Introduced intExp functions; using it where appropriate; make them available in SQL [#CLICKHOUSE-3].

dbms/src/Functions/CMakeLists.txt

@@ -26,6 +26,8 @@ generate_function_register(Arithmetic
   FunctionBitTestAll
   FunctionGCD
   FunctionLCM
+  FunctionIntExp2
+  FunctionIntExp10
 )
 
 generate_function_register(Array

dbms/src/Functions/FunctionsArithmetic.h

@@ -16,6 +16,7 @@
 #include <IO/WriteHelpers.h>
 #include <Interpreters/ExpressionActions.h>
 #include <ext/range.h>
+#include <common/intExp.h>
 #include <boost/math/common_factor.hpp>
 
 
@@ -453,6 +454,29 @@ struct LCMImpl
     }
 };
 
+template <typename A>
+struct IntExp2Impl
+{
+    using ResultType = UInt64;
+
+    static inline ResultType apply(A a)
+    {
+        return intExp2(a);
+    }
+};
+
+template <typename A>
+struct IntExp10Impl
+{
+    using ResultType = UInt64;
+
+    static inline ResultType apply(A a)
+    {
+        return intExp10(a);
+    }
+};
+
+
 /// this one is just for convenience
 template <bool B, typename T1, typename T2> using If = typename std::conditional<B, T1, T2>::type;
 /// these ones for better semantics
@@ -1013,6 +1037,8 @@ struct NameLeast                { static constexpr auto name = "least"; };
 struct NameGreatest             { static constexpr auto name = "greatest"; };
 struct NameGCD                  { static constexpr auto name = "gcd"; };
 struct NameLCM                  { static constexpr auto name = "lcm"; };
+struct NameIntExp2              { static constexpr auto name = "intExp2"; };
+struct NameIntExp10             { static constexpr auto name = "intExp10"; };
 
 using FunctionPlus = FunctionBinaryArithmetic<PlusImpl, NamePlus>;
 using FunctionMinus = FunctionBinaryArithmetic<MinusImpl, NameMinus>;
@@ -1036,6 +1062,10 @@ using FunctionLeast = FunctionBinaryArithmetic<LeastImpl, NameLeast>;
 using FunctionGreatest = FunctionBinaryArithmetic<GreatestImpl, NameGreatest>;
 using FunctionGCD = FunctionBinaryArithmetic<GCDImpl, NameGCD>;
 using FunctionLCM = FunctionBinaryArithmetic<LCMImpl, NameLCM>;
+/// Assumed to be injective for the purpose of query optimization, but in fact it is not injective because of possible overflow.
+using FunctionIntExp2 = FunctionUnaryArithmetic<IntExp2Impl, NameIntExp2, true>;
+using FunctionIntExp10 = FunctionUnaryArithmetic<IntExp10Impl, NameIntExp10, true>;
+
 
 /// Monotonicity properties for some functions.
 
@@ -1072,6 +1102,36 @@ template <> struct FunctionUnaryArithmeticMonotonicity<NameBitNot>
     }
 };
 
+template <> struct FunctionUnaryArithmeticMonotonicity<NameIntExp2>
+{
+    static bool has() { return true; }
+    static IFunction::Monotonicity get(const Field & left, const Field & right)
+    {
+        Float64 left_float = left.isNull() ? -std::numeric_limits<Float64>::infinity() : applyVisitor(FieldVisitorConvertToNumber<Float64>(), left);
+        Float64 right_float = right.isNull() ? std::numeric_limits<Float64>::infinity() : applyVisitor(FieldVisitorConvertToNumber<Float64>(), right);
+
+        if (left_float < 0 || right_float > 63)
+            return {};
+
+        return { true };
+    }
+};
+
+template <> struct FunctionUnaryArithmeticMonotonicity<NameIntExp10>
+{
+    static bool has() { return true; }
+    static IFunction::Monotonicity get(const Field & left, const Field & right)
+    {
+        Float64 left_float = left.isNull() ? -std::numeric_limits<Float64>::infinity() : applyVisitor(FieldVisitorConvertToNumber<Float64>(), left);
+        Float64 right_float = right.isNull() ? std::numeric_limits<Float64>::infinity() : applyVisitor(FieldVisitorConvertToNumber<Float64>(), right);
+
+        if (left_float < 0 || right_float > 19)
+            return {};
+
+        return { true };
+    }
+};
+
 }
 
