249 lines
11 KiB
Plaintext
249 lines
11 KiB
Plaintext
USING: help kernel math ;
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HELP: number=
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{ $values { "x" "a number" } { "y" "a number" } { "?" "a boolean" } }
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{ $description "Tests if two numbers have the same numerical value." }
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{ $notes "Do not call this word directly. Calling " { $link = } " has the same effect and is more concise." } ;
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HELP: <
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{ $values { "x" "a real number" } { "y" "a real number" } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " is less than " { $snippet "y" } "." } ;
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HELP: <=
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{ $values { "x" "a real number" } { "y" "a real number" } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " is less than or equal to " { $snippet "y" } "." } ;
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HELP: >
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{ $values { "x" "a real number" } { "y" "a real number" } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " is greater than " { $snippet "y" } "." } ;
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HELP: >=
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{ $values { "x" "a real number" } { "y" "a real number" } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " is greater than or equal to " { $snippet "y" } "." } ;
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HELP: +
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{ $values { "x" "a number" } { "y" "a number" } { "z" "a number" } }
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{ $description
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"Adds two numbers."
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{ $list
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"Addition of fixnums may overflow and convert the result to a bignum."
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"Addition of bignums always yields a bignum."
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"Addition of floats always yields a float."
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"Addition of ratios and complex numbers proceeds using the relevant mathematical rules."
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}
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} ;
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HELP: -
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{ $values { "x" "a number" } { "y" "a number" } { "z" "a number" } }
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{ $description
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"Subtracts " { $snippet "y" } " from " { $snippet "x" } "."
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{ $list
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"Subtraction of fixnums may overflow and convert the result to a bignum."
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"Subtraction of bignums always yields a bignum."
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"Subtraction of floats always yields a float."
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"Subtraction of ratios and complex numbers proceeds using the relevant mathematical rules."
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}
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} ;
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HELP: *
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{ $values { "x" "a number" } { "y" "a number" } { "z" "a number" } }
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{ $description
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"Multiplies two numbers."
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{ $list
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"Multiplication of fixnums may overflow and convert the result to a bignum."
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"Multiplication of bignums always yields a bignum."
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"Multiplication of floats always yields a float."
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"Multiplication of ratios and complex numbers proceeds using the relevant mathematical rules."
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}
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} ;
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HELP: /
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{ $values { "x" "a number" } { "y" "a number" } { "z" "a number" } }
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{ $description
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"Divides " { $snippet "x" } " by " { $snippet "y" } ", retaining as much precision as possible."
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{ $list
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"Division of fixnums may yield a ratio, or overflow and yield a bignum."
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"Division of bignums may yield a ratio."
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"Division of floats always yields a float."
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"Division of ratios and complex numbers proceeds using the relevant mathematical rules."
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}
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}
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{ $see-also "division-by-zero" } ;
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HELP: /i
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a real number" } }
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{ $description
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"Divides " { $snippet "x" } " by " { $snippet "y" } ", truncating the result to an integer."
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{ $list
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"Integer division of fixnums may overflow and yield a bignum."
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"Integer division of bignums always yields a bignum."
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"Integer division of floats always yields a float."
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"Integer division of ratios and complex numbers proceeds using the relevant mathematical rules."
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}
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}
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{ $see-also "division-by-zero" } ;
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HELP: /f
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a real number" } }
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{ $description
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"Divides " { $snippet "x" } " by " { $snippet "y" } ", representing the result as a floating point number."
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{ $list
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"Integer division of fixnums may overflow and yield a bignum."
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"Integer division of bignums always yields a bignum."
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"Integer division of floats always yields a float."
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"Integer division of ratios and complex numbers proceeds using the relevant mathematical rules."
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}
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}
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{ $see-also "division-by-zero" } ;
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HELP: mod
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{ $values { "x" "an integer" } { "y" "an integer" } { "z" "an integer" } }
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{ $description
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"Computes the remainder of dividing " { $snippet "x" } " by " { $snippet "y" } ", with the remainder being negative if " { $snippet "x" } " is negative."
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{ $list
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"Modulus of fixnums always yields a fixnum."
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"Modulus of bignums always yields a bignum."
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}
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}
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{ $see-also "division-by-zero" rem } ;
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HELP: /mod
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{ $values { "x" "an integer" } { "y" "an integer" } { "z" "an integer" } { "w" "an integer" } }
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{ $description
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"Computes the quotient " { $snippet "z" } " and remainder " { $snippet "w" } " of dividing " { $snippet "x" } " by " { $snippet "y" } ", with the remainder being negative if " { $snippet "x" } " is negative."
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{ $list
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"The quotient of two fixnums may overflow and yield a bignum; the remainder is always a fixnum"
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"The quotient and remainder of two bignums is always a bignum."
