From 830acd3a8927e49c94a4d82817a1364c4dfd0604 Mon Sep 17 00:00:00 2001
From: Mikhail Gorshkov <m.gorshkov@arenadata.io>
Date: Tue, 4 Jun 2024 15:32:38 +0000
Subject: [PATCH] Support non-const scale arguments in rounding functions

---
 .../functions/rounding-functions.md           |    8 +-
 .../functions/rounding-functions.md           |    2 +-
 src/Functions/FunctionsRound.h                |  251 +-
 .../03165_round_scale_as_column.reference     | 2165 +++++++++++++++++
 .../03165_round_scale_as_column.sql           |  125 +
 5 files changed, 2475 insertions(+), 76 deletions(-)
 create mode 100644 tests/queries/0_stateless/03165_round_scale_as_column.reference
 create mode 100644 tests/queries/0_stateless/03165_round_scale_as_column.sql

diff --git a/docs/en/sql-reference/functions/rounding-functions.md b/docs/en/sql-reference/functions/rounding-functions.md
index d18185c5013..55a4b3ce9df 100644
--- a/docs/en/sql-reference/functions/rounding-functions.md
+++ b/docs/en/sql-reference/functions/rounding-functions.md
@@ -9,8 +9,8 @@ sidebar_label: Rounding
 ## floor(x\[, N\])
 
 Returns the largest round number that is less than or equal to `x`. A round number is a multiple of 1/10N, or the nearest number of the appropriate data type if 1 / 10N isn’t exact.
-‘N’ is an integer constant, optional parameter. By default it is zero, which means to round to an integer.
-‘N’ may be negative.
+`N` is an integer, optional parameter. By default it is zero, which means to round to an integer.
+`N` may be negative.
 
 Examples: `floor(123.45, 1) = 123.4, floor(123.45, -1) = 120.`
 
@@ -70,7 +70,7 @@ round(expression [, decimal_places])
 **Arguments**
 
 - `expression` — A number to be rounded. Can be any [expression](../../sql-reference/syntax.md#syntax-expressions) returning the numeric [data type](../data-types/index.md#data_types).
-- `decimal-places` — An integer value.
+- `decimal-places` — The number of decimal places to round to.
     - If `decimal-places > 0` then the function rounds the value to the right of the decimal point.
     - If `decimal-places < 0` then the function rounds the value to the left of the decimal point.
     - If `decimal-places = 0` then the function rounds the value to integer. In this case the argument can be omitted.
@@ -264,7 +264,7 @@ Result:
 
 ## roundDuration
 
-Accepts a number. If the number is less than one, it returns `0`. Otherwise, it rounds the number down to numbers from the set of commonly used durations: `1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000`. 
+Accepts a number. If the number is less than one, it returns `0`. Otherwise, it rounds the number down to numbers from the set of commonly used durations: `1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000`.
 
 **Syntax**
 
diff --git a/docs/ru/sql-reference/functions/rounding-functions.md b/docs/ru/sql-reference/functions/rounding-functions.md
index cc939f69afc..f1dd57505ea 100644
--- a/docs/ru/sql-reference/functions/rounding-functions.md
+++ b/docs/ru/sql-reference/functions/rounding-functions.md
@@ -10,7 +10,7 @@ sidebar_label: "Функции округления"
 
 Возвращает наибольшее круглое число, которое меньше или равно, чем x.
 Круглым называется число, кратное 1 / 10N или ближайшее к нему число соответствующего типа данных, если 1 / 10N не представимо точно.
-N - целочисленная константа, не обязательный параметр. По умолчанию - ноль, что означает - округлять до целого числа.
+N - целочисленный аргумент, не обязательный параметр. По умолчанию - ноль, что означает - округлять до целого числа.
 N может быть отрицательным.
 
 Примеры: `floor(123.45, 1) = 123.4, floor(123.45, -1) = 120.`
diff --git a/src/Functions/FunctionsRound.h b/src/Functions/FunctionsRound.h
index 1f20fbff24e..978b6d88d05 100644
--- a/src/Functions/FunctionsRound.h
+++ b/src/Functions/FunctionsRound.h
@@ -187,13 +187,13 @@ struct IntegerRoundingComputation
 };
 
 
-#ifdef __SSE4_1__
-
-template <typename T>
+template <typename T, bool is_vectorized = true>
 class BaseFloatRoundingComputation;
 
+#ifdef __SSE4_1__
+
 template <>
-class BaseFloatRoundingComputation<Float32>
+class BaseFloatRoundingComputation<Float32, true>
 {
 public:
     using ScalarType = Float32;
@@ -214,7 +214,7 @@ public:
 };
 
 template <>
-class BaseFloatRoundingComputation<Float64>
+class BaseFloatRoundingComputation<Float64, true>
 {
 public:
     using ScalarType = Float64;
@@ -234,9 +234,9 @@ public:
     }
 };
 
-#else
+#endif
 
-/// Implementation for ARM. Not vectorized.
+/// Implementation for ARM/columnar scale argument. Not vectorized.
 
 inline float roundWithMode(float x, RoundingMode mode)
 {
@@ -265,7 +265,7 @@ inline double roundWithMode(double x, RoundingMode mode)
 }
 
 template <typename T>
-class BaseFloatRoundingComputation
+class BaseFloatRoundingComputation<T, false>
 {
 public:
     using ScalarType = T;
@@ -285,15 +285,13 @@ public:
     }
 };
 
-#endif
-
 
 /** Implementation of low-level round-off functions for floating-point values.
   */
-template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode>
-class FloatRoundingComputation : public BaseFloatRoundingComputation<T>
+template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode, bool is_vectorized>
+class FloatRoundingComputation : public BaseFloatRoundingComputation<T, is_vectorized>
 {
-    using Base = BaseFloatRoundingComputation<T>;
+    using Base = BaseFloatRoundingComputation<T, is_vectorized>;
 
 public:
     static void compute(const T * __restrict in, const typename Base::VectorType & scale, T * __restrict out)
@@ -325,15 +323,22 @@ struct FloatRoundingImpl
 private:
     static_assert(!is_decimal<T>);
 
-    using Op = FloatRoundingComputation<T, rounding_mode, scale_mode>;
-    using Data = std::array<T, Op::data_count>;
+    template <bool is_vectorized =
+#ifdef __SSE4_1__
+        true
+#else
+        false
+#endif
+    >
+    using Op = FloatRoundingComputation<T, rounding_mode, scale_mode, is_vectorized>;
+    using Data = std::array<T, Op<>::data_count>;
     using ColumnType = ColumnVector<T>;
     using Container = typename ColumnType::Container;
 
 public:
     static NO_INLINE void apply(const Container & in, size_t scale, Container & out)
     {
-        auto mm_scale = Op::prepare(scale);
+        auto mm_scale = Op<>::prepare(scale);
 
         const size_t data_count = std::tuple_size<Data>();
 
@@ -345,7 +350,7 @@ public:
 
         while (p_in < limit)
         {
-            Op::compute(p_in, mm_scale, p_out);
+            Op<>::compute(p_in, mm_scale, p_out);
             p_in += data_count;
             p_out += data_count;
         }
@@ -358,10 +363,17 @@ public:
             size_t tail_size_bytes = (end_in - p_in) * sizeof(*p_in);
 
             memcpy(&tmp_src, p_in, tail_size_bytes);
-            Op::compute(reinterpret_cast<T *>(&tmp_src), mm_scale, reinterpret_cast<T *>(&tmp_dst));
+            Op<>::compute(reinterpret_cast<T *>(&tmp_src), mm_scale, reinterpret_cast<T *>(&tmp_dst));
             memcpy(p_out, &tmp_dst, tail_size_bytes);
         }
     }
+
+    static void applyOne(const T* __restrict in, size_t scale, T* __restrict out)
+    {
+        using ScalarOp = Op<false>;
+        auto s = ScalarOp::prepare(scale);
+        ScalarOp::compute(in, s, out);
+    }
 };
 
 template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode, TieBreakingMode tie_breaking_mode>
@@ -417,6 +429,11 @@ public:
                 throw Exception(ErrorCodes::BAD_ARGUMENTS, "Unexpected 'scale' parameter passed to function");
         }
     }
+
+    static void applyOne(const T* __restrict in, size_t scale, T* __restrict out)
+    {
+        Op::compute(in, scale, out);
+    }
 };
 
 
@@ -452,11 +469,40 @@ public:
             memcpy(out.data(), in.data(), in.size() * sizeof(T));
         }
     }
-};
 
+    static void applyOne(const NativeType* __restrict in, UInt32 in_scale, NativeType* __restrict out, Scale scale_arg)
+    {
+        scale_arg = in_scale - scale_arg;
+        if (scale_arg > 0)
+        {
+            auto scale = intExp10OfSize<NativeType>(scale_arg);
+            Op::compute(in, scale, out);
+        }
+        else
+        {
+            memcpy(out, in, sizeof(T));
+        }
+    }
+};
 
