From 554fd8c5195424bdbcabf5de30fdc183aba391bd Mon Sep 17 00:00:00 2001 From: upstream source tree Date: Sun, 15 Mar 2015 20:14:05 -0400 Subject: obtained gcc-4.6.4.tar.bz2 from upstream website; verified gcc-4.6.4.tar.bz2.sig; imported gcc-4.6.4 source tree from verified upstream tarball. downloading a git-generated archive based on the 'upstream' tag should provide you with a source tree that is binary identical to the one extracted from the above tarball. if you have obtained the source via the command 'git clone', however, do note that line-endings of files in your working directory might differ from line-endings of the respective files in the upstream repository. --- gcc/ada/eval_fat.adb | 791 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 791 insertions(+) create mode 100644 gcc/ada/eval_fat.adb (limited to 'gcc/ada/eval_fat.adb') diff --git a/gcc/ada/eval_fat.adb b/gcc/ada/eval_fat.adb new file mode 100644 index 000000000..3d0bff6a3 --- /dev/null +++ b/gcc/ada/eval_fat.adb @@ -0,0 +1,791 @@ +------------------------------------------------------------------------------ +-- -- +-- GNAT COMPILER COMPONENTS -- +-- -- +-- E V A L _ F A T -- +-- -- +-- B o d y -- +-- -- +-- Copyright (C) 1992-2010, 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. See the GNU General Public License -- +-- for more details. You should have received a copy of the GNU General -- +-- Public License distributed with GNAT; see file COPYING3. If not, go to -- +-- http://www.gnu.org/licenses for a complete copy of the license. -- +-- -- +-- GNAT was originally developed by the GNAT team at New York University. -- +-- Extensive contributions were provided by Ada Core Technologies Inc. -- +-- -- +------------------------------------------------------------------------------ + +with Einfo; use Einfo; +with Errout; use Errout; +with Targparm; use Targparm; + +package body Eval_Fat is + + Radix : constant Int := 2; + -- This code is currently only correct for the radix 2 case. We use the + -- symbolic value Radix where possible to help in the unlikely case of + -- anyone ever having to adjust this code for another value, and for + -- documentation purposes. + + -- Another assumption is that the range of the floating-point type is + -- symmetric around zero. + + type Radix_Power_Table is array (Int range 1 .. 4) of Int; + + Radix_Powers : constant Radix_Power_Table := + (Radix ** 1, Radix ** 2, Radix ** 3, Radix ** 4); + + ----------------------- + -- Local Subprograms -- + ----------------------- + + procedure Decompose + (RT : R; + X : T; + Fraction : out T; + Exponent : out UI; + Mode : Rounding_Mode := Round); + -- Decomposes a non-zero floating-point number into fraction and exponent + -- parts. The fraction is in the interval 1.0 / Radix .. T'Pred (1.0) and + -- uses Rbase = Radix. The result is rounded to a nearest machine number. + + procedure Decompose_Int + (RT : R; + X : T; + Fraction : out UI; + Exponent : out UI; + Mode : Rounding_Mode); + -- This is similar to Decompose, except that the Fraction value returned + -- is an integer representing the value Fraction * Scale, where Scale is + -- the value (Machine_Radix_Value (RT) ** Machine_Mantissa_Value (RT)). The + -- value is obtained by using biased rounding (halfway cases round away + -- from zero), round to even, a floor operation or a ceiling operation + -- depending on the setting of Mode (see corresponding descriptions in + -- Urealp). + + -------------- + -- Adjacent -- + -------------- + + function Adjacent (RT : R; X, Towards : T) return T is + begin + if Towards = X then + return X; + elsif Towards > X then + return Succ (RT, X); + else + return Pred (RT, X); + end if; + end Adjacent; + + ------------- + -- Ceiling -- + ------------- + + function Ceiling (RT : R; X : T) return T is + XT : constant T := Truncation (RT, X); + begin + if UR_Is_Negative (X) then + return XT; + elsif X = XT then + return X; + else + return XT + Ureal_1; + end if; + end Ceiling; + + ------------- + -- Compose -- + ------------- + + function Compose (RT : R; Fraction : T; Exponent : UI) return T is + Arg_Frac : T; + Arg_Exp : UI; + pragma Warnings (Off, Arg_Exp); + begin + Decompose (RT, Fraction, Arg_Frac, Arg_Exp); + return Scaling (RT, Arg_Frac, Exponent); + end Compose; + + --------------- + -- Copy_Sign -- + --------------- + + function Copy_Sign (RT : R; Value, Sign : T) return T is + pragma Warnings (Off, RT); + Result : T; + + begin + Result := abs Value; + + if UR_Is_Negative (Sign) then + return -Result; + else + return Result; + end if; + end Copy_Sign; + + --------------- + -- Decompose -- + --------------- + + procedure Decompose + (RT : R; + X : T; + Fraction : out T; + Exponent : out UI; + Mode : Rounding_Mode := Round) + is + Int_F : UI; + + begin + Decompose_Int (RT, abs X, Int_F, Exponent, Mode); + + Fraction := UR_From_Components + (Num => Int_F, + Den => Machine_Mantissa_Value (RT), + Rbase => Radix, + Negative => False); + + if UR_Is_Negative (X) then + Fraction := -Fraction; + end if; + + return; + end Decompose; + + ------------------- + -- Decompose_Int -- + ------------------- + + -- This procedure should be modified with care, as there are many non- + -- obvious details that may cause problems that are hard to detect. For + -- zero arguments, Fraction and Exponent are set to zero. Note that sign + -- of zero cannot be preserved. + + procedure Decompose_Int + (RT : R; + X : T; + Fraction : out UI; + Exponent : out UI; + Mode : Rounding_Mode) + is + Base : Int := Rbase (X); + N : UI := abs Numerator (X); + D : UI := Denominator (X); + + N_Times_Radix : UI; + + Even : Boolean; + -- True iff Fraction is even + + Most_Significant_Digit : constant UI := + Radix ** (Machine_Mantissa_Value (RT) - 1); + + Uintp_Mark : Uintp.Save_Mark; + -- The code is divided into blocks that systematically release + -- intermediate values (this routine generates lots of junk!) + + begin + if N = Uint_0 then + Fraction := Uint_0; + Exponent := Uint_0; + return; + end if; + + Calculate_D_And_Exponent_1 : begin + Uintp_Mark := Mark; + Exponent := Uint_0; + + -- In cases where Base > 1, the actual denominator is Base**D. For + -- cases where Base is a power of Radix, use the value 1 for the + -- Denominator and adjust the exponent. + + -- Note: Exponent has different sign from D, because D is a divisor + + for Power in 1 .. Radix_Powers'Last loop + if Base = Radix_Powers (Power) then + Exponent := -D * Power; + Base := 0; + D := Uint_1; + exit; + end if; + end loop; + + Release_And_Save (Uintp_Mark, D, Exponent); + end Calculate_D_And_Exponent_1; + + if Base > 0 then + Calculate_Exponent : begin + Uintp_Mark := Mark; + + -- For bases that are a multiple of the Radix, divide the base by + -- Radix and adjust the Exponent. This will help because D will be + -- much smaller and faster to process. + + -- This occurs for decimal bases on machines with binary floating- + -- point for example. When calculating 1E40, with Radix = 2, N + -- will be 93 bits instead of 133. + + -- N E + -- ------ * Radix + -- D + -- Base + + -- N E + -- = -------------------------- * Radix + -- D D + -- (Base/Radix) * Radix + + -- N E-D + -- = --------------- * Radix + -- D + -- (Base/Radix) + + -- This code is commented out, because it causes numerous + -- failures in the regression suite. To be studied ??? + + while False and then Base > 0 and then Base mod Radix = 0 loop + Base := Base / Radix; + Exponent := Exponent + D; + end loop; + + Release_And_Save (Uintp_Mark, Exponent); + end Calculate_Exponent; + + -- For remaining bases we must actually compute the exponentiation + + -- Because the exponentiation can be negative, and D must be integer, + -- the numerator is corrected instead. + + Calculate_N_And_D : begin + Uintp_Mark := Mark; + + if D < 0 then + N := N * Base ** (-D); + D := Uint_1; + else + D := Base ** D; + end if; + + Release_And_Save (Uintp_Mark, N, D); + end Calculate_N_And_D; + + Base := 0; + end if; + + -- Now scale N and D so that N / D is a value in the interval [1.0 / + -- Radix, 1.0) and adjust Exponent accordingly, so the value N / D * + -- Radix ** Exponent remains unchanged. + + -- Step 1 - Adjust N so N / D >= 1 / Radix, or N = 0 + + -- N and D are positive, so N / D >= 1 / Radix implies N * Radix >= D. + -- As this scaling is not possible for N is Uint_0, zero is handled + -- explicitly at the start of this subprogram. + + Calculate_N_And_Exponent : begin + Uintp_Mark := Mark; + + N_Times_Radix := N * Radix; + while not (N_Times_Radix >= D) loop + N := N_Times_Radix; + Exponent := Exponent - 1; + N_Times_Radix := N * Radix; + end loop; + + Release_And_Save (Uintp_Mark, N, Exponent); + end Calculate_N_And_Exponent; + + -- Step 2 - Adjust D so N / D < 1 + + -- Scale up D so N / D < 1, so N < D + + Calculate_D_And_Exponent_2 : begin + Uintp_Mark := Mark; + + while not (N < D) loop + + -- As N / D >= 1, N / (D * Radix) will be at least 1 / Radix, so + -- the result of Step 1 stays valid + + D := D * Radix; + Exponent := Exponent + 1; + end loop; + + Release_And_Save (Uintp_Mark, D, Exponent); + end Calculate_D_And_Exponent_2; + + -- Here the value N / D is in the range [1.0 / Radix .. 