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! $Id$
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! Copyright (C) 2004 Slava Pestov.
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IN: math
USE: arithmetic
USE: combinators
USE: kernel
USE: logic
USE: real-math
USE: stack

: fib ( n -- nth fibonacci number )
    ! This is the naive implementation, for benchmarking purposes.
    dup 1 <= [
        drop 1
    ] [
        pred dup fib swap pred fib +
    ] ifte ;

: fac ( n -- n! )
    ! This is the naive implementation, for benchmarking purposes.
    1 swap [ succ * ] times* ;

: 2^ ( x -- 2^x )
    1 swap [ 2 * ] times ;

: harmonic ( n -- 1 + 1/2 + 1/3 + ... + 1/n )
    0 swap [ succ recip + ] times* ;

: mag2 ( x y -- mag )
    #! Returns the magnitude of the vector (x,y).
    swap sq swap sq + fsqrt ;

: abs ( z -- abs )
    #! Compute the complex absolute value.
    >rect mag2 ; inline

: conjugate ( z -- z* )
    >rect neg rect> ;

: arg ( z -- arg )
    #! Compute the complex argument.
    >rect swap fatan2 ; inline

: >polar ( z -- abs arg )
    >rect 2dup mag2 transp fatan2 ;

: cis ( theta -- cis )
    dup fcos swap fsin rect> ;

: polar> ( abs arg -- z )
    cis * ; inline