From 95c7edc7a5e31255c35126aec4829f782966b155 Mon Sep 17 00:00:00 2001
From: kzrnm <gengesa@gmail.com>
Date: Sat, 3 Feb 2024 05:58:18 +0900
Subject: [PATCH] Simplify BigInteger.Multiply

---
 .../Numerics/BigIntegerCalculator.SquMul.cs   | 332 ++++++------------
 .../tests/BigInteger/multiply.cs              |   8 +-
 .../tests/BigInteger/op_multiply.cs           |   4 +-
 3 files changed, 106 insertions(+), 238 deletions(-)

diff --git a/src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.SquMul.cs b/src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.SquMul.cs
index a31153ceec8348..54d0bc9f69f6ae 100644
--- a/src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.SquMul.cs
+++ b/src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.SquMul.cs
@@ -155,29 +155,13 @@ internal static
 #else
         internal const
 #endif
-        int MultiplyThreshold = 32;
-
+            int MultiplyKaratsubaThreshold = 32;
         public static void Multiply(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits)
         {
             Debug.Assert(left.Length >= right.Length);
             Debug.Assert(bits.Length >= left.Length + right.Length);
-            Debug.Assert(!bits.ContainsAnyExcept(0u));
-
-            if (left.Length - right.Length < 3)
-            {
-                MultiplyNearLength(left, right, bits);
-            }
-            else
-            {
-                MultiplyFarLength(left, right, bits);
-            }
-        }
-
-        private static void MultiplyFarLength(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits)
-        {
-            Debug.Assert(left.Length - right.Length >= 3);
-            Debug.Assert(bits.Length >= left.Length + right.Length);
-            Debug.Assert(!bits.ContainsAnyExcept(0u));
+            Debug.Assert(bits.Trim(0u).IsEmpty);
+            Debug.Assert(MultiplyKaratsubaThreshold >= 2);
 
             // Executes different algorithms for computing z = a * b
             // based on the actual length of b. If b is "small" enough
@@ -188,120 +172,91 @@ private static void MultiplyFarLength(ReadOnlySpan<uint> left, ReadOnlySpan<uint
             // NOTE: useful thresholds needs some "empirical" testing,
             // which are smaller in DEBUG mode for testing purpose.
 
-            if (right.Length < MultiplyThreshold)
+            if (right.Length < MultiplyKaratsubaThreshold)
             {
-                // Switching to managed references helps eliminating
-                // index bounds check...
-                ref uint resultPtr = ref MemoryMarshal.GetReference(bits);
+                Naive(left, right, bits);
+                return;
+            }
 
-                // Multiplies the bits using the "grammar-school" method.
-                // Envisioning the "rhombus" of a pen-and-paper calculation
-                // should help getting the idea of these two loops...
-                // The inner multiplication operations are safe, because
-                // z_i+j + a_j * b_i + c <= 2(2^32 - 1) + (2^32 - 1)^2 =
-                // = 2^64 - 1 (which perfectly matches with ulong!).
+            //                                            upper           lower
+            // A=   |               |               | a1 = a[n..2n] | a0 = a[0..n] |
+            // B=   |               |               | b1 = b[n..2n] | b0 = b[0..n] |
 
-                for (int i = 0; i < right.Length; i++)
-                {
-                    ulong carry = 0UL;
-                    for (int j = 0; j < left.Length; j++)
-                    {
-                        ref uint elementPtr = ref Unsafe.Add(ref resultPtr, i + j);
-                        ulong digits = elementPtr + carry + (ulong)left[j] * right[i];
-                        elementPtr = unchecked((uint)digits);
-                        carry = digits >> 32;
-                    }
-                    Unsafe.Add(ref resultPtr, i + left.Length) = (uint)carry;
-                }
-            }
-            else
-            {
-                // Based on the Toom-Cook multiplication we split left/right
-                // into two smaller values, doing recursive multiplication.
-                // The special form of this multiplication, where we
-                // split both operands into two operands, is also known
-                // as the Karatsuba algorithm...
+            // Result
+            // z0=  |               |               |            a0 * b0            |
+            // z1=  |               |       a1 * b0 + a0 * b1       |               |
+            // z2=  |            a1 * b1            |               |               |
 
-                // https://en.wikipedia.org/wiki/Toom-Cook_multiplication
-                // https://en.wikipedia.org/wiki/Karatsuba_algorithm
+            // z1 = a1 * b0 + a0 * b1
+            //    = (a0 + a1) * (b0 + b1) - a0 * b0 - a1 * b1
+            //    = (a0 + a1) * (b0 + b1) - z0 - z2
 
-                // Say we want to compute z = a * b ...
 
