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Estimated hours taken: 0.2 Branches: main library/bit_buffer.m: Fix incorrect result type on new_buffer_2. library/math.m: Fix Erlang implementation of math.round/1. library/profiling_builtin.m: library/table_builtin.m: Add Erlang stubs for :- external procedures for deep profiling and tabling.
1017 lines
27 KiB
Mathematica
1017 lines
27 KiB
Mathematica
%---------------------------------------------------------------------------%
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% vim: ft=mercury ts=4 sw=4 et wm=0 tw=0
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%---------------------------------------------------------------------------%
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% Copyright (C) 1995-2007 The University of Melbourne.
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% This file may only be copied under the terms of the GNU Library General
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% Public License - see the file COPYING.LIB in the Mercury distribution.
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%---------------------------------------------------------------------------%
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%
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% File: math.m.
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% Main author: bromage.
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% Stability: high.
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%
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% Higher mathematical operations. (The basics are in float.m.)
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%
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% By default, domain errors are currently handled by throwing an exception.
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%
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% For better performance, it is possible to disable the Mercury domain
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% checking by compiling with `--intermodule-optimization' and the C macro
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% symbol `ML_OMIT_MATH_DOMAIN_CHECKS' defined, e.g. by using
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% `MCFLAGS=--intermodule-optimization' and
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% `MGNUCFLAGS=-DML_OMIT_MATH_DOMAIN_CHECKS' in your Mmakefile,
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% or by compiling with the command
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% `mmc --intermodule-optimization --cflags -DML_OMIT_MATH_DOMAIN_CHECKS'.
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%
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% For maximum performance, all Mercury domain checking can be disabled by
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% recompiling this module using `MGNUCFLAGS=-DML_OMIT_MATH_DOMAIN_CHECKS'
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% or `mmc --cflags -DML_OMIT_MATH_DOMAIN_CHECKS' as above. You can
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% either recompile the entire library, or just copy `math.m' to your
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% application's source directory and link with it directly instead of as
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% part of the library.
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%
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% Note that the above performance improvements are semantically safe,
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% since the C math library and/or floating point hardware perform these
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% checks for you. The benefit of having the Mercury library perform the
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% checks instead is that Mercury will tell you in which function or
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% predicate the error occurred, as well as giving you a stack trace if
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% that is enabled; with the checks disabled you only have the information
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% that the floating-point exception signal handler gives you.
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%
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%---------------------------------------------------------------------------%
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%---------------------------------------------------------------------------%
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:- module math.
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:- interface.
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% A domain error exception, indicates that the inputs to a function
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% were outside the domain of the function. The string indicates
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% where the error occurred.
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%
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% It is possible to switch domain checking off, in which case,
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% depending on the backend, a domain error may cause a program
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% abort.
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%
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:- type domain_error ---> domain_error(string).
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%---------------------------------------------------------------------------%
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%
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% Mathematical constants
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%
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% Pythagoras' number.
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%
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:- func math.pi = float.
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% Base of natural logarithms.
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%
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:- func math.e = float.
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%---------------------------------------------------------------------------%
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%
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% "Next integer" operations
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%
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% math.ceiling(X) = Ceil is true if Ceil is the smallest integer
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% not less than X.
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%
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:- func math.ceiling(float) = float.
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% math.floor(X) = Floor is true if Floor is the largest integer
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% not greater than X.
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%
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:- func math.floor(float) = float.
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% math.round(X) = Round is true if Round is the integer closest to X.
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% If X has a fractional value of 0.5, it is rounded up.
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%
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:- func math.round(float) = float.
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% math.truncate(X) = Trunc is true if Trunc is the integer closest to X
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% such that |Trunc| =< |X|.
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%
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:- func math.truncate(float) = float.
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%---------------------------------------------------------------------------%
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%
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% Polynomial roots
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%
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% math.sqrt(X) = Sqrt is true if Sqrt is the positive square root of X.
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%
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% Domain restriction: X >= 0
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%
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:- func math.sqrt(float) = float.
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:- type math.quadratic_roots
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---> no_roots
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; one_root(float)
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; two_roots(float, float).
