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------------------------------------------------------------------------------
-- --
-- GNAT COMPILER COMPONENTS --
-- --
-- S Y S T E M . D O U B L E _ R E A L --
-- --
-- S p e c --
-- --
-- Copyright (C) 2021-2023, Free Software Foundation, Inc. --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
-- This package contains routines for supporting floating-point computations
-- in double precision, i.e. using a second number to estimate the error due
-- to rounding and more generally performing computations with twice as many
-- bits of mantissa. It is based on the Double-Double library available at
-- https://www.davidhbailey.com/dhbsoftware written by David H.Bailey et al.
generic
type Num is digits <>;
package System.Double_Real is
pragma Pure;
type Double_T is record
Hi, Lo : Num;
end record;
function To_Double (N : Num) return Double_T is ((Hi => N, Lo => 0.0));
-- Convert a single to a double real
function To_Single (D : Double_T) return Num is (D.Hi);
-- Convert a double to a single real
function Quick_Two_Sum (A, B : Num) return Double_T
with Pre => A = 0.0 or else abs (A) >= abs (B);
-- Compute A + B and its rounding error exactly, but assume |A| >= |B|
function Two_Sum (A, B : Num) return Double_T;
-- Compute A + B and its rounding error exactly
function Two_Diff (A, B : Num) return Double_T;
-- Compute A - B and its rounding error exactly
function Two_Prod (A, B : Num) return Double_T;
-- Compute A * B and its rounding error exactly
function Two_Sqr (A : Num) return Double_T;
-- Compute A * A and its rounding error exactly
function "+" (A : Double_T; B : Num) return Double_T;
function "-" (A : Double_T; B : Num) return Double_T;
function "*" (A : Double_T; B : Num) return Double_T;
function "/" (A : Double_T; B : Num) return Double_T
with Pre => B /= 0.0;
-- Mixed precision arithmetic operations
function "+" (A, B : Double_T) return Double_T;
function "-" (A, B : Double_T) return Double_T;
function "*" (A, B : Double_T) return Double_T;
function "/" (A, B : Double_T) return Double_T
with Pre => B.Hi /= 0.0;
-- Double precision arithmetic operations
function Sqr (A : Double_T) return Double_T;
-- Faster version of A * A
function "=" (A : Double_T; B : Num) return Boolean is
(A.Hi = B and then A.Lo = 0.0);
function "<" (A : Double_T; B : Num) return Boolean is
(A.Hi < B or else (A.Hi = B and then A.Lo < 0.0));
function "<=" (A : Double_T; B : Num) return Boolean is
(A.Hi < B or else (A.Hi = B and then A.Lo <= 0.0));
function ">" (A : Double_T; B : Num) return Boolean is
(A.Hi > B or else (A.Hi = B and then A.Lo > 0.0));
function ">=" (A : Double_T; B : Num) return Boolean is
(A.Hi > B or else (A.Hi = B and then A.Lo >= 0.0));
-- Mixed precision comparisons
function "=" (A, B : Double_T) return Boolean is
(A.Hi = B.Hi and then A.Lo = B.Lo);
function "<" (A, B : Double_T) return Boolean is
(A.Hi < B.Hi or else (A.Hi = B.Hi and then A.Lo < B.Lo));
function "<=" (A, B : Double_T) return Boolean is
(A.Hi < B.Hi or else (A.Hi = B.Hi and then A.Lo <= B.Lo));
function ">" (A, B : Double_T) return Boolean is
(A.Hi > B.Hi or else (A.Hi = B.Hi and then A.Lo > B.Lo));
function ">=" (A, B : Double_T) return Boolean is
(A.Hi > B.Hi or else (A.Hi = B.Hi and then A.Lo >= B.Lo));
-- Double precision comparisons
generic
type Uns is mod <>;
function From_Unsigned (U : Uns) return Double_T;
-- Convert Uns to Double_T
generic
type Uns is mod <>;
function To_Unsigned (D : Double_T) return Uns
with Pre => D >= 0.0;
-- Convert Double_T to Uns with truncation
end System.Double_Real;
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