-                // ... we need to determine our new length (just the half)
-                int n = left.Length >> 1;
-                if (right.Length <= n + 1)
-                {
-                    // ... split left like a = (a_1 << n) + a_0
-                    ReadOnlySpan<uint> leftLow = left.Slice(0, n);
-                    ReadOnlySpan<uint> leftHigh = left.Slice(n);
+            // Based on the Toom-Cook multiplication we split left/right
+            // into two smaller values, doing recursive multiplication.
+            // The special form of this multiplication, where we
+            // split both operands into two operands, is also known
+            // as the Karatsuba algorithm...
 
-                    // ... split right like b = (b_1 << n) + b_0
-                    ReadOnlySpan<uint> rightLow;
-                    uint rightHigh;
-                    if (n < right.Length)
-                    {
-                        Debug.Assert(right.Length == n + 1);
-                        rightLow = right.Slice(0, n);
-                        rightHigh = right[n];
-                    }
-                    else
-                    {
-                        rightLow = right;
-                        rightHigh = 0;
-                    }
+            // https://en.wikipedia.org/wiki/Toom-Cook_multiplication
+            // https://en.wikipedia.org/wiki/Karatsuba_algorithm
 
-                    // ... prepare our result array (to reuse its memory)
-                    Span<uint> bitsLow = bits.Slice(0, n + rightLow.Length);
-                    Span<uint> bitsHigh = bits.Slice(n);
+            // Say we want to compute z = a * b ...
 
-                    int carryLength = rightLow.Length;
-                    uint[]? carryFromPool = null;
-                    Span<uint> carry = ((uint)carryLength <= StackAllocThreshold ?
-                                      stackalloc uint[StackAllocThreshold]
-                                      : carryFromPool = ArrayPool<uint>.Shared.Rent(carryLength)).Slice(0, carryLength);
+            // ... we need to determine our new length (just the half)
+            int n = (left.Length + 1) >> 1;
 
-                    // ... compute low
-                    Multiply(leftLow, rightLow, bitsLow);
-                    Span<uint> carryOrig = bits.Slice(n, rightLow.Length);
-                    carryOrig.CopyTo(carry);
-                    carryOrig.Clear();
+            if (right.Length <= n)
+            {
+                // ... split left like a = (a_1 << n) + a_0
+                ReadOnlySpan<uint> leftLow = left.Slice(0, n);
+                ReadOnlySpan<uint> leftHigh = left.Slice(n);
+                Debug.Assert(leftLow.Length >= leftHigh.Length);
 
-                    if (rightHigh != 0)
-                    {
-                        // ... compute high
-                        MultiplyNearLength(leftHigh, rightLow, bitsHigh.Slice(0, leftHigh.Length + n));
+                // ... prepare our result array (to reuse its memory)
+                Span<uint> bitsLow = bits.Slice(0, n + right.Length);
+                Span<uint> bitsHigh = bits.Slice(n);
 
-                        int upperRightLength = left.Length + 1;
-                        uint[]? upperRightFromPool = null;
-                        Span<uint> upperRight = ((uint)upperRightLength <= StackAllocThreshold ?
-                                          stackalloc uint[StackAllocThreshold]
-                                          : upperRightFromPool = ArrayPool<uint>.Shared.Rent(upperRightLength)).Slice(0, upperRightLength);
-                        upperRight.Clear();
+                // ... compute low
+                Multiply(leftLow, right, bitsLow);
 
