------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- S Y S T E M . F A T _ G E N -- -- -- -- S p e c -- -- -- -- Copyright (C) 1992-2024, 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 -- -- . -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ -- This generic package provides a target independent implementation of the -- floating-point attributes that denote functions. The implementations here -- are portable, but very slow. The runtime contains a set of instantiations -- of this package for all predefined floating-point types, and these should -- be replaced by efficient assembly language code where possible. generic type T is digits <>; package System.Fat_Gen is pragma Pure; subtype UI is Integer; -- The runtime representation of universal integer for the purposes of -- this package is integer. The expander generates conversions for the -- actual type used. For functions returning universal integer, there -- is no problem, since the result always is in range of integer. For -- input arguments, the expander has to do some special casing to deal -- with the (very annoying) cases of out of range values. If we used -- Long_Long_Integer to represent universal, then there would be no -- problem, but the resulting inefficiency would be annoying. function Adjacent (X, Towards : T) return T; -- If ``Towards`` = ``X``, the function returns ``X``; oterwise, it yields -- the machien number of the type *T* adjacent to ``X`` in the direction -- ``Towards``, if that machine number exists. function Ceiling (X : T) return T; -- Truncate ``X``. If the truncation is equal to ``X`` return ``X``. If -- ``X`` is less than zero, return the truncation, otherwise add one -- to the truncation. function Compose (Fraction : T; Exponent : UI) return T; -- Decompose the ``Fraction`` into its fraction and exponent parts. Call -- *Scaling* with the returned fraction part and ``Exponent``. function Copy_Sign (Value, Sign : T) return T; -- Take the absolute value of ``Value``. Negate the result if ``Sign`` is -- less than zero. function Exponent (X : T) return UI; -- Decompose `X`` and return the exponent part. function Floor (X : T) return T; -- Truncate ``X``. If the truncation is equal to ``X`` return ``X``. If -- ``X`` is greater than zero, return the truncation, otherwise subtract -- one from the truncation. function Fraction (X : T) return T; -- Decompose `X`` and return the fraction part function Leading_Part (X : T; Radix_Digits : UI) return T; -- Return ``X`` if the ``Radix_Digits`` is larger than the type's machine -- mantissa. Otherwise scale down and truncate ``X`` by the difference -- between the exponent of ``X`` and ``Radix_Digits``, then scale the -- result back up. function Machine (X : T) return T; -- Force ``X`` to be stored in memory and retrieve the result function Machine_Rounding (X : T) return T; -- Truncate the absolute value of ``X`` + 0.5. If ``X`` is negative, negate -- the result. function Model (X : T) return T; -- If ``X`` is a model number of *T*, the function returns ``X``; -- otherwise it yields the value obtained by rounding or truncating ``X`` -- to either one of the adjacent model numbers of *T*. -- -- We treat *Model* as identical to *Machine*. This is true of IEEE and -- other nice floating-point systems, but not necessarily true of all -- systems. function Pred (X : T) return T; -- Return the machine number immediately below the value of ``X``. -- -- If zero, return the negative of *Succ* (``X``). -- -- If ``X`` = *T*'First, return negative infinity. -- -- If ``X`` is already infinity, return ``X``. -- -- Otherwise, subtract from ``X`` a number equivalent to the value of its -- least significant bit. function Remainder (X, Y : T) return T; -- Return the remainder (n) of ``X`` divided by ``Y``. -- If abs(n - ``X`` / ``Y``) = 1/2 then n is chosen to be even. -- -- Calculate the modulus remainder: if abs(``X``) < abs(``Y``) then the -- remainder is abs(``X``). Otherwise, decompose abs(``X``) and abs(``Y``). -- Then: -- -- .. code-block:: ada -- -- P := Compose (Y_Frac, X_Exp); -- K := X_Exp - Y_Exp; -- Rem := |X|; -- for J in reverse 0 .. K loop -- if Rem >= P then -- Rem := Rem - P; -- end if; -- P := P * 0.5; -- end loop; -- -- Return the IEEE remainder by adjusting result such that if -- abs(n - X/Y) = 1/2 then n is even. function Rounding (X : T) return T; -- The function yields the integral value nearest to ``X``, rounding away -- from zero if ``X`` lies exactly halfway between two integers. -- -- The function truncates the absolute value of ``X`` + 0.5. If ``X`` is -- negative, negate the result. function Scaling (X : T; Adjustment : UI) return T; -- Let v be the value ``X`` * *T*'Machine_RadixAdjustment. If v is a -- machine number of the type *T*, or if abs(v) >= *T*'Model_Small, the -- function yields v; otherwise, it yields either one of the machine -- numbers of the type *T* adjacent to v. -- -- If ``X`` or ``Adjustment`` equal zero, return ``X``. Otherwise, return -- ``X`` * Machine_Radix ** ``Adjustment``. function Succ (X : T) return T; -- Returns the machine number immediately above the value of X. -- -- If zero, return the smallest denormal. -- -- If ``X`` = *T*'Last, return infinity. -- -- If ``X`` is already infinity, return ``X``. -- -- Otherwise, add to X a number equivalent to the value of its least -- significant bit. function Truncation (X : T) return T; -- The function yields the value *Ceiling* (``X``) when ``X`` is negative, -- and *Floor* (``X``) otherwise. -- -- Return *T*'Machine (RM1 + N) - RM1 where N is abs(``X``) and -- RM1 = radix ** (mantissa - 1). Negate the result where ``X`` is -- negative. function Unbiased_Rounding (X : T) return T; -- The integral value nearest to ``X``, rounding toward the even integer -- if ``X`` lies exactly halfway between two integers. -- -- This function truncates abs(``X``). If the tail of the result is greater -- than 0.5 add one to the result. If the tail equals 0.5, round to the -- nearest even integer. Negate the result if ``X`` is negative. function Valid (X : not null access T) return Boolean; -- This function checks if the object of type *T* referenced by ``X`` is -- valid, and returns True/False accordingly. The parameter is passed by -- reference (access) here, as the object of type T may be an abnormal -- value that cannot be passed in a floating-point register, and the whole -- point of 'Valid is to prevent exceptions. Note that the object of -- type *T* must have the natural alignment for type *T*. -- -- If denormalized numbers are valid: return True unless ``X`` is infinity -- or NaN. If denormalized numbers are not valid, return False if ``X`` is -- a denormal number. type S is new String (1 .. T'Size / Character'Size); type P is access all S with Storage_Size => 0; -- Buffer and access types used to initialize temporaries for validity -- checks, if the value to be checked has reverse scalar storage order, or -- is not known to be properly aligned (for example it appears in a packed -- record). In this case, we cannot call Valid since Valid assumes proper -- full alignment. Instead, we copy the value to a temporary location using -- type S (we cannot simply do a copy of a T value, because the value might -- be invalid, in which case it might not be possible to copy it through a -- floating point register). private pragma Inline (Compose); pragma Inline (Copy_Sign); pragma Inline (Exponent); pragma Inline (Fraction); pragma Inline (Machine); pragma Inline (Model); pragma Inline (Valid); end System.Fat_Gen;