| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT RUN-TIME COMPONENTS -- |
| -- -- |
| -- S Y S T E M . F O R E _ F -- |
| -- -- |
| -- B o d y -- |
| -- -- |
| -- Copyright (C) 2020-2022, 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. -- |
| -- -- |
| ------------------------------------------------------------------------------ |
| |
| package body System.Fore_F is |
| |
| Maxdigs : constant Natural := Int'Width - 2; |
| -- Maximum number of decimal digits that can be represented in an Int. |
| -- The "-2" accounts for the sign and one extra digit, since we need the |
| -- maximum number of 9's that can be represented, e.g. for the 64-bit case, |
| -- Integer_64'Width is 20 since the maximum value is approximately 9.2E+18 |
| -- and has 19 digits, but the maximum number of 9's that can be represented |
| -- in Integer_64 is only 18. |
| |
| -- The first prerequisite of the implementation is that the scaled divide |
| -- does not overflow, which means that the absolute value of the bounds of |
| -- the subtype must be smaller than 10**Maxdigs * 2**(Int'Size - 1). |
| -- Otherwise Constraint_Error is raised by the scaled divide operation. |
| |
| -- The second prerequisite is that the computation of the operands does not |
| -- overflow, which means that, if the small is larger than 1, it is either |
| -- an integer or its numerator and denominator must be both smaller than |
| -- the power 10**(Maxdigs - 1). |
| |
| ---------------- |
| -- Fore_Fixed -- |
| ---------------- |
| |
| function Fore_Fixed (Lo, Hi, Num, Den : Int; Scale : Integer) return Natural |
| is |
| pragma Assert (Num < 0 and then Den < 0); |
| -- Accept only negative numbers to allow -2**(Int'Size - 1) |
| |
| function Negative_Abs (Val : Int) return Int is |
| (if Val <= 0 then Val else -Val); |
| -- Return the opposite of the absolute value of Val |
| |
| T : Int := Int'Min (Negative_Abs (Lo), Negative_Abs (Hi)); |
| F : Natural; |
| |
| Q, R : Int; |
| |
| begin |
| -- Initial value of 2 allows for sign and mandatory single digit |
| |
| F := 2; |
| |
| -- The easy case is when Num is not larger than Den in magnitude, |
| -- i.e. if S = Num / Den, then S <= 1, in which case we can just |
| -- compute the product Q = T * S. |
| |
| if Num >= Den then |
| Scaled_Divide (T, Num, Den, Q, R, Round => False); |
| T := Q; |
| |
| -- Otherwise S > 1 and thus Scale <= 0, compute Q and R such that |
| |
| -- T * Num = Q * (Den * 10**(-D)) + R |
| |
| -- with |
| |
| -- D = Integer'Max (-Maxdigs, Scale - 1) |
| |
| -- then reason on Q if it is non-zero or else on R / Den. |
| |
| -- This works only if Den * 10**(-D) does not overflow, which is true |
| -- if Den = 1. Suppose that Num corresponds to the maximum value of -D, |
| -- i.e. Maxdigs and 10**(-D) = 10**Maxdigs. If you change Den into 10, |
| -- then S becomes 10 times smaller and, therefore, Scale is incremented |
| -- by 1, which means that -D is decremented by 1 provided that Scale was |
| -- initially not smaller than 1 - Maxdigs, so the multiplication still |
| -- does not overflow. But you need to reach 10 to trigger this effect, |
| -- which means that a leeway of 10 is required, so let's restrict this |
| -- to a Num for which 10**(-D) <= 10**(Maxdigs - 1). To sum up, if S is |
| -- the ratio of two integers with |
| |
| -- 1 < Den < Num <= B |
| |
| -- where B is a fixed limit, then the multiplication does not overflow. |
| -- B can be taken as the largest integer Small such that D = 1 - Maxdigs |
| -- i.e. such that Scale = 2 - Maxdigs, which is 10**(Maxdigs - 1) - 1. |
| |
| else |
| declare |
| D : constant Integer := Integer'Max (-Maxdigs, Scale - 1); |
| |
| begin |
| Scaled_Divide (T, Num, Den * 10**(-D), Q, R, Round => False); |
| |
| if Q /= 0 then |
| T := Q; |
| F := F - D; |
| else |
| T := R / Den; |
| end if; |
| end; |
| end if; |
| |
| -- Loop to increase Fore as needed to include full range of values |
| |
| while T <= -10 or else T >= 10 loop |
| T := T / 10; |
| F := F + 1; |
| end loop; |
| |
| return F; |
| end Fore_Fixed; |
| |
| end System.Fore_F; |