-                        Multiply(left, rightHigh, upperRight);
+                int carryLength = right.Length;
+                uint[]? carryFromPool = null;
+                Span<uint> carry = ((uint)carryLength <= StackAllocThreshold ?
+                                  stackalloc uint[StackAllocThreshold]
+                                  : carryFromPool = ArrayPool<uint>.Shared.Rent(carryLength)).Slice(0, carryLength);
 
-                        AddSelf(bitsHigh, upperRight);
+                Span<uint> carryOrig = bits.Slice(n, right.Length);
+                carryOrig.CopyTo(carry);
+                carryOrig.Clear();
 
-                        if (upperRightFromPool != null)
-                            ArrayPool<uint>.Shared.Return(upperRightFromPool);
-                    }
-                    else
-                    {
-                        // ... compute high
-                        Multiply(leftHigh, rightLow, bitsHigh);
-                    }
+                // ... compute high
+                if (leftHigh.Length < right.Length)
+                    MultiplyKaratsuba(right, leftHigh, bitsHigh.Slice(0, leftHigh.Length + right.Length), (right.Length + 1) >> 1);
+                else
+                    Multiply(leftHigh, right, bitsHigh.Slice(0, leftHigh.Length + right.Length));
+
+                AddSelf(bitsHigh, carry);
 
-                    AddSelf(bitsHigh, carry);
+                if (carryFromPool != null)
+                    ArrayPool<uint>.Shared.Return(carryFromPool);
+            }
+            else
+                MultiplyKaratsuba(left, right, bits, n);
 
-                    if (carryFromPool != null)
-                        ArrayPool<uint>.Shared.Return(carryFromPool);
+            static void MultiplyKaratsuba(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits, int n)
+            {
+                Debug.Assert(left.Length >= right.Length);
+                Debug.Assert(2 * n - left.Length is 0 or 1);
+                Debug.Assert(right.Length > n);
+                Debug.Assert(bits.Length >= left.Length + right.Length);
+
+                if (right.Length < MultiplyKaratsubaThreshold)
+                {
+                    Naive(left, right, bits);
                 }
                 else
                 {
-                    int n2 = n << 1;
-
-                    Debug.Assert(left.Length > right.Length);
-
                     // ... split left like a = (a_1 << n) + a_0
                     ReadOnlySpan<uint> leftLow = left.Slice(0, n);
                     ReadOnlySpan<uint> leftHigh = left.Slice(n);
@@ -311,47 +266,47 @@ stackalloc uint[StackAllocThreshold]
                     ReadOnlySpan<uint> rightHigh = right.Slice(n);
 
                     // ... prepare our result array (to reuse its memory)
-                    Span<uint> bitsLow = bits.Slice(0, n2);
-                    Span<uint> bitsHigh = bits.Slice(n2);
+                    Span<uint> bitsLow = bits.Slice(0, n + n);
+                    Span<uint> bitsHigh = bits.Slice(n + n);
+
+                    Debug.Assert(leftLow.Length >= leftHigh.Length);
+                    Debug.Assert(rightLow.Length >= rightHigh.Length);
+                    Debug.Assert(bitsLow.Length >= bitsHigh.Length);
 
                     // ... compute z_0 = a_0 * b_0 (multiply again)
-                    MultiplyNearLength(rightLow, leftLow, bitsLow);
+                    MultiplyKaratsuba(leftLow, rightLow, bitsLow, (leftLow.Length + 1) >> 1);
 
                     // ... compute z_2 = a_1 * b_1 (multiply again)
-                    MultiplyFarLength(leftHigh, rightHigh, bitsHigh);
+                    Multiply(leftHigh, rightHigh, bitsHigh);
 
-                    int leftFoldLength = leftHigh.Length + 1;
+                    int foldLength = n + 1;
                     uint[]? leftFoldFromPool = null;
-                    Span<uint> leftFold = ((uint)leftFoldLength <= StackAllocThreshold ?
+                    Span<uint> leftFold = ((uint)foldLength <= StackAllocThreshold ?
                                           stackalloc uint[StackAllocThreshold]
-                                          : leftFoldFromPool = ArrayPool<uint>.Shared.Rent(leftFoldLength)).Slice(0, leftFoldLength);
+                                          : leftFoldFromPool = ArrayPool<uint>.Shared.Rent(foldLength)).Slice(0, foldLength);
                     leftFold.Clear();
 