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}
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}
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{ $see-also "division-by-zero" } ;
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HELP: bitand
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{ $values { "x" "an integer" } { "y" "an integer" } { "z" "an integer" } }
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{ $description "Outputs a new integer where each bit is set if and only if the corresponding bit is set in both inputs." }
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{ $examples
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{ $example "BIN: 101 BIN: 10 bitand .b" "0" }
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{ $example "BIN: 110 BIN: 10 bitand .b" "10" }
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} ;
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HELP: bitor
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{ $values { "x" "an integer" } { "y" "an integer" } { "z" "an integer" } }
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{ $description "Outputs a new integer where each bit is set if and only if the corresponding bit is set in at least one of the inputs." }
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{ $examples
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{ $example "BIN: 101 BIN: 10 bitor .b" "111" }
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{ $example "BIN: 110 BIN: 10 bitor .b" "110" }
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} ;
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HELP: bitxor
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{ $values { "x" "an integer" } { "y" "an integer" } { "z" "an integer" } }
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{ $description "Outputs a new integer where each bit is set if and only if the corresponding bit is set in exactly one of the inputs." }
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{ $examples
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{ $example "BIN: 101 BIN: 10 bitxor .b" "111" }
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{ $example "BIN: 110 BIN: 10 bitxor .b" "100" }
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} ;
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HELP: shift
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{ $values { "x" "an integer" } { "n" "an integer" } { "y" "an integer" } }
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{ $description "Shifts " { $snippet "x" } " to the left by " { $snippet "y" } " bits if " { $snippet "y" } " is positive, or " { $snippet "-y" } " bits to the right if " { $snippet "y" } " is negative. A left shift of a fixnum may overflow, yielding a bignum. A right shift may result in bits ``falling off'' the right hand side and being discarded." }
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{ $examples { $example "BIN: 101 5 shift .b" "10100000" } { $example "BIN: 11111 -2 shift .b" "111" } } ;
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HELP: bitnot
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{ $values { "x" "an integer" } { "y" "an integer" } }
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{ $description "Computes the bitwise complement of the input; that is, each bit in the input number is flipped." }
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{ $notes "Due to the two's complement representation of signed integers, the following two lines are equivalent:" { $code "bitnot" "neg 1-" } } ;
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HELP: 1+
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{ $values { "x" "a number" } { "y" "a number" } }
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{ $description
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"Increments a number by 1. The following two lines are equivalent, but the first is more efficient:"
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{ $code "1+" "1 +" }
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} ;
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HELP: 1-
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{ $values { "x" "a number" } { "y" "a number" } }
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{ $description
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"Decrements a number by 1. The following two lines are equivalent, but the first is more efficient:"
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{ $code "1-" "1 -" }
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} ;
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HELP: truncate
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{ $values { "x" "a real number" } { "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" "a real number" } { "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" "a real number" } { "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: abs
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{ $values { "x" "a complex 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" "a complex 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: sq
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{ $values { "x" "a number" } { "y" "a number" } }
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{ $description "Multiplies a number by itself." } ;
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HELP: neg
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{ $values { "x" "a number" } { "-x" "a number" } }
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{ $description "Computes a number's additive inverse." } ;
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HELP: recip
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{ $values { "x" "a number" } { "y" "a number" } }
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{ $description "Computes a number's multiplicative inverse." }
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{ $errors "Throws an error if " { $snippet "x" } " is the integer 0." } ;
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HELP: max
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a real number" } }
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{ $description "Outputs the greatest of two real numbers." } ;
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HELP: min
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a real number" } }
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{ $description "Outputs the smallest of two real numbers." } ;
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HELP: between?
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{ $values { "x" "a real number" } { "y" "a real number" } { "z" "a real number" } { "?" "a boolean" } }
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{ $description "Tests if " { $snippet "x" } " is in the interval " { $snippet "[y,z]" } "." }
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{ $notes "As per the closed interval notation, the end-points are included in the interval." } ;
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HELP: rem
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{ $values { "x" "an integer" } { "y" "an integer" } { "z" "an integer" } }
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{ $description
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"Computes the remainder of dividing " { $snippet "x" } " by " { $snippet "y" } ", with the remainder always positive."
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{ $list
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"Modulus of fixnums always yields a fixnum."
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"Modulus of bignums always yields a bignum."
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}
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}
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{ $see-also "division-by-zero" mod } ;
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HELP: sgn
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{ $values { "x" "a real number" } { "n" "-1, 0 or 1" } }
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{ $description
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"Outputs one of the following:"
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{ $list
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"-1 if " { $snippet "x" } " is negative"
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"0 if " { $snippet "x" } " is equal to 0"
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"1 if " { $snippet "x" } " is positive"
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}
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} ;
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HELP: align
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{ $values { "m" "an 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: number>string
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{ $values { "n" "a real number" } { "str" "a string" } }
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{ $description "Converts a real number to a string." }
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{ $notes "Printing complex numbers requires the more general prettyprinter facility (see " { $link "prettyprint" } ")." } ;
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