 /** Select the appropriate processing algorithm depending on the scale.
   */
+inline void validateScale(Int64 scale64)
+{
+    if (scale64 > std::numeric_limits<Scale>::max() || scale64 < std::numeric_limits<Scale>::min())
+        throw Exception(ErrorCodes::ARGUMENT_OUT_OF_BOUND, "Scale argument for rounding function is too large");
+}
+
+inline Scale getScaleArg(const ColumnConst* scale_col)
+{
+    const auto& scale_field = scale_col->getField();
+
+    Int64 scale64 = scale_field.get<Int64>();
+    validateScale(scale64);
+
+    return scale64;
+}
+
 template <typename T, RoundingMode rounding_mode, TieBreakingMode tie_breaking_mode>
 struct Dispatcher
 {
@@ -465,9 +511,10 @@ struct Dispatcher
         FloatRoundingImpl<T, rounding_mode, scale_mode>,
         IntegerRoundingImpl<T, rounding_mode, scale_mode, tie_breaking_mode>>;
 
-    static ColumnPtr apply(const IColumn * col_general, Scale scale_arg)
+    template <typename ScaleType>
+    static ColumnPtr apply(const IColumn * data_col, const IColumn * scale_col = nullptr)
     {
-        const auto & col = checkAndGetColumn<ColumnVector<T>>(*col_general);
+        const auto & col = checkAndGetColumn<ColumnVector<T>>(*data_col);
         auto col_res = ColumnVector<T>::create();
 
         typename ColumnVector<T>::Container & vec_res = col_res->getData();
@@ -475,20 +522,62 @@ struct Dispatcher
 
         if (!vec_res.empty())
         {
-            if (scale_arg == 0)
+            using ColVecScale = ColumnVector<ScaleType>;
+            if (scale_col == nullptr || isColumnConst(*scale_col))
             {
-                size_t scale = 1;
-                FunctionRoundingImpl<ScaleMode::Zero>::apply(col.getData(), scale, vec_res);
+                auto scale_arg = scale_col == nullptr ? 0 : getScaleArg(checkAndGetColumnConst<ColVecScale>(scale_col));
+                if (scale_arg == 0)
+                {
+                    size_t scale = 1;
+                    FunctionRoundingImpl<ScaleMode::Zero>::apply(col.getData(), scale, vec_res);
+                }
+                else if (scale_arg > 0)
+                {
+                    size_t scale = intExp10(scale_arg);
+                    FunctionRoundingImpl<ScaleMode::Positive>::apply(col.getData(), scale, vec_res);
+                }
+                else
+                {
+                    size_t scale = intExp10(-scale_arg);
+                    FunctionRoundingImpl<ScaleMode::Negative>::apply(col.getData(), scale, vec_res);
+                }
             }
-            else if (scale_arg > 0)
+            else if (const auto scale_typed = checkAndGetColumn<ColVecScale>(scale_col))
             {
-                size_t scale = intExp10(scale_arg);
-                FunctionRoundingImpl<ScaleMode::Positive>::apply(col.getData(), scale, vec_res);
-            }
-            else
-            {
-                size_t scale = intExp10(-scale_arg);
-                FunctionRoundingImpl<ScaleMode::Negative>::apply(col.getData(), scale, vec_res);
+                const auto & in = col.getData();
+                const auto & scale_data = scale_typed->getData();
+                const size_t count = in.size();
+
+                const T * end_in = in.data() + count;
+                const T * __restrict p_in = in.data();
+                const ScaleType * __restrict p_scale = scale_data.data();
+                T * __restrict p_out = vec_res.data();
+
+                while (p_in < end_in)
+                {
+                    Int64 scale64 = *p_scale;
+                    validateScale(scale64);
+                    Scale raw_scale = scale64;
+
+                    if (raw_scale == 0)
+                    {
+                        size_t scale = 1;
+                        FunctionRoundingImpl<ScaleMode::Zero>::applyOne(p_in, scale, p_out);
+                    }
+                    else if (raw_scale > 0)
+                    {
+                        size_t scale = intExp10(raw_scale);
+                        FunctionRoundingImpl<ScaleMode::Positive>::applyOne(p_in, scale, p_out);
+                    }
+                    else
+                    {
+                        size_t scale = intExp10(-raw_scale);
+                        FunctionRoundingImpl<ScaleMode::Negative>::applyOne(p_in, scale, p_out);
+                    }
+                    ++p_in;
+                    ++p_scale;
+                    ++p_out;
+                }
             }
         }
 
@@ -500,16 +589,46 @@ template <is_decimal T, RoundingMode rounding_mode, TieBreakingMode tie_breaking
 struct Dispatcher<T, rounding_mode, tie_breaking_mode>
 {
 public:
-    static ColumnPtr apply(const IColumn * col_general, Scale scale_arg)
+    template <typename ScaleType>
+    static ColumnPtr apply(const IColumn * data_col, const IColumn* scale_col = nullptr)
     {
-        const auto & col = checkAndGetColumn<ColumnDecimal<T>>(*col_general);
+        const auto & col = checkAndGetColumn<ColumnDecimal<T>>(*data_col);
         const typename ColumnDecimal<T>::Container & vec_src = col.getData();
 
         auto col_res = ColumnDecimal<T>::create(vec_src.size(), col.getScale());
         auto & vec_res = col_res->getData();
 
         if (!vec_res.empty())
-            DecimalRoundingImpl<T, rounding_mode, tie_breaking_mode>::apply(col.getData(), col.getScale(), vec_res, scale_arg);
+        {
+            using ColVecScale = ColumnVector<ScaleType>;
+            if (scale_col == nullptr || isColumnConst(*scale_col))
+            {
+                auto scale_arg = scale_col == nullptr ? 0 : getScaleArg(checkAndGetColumnConst<ColVecScale>(scale_col));
+                DecimalRoundingImpl<T, rounding_mode, tie_breaking_mode>::apply(col.getData(), col.getScale(), vec_res, scale_arg);
+            }
+            else if (const auto scale_typed = checkAndGetColumn<ColVecScale>(scale_col))
+            {
+                const auto & scale = scale_typed->getData();
+                const size_t count = vec_src.size();
+
+                using NativeType = typename T::NativeType;
+                const NativeType * __restrict p_in = reinterpret_cast<const NativeType *>(vec_src.data());
+                const ScaleType * __restrict p_scale = scale.data();
+                const NativeType * end_in = p_in + count;
+                NativeType * __restrict p_out = reinterpret_cast<NativeType *>(vec_res.data());
+                while (p_in < end_in)
+                {
+                    Int64 scale64 = *p_scale;
+                    validateScale(scale64);
+                    Scale raw_scale = scale64;
+
+                    DecimalRoundingImpl<T, rounding_mode, tie_breaking_mode>::applyOne(p_in, col.getScale(), p_out, raw_scale);
+                    ++p_in;
+                    ++p_scale;
+                    ++p_out;
+                }
+            }
+        }
 
         return col_res;
     }
@@ -550,50 +669,41 @@ public:
         return arguments[0];
     }
 
-    static Scale getScaleArg(const ColumnsWithTypeAndName & arguments)
-    {
-        if (arguments.size() == 2)
-        {
-            const IColumn & scale_column = *arguments[1].column;
-            if (!isColumnConst(scale_column))
-                throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Scale argument for rounding functions must be constant");
-
-            Field scale_field = assert_cast<const ColumnConst &>(scale_column).getField();
-            if (scale_field.getType() != Field::Types::UInt64
-                && scale_field.getType() != Field::Types::Int64)
-                throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Scale argument for rounding functions must have integer type");
-
-            Int64 scale64 = scale_field.get<Int64>();
-            if (scale64 > std::numeric_limits<Scale>::max()
-                || scale64 < std::numeric_limits<Scale>::min())
-                throw Exception(ErrorCodes::ARGUMENT_OUT_OF_BOUND, "Scale argument for rounding function is too large");
-
-            return scale64;
-        }
-        return 0;
-    }
-
     bool useDefaultImplementationForConstants() const override { return true; }
-    ColumnNumbers getArgumentsThatAreAlwaysConstant() const override { return {1}; }
 
     ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr &, size_t /*input_rows_count*/) const override
     {
-        const ColumnWithTypeAndName & column = arguments[0];
-        Scale scale_arg = getScaleArg(arguments);
+        const ColumnWithTypeAndName & data_column = arguments[0];
 