-                    int rightFoldLength = n + 1;
                     uint[]? rightFoldFromPool = null;
-                    Span<uint> rightFold = ((uint)rightFoldLength <= StackAllocThreshold ?
+                    Span<uint> rightFold = ((uint)foldLength <= StackAllocThreshold ?
                                            stackalloc uint[StackAllocThreshold]
-                                           : rightFoldFromPool = ArrayPool<uint>.Shared.Rent(rightFoldLength)).Slice(0, rightFoldLength);
+                                           : rightFoldFromPool = ArrayPool<uint>.Shared.Rent(foldLength)).Slice(0, foldLength);
                     rightFold.Clear();
 
-                    int coreLength = leftFoldLength + rightFoldLength;
+                    // ... compute z_a = a_1 + a_0 (call it fold...)
+                    Add(leftLow, leftHigh, leftFold);
+
+                    // ... compute z_b = b_1 + b_0 (call it fold...)
+                    Add(rightLow, rightHigh, rightFold);
+
+                    int coreLength = foldLength + foldLength;
                     uint[]? coreFromPool = null;
                     Span<uint> core = ((uint)coreLength <= StackAllocThreshold ?
                                       stackalloc uint[StackAllocThreshold]
                                       : coreFromPool = ArrayPool<uint>.Shared.Rent(coreLength)).Slice(0, coreLength);
                     core.Clear();
 
-                    Debug.Assert(bits.Length - n >= core.Length);
-                    Debug.Assert(rightLow.Length >= rightHigh.Length);
-
-                    // ... compute z_a = a_1 + a_0 (call it fold...)
-                    Add(leftHigh, leftLow, leftFold);
-
-                    // ... compute z_b = b_1 + b_0 (call it fold...)
-                    Add(rightLow, rightHigh, rightFold);
-
-                    // ... compute z_1 = z_a * z_b - z_0 - z_2
-                    MultiplyNearLength(leftFold, rightFold, core);
+                    // ... compute z_ab = z_a * z_b
+                    MultiplyKaratsuba(leftFold, rightFold, core, (leftFold.Length + 1) >> 1);
 
                     if (leftFoldFromPool != null)
                         ArrayPool<uint>.Shared.Return(leftFoldFromPool);
@@ -359,33 +314,24 @@ stackalloc uint[StackAllocThreshold]
                     if (rightFoldFromPool != null)
                         ArrayPool<uint>.Shared.Return(rightFoldFromPool);
 
+                    // ... compute z_1 = z_a * z_b - z_0 - z_2 = a_0 * b_1 + a_1 * b_0
                     SubtractCore(bitsLow, bitsHigh, core);
 
+                    Debug.Assert(ActualLength(core) <= left.Length + 1);
+
                     // ... and finally merge the result! :-)
-                    AddSelf(bits.Slice(n), core);
+                    AddSelf(bits.Slice(n), core.Slice(0, ActualLength(core)));
 
                     if (coreFromPool != null)
                         ArrayPool<uint>.Shared.Return(coreFromPool);
                 }
             }
-        }
-        private static void MultiplyNearLength(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits)
-        {
-            Debug.Assert(left.Length - right.Length < 3);
-            Debug.Assert(bits.Length >= left.Length + right.Length);
-            Debug.Assert(!bits.ContainsAnyExcept(0u));
 
-            // Executes different algorithms for computing z = a * b
-            // based on the actual length of b. If b is "small" enough
-            // we stick to the classic "grammar-school" method; for the
-            // rest we switch to implementations with less complexity
-            // albeit more overhead (which needs to pay off!).
-
-            // NOTE: useful thresholds needs some "empirical" testing,
-            // which are smaller in DEBUG mode for testing purpose.
-
-            if (right.Length < MultiplyThreshold)
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            static void Naive(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits)
             {
+                Debug.Assert(right.Length < MultiplyKaratsubaThreshold);
+
                 // Switching to managed references helps eliminating
                 // index bounds check...
                 ref uint resultPtr = ref MemoryMarshal.GetReference(bits);
@@ -399,96 +345,18 @@ private static void MultiplyNearLength(ReadOnlySpan<uint> left, ReadOnlySpan<uin
 
