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mpfi

Description

The mpfi egg contains bindings for the mpfi library for interval arithmetic (a short introduction to interval arithmetic can be found at the mpfi site).

Author

Jeronimo Pellegrini

Requirements

Example

Examples:

(use mpfi)

(let ((a (make-ia-interval-f64 1 10))
      (b (make-ia-interval-f64 -0.5 1)))
  (when (ia-has-zero? b)
      (display "b contains zero!")
      (newline))
  (display "a = ")
  (display (ia->string a))
  (newline)
  (display "b = ")
  (display (ia->string b))
  (newline)
  (display "a x b = ")
  (display (ia->string (ia* a b)))
  (newline))

==>

b contains zero!
a = [1.0__10.0]
b = [-0.5__1.0]
a x b = [-5.0__10.0]

Documentation

[procedure] (make-ia-interval-empty)
[procedure] (make-ia-interval-f64 LO HI)

The following procedures are available:

Arithmetic:

(ia+ A B)
(ia+f64 A F)
(ia- A B)
(ia-f64 A F)
(f64-ia F A)
(ia* A B)
(ia*f64 A F)
(ia/ A B)
(ia/f64 A F)
(f64/ia F A)

Unary functions:

(ia-neg A)
(ia-sqr A)
(ia-inv A)
(ia-sqrt A)
(ia-abs A)
(ia-log A)
(ia-exp A)
(ia-exp2 A)
(ia-log1p A)
(ia-expm1 A)
(ia-log2 A)
(ia-log10 A)

Trigonometric functions:

(ia-cos A)
(ia-sin A)
(ia-tan A)
(ia-acos A)
(ia-asin A)
(ia-atan A)
(ia-cosh A)
(ia-sinh A)
(ia-tanh A)
(ia-acosh A)
(ia-asinh A)
(ia-atanh A) 

Constants:

(ia-const-log2)
(ia-const-pi)
(ia-const-e)

Comparisons:

(ia< A B)
(ia> A B)
(ia>= A B)
(ia<= A B)
(ia-overlap? A B)
(ia-nan? A)
(ia-inf? A)
(ia-zero? A)
(ia-has-zero? A)
(ia-positive? A)
(ia-negative? A)
(ia-strictly-positive? A)
(ia-strictly-negative? A)
(ia-nonpositive? A)
(ia-nonnegative? A)
(ia-bounded? A)
(ia-empty? A)
(ia-inside?  A B)
(ia-f64-inside? A B)
[procedure] (ia-lo A)
[procedure] (ia-hi A)

Return the low and high endpoints of the interval.

[procedure] (ia->string)

Converts interval into a string.

Each nondestructive procedure described above (like ia/ for example) has a destructive counterpart in which there is one extra argument where the result goes:

(ia/ a b)
(ia/! result a b)

The destructive operation does not allocate memory; the nondestructive one does.

Changelog

License

 Copyright (c) 2010, Jeronimo C. Pellegrini
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following
 conditions are met:
 
   Redistributions of source code must retain the above copyright notice, this list of conditions and the following
     disclaimer. 
   Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following
     disclaimer in the documentation and/or other materials provided with the distribution. 
   Neither the name of the author nor the names of its contributors may be used to endorse or promote
     products derived from this software without specific prior written permission. 
 
 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS
 OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
 AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR
 CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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