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% math.solve_quadratic(A, B, C) = Roots is true if Roots are
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% the solutions to the equation Ax^2 + Bx + C.
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%
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% Domain restriction: A \= 0
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%
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:- func math.solve_quadratic(float, float, float) = quadratic_roots.
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%---------------------------------------------------------------------------%
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%
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% Power/logarithm operations
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%
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% math.pow(X, Y) = Res is true if Res is X raised to the power of Y.
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%
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% Domain restriction: X >= 0 and (X = 0 implies Y > 0)
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%
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:- func math.pow(float, float) = float.
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% math.exp(X) = Exp is true if Exp is e raised to the power of X.
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%
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:- func math.exp(float) = float.
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% math.ln(X) = Log is true if Log is the natural logarithm of X.
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%
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% Domain restriction: X > 0
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%
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:- func math.ln(float) = float.
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% math.log10(X) = Log is true if Log is the logarithm to base 10 of X.
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%
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% Domain restriction: X > 0
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%
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:- func math.log10(float) = float.
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% math.log2(X) = Log is true if Log is the logarithm to base 2 of X.
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%
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% Domain restriction: X > 0
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%
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:- func math.log2(float) = float.
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% math.log(B, X) = Log is true if Log is the logarithm to base B of X.
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%
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% Domain restriction: X > 0 and B > 0 and B \= 1
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%
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:- func math.log(float, float) = float.
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%---------------------------------------------------------------------------%
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%
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% Trigonometric operations
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%
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% math.sin(X) = Sin is true if Sin is the sine of X.
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%
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:- func math.sin(float) = float.
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% math.cos(X) = Cos is true if Cos is the cosine of X.
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%
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:- func math.cos(float) = float.
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% math.tan(X) = Tan is true if Tan is the tangent of X.
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%
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:- func math.tan(float) = float.
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% math.asin(X) = ASin is true if ASin is the inverse sine of X,
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% where ASin is in the range [-pi/2,pi/2].
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%
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% Domain restriction: X must be in the range [-1,1]
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%
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:- func math.asin(float) = float.
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% math.acos(X) = ACos is true if ACos is the inverse cosine of X,
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% where ACos is in the range [0, pi].
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%
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% Domain restriction: X must be in the range [-1,1]
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%
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:- func math.acos(float) = float.
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% math.atan(X) = ATan is true if ATan is the inverse tangent of X,
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% where ATan is in the range [-pi/2,pi/2].
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%
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:- func math.atan(float) = float.
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% math.atan2(Y, X) = ATan is true if ATan is the inverse tangent of Y/X,
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% where ATan is in the range [-pi,pi].
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%
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:- func math.atan2(float, float) = float.
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%---------------------------------------------------------------------------%
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%
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% Hyperbolic functions
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%
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% math.sinh(X) = Sinh is true if Sinh is the hyperbolic sine of X.
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%
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:- func math.sinh(float) = float.
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% math.cosh(X) = Cosh is true if Cosh is the hyperbolic cosine of X.
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%
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:- func math.cosh(float) = float.
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% math.tanh(X) = Tanh is true if Tanh is the hyperbolic tangent of X.
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%
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:- func math.tanh(float) = float.
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%---------------------------------------------------------------------------%
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%---------------------------------------------------------------------------%
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:- implementation.
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:- import_module exception.
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:- import_module float.
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% These operations are mostly implemented using the C interface.
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:- pragma foreign_decl("C", "
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#include <math.h>
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/*
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** Mathematical constants.
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**
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** The maximum number of significant decimal digits which
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** can be packed into an IEEE-754 extended precision
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** floating point number is 18. Therefore 20 significant
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** decimal digits for these constants should be plenty.
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*/
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#define ML_FLOAT_E 2.7182818284590452354
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#define ML_FLOAT_PI 3.1415926535897932384
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#define ML_FLOAT_LN2 0.69314718055994530941
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"). % end pragma foreign_decl
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:- pragma foreign_code("C#", "
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// This is not defined in the .NET Frameworks.
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// For pi and e we use the constants defined in System.Math.
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public static double ML_FLOAT_LN2 = 0.69314718055994530941;
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").
