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Creating PDF 417 in Font Bitwise Operations

All the integer types listed in Table 3-1 support bitwise manipulations on their underlying representations. Table 3-3 shows the bitwise manipulation operators.

Bitwise and Bitwise or Bitwise exclusive or Bitwise negation Left shift Right shift (arithmetic if signed)

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]

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.

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

sbyte (-17) byte 255 int16 0 uint16 65535 int 17.8 uint32 12 int64 (-100.4) uint64 1 float32 65 float 65

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.

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).

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.

abs cos, sin, tan cosh, sinh, tanh acos, asin, atan, atan2 ceil, floor truncate exp, log, log10 ( ** )

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

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

10.0f 1.0 1.543080635 0.0 2.0 8.0 2.718281828 16.0

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.