                 for (int i = 0; i < right.Length; i++)
                 {
+                    uint rv = right[i];
                     ulong carry = 0UL;
                     for (int j = 0; j < left.Length; j++)
                     {
                         ref uint elementPtr = ref Unsafe.Add(ref resultPtr, i + j);
-                        ulong digits = elementPtr + carry + (ulong)left[j] * right[i];
+                        ulong digits = elementPtr + carry + (ulong)left[j] * rv;
                         elementPtr = unchecked((uint)digits);
                         carry = digits >> 32;
                     }
                     Unsafe.Add(ref resultPtr, i + left.Length) = (uint)carry;
                 }
             }
-            else
-            {
-                // Based on the Toom-Cook multiplication we split left/right
-                // into two smaller values, doing recursive multiplication.
-                // The special form of this multiplication, where we
-                // split both operands into two operands, is also known
-                // as the Karatsuba algorithm...
-
-                // https://en.wikipedia.org/wiki/Toom-Cook_multiplication
-                // https://en.wikipedia.org/wiki/Karatsuba_algorithm
-
-                // Say we want to compute z = a * b ...
-
-                // ... we need to determine our new length (just the half)
-                int n = right.Length >> 1;
-                int n2 = n << 1;
-
-                // ... split left like a = (a_1 << n) + a_0
-                ReadOnlySpan<uint> leftLow = left.Slice(0, n);
-                ReadOnlySpan<uint> leftHigh = left.Slice(n);
-
-                // ... split right like b = (b_1 << n) + b_0
-                ReadOnlySpan<uint> rightLow = right.Slice(0, n);
-                ReadOnlySpan<uint> rightHigh = right.Slice(n);
-
-                // ... prepare our result array (to reuse its memory)
-                Span<uint> bitsLow = bits.Slice(0, n2);
-                Span<uint> bitsHigh = bits.Slice(n2);
-
-                // ... compute z_0 = a_0 * b_0 (multiply again)
-                MultiplyNearLength(leftLow, rightLow, bitsLow);
-
-                // ... compute z_2 = a_1 * b_1 (multiply again)
-                MultiplyNearLength(leftHigh, rightHigh, bitsHigh);
-
-                int leftFoldLength = leftHigh.Length + 1;
-                uint[]? leftFoldFromPool = null;
-                Span<uint> leftFold = ((uint)leftFoldLength <= StackAllocThreshold ?
-                                      stackalloc uint[StackAllocThreshold]
-                                      : leftFoldFromPool = ArrayPool<uint>.Shared.Rent(leftFoldLength)).Slice(0, leftFoldLength);
-                leftFold.Clear();
-
-                int rightFoldLength = rightHigh.Length + 1;
-                uint[]? rightFoldFromPool = null;
-                Span<uint> rightFold = ((uint)rightFoldLength <= StackAllocThreshold ?
-                                       stackalloc uint[StackAllocThreshold]
-                                       : rightFoldFromPool = ArrayPool<uint>.Shared.Rent(rightFoldLength)).Slice(0, rightFoldLength);
-                rightFold.Clear();
-
-                int coreLength = leftFoldLength + rightFoldLength;
-                uint[]? coreFromPool = null;
-                Span<uint> core = ((uint)coreLength <= StackAllocThreshold ?
-                                  stackalloc uint[StackAllocThreshold]
-                                  : coreFromPool = ArrayPool<uint>.Shared.Rent(coreLength)).Slice(0, coreLength);
-                core.Clear();
-
-                // ... compute z_a = a_1 + a_0 (call it fold...)
-                Add(leftHigh, leftLow, leftFold);
-
-                // ... compute z_b = b_1 + b_0 (call it fold...)
-                Add(rightHigh, rightLow, rightFold);
-
-                // ... compute z_1 = z_a * z_b - z_0 - z_2
-                MultiplyNearLength(leftFold, rightFold, core);
-
-                if (leftFoldFromPool != null)
-                    ArrayPool<uint>.Shared.Return(leftFoldFromPool);
-
-                if (rightFoldFromPool != null)
-                    ArrayPool<uint>.Shared.Return(rightFoldFromPool);
-
-                SubtractCore(bitsHigh, bitsLow, core);
-
-                // ... and finally merge the result! :-)
-                AddSelf(bits.Slice(n), core);
-
-                if (coreFromPool != null)
-                    ArrayPool<uint>.Shared.Return(coreFromPool);
-            }
         }
 