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:- pragma foreign_code("Java", "
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// As for .NET, java does not have a built-in ln2
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private static final double ML_FLOAT_LN2 = 0.69314718055994530941;
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").
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:- pred math_domain_checks is semidet.
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:- pragma foreign_proc("C",
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math_domain_checks,
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[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
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does_not_affect_liveness],
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"
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#ifdef ML_OMIT_MATH_DOMAIN_CHECKS
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SUCCESS_INDICATOR = MR_FALSE;
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#else
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SUCCESS_INDICATOR = MR_TRUE;
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#endif
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").
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:- pragma foreign_proc("C#",
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math_domain_checks,
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[thread_safe, promise_pure],
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"
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#if ML_OMIT_MATH_DOMAIN_CHECKS
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SUCCESS_INDICATOR = false;
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#else
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SUCCESS_INDICATOR = true;
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#endif
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").
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:- pragma foreign_proc("Java",
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math_domain_checks,
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[thread_safe, promise_pure],
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"
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succeeded = true;
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").
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:- pragma foreign_proc("Erlang",
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math_domain_checks,
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[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
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does_not_affect_liveness],
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"
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SUCCESS_INDICATOR = true
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").
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%
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% Mathematical constants from math.m
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%
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% Pythagoras' number
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:- pragma foreign_proc("C",
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math.pi = (Pi::out),
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[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
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does_not_affect_liveness],
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"
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Pi = ML_FLOAT_PI;
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").
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:- pragma foreign_proc("C#",
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math.pi = (Pi::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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Pi = System.Math.PI;
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").
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:- pragma foreign_proc("Java",
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math.pi = (Pi::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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Pi = java.lang.Math.PI;
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").
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:- pragma foreign_proc("Erlang",
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math.pi = (Pi::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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Pi = math:pi()
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").
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% This version is only used for back-ends for which there is no
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% matching foreign_proc version. We define this with sufficient
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% digits that if the underlying implementation's
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% floating point parsing routines are good, it should
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% to be accurate enough for 128-bit IEEE float.
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math.pi = 3.1415926535897932384626433832795029.
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% Base of natural logarithms
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:- pragma foreign_proc("C",
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math.e = (E::out),
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[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
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does_not_affect_liveness],
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"
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E = ML_FLOAT_E;
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").
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:- pragma foreign_proc("C#",
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math.e = (E::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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E = System.Math.E;
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").
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:- pragma foreign_proc("Java",
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math.e = (E::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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E = java.lang.Math.E;
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").
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% This version is only used for back-ends for which there is no
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% matching foreign_proc version. We define this with sufficient
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% digits that if the underlying implementation's
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% floating point parsing routines are good, it should
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% to be accurate enough for 128-bit IEEE float.
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math.e = 2.7182818284590452353602874713526625.
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:- pragma foreign_proc("C",
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math.ceiling(Num::in) = (Ceil::out),
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[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
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does_not_affect_liveness],
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"
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Ceil = ceil(Num);
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").
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:- pragma foreign_proc("C#",
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math.ceiling(Num::in) = (Ceil::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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Ceil = System.Math.Ceiling(Num);
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").
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:- pragma foreign_proc("Java",
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math.ceiling(Num::in) = (Ceil::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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Ceil = java.lang.Math.ceil(Num);
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").
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:- pragma foreign_proc("Erlang",
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math.ceiling(Num::in) = (Ceil::out),
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[will_not_call_mercury, promise_pure, thread_safe],
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"
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T = erlang:trunc(Num),
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case (Num - T) > 0 of
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true ->
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Ceil = float(T + 1);
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false ->
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Ceil = float(T)
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end
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").
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:- pragma foreign_proc("C",
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math.floor(Num::in) = (Floor::out),
|
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[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
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does_not_affect_liveness],
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"
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Floor = floor(Num);
|
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").
|
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:- pragma foreign_proc("C#",
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math.floor(Num::in) = (Floor::out),
|
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[will_not_call_mercury, promise_pure, thread_safe],
|
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"
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Floor = System.Math.Floor(Num);
|
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").
|
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:- pragma foreign_proc("Java",
|
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math.floor(Num::in) = (Floor::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
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Floor = java.lang.Math.floor(Num);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
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math.floor(Num::in) = (Floor::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
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T = erlang:trunc(Num),
|
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case (Num - T) < 0 of
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true ->
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Floor = float(T - 1);
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false ->
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Floor = float(T)
|
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end
|
|
").