 /// Optimizations for integer division by a constant.

dbms/src/Parsers/ParserSampleRatio.cpp

@@ -1,4 +1,4 @@
-#include <common/exp10.h>
+#include <common/intExp.h>
 
 #include <Parsers/CommonParsers.h>
 #include <Parsers/ParserSampleRatio.h>
@@ -48,13 +48,13 @@ static bool parseDecimal(const char * pos, const char * end, ASTSampleRatio::Rat
             return false;
     }
 
-    res.numerator = num_before * exp10(number_of_digits_after_point) + num_after;
-    res.denominator = exp10(number_of_digits_after_point);
+    res.numerator = num_before * intExp10(number_of_digits_after_point) + num_after;
+    res.denominator = intExp10(number_of_digits_after_point);
 
     if (exponent > 0)
-        res.numerator *= exp10(exponent);
+        res.numerator *= intExp10(exponent);
     if (exponent < 0)
-        res.denominator *= exp10(-exponent);
+        res.denominator *= intExp10(-exponent);
 
     /// NOTE You do not need to remove the common power of ten from the numerator and denominator.
     return true;

dbms/tests/queries/0_stateless/00534_exp10.sql

@@ -1 +1 @@
-SELECT number, exp10(number) FROM system.numbers LIMIT 310;
+SELECT number, exp10(number) FROM system.numbers LIMIT 310;