         ColumnPtr res;
-        auto call = [&](const auto & types) -> bool
+        auto callData = [&](const auto & types) -> bool
         {
             using Types = std::decay_t<decltype(types)>;
-            using DataType = typename Types::LeftType;
+            using DataType = typename Types::RightType;
 
-            if constexpr (IsDataTypeNumber<DataType> || IsDataTypeDecimal<DataType>)
+            if (arguments.size() > 1)
             {
-                using FieldType = typename DataType::FieldType;
-                res = Dispatcher<FieldType, rounding_mode, tie_breaking_mode>::apply(column.column.get(), scale_arg);
+                const ColumnWithTypeAndName & scale_column = arguments[1];
+
+                auto callScale = [&](const auto & scaleTypes) -> bool
+                {
+                    using ScaleTypes = std::decay_t<decltype(scaleTypes)>;
+                    using ScaleType = typename ScaleTypes::RightType;
+
+                    if (isColumnConst(*data_column.column) && !isColumnConst(*scale_column.column))
+                        throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Scale column must be const for const data column");
+
+                    res = Dispatcher<DataType, rounding_mode, tie_breaking_mode>::template apply<ScaleType>(data_column.column.get(), scale_column.column.get());
+                    return true;
+                };
+
+                TypeIndex right_index = scale_column.type->getTypeId();
+                if (!callOnBasicType<void, true, false, false, false>(right_index, callScale))
+                    throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Scale argument for rounding functions must have integer type");
                 return true;
             }
-            return false;
+            res = Dispatcher<DataType, rounding_mode, tie_breaking_mode>::template apply<int>(data_column.column.get());
+            return true;
         };
 
 #if !defined(__SSE4_1__)
@@ -605,10 +715,9 @@ public:
                 throw Exception(ErrorCodes::CANNOT_SET_ROUNDING_MODE, "Cannot set floating point rounding mode");
 #endif
 
-        if (!callOnIndexAndDataType<void>(column.type->getTypeId(), call))
-        {
-            throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Illegal column {} of argument of function {}", column.name, getName());
-        }
+        TypeIndex left_index = data_column.type->getTypeId();
+        if (!callOnBasicType<void, true, true, true, false>(left_index, callData))
+            throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Illegal column {} of argument of function {}", data_column.name, getName());
 