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.round(Num::in) = (Rounded::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Rounded = floor(Num+0.5);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.round(Num::in) = (Rounded::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
// XXX the semantics of System.Math.Round() are not the same as ours.
|
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// Unfortunately they are better (round to nearest even number).
|
|
Rounded = System.Math.Floor(Num+0.5);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.round(Num::in) = (Rounded::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Rounded = java.lang.Math.round(Num);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.round(Num::in) = (Rounded::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Rounded = java.lang.Math.round(Num);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.round(Num::in) = (Rounded::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Rounded = float(round(Num))
|
|
").
|
|
math.round(Num) = math.floor(Num + 0.5).
|
|
|
|
math.truncate(X) = (X < 0.0 -> math.ceiling(X) ; math.floor(X)).
|
|
|
|
math.sqrt(X) = SquareRoot :-
|
|
( math_domain_checks, X < 0.0 ->
|
|
throw(domain_error("math.sqrt"))
|
|
;
|
|
SquareRoot = math.sqrt_2(X)
|
|
).
|
|
|
|
:- func math.sqrt_2(float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.sqrt_2(X::in) = (SquareRoot::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
SquareRoot = sqrt(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.sqrt_2(X::in) = (SquareRoot::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
SquareRoot = System.Math.Sqrt(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.sqrt_2(X::in) = (SquareRoot::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
SquareRoot = java.lang.Math.sqrt(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.sqrt_2(X::in) = (SquareRoot::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
SquareRoot = math:sqrt(X)
|
|
").
|
|
% This version is only used for back-ends for which there is no
|
|
% matching foreign_proc version.
|
|
math.sqrt_2(X) = math.exp(math.ln(X) / 2.0).
|
|
|
|
math.solve_quadratic(A, B, C) = Roots :-
|
|
% This implementation is designed to minimise numerical errors;
|
|
% it is adapted from "Numerical recipes in C".
|
|
DSquared = B * B - 4.0 * A * C,
|
|
compare(CmpD, DSquared, 0.0),
|
|
(
|
|
CmpD = (<),
|
|
Roots = no_roots
|
|
;
|
|
CmpD = (=),
|
|
Root = -0.5 * B / A,
|
|
Roots = one_root(Root)
|
|
;
|
|
CmpD = (>),
|
|
D = sqrt(DSquared),
|
|
compare(CmpB, B, 0.0),
|
|
(
|
|
CmpB = (<),
|
|
Q = -0.5 * (B - D),
|
|
Root1 = Q / A,
|
|
Root2 = C / Q
|
|
;
|
|
CmpB = (=),
|
|
Root1 = -0.5 * D / A,
|
|
Root2 = -Root1
|
|
;
|
|
CmpB = (>),
|
|
Q = -0.5 * (B + D),
|
|
Root1 = Q / A,
|
|
Root2 = C / Q
|
|
),
|
|
Roots = two_roots(Root1, Root2)
|
|
).
|
|
|
|
math.pow(X, Y) = Res :-
|
|
( math_domain_checks, X < 0.0 ->
|
|
throw(domain_error("math.pow"))
|
|
; X = 0.0 ->
|
|
( Y =< 0.0 ->
|
|
throw(domain_error("math.pow"))
|
|
;
|
|
Res = 0.0
|
|
)
|
|
;
|
|
Res = math.pow_2(X, Y)
|
|
).
|
|
|
|
:- func math.pow_2(float, float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.pow_2(X::in, Y::in) = (Res::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Res = pow(X, Y);
|
|
").
|
|
|
|
:- pragma foreign_proc("C#",
|
|
math.pow_2(X::in, Y::in) = (Res::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Res = System.Math.Pow(X, Y);
|
|
").
|
|
|
|
:- pragma foreign_proc("Java",
|
|
math.pow_2(X::in, Y::in) = (Res::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Res = java.lang.Math.pow(X, Y);
|
|
").
|
|
|
|
:- pragma foreign_proc("Erlang",
|
|
math.pow_2(X::in, Y::in) = (Res::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Res = math:pow(X, Y)
|
|
").