         private static void SubtractCore(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> core)
diff --git a/src/libraries/System.Runtime.Numerics/tests/BigInteger/multiply.cs b/src/libraries/System.Runtime.Numerics/tests/BigInteger/multiply.cs
index d1abae863ea102..d94c235c65b628 100644
--- a/src/libraries/System.Runtime.Numerics/tests/BigInteger/multiply.cs
+++ b/src/libraries/System.Runtime.Numerics/tests/BigInteger/multiply.cs
@@ -38,12 +38,12 @@ public static void RunMultiply_TwoLargeBigIntegers_Threshold()
         {
             // Again, with lower threshold
             BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.SquareThreshold, 8, () =>
-                BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.MultiplyThreshold, 8, RunMultiply_TwoLargeBigIntegers)
+                BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.MultiplyKaratsubaThreshold, 8, RunMultiply_TwoLargeBigIntegers)
             );
 
             // Again, with lower threshold
             BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.SquareThreshold, 8, () =>
-                BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.MultiplyThreshold, 8, () =>
+                BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.MultiplyKaratsubaThreshold, 8, () =>
                     BigIntTools.Utils.RunWithFakeThreshold(BigIntegerCalculator.StackAllocThreshold, 8, RunMultiply_TwoLargeBigIntegers)
                 )
             );
@@ -216,10 +216,10 @@ public static void RunMultiplyKaratsubaBoundary()
             {
                 for (int d1 = -2; d1 <= 2; d1++)
                 {
-                    tempByteArray1 = GetRandomByteArray(random, BigIntegerCalculator.MultiplyThreshold + d1);
+                    tempByteArray1 = GetRandomByteArray(random, BigIntegerCalculator.MultiplyKaratsubaThreshold + d1);
                     for (int d2 = -4; d2 <= 4; d2++)
                     {
-                        tempByteArray2 = GetRandomByteArray(random, (BigIntegerCalculator.MultiplyThreshold + 1) * 2 + d2);
+                        tempByteArray2 = GetRandomByteArray(random, (BigIntegerCalculator.MultiplyKaratsubaThreshold + 1) * 2 + d2);
                         VerifyMultiplyString(Print(tempByteArray1) + Print(tempByteArray2) + "bMultiply");
                     }
                 }
diff --git a/src/libraries/System.Runtime.Numerics/tests/BigInteger/op_multiply.cs b/src/libraries/System.Runtime.Numerics/tests/BigInteger/op_multiply.cs
index 08f73afe18198d..9b09a402df5953 100644
--- a/src/libraries/System.Runtime.Numerics/tests/BigInteger/op_multiply.cs
+++ b/src/libraries/System.Runtime.Numerics/tests/BigInteger/op_multiply.cs
@@ -169,10 +169,10 @@ public static void RunMultiplyKaratsubaBoundary()
             {
                 for (int d1 = -2; d1 <= 2; d1++)
                 {
-                    tempByteArray1 = GetRandomByteArray(s_random, BigIntegerCalculator.MultiplyThreshold + d1);
+                    tempByteArray1 = GetRandomByteArray(s_random, BigIntegerCalculator.MultiplyKaratsubaThreshold + d1);
                     for (int d2 = -4; d2 <= 4; d2++)
                     {
-                        tempByteArray2 = GetRandomByteArray(s_random, (BigIntegerCalculator.MultiplyThreshold + 1) * 2 + d2);
+                        tempByteArray2 = GetRandomByteArray(s_random, (BigIntegerCalculator.MultiplyKaratsubaThreshold + 1) * 2 + d2);
                         VerifyMultiplyString(Print(tempByteArray1) + Print(tempByteArray2) + "b*");
                     }
                 }