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98 lines
2.8 KiB
Mathematica
98 lines
2.8 KiB
Mathematica
%-----------------------------------------------------------------------------%
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% vim: ft=mercury ts=4 sw=4 et
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%-----------------------------------------------------------------------------%
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% Copyright (C) 1997-1998,2001, 2004-2006 The University of Melbourne.
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% Copyright (C) 2015, 2018, 2022 The Mercury team.
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% This file is distributed under the terms specified in COPYING.LIB.
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%-----------------------------------------------------------------------------%
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%
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% File: imag.m.
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% Main author: fjh.
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% Stability: medium.
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%
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% Imaginary numbers.
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%
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% There are several reasons for supporting a separate type for imaginary
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% numbers rather than just treating them as a special case of complex numbers.
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% It is sometimes more convenient, and can be slightly more efficient. But
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% perhaps the most important reason is to get correct handling of infinity and
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% not-a-number on platforms that support IEEE floating point.
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%
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% Note that the overloaded versions of the binary operators that provide
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% mixed type arithmetic are defined in different modules.
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%
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% See also:
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% float.m, imag_float.m, float_imag.m,
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% complex.m, imag_complex.m, complex_imag.m.
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%
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%-----------------------------------------------------------------------------%
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%-----------------------------------------------------------------------------%
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:- module complex_numbers.imag.
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:- interface.
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:- import_module float.
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%-----------------------------------------------------------------------------%
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:- type imag
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---> im(float).
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:- func i = imag. % i = sqrt(-1)
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:- func j = imag. % another name for `i'
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%-----------------------------------------------------------------------------%
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% Addition.
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%
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:- func imag + imag = imag.
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:- mode in + in = uo is det.
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% Subtraction.
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%
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:- func imag - imag = imag.
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:- mode in - in = uo is det.
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% Multiplication.
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%
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:- func imag * imag = float.
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:- mode in * in = uo is det.
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% Division.
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%
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:- func imag / imag = float.
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:- mode in / in = uo is det.
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% Unary plus.
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%
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:- func + imag = imag.
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:- mode + in = uo is det.
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% Unary minus.
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%
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:- func - imag = imag.
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:- mode - in = uo is det.
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%-----------------------------------------------------------------------------%
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%-----------------------------------------------------------------------------%
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:- implementation.
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%-----------------------------------------------------------------------------%
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i = im(1.0).
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j = i.
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%-----------------------------------------------------------------------------%
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+im(X) = im(X + 0.0).
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-im(X) = im(-X).
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im(X) + im(Y) = im(X + Y).
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im(X) - im(Y) = im(X - Y).
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im(X) * im(Y) = 0.0 - X * Y.
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im(X) / im(Y) = X / Y.
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%-----------------------------------------------------------------------------%
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:- end_module complex_numbers.imag.
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%-----------------------------------------------------------------------------%
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