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.exp(X::in) = (Exp::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Exp = exp(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.exp(X::in) = (Exp::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Exp = System.Math.Exp(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.exp(X::in) = (Exp::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Exp = java.lang.Math.exp(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.exp(X::in) = (Exp::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Exp = math:exp(X)
|
|
").
|
|
|
|
math.ln(X) = Log :-
|
|
( math_domain_checks, X =< 0.0 ->
|
|
throw(domain_error("math.ln"))
|
|
;
|
|
Log = math.ln_2(X)
|
|
).
|
|
|
|
:- func math.ln_2(float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.ln_2(X::in) = (Log::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Log = log(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.ln_2(X::in) = (Log::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log = System.Math.Log(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.ln_2(X::in) = (Log::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log = java.lang.Math.log(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.ln_2(X::in) = (Log::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log = math:log(X)
|
|
").
|
|
|
|
math.log10(X) = Log :-
|
|
( math_domain_checks, X =< 0.0 ->
|
|
throw(domain_error("math.log10"))
|
|
;
|
|
Log = math.log10_2(X)
|
|
).
|
|
|
|
:- func math.log10_2(float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.log10_2(X::in) = (Log10::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Log10 = log10(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.log10_2(X::in) = (Log10::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log10 = System.Math.Log10(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.log10_2(X::in) = (Log10::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log10 = math:log10(X)
|
|
").
|
|
% Java doesn't have a built-in log10, so default to mercury here.
|
|
math.log10_2(X) = math.ln_2(X) / math.ln_2(10.0).
|
|
|
|
math.log2(X) = Log :-
|
|
( math_domain_checks, X =< 0.0 ->
|
|
throw(domain_error("math.log2"))
|
|
;
|
|
Log = math.log2_2(X)
|
|
).
|
|
|
|
:- func math.log2_2(float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.log2_2(X::in) = (Log2::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Log2 = log(X) / ML_FLOAT_LN2;
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.log2_2(X::in) = (Log2::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log2 = System.Math.Log(X) / ML_FLOAT_LN2;
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.log2_2(X::in) = (Log2::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log2 = java.lang.Math.log(X) / ML_FLOAT_LN2;
|
|
").
|
|
math.log2_2(X) = math.ln_2(X) / math.ln_2(2.0).
|
|
|
|
math.log(B, X) = Log :-
|
|
(
|
|
math_domain_checks,
|
|
( X =< 0.0
|
|
; B =< 0.0
|
|
; B = 1.0
|
|
)
|
|
->
|
|
throw(domain_error("math.log"))
|
|
;
|
|
Log = math.log_2(B, X)
|
|
).
|
|
|
|
:- func math.log_2(float, float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.log_2(B::in, X::in) = (Log::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Log = log(X) / log(B);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.log_2(B::in, X::in) = (Log::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
Log = System.Math.Log(X, B);
|
|
").
|
|
% Java implementation will default to mercury here.
|
|
% Erlang implementation will default to mercury here.
|
|
math.log_2(B, X) = math.ln_2(X) / math.ln_2(B).
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.sin(X::in) = (Sin::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Sin = sin(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.sin(X::in) = (Sin::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Sin = System.Math.Sin(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.sin(X::in) = (Sin::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Sin = java.lang.Math.sin(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.sin(X::in) = (Sin::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Sin = math:sin(X)
|
|
").
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.cos(X::in) = (Cos::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Cos = cos(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.cos(X::in) = (Cos::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Cos = System.Math.Cos(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.cos(X::in) = (Cos::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Cos = java.lang.Math.cos(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.cos(X::in) = (Cos::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Cos = math:cos(X)
|
|
").
