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41 math

%--------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et wm=0 tw=0
%--------------------------------------------------%
% Copyright (C) 1995-2007, 2011-2012 The University of Melbourne.
% This file may only be copied under the terms of the GNU Library General
% Public License - see the file COPYING.LIB in the Mercury distribution.
%--------------------------------------------------%
%
% File: math.m.
% Main author: bromage.
% Stability: high.
%
% Higher mathematical operations.  (The basics are in float.m.)
%
% By default, domain errors are currently handled by throwing an exception.
% For better performance, each operation in this module that can throw a domain
% exception also has an unchecked version that omits the domain check.
%
% The unchecked operations are semantically safe, since the target math
% library and/or floating point hardware perform these checks for you.
% The benefit of having the Mercury library perform the checks instead is
% that Mercury will tell you in which function or predicate the error
% occurred, as well as giving you a stack trace if that is enabled; with
% the unchecked operations  you only have the information that the
% floating-point exception signal handler gives you.
%
%--------------------------------------------------%
%--------------------------------------------------%

:- module math.
:- interface.

    % A domain error exception, indicates that the inputs to a function
    % were outside the domain of the function.  The string indicates
    % where the error occurred.
    %
:- type domain_error ---> domain_error(string).

%--------------------------------------------------%
%
% Mathematical constants
%

    % Pythagoras' number.
    %
:- func math.pi = float.

    % Base of natural logarithms.
    %
:- func math.e = float.

%--------------------------------------------------%
%
% "Next integer" operations
%

    % math.ceiling(X) = Ceil is true if Ceil is the smallest integer
    % not less than X.
    %
:- func math.ceiling(float) = float.

    % math.floor(X) = Floor is true if Floor is the largest integer
    % not greater than X.
    %
:- func math.floor(float) = float.

    % math.round(X) = Round is true if Round is the integer closest to X.
    % If X has a fractional value of 0.5, it is rounded up.
    %
:- func math.round(float) = float.

    % math.truncate(X) = Trunc is true if Trunc is the integer closest to X
    % such that |Trunc| =< |X|.
    %
:- func math.truncate(float) = float.

%--------------------------------------------------%
%
% Polynomial roots
%

    % math.sqrt(X) = Sqrt is true if Sqrt is the positive square root of X.
    %
    % Domain restriction: X >= 0
    %
:- func math.sqrt(float) = float.
:- func math.unchecked_sqrt(float) = float.

:- type math.quadratic_roots
    --->    no_roots
    ;       one_root(float)
    ;       two_roots(float, float).

    % math.solve_quadratic(A, B, C) = Roots is true if Roots are
    % the solutions to the equation Ax^2 + Bx + C.
    %
    % Domain restriction: A \= 0
    %
:- func math.solve_quadratic(float, float, float) = quadratic_roots.

%--------------------------------------------------%
%
% Power/logarithm operations
%

    % math.pow(X, Y) = Res is true if Res is X raised to the power of Y.
    %
    % Domain restriction: X >= 0 and (X = 0 implies Y > 0)
    %
:- func math.pow(float, float) = float.
:- func math.unchecked_pow(float, float) = float.

    % math.exp(X) = Exp is true if Exp is e raised to the power of X.
    %
:- func math.exp(float) = float.

    % math.ln(X) = Log is true if Log is the natural logarithm of X.
    %
    % Domain restriction: X > 0
    %
:- func math.ln(float) = float.
:- func math.unchecked_ln(float) = float.

    % math.log10(X) = Log is true if Log is the logarithm to base 10 of X.
    %
    % Domain restriction: X > 0
    %
:- func math.log10(float) = float.
:- func math.unchecked_log10(float) = float.

    % math.log2(X) = Log is true if Log is the logarithm to base 2 of X.
    %
    % Domain restriction: X > 0
    %
:- func math.log2(float) = float.
:- func math.unchecked_log2(float) = float.

    % math.log(B, X) = Log is true if Log is the logarithm to base B of X.
    %
    % Domain restriction: X > 0 and B > 0 and B \= 1
    %
:- func math.log(float, float) = float.
:- func math.unchecked_log(float, float) = float.

%--------------------------------------------------%
%
% Trigonometric operations
%

    % math.sin(X) = Sin is true if Sin is the sine of X.
    %
:- func math.sin(float) = float.

    % math.cos(X) = Cos is true if Cos is the cosine of X.
    %
:- func math.cos(float) = float.

    % math.tan(X) = Tan is true if Tan is the tangent of X.
    %
:- func math.tan(float) = float.

    % math.asin(X) = ASin is true if ASin is the inverse sine of X,
    % where ASin is in the range [-pi/2,pi/2].
    %
    % Domain restriction: X must be in the range [-1,1]
    %
:- func math.asin(float) = float.
:- func math.unchecked_asin(float) = float.

    % math.acos(X) = ACos is true if ACos is the inverse cosine of X,
    % where ACos is in the range [0, pi].
    %
    % Domain restriction: X must be in the range [-1,1]
    %
:- func math.acos(float) = float.
:- func math.unchecked_acos(float) = float.

    % math.atan(X) = ATan is true if ATan is the inverse tangent of X,
    % where ATan is in the range [-pi/2,pi/2].
    %
:- func math.atan(float) = float.

    % math.atan2(Y, X) = ATan is true if ATan is the inverse tangent of Y/X,
    % where ATan is in the range [-pi,pi].
    %
:- func math.atan2(float, float) = float.

%--------------------------------------------------%
%
% Hyperbolic functions
%

    % math.sinh(X) = Sinh is true if Sinh is the hyperbolic sine of X.
    %
:- func math.sinh(float) = float.

    % math.cosh(X) = Cosh is true if Cosh is the hyperbolic cosine of X.
    %
:- func math.cosh(float) = float.

    % math.tanh(X) = Tanh is true if Tanh is the hyperbolic tangent of X.
    %
:- func math.tanh(float) = float.

%--------------------------------------------------%
%--------------------------------------------------%


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