313 lines
9.5 KiB
Factor
313 lines
9.5 KiB
Factor
USING: help.markup help.syntax kernel math math.order
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sequences quotations math.functions.private ;
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IN: math.functions
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ARTICLE: "integer-functions" "Integer functions"
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{ $subsection align }
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{ $subsection gcd }
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{ $subsection log2 }
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{ $subsection next-power-of-2 }
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"Modular exponentiation:"
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{ $subsection ^mod }
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{ $subsection mod-inv }
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"Tests:"
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{ $subsection power-of-2? }
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{ $subsection even? }
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{ $subsection odd? }
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{ $subsection divisor? } ;
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ARTICLE: "arithmetic-functions" "Arithmetic functions"
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"Computing additive and multiplicative inverses:"
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{ $subsection neg }
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{ $subsection recip }
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"Incrementing, decrementing:"
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{ $subsection 1+ }
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{ $subsection 1- }
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"Minimum, maximum, clamping:"
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{ $subsection min }
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{ $subsection max }
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{ $subsection clamp }
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"Complex conjugation:"
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{ $subsection conjugate }
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"Tests:"
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{ $subsection zero? }
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{ $subsection between? }
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"Sign:"
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{ $subsection sgn }
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"Rounding:"
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{ $subsection ceiling }
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{ $subsection floor }
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{ $subsection truncate }
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{ $subsection round }
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"Inexact comparison:"
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{ $subsection ~ } ;
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ARTICLE: "power-functions" "Powers and logarithms"
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"Squares:"
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{ $subsection sq }
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{ $subsection sqrt }
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"Exponential and natural logarithm:"
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{ $subsection exp }
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{ $subsection cis }
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{ $subsection log }
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"Raising a number to a power:"
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{ $subsection ^ }
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"Converting between rectangular and polar form:"
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{ $subsection abs }
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{ $subsection absq }
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{ $subsection arg }
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{ $subsection >polar }
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{ $subsection polar> } ;
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ARTICLE: "trig-hyp-functions" "Trigonometric and hyperbolic functions"
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"Trigonometric functions:"
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{ $subsection cos }
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{ $subsection sin }
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{ $subsection tan }
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"Reciprocals:"
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{ $subsection sec }
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{ $subsection cosec }
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{ $subsection cot }
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"Inverses:"
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{ $subsection acos }
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{ $subsection asin }
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{ $subsection atan }
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"Inverse reciprocals:"
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{ $subsection asec }
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{ $subsection acosec }
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{ $subsection acot }
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"Hyperbolic functions:"
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{ $subsection cosh }
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{ $subsection sinh }
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{ $subsection tanh }
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"Reciprocals:"
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{ $subsection sech }
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{ $subsection cosech }
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{ $subsection coth }
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"Inverses:"
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{ $subsection acosh }
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{ $subsection asinh }
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{ $subsection atanh }
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"Inverse reciprocals:"
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{ $subsection asech }
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{ $subsection acosech }
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{ $subsection acoth } ;
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ARTICLE: "math-functions" "Mathematical functions"
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{ $subsection "integer-functions" }
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{ $subsection "arithmetic-functions" }
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{ $subsection "power-functions" }
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{ $subsection "trig-hyp-functions" } ;
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ABOUT: "math-functions"
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HELP: rect>
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{ $values { "x" real } { "y" real } { "z" number } }
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{ $description "Creates a complex number from real and imaginary components. If " { $snippet "z" } " is an integer zero, this will simply output " { $snippet "x" } "." } ;
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HELP: >rect
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{ $values { "z" number } { "x" real } { "y" real } }
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{ $description "Extracts the real and imaginary components of a complex number." } ;
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HELP: align
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{ $values { "m" integer } { "w" "a power of 2" } { "n" "an integer multiple of " { $snippet "w" } } }
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{ $description "Outputs the least multiple of " { $snippet "w" } " greater than " { $snippet "m" } "." }
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{ $notes "This word will give an incorrect result if " { $snippet "w" } " is not a power of 2." } ;
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HELP: exp
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{ $values { "x" number } { "y" number } }
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{ $description "Exponential function, " { $snippet "y=e^x" } "." } ;
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HELP: log
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{ $values { "x" number } { "y" number } }
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{ $description "Natural logarithm function. Outputs negative infinity if " { $snippet "x" } " is 0." } ;
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HELP: sqrt
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{ $values { "x" number } { "y" number } }
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{ $description "Square root function." } ;
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HELP: cosh
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$values-x/y
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{ $description "Hyperbolic cosine." } ;
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HELP: sech
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$values-x/y
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{ $description "Hyperbolic secant." } ;
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HELP: sinh
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$values-x/y
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{ $description "Hyperbolic sine." } ;
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HELP: cosech
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$values-x/y
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{ $description "Hyperbolic cosecant." } ;
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HELP: tanh
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$values-x/y
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{ $description "Hyperbolic tangent." } ;
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HELP: coth
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$values-x/y
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{ $description "Hyperbolic cotangent." } ;
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HELP: cos
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$values-x/y
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{ $description "Trigonometric cosine." } ;
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HELP: sec
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$values-x/y
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{ $description "Trigonometric secant." } ;
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HELP: sin
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$values-x/y
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{ $description "Trigonometric sine." } ;