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.tan(X::in) = (Tan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Tan = tan(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.tan(X::in) = (Tan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Tan = System.Math.Tan(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.tan(X::in) = (Tan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Tan = java.lang.Math.tan(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.tan(X::in) = (Tan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Tan = math:tan(X)
|
|
").
|
|
|
|
math.asin(X) = ASin :-
|
|
(
|
|
math_domain_checks,
|
|
( X < -1.0
|
|
; X > 1.0
|
|
)
|
|
->
|
|
throw(domain_error("math.asin"))
|
|
;
|
|
ASin = math.asin_2(X)
|
|
).
|
|
|
|
:- func math.asin_2(float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.asin_2(X::in) = (ASin::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
ASin = asin(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.asin_2(X::in) = (ASin::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
ASin = System.Math.Asin(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.asin_2(X::in) = (ASin::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
ASin = java.lang.Math.asin(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.asin_2(X::in) = (ASin::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
ASin = math:asin(X)
|
|
").
|
|
|
|
math.acos(X) = ACos :-
|
|
(
|
|
math_domain_checks,
|
|
( X < -1.0
|
|
; X > 1.0
|
|
)
|
|
->
|
|
throw(domain_error("math.acos"))
|
|
;
|
|
ACos = math.acos_2(X)
|
|
).
|
|
|
|
:- func math.acos_2(float) = float.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.acos_2(X::in) = (ACos::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
ACos = acos(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.acos_2(X::in) = (ACos::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
ACos = System.Math.Acos(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.acos_2(X::in) = (ACos::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
ACos = java.lang.Math.acos(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.acos_2(X::in) = (ACos::out),
|
|
[thread_safe, promise_pure],
|
|
"
|
|
ACos = math:acos(X)
|
|
").
|
|
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.atan(X::in) = (ATan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
ATan = atan(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.atan(X::in) = (ATan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
ATan = System.Math.Atan(X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.atan(X::in) = (ATan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
ATan = java.lang.Math.atan(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.atan(X::in) = (ATan::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
ATan = math:atan(X)
|
|
").
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.atan2(Y::in, X::in) = (ATan2::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
ATan2 = atan2(Y, X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.atan2(Y::in, X::in) = (ATan2::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
ATan2 = System.Math.Atan2(Y, X);
|
|
").
|
|
:- pragma foreign_proc("Java",
|
|
math.atan2(Y::in, X::in) = (ATan2::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
ATan2 = java.lang.Math.atan2(Y, X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.atan2(Y::in, X::in) = (ATan2::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
ATan2 = math:atan2(Y, X)
|
|
").
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.sinh(X::in) = (Sinh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Sinh = sinh(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.sinh(X::in) = (Sinh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Sinh = System.Math.Sinh(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.sinh(X::in) = (Sinh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Sinh = math:sinh(X)
|
|
").
|
|
% Java doesn't have any hyperbolic functions built in.
|
|
math.sinh(X) = Sinh :-
|
|
Sinh = (exp(X)-exp(-X)) / 2.0.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.cosh(X::in) = (Cosh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Cosh = cosh(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.cosh(X::in) = (Cosh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Cosh = System.Math.Cosh(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.cosh(X::in) = (Cosh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Cosh = math:cosh(X)
|
|
").
|
|
% Java doesn't have any hyperbolic functions built in.
|
|
math.cosh(X) = Cosh :-
|
|
Cosh = (exp(X)+exp(-X)) / 2.0.
|
|
|
|
:- pragma foreign_proc("C",
|
|
math.tanh(X::in) = (Tanh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe, will_not_modify_trail,
|
|
does_not_affect_liveness],
|
|
"
|
|
Tanh = tanh(X);
|
|
").
|
|
:- pragma foreign_proc("C#",
|
|
math.tanh(X::in) = (Tanh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Tanh = System.Math.Tanh(X);
|
|
").
|
|
:- pragma foreign_proc("Erlang",
|
|
math.tanh(X::in) = (Tanh::out),
|
|
[will_not_call_mercury, promise_pure, thread_safe],
|
|
"
|
|
Tanh = math:tanh(X)
|
|
").
|
|
% Java doesn't have any hyperbolic functions built in.
|
|
math.tanh(X) = Tanh :-
|
|
Tanh = (exp(X)-exp(-X)) / (exp(X)+exp(-X)).
|
|
|
|
%---------------------------------------------------------------------------%
|
|
%---------------------------------------------------------------------------%
|