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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).

Requirements

You need the 'development' libraries below in order to install the mpfi egg.

the mpfi library (mpfi-dev)
the mpfr library, needed by mpfi (mpfr-dev)

Example

(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]

In the description below, A and B are mpfi intervals; F is a floating-point number (double in FFI); U is an unsigned integer number (unsigned-long in FFI); S is a signed integer number (long in FFI).

[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+u64 A U)
(ia+s64 A S) 
(ia- A B)
(ia-f64 A F)
(f64-ia F A)
(ia-u64 A U)
(u64-ia U A)
(ia-s64 A S)
(s64-ia S A)
(ia* A B)
(ia*f64 A F)
(ia*u64 A U)
(ia*s64 A S)
(ia/ A B)
(ia/f64 A F)
(f64/ia F A)
(ia/u64 A U)
(u64/ia U A)
(ia/s64 A S)
(s64/ia S A)

The procedures ending with +, -, * and / operate on two intervals and give an interval as result. The procedures that have f64 in their name take one flonum argument.

Unary functions:

(ia-neg A)
(ia-sqr A)  ;; square, (* x x)
(ia-inv A)  ;; inverse, (/ 1 x)
(ia-sqrt A) ;; square root
(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)

These procedures calculate e, pi and the logarithm of two and give back intervals representing them.

Comparisons:

(ia< A B)
(ia> A B)

Given two intervals A and B, A is considered greater than B is and only if all elements of A are greater than all elements of B.

(ia-overlap? A B)

Returns true if A overlap with or contains 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)

Procedures returning flonum:

(ia-diameter A)
(ia-diameter-absolute A)
(ia-diameter-relative A)
(ia-magnitude A)
(ia-mignitude A)
(ia-random A)
(ia-middle A)

Other procedures:

[procedure] (ia-lo A)
[procedure] (ia-hi A)

Return the low and high endpoints of the interval.

[procedure] (ia->string)

Converts an 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.

Bugs and limitations

the mpfi egg is still not tested enough
There is only support for floating point intervals. Although there are procedures to set interval endpoints to flonums, fixnums, exact integers, and so on, this egg will only return the endpoints as flonums. The mpfi library itself won't return an integer.

Changelog

0.2 Added functions to add, multiply, subtract and divide intervals and constants. Also fixed some bugs.
0.1 Initial Release

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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