         return res;
     }
diff --git a/tests/queries/0_stateless/03165_round_scale_as_column.reference b/tests/queries/0_stateless/03165_round_scale_as_column.reference
new file mode 100644
index 00000000000..9ad25ed466a
--- /dev/null
+++ b/tests/queries/0_stateless/03165_round_scale_as_column.reference
@@ -0,0 +1,2165 @@
+0	0	0	0	0	0
+1	1	1	1	1	1
+2	2	2	2	2	2
+3	3	3	3	3	3
+4	4	4	4	4	4
+5	5	5	5	5	5
+6	6	6	6	6	6
+7	7	7	7	7	7
+8	8	8	8	8	8
+9	9	9	9	9	9
+10	10	10	10	10	10
+11	11	11	11	11	11
+12	12	12	12	12	12
+13	13	13	13	13	13
+14	14	14	14	14	14
+15	15	15	15	15	15
+16	16	16	16	16	16
+17	17	17	17	17	17
+18	18	18	18	18	18
+19	19	19	19	19	19
+0	0	0	0	0	0
+1	1	1	1	1	1
+2	2	2	2	2	2
+3	3	3	3	3	3
+4	4	4	4	4	4
+5	5	5	5	5	5
+6	6	6	6	6	6
+7	7	7	7	7	7
+8	8	8	8	8	8
+9	9	9	9	9	9
+10	10	10	10	10	10
+11	11	11	11	11	11
+12	12	12	12	12	12
+13	13	13	13	13	13
+14	14	14	14	14	14
+15	15	15	15	15	15
+16	16	16	16	16	16
+17	17	17	17	17	17
+18	18	18	18	18	18
+19	19	19	19	19	19
+0	0	0	0	0	0
+1	1	1	1	1	1
+2	2	2	2	2	2
+3	3	3	3	3	3
+4	4	4	4	4	4
+5	5	5	5	5	5
+6	6	6	6	6	6
+7	7	7	7	7	7
+8	8	8	8	8	8
+9	9	9	9	9	9
+10	10	10	10	10	10
+11	11	11	11	11	11
+12	12	12	12	12	12
+13	13	13	13	13	13
+14	14	14	14	14	14
+15	15	15	15	15	15
+16	16	16	16	16	16
+17	17	17	17	17	17
+18	18	18	18	18	18
+19	19	19	19	19	19
+0	0	0	0	0	0
+1	1	1	1	1	1
+2	2	2	2	2	2
+3	3	3	3	3	3
+4	4	4	4	4	4
+5	5	5	5	5	5
+6	6	6	6	6	6
+7	7	7	7	7	7
+8	8	8	8	8	8
+9	9	9	9	9	9
+10	10	10	10	10	10
+11	11	11	11	11	11
+12	12	12	12	12	12
+13	13	13	13	13	13
+14	14	14	14	14	14
+15	15	15	15	15	15
+16	16	16	16	16	16
+17	17	17	17	17	17
+18	18	18	18	18	18
+19	19	19	19	19	19
+-10	-10	-10	-10	-10	-10
+-9	-9	-9	-9	-9	-9
+-8	-8	-8	-8	-8	-8
+-7	-7	-7	-7	-7	-7
+-6	-6	-6	-6	-6	-6
+-5	-5	-5	-5	-5	-5
+-4	-4	-4	-4	-4	-4
+-3	-3	-3	-3	-3	-3
+-2	-2	-2	-2	-2	-2
+-1	-1	-1	-1	-1	-1
+0	0	0	0	0	0
+1	1	1	1	1	1
+2	2	2	2	2	2
+3	3	3	3	3	3
+4	4	4	4	4	4
+5	5	5	5	5	5
+6	6	6	6	6	6
+7	7	7	7	7	7
+8	8	8	8	8	8
+9	9	9	9	9	9
+-10	-10	-10	-10	-10	-10
+-9	-9	-9	-9	-9	-9
+-8	-8	-8	-8	-8	-8
+-7	-7	-7	-7	-7	-7
+-6	-6	-6	-6	-6	-6
+-5	-5	-5	-5	-5	-5
+-4	-4	-4	-4	-4	-4
+-3	-3	-3	-3	-3	-3
+-2	-2	-2	-2	-2	-2
+-1	-1	-1	-1	-1	-1
+0	0	0	0	0	0
+1	1	1	1	1	1
+2	2	2	2	2	2
+3	3	3	3	3	3
+4	4	4	4	4	4
+5	5	5	5	5	5
+6	6	6	6	6	6
+7	7	7	7	7	7
+8	8	8	8	8	8
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+-7	0	0	-100	0	0
+-6	0	0	-100	0	0
+-5	0	0	-100	0	0
+-4	0	0	-100	0	0
+-3	0	0	-100	0	0
+-2	0	0	-100	0	0
+-1	0	0	-100	0	0
+0	0	0	0	0	0
+1	0	0	0	100	0
+2	0	0	0	100	0
+3	0	0	0	100	0
+4	0	0	0	100	0
+5	0	0	0	100	0
+6	0	0	0	100	0
+7	0	0	0	100	0
+8	0	0	0	100	0
+9	0	0	0	100	0
+-10	-0	-0	-100	-0	-0
+-9	-0	-0	-100	-0	-0
+-8	-0	-0	-100	-0	-0
+-7	-0	-0	-100	-0	-0
+-6	-0	-0	-100	-0	-0
+-5	-0	-0	-100	-0	-0
+-4	-0	-0	-100	-0	-0
+-3	-0	-0	-100	-0	-0
+-2	-0	-0	-100	-0	-0
+-1	-0	-0	-100	-0	-0
+0	0	0	0	0	0
+1	0	0	0	100	0
+2	0	0	0	100	0
+3	0	0	0	100	0
+4	0	0	0	100	0
+5	0	0	0	100	0
+6	0	0	0	100	0
+7	0	0	0	100	0
+8	0	0	0	100	0
+9	0	0	0	100	0
+-10	-0	-0	-100	-0	-0
+-9	-0	-0	-100	-0	-0
+-8	-0	-0	-100	-0	-0
+-7	-0	-0	-100	-0	-0
+-6	-0	-0	-100	-0	-0
+-5	-0	-0	-100	-0	-0
+-4	-0	-0	-100	-0	-0
+-3	-0	-0	-100	-0	-0
+-2	-0	-0	-100	-0	-0
+-1	-0	-0	-100	-0	-0
+0	0	0	0	0	0
+1	0	0	0	100	0
+2	0	0	0	100	0
+3	0	0	0	100	0
+4	0	0	0	100	0
+5	0	0	0	100	0
+6	0	0	0	100	0
+7	0	0	0	100	0
+8	0	0	0	100	0
+9	0	0	0	100	0
+CHECKPOINT1
+id u8 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	10	0	10	10	10	10	10
+21	11	0	11	11	11	11	11
+22	12	0	12	12	12	12	12
+23	13	0	13	13	13	13	13
+24	14	0	14	14	14	14	14
+25	15	0	15	15	15	15	15
+26	16	0	16	16	16	16	16
+27	17	0	17	17	17	17	17
+28	18	0	18	18	18	18	18
+29	19	0	19	19	19	19	19
+30	20	0	20	20	20	20	20
+31	21	0	21	21	21	21	21
+32	22	0	22	22	22	22	22
+33	23	0	23	23	23	23	23
+34	24	0	24	24	24	24	24
+35	25	0	25	25	25	25	25
+36	26	0	26	26	26	26	26
+37	27	0	27	27	27	27	27
+38	28	0	28	28	28	28	28
+39	29	0	29	29	29	29	29
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	10	-1	10	10	10	10	10
+61	11	-1	10	10	10	20	10
+62	12	-1	10	10	10	20	10
+63	13	-1	10	10	10	20	10
+64	14	-1	10	10	10	20	10
+65	15	-1	20	20	10	20	10
+66	16	-1	20	20	10	20	10
+67	17	-1	20	20	10	20	10
+68	18	-1	20	20	10	20	10
+69	19	-1	20	20	10	20	10
+70	20	-1	20	20	20	20	20
+71	21	-1	20	20	20	30	20
+72	22	-1	20	20	20	30	20
+73	23	-1	20	20	20	30	20
+74	24	-1	20	20	20	30	20
+75	25	-1	30	20	20	30	20
+76	26	-1	30	30	20	30	20
+77	27	-1	30	30	20	30	20
+78	28	-1	30	30	20	30	20
+79	29	-1	30	30	20	30	20
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	10	-2	0	0	0	100	0
+101	11	-2	0	0	0	100	0
+102	12	-2	0	0	0	100	0
+103	13	-2	0	0	0	100	0
+104	14	-2	0	0	0	100	0
+105	15	-2	0	0	0	100	0
+106	16	-2	0	0	0	100	0
+107	17	-2	0	0	0	100	0
+108	18	-2	0	0	0	100	0
+109	19	-2	0	0	0	100	0
+110	20	-2	0	0	0	100	0
+111	21	-2	0	0	0	100	0
+112	22	-2	0	0	0	100	0
+113	23	-2	0	0	0	100	0
+114	24	-2	0	0	0	100	0
+115	25	-2	0	0	0	100	0
+116	26	-2	0	0	0	100	0
+117	27	-2	0	0	0	100	0
+118	28	-2	0	0	0	100	0
+119	29	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	244	4	244	244	244	244	244
+id u16 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	10	0	10	10	10	10	10
+21	11	0	11	11	11	11	11
+22	12	0	12	12	12	12	12
+23	13	0	13	13	13	13	13
+24	14	0	14	14	14	14	14
+25	15	0	15	15	15	15	15
+26	16	0	16	16	16	16	16
+27	17	0	17	17	17	17	17
+28	18	0	18	18	18	18	18
+29	19	0	19	19	19	19	19
+30	20	0	20	20	20	20	20
+31	21	0	21	21	21	21	21
+32	22	0	22	22	22	22	22
+33	23	0	23	23	23	23	23
+34	24	0	24	24	24	24	24
+35	25	0	25	25	25	25	25
+36	26	0	26	26	26	26	26
+37	27	0	27	27	27	27	27
+38	28	0	28	28	28	28	28
+39	29	0	29	29	29	29	29
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	10	-1	10	10	10	10	10
+61	11	-1	10	10	10	20	10
+62	12	-1	10	10	10	20	10
+63	13	-1	10	10	10	20	10
+64	14	-1	10	10	10	20	10
+65	15	-1	20	20	10	20	10
+66	16	-1	20	20	10	20	10
+67	17	-1	20	20	10	20	10
+68	18	-1	20	20	10	20	10
+69	19	-1	20	20	10	20	10
+70	20	-1	20	20	20	20	20
+71	21	-1	20	20	20	30	20
+72	22	-1	20	20	20	30	20
+73	23	-1	20	20	20	30	20
+74	24	-1	20	20	20	30	20
+75	25	-1	30	20	20	30	20
+76	26	-1	30	30	20	30	20
+77	27	-1	30	30	20	30	20
+78	28	-1	30	30	20	30	20
+79	29	-1	30	30	20	30	20
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	10	-2	0	0	0	100	0
+101	11	-2	0	0	0	100	0
+102	12	-2	0	0	0	100	0
+103	13	-2	0	0	0	100	0
+104	14	-2	0	0	0	100	0
+105	15	-2	0	0	0	100	0
+106	16	-2	0	0	0	100	0
+107	17	-2	0	0	0	100	0
+108	18	-2	0	0	0	100	0
+109	19	-2	0	0	0	100	0
+110	20	-2	0	0	0	100	0
+111	21	-2	0	0	0	100	0
+112	22	-2	0	0	0	100	0
+113	23	-2	0	0	0	100	0
