------------------------------------------------------------------------------ | |

-- -- | |

-- 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, 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; |