInt32> (n), i;
@@ -1401,17 +1436,27 @@ void ScInterpreter::ScCritBinom()
                     }
                     PushDouble(n-i);
                 }
-            }
-            else
-            {
-                double fSum = fFactor;
-                sal_uInt32 max = static_cast<sal_uInt32> (n), i;
-                for (i = 0; i < max && fSum < alpha; i++)
+                else
                 {
-                    fFactor *= (n-i)/(i+1)*p/q;
-                    fSum += fFactor;
+                    // accumulate BinomDist until accumulated BinomDist reaches alpha
+                    double fSum = 0.0, x;
+                    sal_uInt32 max = static_cast<sal_uInt32> (n), i;
+                    alpha = 1 - alpha;
+                    for (i = 0; i < max && fSum < alpha; i++)
+                    {
+                        x = GetBetaDistPDF( q, ( i + 1 ), ( n - i + 1 ) )/( n + 1 );
+                        if ( !nGlobalError )
+                        {
+                            fSum += x;
+                        }
+                        else
+                        {
+                            PushNoValue();
+                            return;
+                        }
+                    }
+                    PushDouble( n - i + 1 );
                 }
-                PushDouble(i);
             }
         }
     }