+114	24	-2	0	0	0	100	0
+115	25	-2	0	0	0	100	0
+116	26	-2	0	0	0	100	0
+117	27	-2	0	0	0	100	0
+118	28	-2	0	0	0	100	0
+119	29	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id u32 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	10	0	10	10	10	10	10
+21	11	0	11	11	11	11	11
+22	12	0	12	12	12	12	12
+23	13	0	13	13	13	13	13
+24	14	0	14	14	14	14	14
+25	15	0	15	15	15	15	15
+26	16	0	16	16	16	16	16
+27	17	0	17	17	17	17	17
+28	18	0	18	18	18	18	18
+29	19	0	19	19	19	19	19
+30	20	0	20	20	20	20	20
+31	21	0	21	21	21	21	21
+32	22	0	22	22	22	22	22
+33	23	0	23	23	23	23	23
+34	24	0	24	24	24	24	24
+35	25	0	25	25	25	25	25
+36	26	0	26	26	26	26	26
+37	27	0	27	27	27	27	27
+38	28	0	28	28	28	28	28
+39	29	0	29	29	29	29	29
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	10	-1	10	10	10	10	10
+61	11	-1	10	10	10	20	10
+62	12	-1	10	10	10	20	10
+63	13	-1	10	10	10	20	10
+64	14	-1	10	10	10	20	10
+65	15	-1	20	20	10	20	10
+66	16	-1	20	20	10	20	10
+67	17	-1	20	20	10	20	10
+68	18	-1	20	20	10	20	10
+69	19	-1	20	20	10	20	10
+70	20	-1	20	20	20	20	20
+71	21	-1	20	20	20	30	20
+72	22	-1	20	20	20	30	20
+73	23	-1	20	20	20	30	20
+74	24	-1	20	20	20	30	20
+75	25	-1	30	20	20	30	20
+76	26	-1	30	30	20	30	20
+77	27	-1	30	30	20	30	20
+78	28	-1	30	30	20	30	20
+79	29	-1	30	30	20	30	20
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	10	-2	0	0	0	100	0
+101	11	-2	0	0	0	100	0
+102	12	-2	0	0	0	100	0
+103	13	-2	0	0	0	100	0
+104	14	-2	0	0	0	100	0
+105	15	-2	0	0	0	100	0
+106	16	-2	0	0	0	100	0
+107	17	-2	0	0	0	100	0
+108	18	-2	0	0	0	100	0
+109	19	-2	0	0	0	100	0
+110	20	-2	0	0	0	100	0
+111	21	-2	0	0	0	100	0
+112	22	-2	0	0	0	100	0
+113	23	-2	0	0	0	100	0
+114	24	-2	0	0	0	100	0
+115	25	-2	0	0	0	100	0
+116	26	-2	0	0	0	100	0
+117	27	-2	0	0	0	100	0
+118	28	-2	0	0	0	100	0
+119	29	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id u64 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	10	0	10	10	10	10	10
+21	11	0	11	11	11	11	11
+22	12	0	12	12	12	12	12
+23	13	0	13	13	13	13	13
+24	14	0	14	14	14	14	14
+25	15	0	15	15	15	15	15
+26	16	0	16	16	16	16	16
+27	17	0	17	17	17	17	17
+28	18	0	18	18	18	18	18
+29	19	0	19	19	19	19	19
+30	20	0	20	20	20	20	20
+31	21	0	21	21	21	21	21
+32	22	0	22	22	22	22	22
+33	23	0	23	23	23	23	23
+34	24	0	24	24	24	24	24
+35	25	0	25	25	25	25	25
+36	26	0	26	26	26	26	26
+37	27	0	27	27	27	27	27
+38	28	0	28	28	28	28	28
+39	29	0	29	29	29	29	29
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	10	-1	10	10	10	10	10
+61	11	-1	10	10	10	20	10
+62	12	-1	10	10	10	20	10
+63	13	-1	10	10	10	20	10
+64	14	-1	10	10	10	20	10
+65	15	-1	20	20	10	20	10
+66	16	-1	20	20	10	20	10
+67	17	-1	20	20	10	20	10
+68	18	-1	20	20	10	20	10
+69	19	-1	20	20	10	20	10
+70	20	-1	20	20	20	20	20
+71	21	-1	20	20	20	30	20
+72	22	-1	20	20	20	30	20
+73	23	-1	20	20	20	30	20
+74	24	-1	20	20	20	30	20
+75	25	-1	30	20	20	30	20
+76	26	-1	30	30	20	30	20
+77	27	-1	30	30	20	30	20
+78	28	-1	30	30	20	30	20
+79	29	-1	30	30	20	30	20
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	10	-2	0	0	0	100	0
+101	11	-2	0	0	0	100	0
+102	12	-2	0	0	0	100	0
+103	13	-2	0	0	0	100	0
+104	14	-2	0	0	0	100	0
+105	15	-2	0	0	0	100	0
+106	16	-2	0	0	0	100	0
+107	17	-2	0	0	0	100	0
+108	18	-2	0	0	0	100	0
+109	19	-2	0	0	0	100	0
+110	20	-2	0	0	0	100	0
+111	21	-2	0	0	0	100	0
+112	22	-2	0	0	0	100	0
+113	23	-2	0	0	0	100	0
+114	24	-2	0	0	0	100	0
+115	25	-2	0	0	0	100	0
+116	26	-2	0	0	0	100	0
+117	27	-2	0	0	0	100	0
+118	28	-2	0	0	0	100	0
+119	29	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id i8 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	-10	0	-10	-10	-10	-10	-10
+21	-9	0	-9	-9	-9	-9	-9
+22	-8	0	-8	-8	-8	-8	-8
+23	-7	0	-7	-7	-7	-7	-7
+24	-6	0	-6	-6	-6	-6	-6
+25	-5	0	-5	-5	-5	-5	-5
+26	-4	0	-4	-4	-4	-4	-4
+27	-3	0	-3	-3	-3	-3	-3
+28	-2	0	-2	-2	-2	-2	-2
+29	-1	0	-1	-1	-1	-1	-1
+30	0	0	0	0	0	0	0
+31	1	0	1	1	1	1	1
+32	2	0	2	2	2	2	2
+33	3	0	3	3	3	3	3
+34	4	0	4	4	4	4	4
+35	5	0	5	5	5	5	5
+36	6	0	6	6	6	6	6
+37	7	0	7	7	7	7	7
+38	8	0	8	8	8	8	8
+39	9	0	9	9	9	9	9
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	-10	-1	-10	-10	-10	-10	-10
+61	-9	-1	-10	-10	-10	0	0
+62	-8	-1	-10	-10	-10	0	0
+63	-7	-1	-10	-10	-10	0	0
+64	-6	-1	-10	-10	-10	0	0
+65	-5	-1	-10	0	-10	0	0
+66	-4	-1	0	0	-10	0	0
+67	-3	-1	0	0	-10	0	0
+68	-2	-1	0	0	-10	0	0
+69	-1	-1	0	0	-10	0	0
+70	0	-1	0	0	0	0	0
+71	1	-1	0	0	0	10	0
+72	2	-1	0	0	0	10	0
+73	3	-1	0	0	0	10	0
+74	4	-1	0	0	0	10	0
+75	5	-1	10	0	0	10	0
+76	6	-1	10	10	0	10	0
+77	7	-1	10	10	0	10	0
+78	8	-1	10	10	0	10	0
+79	9	-1	10	10	0	10	0
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	-10	-2	0	0	-100	0	0
+101	-9	-2	0	0	-100	0	0
+102	-8	-2	0	0	-100	0	0
+103	-7	-2	0	0	-100	0	0
+104	-6	-2	0	0	-100	0	0
+105	-5	-2	0	0	-100	0	0
+106	-4	-2	0	0	-100	0	0
+107	-3	-2	0	0	-100	0	0
+108	-2	-2	0	0	-100	0	0
+109	-1	-2	0	0	-100	0	0
+110	0	-2	0	0	0	0	0
+111	1	-2	0	0	0	100	0
+112	2	-2	0	0	0	100	0
+113	3	-2	0	0	0	100	0
+114	4	-2	0	0	0	100	0
+115	5	-2	0	0	0	100	0
+116	6	-2	0	0	0	100	0
+117	7	-2	0	0	0	100	0
+118	8	-2	0	0	0	100	0
+119	9	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	-56	4	-56	-56	-56	-56	-56
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	-12	4	-12	-12	-12	-12	-12
+id i16 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	-10	0	-10	-10	-10	-10	-10
+21	-9	0	-9	-9	-9	-9	-9
+22	-8	0	-8	-8	-8	-8	-8
+23	-7	0	-7	-7	-7	-7	-7
+24	-6	0	-6	-6	-6	-6	-6
+25	-5	0	-5	-5	-5	-5	-5
+26	-4	0	-4	-4	-4	-4	-4
+27	-3	0	-3	-3	-3	-3	-3
+28	-2	0	-2	-2	-2	-2	-2
+29	-1	0	-1	-1	-1	-1	-1
+30	0	0	0	0	0	0	0
+31	1	0	1	1	1	1	1
+32	2	0	2	2	2	2	2
+33	3	0	3	3	3	3	3
+34	4	0	4	4	4	4	4
+35	5	0	5	5	5	5	5
+36	6	0	6	6	6	6	6
+37	7	0	7	7	7	7	7
+38	8	0	8	8	8	8	8
+39	9	0	9	9	9	9	9
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	-10	-1	-10	-10	-10	-10	-10
+61	-9	-1	-10	-10	-10	0	0
+62	-8	-1	-10	-10	-10	0	0
+63	-7	-1	-10	-10	-10	0	0
+64	-6	-1	-10	-10	-10	0	0
+65	-5	-1	-10	0	-10	0	0
+66	-4	-1	0	0	-10	0	0
+67	-3	-1	0	0	-10	0	0
+68	-2	-1	0	0	-10	0	0
+69	-1	-1	0	0	-10	0	0
+70	0	-1	0	0	0	0	0
+71	1	-1	0	0	0	10	0
+72	2	-1	0	0	0	10	0
+73	3	-1	0	0	0	10	0
+74	4	-1	0	0	0	10	0
+75	5	-1	10	0	0	10	0
+76	6	-1	10	10	0	10	0
+77	7	-1	10	10	0	10	0
+78	8	-1	10	10	0	10	0
+79	9	-1	10	10	0	10	0
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	-10	-2	0	0	-100	0	0
+101	-9	-2	0	0	-100	0	0
+102	-8	-2	0	0	-100	0	0
+103	-7	-2	0	0	-100	0	0
+104	-6	-2	0	0	-100	0	0
+105	-5	-2	0	0	-100	0	0
+106	-4	-2	0	0	-100	0	0
+107	-3	-2	0	0	-100	0	0
+108	-2	-2	0	0	-100	0	0
+109	-1	-2	0	0	-100	0	0
+110	0	-2	0	0	0	0	0
+111	1	-2	0	0	0	100	0
+112	2	-2	0	0	0	100	0
