| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT COMPILER COMPONENTS -- |
| -- -- |
| -- S Y S T E M . F A T _ G E N -- |
| -- -- |
| -- S p e c -- |
| -- -- |
| -- Copyright (C) 1992-2025, 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 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; |