dbms/tests/queries/0_stateless/00536_int_exp.reference

@@ -0,0 +1,70 @@
+1	1	1	1	1	1
+2	2	1	10	10	1
+4	4	1	100	100	1
+8	8	1	1000	1000	1
+16	16	1	10000	10000	1
+32	32	1	100000	100000	1
+64	64	1	1000000	1000000	1
+128	128	1	10000000	10000000	1
+256	256	1	100000000	100000000	1
+512	512	1	1000000000	1000000000	1
+1024	1024	1	10000000000	10000000000	1
+2048	2048	1	100000000000	100000000000	1
+4096	4096	1	1000000000000	1000000000000	1
+8192	8192	1	10000000000000	10000000000000	1
+16384	16384	1	100000000000000	100000000000000	1
+32768	32768	1	1000000000000000	1000000000000000	1
+65536	65536	1	10000000000000000	10000000000000000	1
+131072	131072	1	100000000000000000	100000000000000000	1
+262144	262144	1	1000000000000000000	1000000000000000000	1
+524288	524288	1	10000000000000000000	10000000000000000000	1
+1048576	1048576	1	100000000000000000000	18446744073709551615	0
+2097152	2097152	1	1e21	18446744073709551615	0
+4194304	4194304	1	1e22	18446744073709551615	0
+8388608	8388608	1	1e23	18446744073709551615	0
+16777216	16777216	1	1e24	18446744073709551615	0
+33554432	33554432	1	1e25	18446744073709551615	0
+67108864	67108864	1	1e26	18446744073709551615	0
+134217728	134217728	1	1e27	18446744073709551615	0
+268435456	268435456	1	1e28	18446744073709551615	0
+536870912	536870912	1	1e29	18446744073709551615	0
+1073741824	1073741824	1	1e30	18446744073709551615	0
+2147483648	2147483648	1	1e31	18446744073709551615	0
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+549755813888	549755813888	1	1e39	18446744073709551615	0
+1099511627776	1099511627776	1	1e40	18446744073709551615	0
+2199023255552	2199023255552	1	1e41	18446744073709551615	0
+4398046511104	4398046511104	1	1e42	18446744073709551615	0
+8796093022208	8796093022208	1	1e43	18446744073709551615	0
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+35184372088832	35184372088832	1	1e45	18446744073709551615	0
+70368744177664	70368744177664	1	1e46	18446744073709551615	0
+140737488355328	140737488355328	1	1e47	18446744073709551615	0
+281474976710656	281474976710656	1	1e48	18446744073709551615	0
+562949953421312	562949953421312	1	1e49	18446744073709551615	0
+1125899906842624	1125899906842624	1	1e50	18446744073709551615	0
+2251799813685248	2251799813685248	1	1e51	18446744073709551615	0
+4503599627370496	4503599627370496	1	1e52	18446744073709551615	0
+9007199254740992	9007199254740992	1	1e53	18446744073709551615	0
+18014398509481984	18014398509481984	1	1e54	18446744073709551615	0
+36028797018963970	36028797018963968	1	1e55	18446744073709551615	0
+72057594037927940	72057594037927936	1	1e56	18446744073709551615	0
+144115188075855870	144115188075855872	1	1e57	18446744073709551615	0
+288230376151711740	288230376151711744	1	1e58	18446744073709551615	0
+576460752303423500	576460752303423488	1	1e59	18446744073709551615	0
+1152921504606847000	1152921504606846976	1	1e60	18446744073709551615	0
+2305843009213694000	2305843009213693952	1	1e61	18446744073709551615	0
+4611686018427388000	4611686018427387904	1	1e62	18446744073709551615	0
+9223372036854776000	9223372036854775808	1	1e63	18446744073709551615	0
+18446744073709552000	1	0	1e64	18446744073709551615	0
+36893488147419103000	2	0	1e65	18446744073709551615	0
+73786976294838210000	4	0	1e66	18446744073709551615	0
+147573952589676410000	8	0	1e67	18446744073709551615	0
+295147905179352830000	16	0	1e68	18446744073709551615	0
+590295810358705700000	32	0	1e69	18446744073709551615	0

dbms/tests/queries/0_stateless/00536_int_exp.sql

@@ -0,0 +1 @@
+SELECT exp2(number) AS e2d, intExp2(number) AS e2i, e2d = e2i AS e2eq, exp10(number) AS e10d, intExp10(number) AS e10i, e10d = e10i AS e10eq FROM system.numbers LIMIT 70;

libs/libcommon/CMakeLists.txt

@@ -34,6 +34,7 @@ add_library (common
     include/common/LocalDateTime.h
     include/common/ErrorHandlers.h
     include/common/exp10.h
+    include/common/intExp.h
     include/common/mremap.h
     include/common/likely.h
     include/common/logger_useful.h

libs/libcommon/include/common/intExp.h

@@ -0,0 +1,33 @@
+#pragma once
+
+#include <cstdint>
+#include <limits>
+
+
+/// On overlow, the function returns unspecified value.
+
+inline uint64_t intExp2(int x)
+{
+    return 1ULL << x;
+}
+
+inline uint64_t intExp10(int x)
+{
+    if (x < 0)
+        return 0;
+    if (x > 19)
+        return std::numeric_limits<uint64_t>::max();
+
+    static const uint64_t table[20] =
+    {
+        1ULL,                   10ULL,                   100ULL,
+        1000ULL,                10000ULL,                100000ULL,
+        1000000ULL,             10000000ULL,             100000000ULL,
+        1000000000ULL,          10000000000ULL,          100000000000ULL,
+        1000000000000ULL,       10000000000000ULL,       100000000000000ULL,
+        1000000000000000ULL,    10000000000000000ULL,    100000000000000000ULL,
+        1000000000000000000ULL, 10000000000000000000ULL
+    };
+
+    return table[x];
+}