+113	3	-2	0	0	0	100	0
+114	4	-2	0	0	0	100	0
+115	5	-2	0	0	0	100	0
+116	6	-2	0	0	0	100	0
+117	7	-2	0	0	0	100	0
+118	8	-2	0	0	0	100	0
+119	9	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id i32 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	-10	0	-10	-10	-10	-10	-10
+21	-9	0	-9	-9	-9	-9	-9
+22	-8	0	-8	-8	-8	-8	-8
+23	-7	0	-7	-7	-7	-7	-7
+24	-6	0	-6	-6	-6	-6	-6
+25	-5	0	-5	-5	-5	-5	-5
+26	-4	0	-4	-4	-4	-4	-4
+27	-3	0	-3	-3	-3	-3	-3
+28	-2	0	-2	-2	-2	-2	-2
+29	-1	0	-1	-1	-1	-1	-1
+30	0	0	0	0	0	0	0
+31	1	0	1	1	1	1	1
+32	2	0	2	2	2	2	2
+33	3	0	3	3	3	3	3
+34	4	0	4	4	4	4	4
+35	5	0	5	5	5	5	5
+36	6	0	6	6	6	6	6
+37	7	0	7	7	7	7	7
+38	8	0	8	8	8	8	8
+39	9	0	9	9	9	9	9
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	-10	-1	-10	-10	-10	-10	-10
+61	-9	-1	-10	-10	-10	0	0
+62	-8	-1	-10	-10	-10	0	0
+63	-7	-1	-10	-10	-10	0	0
+64	-6	-1	-10	-10	-10	0	0
+65	-5	-1	-10	0	-10	0	0
+66	-4	-1	0	0	-10	0	0
+67	-3	-1	0	0	-10	0	0
+68	-2	-1	0	0	-10	0	0
+69	-1	-1	0	0	-10	0	0
+70	0	-1	0	0	0	0	0
+71	1	-1	0	0	0	10	0
+72	2	-1	0	0	0	10	0
+73	3	-1	0	0	0	10	0
+74	4	-1	0	0	0	10	0
+75	5	-1	10	0	0	10	0
+76	6	-1	10	10	0	10	0
+77	7	-1	10	10	0	10	0
+78	8	-1	10	10	0	10	0
+79	9	-1	10	10	0	10	0
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	-10	-2	0	0	-100	0	0
+101	-9	-2	0	0	-100	0	0
+102	-8	-2	0	0	-100	0	0
+103	-7	-2	0	0	-100	0	0
+104	-6	-2	0	0	-100	0	0
+105	-5	-2	0	0	-100	0	0
+106	-4	-2	0	0	-100	0	0
+107	-3	-2	0	0	-100	0	0
+108	-2	-2	0	0	-100	0	0
+109	-1	-2	0	0	-100	0	0
+110	0	-2	0	0	0	0	0
+111	1	-2	0	0	0	100	0
+112	2	-2	0	0	0	100	0
+113	3	-2	0	0	0	100	0
+114	4	-2	0	0	0	100	0
+115	5	-2	0	0	0	100	0
+116	6	-2	0	0	0	100	0
+117	7	-2	0	0	0	100	0
+118	8	-2	0	0	0	100	0
+119	9	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id i64 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	-10	0	-10	-10	-10	-10	-10
+21	-9	0	-9	-9	-9	-9	-9
+22	-8	0	-8	-8	-8	-8	-8
+23	-7	0	-7	-7	-7	-7	-7
+24	-6	0	-6	-6	-6	-6	-6
+25	-5	0	-5	-5	-5	-5	-5
+26	-4	0	-4	-4	-4	-4	-4
+27	-3	0	-3	-3	-3	-3	-3
+28	-2	0	-2	-2	-2	-2	-2
+29	-1	0	-1	-1	-1	-1	-1
+30	0	0	0	0	0	0	0
+31	1	0	1	1	1	1	1
+32	2	0	2	2	2	2	2
+33	3	0	3	3	3	3	3
+34	4	0	4	4	4	4	4
+35	5	0	5	5	5	5	5
+36	6	0	6	6	6	6	6
+37	7	0	7	7	7	7	7
+38	8	0	8	8	8	8	8
+39	9	0	9	9	9	9	9
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	10	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	-10	-1	-10	-10	-10	-10	-10
+61	-9	-1	-10	-10	-10	0	0
+62	-8	-1	-10	-10	-10	0	0
+63	-7	-1	-10	-10	-10	0	0
+64	-6	-1	-10	-10	-10	0	0
+65	-5	-1	-10	0	-10	0	0
+66	-4	-1	0	0	-10	0	0
+67	-3	-1	0	0	-10	0	0
+68	-2	-1	0	0	-10	0	0
+69	-1	-1	0	0	-10	0	0
+70	0	-1	0	0	0	0	0
+71	1	-1	0	0	0	10	0
+72	2	-1	0	0	0	10	0
+73	3	-1	0	0	0	10	0
+74	4	-1	0	0	0	10	0
+75	5	-1	10	0	0	10	0
+76	6	-1	10	10	0	10	0
+77	7	-1	10	10	0	10	0
+78	8	-1	10	10	0	10	0
+79	9	-1	10	10	0	10	0
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	-10	-2	0	0	-100	0	0
+101	-9	-2	0	0	-100	0	0
+102	-8	-2	0	0	-100	0	0
+103	-7	-2	0	0	-100	0	0
+104	-6	-2	0	0	-100	0	0
+105	-5	-2	0	0	-100	0	0
+106	-4	-2	0	0	-100	0	0
+107	-3	-2	0	0	-100	0	0
+108	-2	-2	0	0	-100	0	0
+109	-1	-2	0	0	-100	0	0
+110	0	-2	0	0	0	0	0
+111	1	-2	0	0	0	100	0
+112	2	-2	0	0	0	100	0
+113	3	-2	0	0	0	100	0
+114	4	-2	0	0	0	100	0
+115	5	-2	0	0	0	100	0
+116	6	-2	0	0	0	100	0
+117	7	-2	0	0	0	100	0
+118	8	-2	0	0	0	100	0
+119	9	-2	0	0	0	100	0
+200	0	0	0	0	0	0	0
+201	0	-1	0	0	0	0	0
+202	0	-2	0	0	0	0	0
+203	0	-3	0	0	0	0	0
+204	0	-4	0	0	0	0	0
+205	0	-5	0	0	0	0	0
+206	0	-6	0	0	0	0	0
+207	0	-7	0	0	0	0	0
+208	0	-8	0	0	0	0	0
+209	0	-9	0	0	0	0	0
+210	0	0	0	0	0	0	0
+211	0	-1	0	0	0	0	0
+212	0	-2	0	0	0	0	0
+213	0	-3	0	0	0	0	0
+214	0	-4	0	0	0	0	0
+215	0	-5	0	0	0	0	0
+216	0	-6	0	0	0	0	0
+217	0	-7	0	0	0	0	0
+218	0	-8	0	0	0	0	0
+219	0	-9	0	0	0	0	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id f32 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	-1	0	-1	-1	-1	-1	-1
+21	-0.9	0	-1	-1	-1	-0	-0
+22	-0.8	0	-1	-1	-1	-0	-0
+23	-0.7	0	-1	-1	-1	-0	-0
+24	-0.6	0	-1	-1	-1	-0	-0
+25	-0.5	0	-0	-0	-1	-0	-0
+26	-0.4	0	-0	-0	-1	-0	-0
+27	-0.3	0	-0	-0	-1	-0	-0
+28	-0.2	0	-0	-0	-1	-0	-0
+29	-0.1	0	-0	-0	-1	-0	-0
+30	0	0	0	0	0	0	0
+31	0.1	0	0	0	0	1	0
+32	0.2	0	0	0	0	1	0
+33	0.3	0	0	0	0	1	0
+34	0.4	0	0	0	0	1	0
+35	0.5	0	0	0	0	1	0
+36	0.6	0	1	1	0	1	0
+37	0.7	0	1	1	0	1	0
+38	0.8	0	1	1	0	1	0
+39	0.9	0	1	1	0	1	0
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	0	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	-1	-1	-0	-0	-10	-0	-0
+61	-0.9	-1	-0	-0	-10	-0	-0
+62	-0.8	-1	-0	-0	-10	-0	-0
+63	-0.7	-1	-0	-0	-10	-0	-0
+64	-0.6	-1	-0	-0	-10	-0	-0
+65	-0.5	-1	-0	-0	-10	-0	-0
+66	-0.4	-1	-0	-0	-10	-0	-0
+67	-0.3	-1	-0	-0	-10	-0	-0
+68	-0.2	-1	-0	-0	-10	-0	-0
+69	-0.1	-1	-0	-0	-10	-0	-0
+70	0	-1	0	0	0	0	0
+71	0.1	-1	0	0	0	10	0
+72	0.2	-1	0	0	0	10	0
+73	0.3	-1	0	0	0	10	0
+74	0.4	-1	0	0	0	10	0
+75	0.5	-1	0	0	0	10	0
+76	0.6	-1	0	0	0	10	0
+77	0.7	-1	0	0	0	10	0
+78	0.8	-1	0	0	0	10	0
+79	0.9	-1	0	0	0	10	0
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	-1	-2	-0	-0	-100	-0	-0
+101	-0.9	-2	-0	-0	-100	-0	-0
+102	-0.8	-2	-0	-0	-100	-0	-0
+103	-0.7	-2	-0	-0	-100	-0	-0
+104	-0.6	-2	-0	-0	-100	-0	-0
+105	-0.5	-2	-0	-0	-100	-0	-0
+106	-0.4	-2	-0	-0	-100	-0	-0
+107	-0.3	-2	-0	-0	-100	-0	-0
+108	-0.2	-2	-0	-0	-100	-0	-0
+109	-0.1	-2	-0	-0	-100	-0	-0
+110	0	-2	0	0	0	0	0
+111	0.1	-2	0	0	0	100	0
+112	0.2	-2	0	0	0	100	0
+113	0.3	-2	0	0	0	100	0
+114	0.4	-2	0	0	0	100	0
+115	0.5	-2	0	0	0	100	0
+116	0.6	-2	0	0	0	100	0
+117	0.7	-2	0	0	0	100	0
+118	0.8	-2	0	0	0	100	0
+119	0.9	-2	0	0	0	100	0
+200	12345.679	0	12346	12346	12345	12346	12345
+201	12345.679	-1	12350	12350	12340	12350	12340
+202	12345.679	-2	12300	12300	12300	12400	12300
+203	12345.679	-3	12000	12000	12000	13000	12000
+204	12345.679	-4	10000	10000	10000	20000	10000
+205	12345.679	-5	0	0	0	100000	0
+206	12345.679	-6	0	0	0	1000000	0
+207	12345.679	-7	0	0	0	10000000	0
+208	12345.679	-8	0	0	0	100000000	0
+209	12345.679	-9	0	0	0	1000000000	0
+210	12345.679	0	12346	12346	12345	12346	12345
+211	12345.679	-1	12350	12350	12340	12350	12340
+212	12345.679	-2	12300	12300	12300	12400	12300
+213	12345.679	-3	12000	12000	12000	13000	12000
+214	12345.679	-4	10000	10000	10000	20000	10000
+215	12345.679	-5	0	0	0	100000	0
+216	12345.679	-6	0	0	0	1000000	0
+217	12345.679	-7	0	0	0	10000000	0
+218	12345.679	-8	0	0	0	100000000	0
+219	12345.679	-9	0	0	0	1000000000	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+id f64 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)
+0	0	0	0	0	0	0	0
+1	1	0	1	1	1	1	1
+2	2	0	2	2	2	2	2
+3	3	0	3	3	3	3	3