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HELP: cosec
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$values-x/y
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{ $description "Trigonometric cosecant." } ;
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HELP: tan
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$values-x/y
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{ $description "Trigonometric tangent." } ;
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HELP: cot
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$values-x/y
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{ $description "Trigonometric cotangent." } ;
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HELP: acosh
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$values-x/y
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{ $description "Inverse hyperbolic cosine." } ;
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HELP: asech
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$values-x/y
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{ $description "Inverse hyperbolic secant." } ;
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HELP: asinh
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$values-x/y
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{ $description "Inverse hyperbolic sine." } ;
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HELP: acosech
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$values-x/y
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{ $description "Inverse hyperbolic cosecant." } ;
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HELP: atanh
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$values-x/y
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{ $description "Inverse hyperbolic tangent." } ;
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HELP: acoth
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$values-x/y
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{ $description "Inverse hyperbolic cotangent." } ;
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HELP: acos
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$values-x/y
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{ $description "Inverse trigonometric cosine." } ;
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HELP: asec
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$values-x/y
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{ $description "Inverse trigonometric secant." } ;
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HELP: asin
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$values-x/y
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{ $description "Inverse trigonometric sine." } ;
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HELP: acosec
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$values-x/y
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{ $description "Inverse trigonometric cosecant." } ;
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HELP: atan
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$values-x/y
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{ $description "Inverse trigonometric tangent." } ;
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HELP: acot
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$values-x/y
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{ $description "Inverse trigonometric cotangent." } ;
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HELP: conjugate
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{ $values { "z" number } { "z*" number } }
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{ $description "Computes the complex conjugate by flipping the sign of the imaginary part of " { $snippet "z" } "." } ;
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HELP: arg
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{ $values { "z" number } { "arg" "a number in the interval " { $snippet "(-pi,pi]" } } }
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{ $description "Computes the complex argument." } ;
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HELP: >polar
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{ $values { "z" number } { "abs" "a non-negative real number" } { "arg" "a number in the interval " { $snippet "(-pi,pi]" } } }
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{ $description "Converts a complex number into an absolute value and argument (polar form)." } ;
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HELP: cis
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{ $values { "arg" "a real number" } { "z" "a complex number on the unit circle" } }
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{ $description "Computes a point on the unit circle using Euler's formula for " { $snippet "exp(arg*i)" } "." } ;
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{ cis exp } related-words
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HELP: polar>
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{ $values { "z" number } { "abs" "a non-negative real number" } { "arg" real } }
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{ $description "Converts an absolute value and argument (polar form) to a complex number." } ;
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HELP: [-1,1]?
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{ $values { "x" number } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " is a real number between -1 and 1, inclusive." } ;
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HELP: abs
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{ $values { "x" number } { "y" "a non-negative real number" } }
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{ $description "Computes the absolute value of a complex number." } ;
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HELP: absq
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{ $values { "x" number } { "y" "a non-negative real number" } }
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{ $description "Computes the squared absolute value of a complex number. This is marginally more efficient than " { $link abs } "." } ;
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HELP: ^
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{ $values { "x" number } { "y" number } { "z" number } }
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{ $description "Raises " { $snippet "x" } " to the power of " { $snippet "y" } ". If " { $snippet "y" } " is an integer the answer is computed exactly, otherwise a floating point approximation is used." }
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{ $errors "Throws an error if " { $snippet "x" } " and " { $snippet "y" } " are both integer 0." } ;
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HELP: gcd
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{ $values { "x" integer } { "y" integer } { "a" integer } { "d" integer } }
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{ $description "Computes the positive greatest common divisor " { $snippet "d" } " of " { $snippet "x" } " and " { $snippet "y" } ", and another value " { $snippet "a" } " satisfying:" { $code "a*y = d mod x" } }
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{ $notes "If " { $snippet "d" } " is 1, then " { $snippet "a" } " is the inverse of " { $snippet "y" } " modulo " { $snippet "x" } "." } ;
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HELP: divisor?
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{ $values { "m" integer } { "n" integer } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "n" } " is a divisor of " { $snippet "m" } ". This is the same thing as asking if " { $snippet "m" } " is divisible by " { $snippet "n" } "." }
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{ $notes "Returns t for both negative and positive divisors, as well as for trivial and non-trivial divisors." } ;
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HELP: mod-inv
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{ $values { "x" integer } { "n" integer } { "y" integer } }
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{ $description "Outputs an integer " { $snippet "y" } " such that " { $snippet "xy = 1 (mod n)" } "." }
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{ $errors "Throws an error if " { $snippet "n" } " is not invertible modulo " { $snippet "n" } "." }
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{ $examples
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{ $example "USING: math.functions prettyprint ;" "173 1119 mod-inv ." "815" }
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{ $example "USING: math prettyprint ;" "173 815 * 1119 mod ." "1" }
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} ;
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HELP: ~
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{ $values { "x" real } { "y" real } { "epsilon" real } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " and " { $snippet "y" } " are approximately equal to each other. There are three possible comparison tests, chosen based on the sign of " { $snippet "epsilon" } ":"
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{ $list
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{ { $snippet "epsilon" } " is zero: exact comparison." }
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{ { $snippet "epsilon" } " is positive: absolute distance test." }
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{ { $snippet "epsilon" } " is negative: relative distance test." }
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}
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} ;
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HELP: truncate
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{ $values { "x" real } { "y" "a whole real number" } }
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{ $description "Outputs the number that results from subtracting the fractional component of " { $snippet "x" } "." }
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{ $notes "The result is not necessarily an integer." } ;
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HELP: floor
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{ $values { "x" real } { "y" "a whole real number" } }
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{ $description "Outputs the greatest whole number smaller than or equal to " { $snippet "x" } "." }
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{ $notes "The result is not necessarily an integer." } ;
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HELP: ceiling
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{ $values { "x" real } { "y" "a whole real number" } }
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{ $description "Outputs the least whole number greater than or equal to " { $snippet "x" } "." }
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{ $notes "The result is not necessarily an integer." } ;
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HELP: round
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{ $values { "x" real } { "y" "a whole real number" } }
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{ $description "Outputs the whole number closest to " { $snippet "x" } "." }
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{ $notes "The result is not necessarily an integer." } ;
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