164 lines
8.6 KiB
Factor
164 lines
8.6 KiB
Factor
USING: help.markup help.syntax math math.private ;
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IN: math.floats
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HELP: float
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{ $class-description "The class of double-precision floating point numbers." } ;
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HELP: >float
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{ $values { "x" real } { "y" float } }
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{ $description "Converts a real to a float. This is the identity on floats, and performs a floating point division on rationals." } ;
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HELP: bits>double ( n -- x )
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{ $values { "n" "a 64-bit integer representing an IEEE 754 double-precision float" } { "x" float } }
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{ $description "Creates a " { $link float } " object from a 64-bit binary representation. This word is usually used to reconstruct floats read from streams." } ;
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{ bits>double bits>float double>bits float>bits } related-words
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HELP: bits>float ( n -- x )
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{ $values { "n" "a 32-bit integer representing an IEEE 754 single-precision float" } { "x" float } }
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{ $description "Creates a " { $link float } " object from a 32-bit binary representation. This word is usually used to reconstruct floats read from streams." } ;
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HELP: double>bits ( x -- n )
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{ $values { "x" float } { "n" "a 64-bit integer representing an IEEE 754 double-precision float" } }
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{ $description "Creates a 64-bit binary representation of a " { $link float } " object. This can be used in the process of writing a float to a stream." } ;
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HELP: float>bits ( x -- n )
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{ $values { "x" float } { "n" "a 32-bit integer representing an IEEE 754 single-precision float" } }
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{ $description "Creates a 32-bit binary representation of a " { $link float } " object. This can be used in the process of writing a float to a stream." } ;
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! Unsafe primitives
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HELP: float+ ( x y -- z )
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{ $values { "x" float } { "y" float } { "z" float } }
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{ $description "Primitive version of " { $link + } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link + } " instead." } ;
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HELP: float- ( x y -- z )
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{ $values { "x" float } { "y" float } { "z" float } }
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{ $description "Primitive version of " { $link - } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link - } " instead." } ;
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HELP: float* ( x y -- z )
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{ $values { "x" float } { "y" float } { "z" float } }
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{ $description "Primitive version of " { $link * } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link * } " instead." } ;
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HELP: float/f ( x y -- z )
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{ $values { "x" float } { "y" float } { "z" float } }
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{ $description "Primitive version of " { $link /f } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link /f } " instead." } ;
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HELP: float< ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link < } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link < } " instead." } ;
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HELP: float<= ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link <= } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link <= } " instead." } ;
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HELP: float> ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link > } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link > } " instead." } ;
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HELP: float>= ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link u>= } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link u>= } " instead." } ;
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HELP: float-u< ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link u< } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link u< } " instead." } ;
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HELP: float-u<= ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link u<= } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link u<= } " instead." } ;
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HELP: float-u> ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link u> } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link u> } " instead." } ;
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HELP: float-u>= ( x y -- ? )
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{ $values { "x" float } { "y" float } { "?" "a boolean" } }
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{ $description "Primitive version of " { $link u>= } "." }
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{ $warning "This word does not perform type checking, and passing objects of the wrong type can crash the runtime. User code should call the generic word " { $link u>= } " instead." } ;
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ARTICLE: "math.floats.compare" "Floating point comparison operations"
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"In mathematics, real numbers are linearly ordered; for any two numbers " { $snippet "a" } " and " { $snippet "b" } ", exactly one of the following is true:"
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{ $code
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"a < b"
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"a = b"
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"a > b"
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}
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"With floating point values, there is a fourth possibility; " { $snippet "a" } " and " { $snippet "b" } " may be " { $emphasis "unordered" } ". This happens if one or both values are Not-a-Number values."
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$nl
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"All comparison operators, including " { $link number= } ", return " { $link f } " in the unordered case (and in particular, this means that a NaN is not equal to itself)."
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$nl
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"The " { $emphasis "ordered" } " comparison operators set floating point exception flags if the result of the comparison is unordered. The standard comparison operators (" { $link < } ", " { $link <= } ", " { $link > } ", " { $link >= } ") perform ordered comparisons."
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$nl
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"The " { $link number= } " operation performs an unordered comparison. The following set of operators also perform unordered comparisons:"
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{ $subsections
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u<
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u<=
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u>
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u>=
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}
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"A word to check if two values are unordered with respect to each other:"
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{ $subsections unordered? }
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"To test for floating point exceptions, use the " { $vocab-link "math.floats.env" } " vocabulary."
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$nl
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"If neither input to a comparison operator is a floating point value, then " { $link u< } ", " { $link u<= } ", " { $link u> } " and " { $link u>= } " are equivalent to the ordered operators." ;
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ARTICLE: "math.floats.bitwise" "Bitwise operations on floats"
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"Floating point numbers are represented internally in IEEE 754 double-precision format. This internal representation can be accessed for advanced operations and input/output purposes."
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{ $subsections
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float>bits
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double>bits
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bits>float
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bits>double
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}
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"Constructing floating point NaNs:"
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{ $subsections <fp-nan> }
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"Floating point numbers are discrete:"
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{ $subsections
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prev-float
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next-float
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}
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"Introspection on floating point numbers:"
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{ $subsections
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fp-special?
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fp-nan?
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fp-qnan?
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fp-snan?
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fp-infinity?
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fp-nan-payload
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}
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"Comparing two floating point numbers for bitwise equality:"
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{ $subsections fp-bitwise= }
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{ $see-also POSTPONE: NAN: } ;
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ARTICLE: "floats" "Floats"
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{ $subsections float }
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"Rational numbers represent " { $emphasis "exact" } " quantities. On the other hand, a floating point number is an " { $emphasis "approximate" } " value. While rationals can grow to any required precision, floating point numbers have limited precision, and manipulating them is usually faster than manipulating ratios or bignums."
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$nl
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"Introducing a floating point number in a computation forces the result to be expressed in floating point."
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{ $example "5/4 1/2 + ." "1+3/4" }
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{ $example "5/4 0.5 + ." "1.75" }
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"Floating point literal syntax is documented in " { $link "syntax-floats" } "."
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$nl
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"Integers and rationals can be converted to floats:"
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{ $subsections >float }
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"Two real numbers can be divided yielding a float result:"
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{ $subsections
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/f
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"math.floats.bitwise"
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"math.floats.compare"
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}
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"The " { $vocab-link "math.floats.env" } " vocabulary provides functionality for controlling floating point exceptions, rounding modes, and denormal behavior." ;
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ABOUT: "floats"
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