+4	4	0	4	4	4	4	4
+5	5	0	5	5	5	5	5
+6	6	0	6	6	6	6	6
+7	7	0	7	7	7	7	7
+8	8	0	8	8	8	8	8
+9	9	0	9	9	9	9	9
+10	10	0	10	10	10	10	10
+11	11	0	11	11	11	11	11
+12	12	0	12	12	12	12	12
+13	13	0	13	13	13	13	13
+14	14	0	14	14	14	14	14
+15	15	0	15	15	15	15	15
+16	16	0	16	16	16	16	16
+17	17	0	17	17	17	17	17
+18	18	0	18	18	18	18	18
+19	19	0	19	19	19	19	19
+20	-1	0	-1	-1	-1	-1	-1
+21	-0.9	0	-1	-1	-1	-0	-0
+22	-0.8	0	-1	-1	-1	-0	-0
+23	-0.7	0	-1	-1	-1	-0	-0
+24	-0.6	0	-1	-1	-1	-0	-0
+25	-0.5	0	-0	-0	-1	-0	-0
+26	-0.4	0	-0	-0	-1	-0	-0
+27	-0.3	0	-0	-0	-1	-0	-0
+28	-0.2	0	-0	-0	-1	-0	-0
+29	-0.1	0	-0	-0	-1	-0	-0
+30	0	0	0	0	0	0	0
+31	0.1	0	0	0	0	1	0
+32	0.2	0	0	0	0	1	0
+33	0.3	0	0	0	0	1	0
+34	0.4	0	0	0	0	1	0
+35	0.5	0	0	0	0	1	0
+36	0.6	0	1	1	0	1	0
+37	0.7	0	1	1	0	1	0
+38	0.8	0	1	1	0	1	0
+39	0.9	0	1	1	0	1	0
+40	0	-1	0	0	0	0	0
+41	1	-1	0	0	0	10	0
+42	2	-1	0	0	0	10	0
+43	3	-1	0	0	0	10	0
+44	4	-1	0	0	0	10	0
+45	5	-1	0	0	0	10	0
+46	6	-1	10	10	0	10	0
+47	7	-1	10	10	0	10	0
+48	8	-1	10	10	0	10	0
+49	9	-1	10	10	0	10	0
+50	10	-1	10	10	10	10	10
+51	11	-1	10	10	10	20	10
+52	12	-1	10	10	10	20	10
+53	13	-1	10	10	10	20	10
+54	14	-1	10	10	10	20	10
+55	15	-1	20	20	10	20	10
+56	16	-1	20	20	10	20	10
+57	17	-1	20	20	10	20	10
+58	18	-1	20	20	10	20	10
+59	19	-1	20	20	10	20	10
+60	-1	-1	-0	-0	-10	-0	-0
+61	-0.9	-1	-0	-0	-10	-0	-0
+62	-0.8	-1	-0	-0	-10	-0	-0
+63	-0.7	-1	-0	-0	-10	-0	-0
+64	-0.6	-1	-0	-0	-10	-0	-0
+65	-0.5	-1	-0	-0	-10	-0	-0
+66	-0.4	-1	-0	-0	-10	-0	-0
+67	-0.3	-1	-0	-0	-10	-0	-0
+68	-0.2	-1	-0	-0	-10	-0	-0
+69	-0.1	-1	-0	-0	-10	-0	-0
+70	0	-1	0	0	0	0	0
+71	0.1	-1	0	0	0	10	0
+72	0.2	-1	0	0	0	10	0
+73	0.3	-1	0	0	0	10	0
+74	0.4	-1	0	0	0	10	0
+75	0.5	-1	0	0	0	10	0
+76	0.6	-1	0	0	0	10	0
+77	0.7	-1	0	0	0	10	0
+78	0.8	-1	0	0	0	10	0
+79	0.9	-1	0	0	0	10	0
+80	0	-2	0	0	0	0	0
+81	1	-2	0	0	0	100	0
+82	2	-2	0	0	0	100	0
+83	3	-2	0	0	0	100	0
+84	4	-2	0	0	0	100	0
+85	5	-2	0	0	0	100	0
+86	6	-2	0	0	0	100	0
+87	7	-2	0	0	0	100	0
+88	8	-2	0	0	0	100	0
+89	9	-2	0	0	0	100	0
+90	10	-2	0	0	0	100	0
+91	11	-2	0	0	0	100	0
+92	12	-2	0	0	0	100	0
+93	13	-2	0	0	0	100	0
+94	14	-2	0	0	0	100	0
+95	15	-2	0	0	0	100	0
+96	16	-2	0	0	0	100	0
+97	17	-2	0	0	0	100	0
+98	18	-2	0	0	0	100	0
+99	19	-2	0	0	0	100	0
+100	-1	-2	-0	-0	-100	-0	-0
+101	-0.9	-2	-0	-0	-100	-0	-0
+102	-0.8	-2	-0	-0	-100	-0	-0
+103	-0.7	-2	-0	-0	-100	-0	-0
+104	-0.6	-2	-0	-0	-100	-0	-0
+105	-0.5	-2	-0	-0	-100	-0	-0
+106	-0.4	-2	-0	-0	-100	-0	-0
+107	-0.3	-2	-0	-0	-100	-0	-0
+108	-0.2	-2	-0	-0	-100	-0	-0
+109	-0.1	-2	-0	-0	-100	-0	-0
+110	0	-2	0	0	0	0	0
+111	0.1	-2	0	0	0	100	0
+112	0.2	-2	0	0	0	100	0
+113	0.3	-2	0	0	0	100	0
+114	0.4	-2	0	0	0	100	0
+115	0.5	-2	0	0	0	100	0
+116	0.6	-2	0	0	0	100	0
+117	0.7	-2	0	0	0	100	0
+118	0.8	-2	0	0	0	100	0
+119	0.9	-2	0	0	0	100	0
+200	12345.6789	0	12346	12346	12345	12346	12345
+201	12345.6789	-1	12350	12350	12340	12350	12340
+202	12345.6789	-2	12300	12300	12300	12400	12300
+203	12345.6789	-3	12000	12000	12000	13000	12000
+204	12345.6789	-4	10000	10000	10000	20000	10000
+205	12345.6789	-5	0	0	0	100000	0
+206	12345.6789	-6	0	0	0	1000000	0
+207	12345.6789	-7	0	0	0	10000000	0
+208	12345.6789	-8	0	0	0	100000000	0
+209	12345.6789	-9	0	0	0	1000000000	0
+210	12345.6789	0	12346	12346	12345	12346	12345
+211	12345.6789	-1	12350	12350	12340	12350	12340
+212	12345.6789	-2	12300	12300	12300	12400	12300
+213	12345.6789	-3	12000	12000	12000	13000	12000
+214	12345.6789	-4	10000	10000	10000	20000	10000
+215	12345.6789	-5	0	0	0	100000	0
+216	12345.6789	-6	0	0	0	1000000	0
+217	12345.6789	-7	0	0	0	10000000	0
+218	12345.6789	-8	0	0	0	100000000	0
+219	12345.6789	-9	0	0	0	1000000000	0
+300	2	4	2	2	2	2	2
+301	20	4	20	20	20	20	20
+302	200	4	200	200	200	200	200
+303	5	4	5	5	5	5	5
+304	50	4	50	50	50	50	50
+305	500	4	500	500	500	500	500
+CHECKPOINT2
+1	42.42	42.42	42.42	42.42
+2	0.0084	0.0084	0.0084	0.0084
+3	6.513	6.513	6.513	6.513
+4	115.6011	115.6011	115.6011	115.6011
+5	1.6029	1.6029	1.6029	1.6029
+6	-0.9999	-0.9999	-0.9999	-0.9999
+7	0.0084	0.0084	0.0084	0.0084
+8	3.7476	3.7476	3.7476	3.7476
+9	5.4066	5.4066	5.4066	5.4066
+10	1.6275	1.6275	1.6275	1.6275
+1
+1
+1
diff --git a/tests/queries/0_stateless/03165_round_scale_as_column.sql b/tests/queries/0_stateless/03165_round_scale_as_column.sql
new file mode 100644
index 00000000000..60940b22fc1
--- /dev/null
+++ b/tests/queries/0_stateless/03165_round_scale_as_column.sql
@@ -0,0 +1,125 @@
+-- Regression test that functions round(), roundBankers(), floor(), ceil() and trunc() work with default 'scale' argument (= the 2nd argument)
+SELECT toUInt8(number) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toUInt16(number) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toUInt32(number) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toUInt64(number) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toInt8(number - 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toInt16(number - 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toInt32(number - 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toInt64(number - 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toFloat32(number - 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toFloat64(number - 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+
+SELECT toFloat32((number - 10) / 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+SELECT toFloat64((number - 10) / 10) AS x, round(x), roundBankers(x), floor(x), ceil(x), trunc(x) FROM system.numbers LIMIT 20;
+
+-- Test that functions round(), roundBankers(), floor(), ceil() and trunc() accept non-const 'scale' argument
+SELECT toFloat32((number - 10) / 10) AS x, round(x, materialize(1)), roundBankers(x, materialize(1)), floor(x, materialize(1)), ceil(x, materialize(1)), trunc(x, materialize(1)) FROM system.numbers LIMIT 20;
+SELECT toFloat64((number - 10) / 10) AS x, round(x, materialize(1)), roundBankers(x, materialize(1)), floor(x, materialize(1)), ceil(x, materialize(1)), trunc(x, materialize(1)) FROM system.numbers LIMIT 20;
+SELECT toUInt8(number) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toUInt16(number) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toUInt32(number) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toUInt64(number) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+
