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All the integer types listed in Table 3-1 support bitwise manipulations on their underlying representations. Table 3-3 shows the bitwise manipulation operators.
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Table 3-3. Bitwise Arithmetic Operators and Examples
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&&& ||| ~~~ <<< >>>
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Bitwise and Bitwise or Bitwise exclusive or Bitwise negation Left shift Right shift (arithmetic if signed)
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0x65 &&& 0x0F 0x65 ||| 0x18 0x65 0x0F ~~~0x65 0x01 <<< 3 0x65 >>> 3
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0x05 0x7D 0x6A 0xFFFFFF9a 0x08 0x0C
CH APT ER 3 I NTRO D UCI NG F UNC TI O NAL PRO GRA MMI NG
The following sample shows how to use these operators to encode 32-bit integers into 1, 2, or 5 bytes, represented by returning a list of integers. Integers in the range 0 to 127 return a list of length 1: let encode (n: int32) = if (n >= 0 && n <= 0x7F) then [ n ] elif (n >= 0x80 && n <= 0x3FFF) then [ (0x80 ||| (n >>> 8)) &&& 0xFF; (n &&& 0xFF) ] else [ 0xC0; ((n >>> 24) &&& 0xFF); ((n >>> 16) &&& 0xFF); ((n >>> 8) &&& 0xFF); (n &&& 0xFF) ] Here s an example of the function in action: > encode 32;; val it : int32 list = [32] > encode 320;; val it : int32 list = [129; 64] > encode 32000;; val it : int32 list = [192; 0; 0; 125; 0]
Arithmetic Conversions
Numeric types are not implicitly converted conversions between different numeric types must be made explicitly. You do this by using overloaded conversion operators. These work in the same way as overloaded infix operators such as + and *. Table 3-4 shows the primary conversion operators.
Table 3-4. Overloaded Arithmetic Conversions and Examples
Operator
sbyte byte int16 uint16 int/int32 uint32 int64 uint64 float32 float
Description
Convert/truncate to sbyte Convert/truncate to byte Convert/truncate to int16 Convert/truncate to uint16 Convert/truncate to int32 Convert/truncate to uint32 Convert/truncate to int64 Convert/truncate to uint64 Convert to float32/single Convert to float/double
Sample Use
sbyte (-17) byte 255 int16 0 uint16 65535 int 17.8 uint32 12 int64 (-100.4) uint64 1 float32 65 float 65
Result
-17y 255uy 0s 65535us 17 12u -100L 1UL 65.0f 65.0
C HAPTE R 3 INTRODU CING FUNCTION AL PROGRAM MIN G
These conversions are all unchecked in the sense that they will not raise exceptions. Again, the Microsoft.FSharp.Core.Operators.Checked module has corresponding definitions of these operators. An alternative is to use the .NET static methods contained in the type System.Convert, such as System.Convert.ToDouble( ). These do perform checking, which means they raise an exception if the source number can t be represented within the numeric range of the target type. As with many .NET constructs, uses of System.Convert methods may require type annotations to resolve overloading, discussed further in 5 and 6.
Arithmetic Comparisons
When used with numeric values, the binary comparison operators =, <>, <, <=, >, >=, min, and max perform comparisons according to the natural ordering for each particular numeric type. You can also use these operators on other data types, such as to compare lists of integers, and you can customize their behavior for new types you define. We discuss generic comparison in detail in 5, and we discuss customizing generic comparison in 8. When used with floating-point values, these operators implement the IEEE semantics for NaN (Not a Number) values. For example, (NaN = NaN) is false, as is (NaN <= NaN) and (NaN < NaN).
Overloaded Math Functions
The module Microsoft.FSharp.Core.Operators includes the definition of a number of useful overloaded math operators. These are shown in Table 3-5 and are overloaded either on a suitable range of integer types or on the basic floating-point types.
Table 3-5. Overloaded Math Functions and Examples
Function
abs cos, sin, tan cosh, sinh, tanh acos, asin, atan, atan2 ceil, floor truncate exp, log, log10 ( ** )
Description
Absolute value of signed numeric types Trigonometric functions Hyperbolic trigonometric functions Inverse trigonometric functions Round up, round down Round toward zero Exponent, logarithm, base-10 logarithm Power
Sample Use
abs (-10.0f) cos 0.0 cos 1.0 acos 1.0 ceil 1.001 truncate 8.9 exp 1.0 2.0 ** 4.0
Result
10.0f 1.0 1.543080635 0.0 2.0 8.0 2.718281828 16.0
Introducing Simple Strings
The F# type string is an abbreviation for .NET type System.String and represents a sequence of Unicode UTF-16 characters. In the following sections, we briefly introduce strings and the most useful functions for formatting them.
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