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% vim: ft=mercury ts=4 sw=4 et
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% Copyright (C) 1995-2007, 2011-2012 The University of Melbourne.
% Copyright (C) 2014, 2016-2023 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
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%
% 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.
%--------------------------------------------------%
%
% Mathematical constants
%
% Pythagoras' number.
%
:- func pi = float.
% Base of natural logarithms.
%
:- func e = float.
%--------------------------------------------------%
%
% "Next integer" operations
%
% ceiling(X) = Ceil is true if Ceil is the smallest integer
% not less than X.
% If X is of infinite magnitude then Ceil = X.
%
:- func ceiling(float) = float.
% floor(X) = Floor is true if Floor is the largest integer
% not greater than X.
% If X is of infinite magnitude then Floor = X.
%
:- func floor(float) = float.
% 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.
% If X is of infinite magnitude then Round = X.
%
:- func round(float) = float.
% truncate(X) = Trunc is true if Trunc is the integer closest to X
% such that |Trunc| =< |X|.
% If X is of infinite magnitude then Trunc = X.
%
:- func truncate(float) = float.
%--------------------------------------------------%
%
% Polynomial roots
%
% sqrt(X) = Sqrt is true if Sqrt is the positive square root of X.
%
% Domain restriction: X >= 0
%
:- func sqrt(float) = float.
:- func unchecked_sqrt(float) = float.
:- type quadratic_roots
---> no_roots
; one_root(float)
; two_roots(float, float).
% 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 solve_quadratic(float, float, float) = quadratic_roots.
%--------------------------------------------------%
%
% Power/logarithm operations
%
% 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 pow(float, float) = float.
:- func unchecked_pow(float, float) = float.
% exp(X) = Exp is true if Exp is e raised to the power of X.
%
:- func exp(float) = float.
% ln(X) = Log is true if Log is the natural logarithm of X.
%
% Domain restriction: X > 0
%
:- func ln(float) = float.
:- func unchecked_ln(float) = float.
% log10(X) = Log is true if Log is the logarithm to base 10 of X.
%
% Domain restriction: X > 0
%
:- func log10(float) = float.
:- func unchecked_log10(float) = float.
% log2(X) = Log is true if Log is the logarithm to base 2 of X.
%
% Domain restriction: X > 0
%
:- func log2(float) = float.
:- func unchecked_log2(float) = float.
% 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 log(float, float) = float.
:- func unchecked_log(float, float) = float.
%--------------------------------------------------%
%
% Trigonometric operations
%
% sin(X) = Sin is true if Sin is the sine of X.
%
:- func sin(float) = float.
% cos(X) = Cos is true if Cos is the cosine of X.
%
:- func cos(float) = float.
% tan(X) = Tan is true if Tan is the tangent of X.
%
:- func tan(float) = float.
% 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 asin(float) = float.
:- func unchecked_asin(float) = float.
% 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 acos(float) = float.
:- func unchecked_acos(float) = float.
% atan(X) = ATan is true if ATan is the inverse tangent of X,
% where ATan is in the range [-pi/2,pi/2].
%
:- func atan(float) = float.
% atan2(Y, X) = ATan is true if ATan is the inverse tangent of Y/X,
% where ATan is in the range [-pi,pi].
%
:- func atan2(float, float) = float.
%--------------------------------------------------%
%
% Hyperbolic functions
%
% sinh(X) = Sinh is true if Sinh is the hyperbolic sine of X.
%
:- func sinh(float) = float.
% cosh(X) = Cosh is true if Cosh is the hyperbolic cosine of X.
%
:- func cosh(float) = float.
% tanh(X) = Tanh is true if Tanh is the hyperbolic tangent of X.
%
:- func tanh(float) = float.
%--------------------------------------------------%
%
% Fused multiply-add operation.
%
% Succeeds if this grade and platform provide the fused multiply-add
% operation.
%
:- pred have_fma is semidet.
% fma(X, Y, Z) = FMA is true if FMA = (X * Y) + Z, rounded as one
% floating-point operation.
%
% This function is (currently) only available on the C backends and only if
% the target math library supports it.
% Use have_fma/0 to check whether it is supported.
%
:- func fma(float, float, float) = float.
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