+SELECT toInt8(number - 10) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toInt16(number - 10) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toInt32(number - 10) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toInt64(number - 10) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toFloat32(number - 10) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+SELECT toFloat64(number - 10) AS x, round(x, materialize(-1)), roundBankers(x, materialize(-1)), floor(x, materialize(-1)), ceil(x, materialize(-1)), trunc(x, materialize(-1)) FROM system.numbers LIMIT 20;
+
+SELECT toUInt8(number) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toUInt16(number) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toUInt32(number) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toUInt64(number) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toInt8(number - 10) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toInt16(number - 10) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toInt32(number - 10) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toInt64(number - 10) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toFloat32(number - 10) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+SELECT toFloat64(number - 10) AS x, round(x, materialize(-2)), roundBankers(x, materialize(-2)), floor(x, materialize(-2)), ceil(x, materialize(-2)), trunc(x, materialize(-2)) FROM system.numbers LIMIT 20;
+
+SELECT toString('CHECKPOINT1');
+
+DROP TABLE IF EXISTS tround;
+
+CREATE TABLE tround (
+    id Int32,
+    scale Int16,
+    u8 UInt8, u16 UInt16, u32 UInt32, u64 UInt64,
+    i8 Int8, i16 Int16, i32 Int32, i64 Int64,
+    f32 Float32, f64 Float64
+) ENGINE = Memory;
+
+INSERT INTO tround SELECT number    ,  0, number, number, number, number, number, number, number, number, number, number, FROM system.numbers LIMIT 20;
+INSERT INTO tround SELECT number+20 ,  0, number+10, number+10, number+10, number+10, number-10, number-10, number-10, number-10, (toFloat32(number)-10)/10, (toFloat64(number)-10)/10, FROM system.numbers LIMIT 20;
+INSERT INTO tround SELECT number+40 , -1, number, number, number, number, number, number, number, number, number, number, FROM system.numbers LIMIT 20;
+INSERT INTO tround SELECT number+60 , -1, number+10, number+10, number+10, number+10, number-10, number-10, number-10, number-10, (toFloat32(number)-10)/10, (toFloat64(number)-10)/10, FROM system.numbers LIMIT 20;
+INSERT INTO tround SELECT number+80 , -2, number, number, number, number, number, number, number, number, number, number, FROM system.numbers LIMIT 20;
+INSERT INTO tround SELECT number+100, -2, number+10, number+10, number+10, number+10, number-10, number-10, number-10, number-10, (toFloat32(number)-10)/10, (toFloat64(number)-10)/10, FROM system.numbers LIMIT 20;
+
+INSERT INTO tround SELECT number+200, -number, 0, 0, 0, 0, 0, 0, 0, 0, 12345.6789, 12345.6789, FROM system.numbers LIMIT 10;
+INSERT INTO tround SELECT number+210, -number, 0, 0, 0, 0, 0, 0, 0, 0, 12345.6789, 12345.6789, FROM system.numbers LIMIT 10;
+
+INSERT INTO tround VALUES (300, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2.0, 2.0);
+INSERT INTO tround VALUES (301, 4, 20, 20, 20, 20, 20, 20, 20, 20, 20.0, 20.0);
+INSERT INTO tround VALUES (302, 4, 200, 200, 200, 200, 200, 200, 200, 200, 200.0, 200.0);
+INSERT INTO tround VALUES (303, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5.0, 5.0);
+INSERT INTO tround VALUES (304, 4, 50, 50, 50, 50, 50, 50, 50, 50, 50.0, 50.0);
+INSERT INTO tround VALUES (305, 4, 500, 500, 500, 500, 500, 500, 500, 500, 500.0, 500.0);
+
+SELECT toString('id u8 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, u8   AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id u16 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, u16  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id u32 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, u32  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id u64 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, u64  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id i8 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, i8   AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id i16 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, i16  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id i32 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, i32  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id i64 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, i64  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id f32 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, f32  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+SELECT toString('id f64 scale round(u8, scale) roundBankers(x, scale) floor(x, scale) ceil(x, scale) trunc(x, scale)');
+SELECT id, f64  AS x, scale, round(x, scale), roundBankers(x, scale), floor(x, scale), ceil(x, scale), trunc(x, scale) FROM tround ORDER BY id;
+
+DROP TABLE IF EXISTS tround;
+--
+SELECT toString('CHECKPOINT2');
+
+DROP TABLE IF EXISTS tround2;
+
+CREATE TABLE tround2 (
+    id Int32,
+    scale Int16,
+    d32 Decimal32(4), d64 Decimal64(4), d128 Decimal128(4), d256 Decimal256(4)
+) ENGINE = Memory;
+
+INSERT INTO tround2 VALUES (1, 6, toDecimal32('42.42', 4), toDecimal64('42.42', 4), toDecimal128('42.42', 4), toDecimal256('42.42', 4));
+INSERT INTO tround2 SELECT 2 , 6, cos(d32), cos(d64), cos(d128), cos(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 3 , 6, sqrt(d32), sqrt(d64), sqrt(d128), sqrt(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 4 , 6, lgamma(d32), lgamma(d64), lgamma(d128), lgamma(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 5 , 6, tgamma(d32)/1e50, tgamma(d64)/1e50, tgamma(d128)/1e50, tgamma(d256)/1e50 FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 6 , 8, sin(d32), sin(d64), sin(d128), sin(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 7 , 8, cos(d32), cos(d64), cos(d128), cos(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 8 , 8, log(d32), log(d64), log(d128), log(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 9 , 8, log2(d32), log2(d64), log2(d128), log2(d256) FROM tround2 WHERE id = 1;
+INSERT INTO tround2 SELECT 10, 8, log10(d32), log10(d64), log10(d128), log10(d256) FROM tround2 WHERE id = 1;
+
+SELECT id, round(d32, scale), round(d64, scale), round(d128, scale), round(d256, scale) FROM tround2 ORDER BY id;
+
+DROP TABLE IF EXISTS tround2;
+
+SELECT round(1, 1);
+SELECT round(materialize(1), materialize(1));
+SELECT round(1, materialize(1)); --{serverError ILLEGAL_COLUMN}
+SELECT round(materialize(1), 1);
+
+
+