1.0) + + -- Now find the fraction by doing a very simple-minded division until + -- enough digits have been computed. + + -- This division works for all radices, but is only efficient for a + -- binary radix. It is just like a manual division algorithm, but + -- instead of moving the denominator one digit right, we move the + -- numerator one digit left so the numerator and denominator remain + -- integral. + + Fraction := Uint_0; + Even := True; + + Calculate_Fraction_And_N : begin + Uintp_Mark := Mark; + + loop + while N >= D loop + N := N - D; + Fraction := Fraction + 1; + Even := not Even; + end loop; + + -- Stop when the result is in [1.0 / Radix, 1.0) + + exit when Fraction >= Most_Significant_Digit; + + N := N * Radix; + Fraction := Fraction * Radix; + Even := True; + end loop; + + Release_And_Save (Uintp_Mark, Fraction, N); + end Calculate_Fraction_And_N; + + Calculate_Fraction_And_Exponent : begin + Uintp_Mark := Mark; + + -- Determine correct rounding based on the remainder which is in + -- N and the divisor D. The rounding is performed on the absolute + -- value of X, so Ceiling and Floor need to check for the sign of + -- X explicitly. + + case Mode is + when Round_Even => + + -- This rounding mode should not be used for static + -- expressions, but only for compile-time evaluation of + -- non-static expressions. + + if (Even and then N * 2 > D) + or else + (not Even and then N * 2 >= D) + then + Fraction := Fraction + 1; + end if; + + when Round => + + -- Do not round to even as is done with IEEE arithmetic, but + -- instead round away from zero when the result is exactly + -- between two machine numbers. See RM 4.9(38). + + if N * 2 >= D then + Fraction := Fraction + 1; + end if; + + when Ceiling => + if N > Uint_0 and then not UR_Is_Negative (X) then + Fraction := Fraction + 1; + end if; + + when Floor => + if N > Uint_0 and then UR_Is_Negative (X) then + Fraction := Fraction + 1; + end if; + end case; + + -- The result must be normalized to [1.0/Radix, 1.0), so adjust if + -- the result is 1.0 because of rounding. + + if Fraction = Most_Significant_Digit * Radix then + Fraction := Most_Significant_Digit; + Exponent := Exponent + 1; + end if; + + -- Put back sign after applying the rounding + + if UR_Is_Negative (X) then + Fraction := -Fraction; + end if; + + Release_And_Save (Uintp_Mark, Fraction, Exponent); + end Calculate_Fraction_And_Exponent; + end Decompose_Int; + + -------------- + -- Exponent -- + -------------- + + function Exponent (RT : R; X : T) return UI is + X_Frac : UI; + X_Exp : UI; + pragma Warnings (Off, X_Frac); + begin + Decompose_Int (RT, X, X_Frac, X_Exp, Round_Even); + return X_Exp; + end Exponent; + + ----------- + -- Floor -- + ----------- + + function Floor (RT : R; X : T) return T is + XT : constant T := Truncation (RT, X); + + begin + if UR_Is_Positive (X) then + return XT; + + elsif XT = X then + return X; + + else + return XT - Ureal_1; + end if; + end Floor; + + -------------- + -- Fraction -- + -------------- + + function Fraction (RT : R; X : T) return T is + X_Frac : T; + X_Exp : UI; + pragma Warnings (Off, X_Exp); + begin + Decompose (RT, X, X_Frac, X_Exp); + return X_Frac; + end Fraction; + + ------------------ + -- Leading_Part -- + ------------------ + + function Leading_Part (RT : R; X : T; Radix_Digits : UI) return T is + RD : constant UI := UI_Min (Radix_Digits, Machine_Mantissa_Value (RT)); + L : UI; + Y : T; + begin + L := Exponent (RT, X) - RD; + Y := UR_From_Uint (UR_Trunc (Scaling (RT, X, -L))); + return Scaling (RT, Y, L); + end Leading_Part; + + ------------- + -- Machine -- + ------------- + + function Machine + (RT : R; + X : T; + Mode : Rounding_Mode; + Enode : Node_Id) return T + is + X_Frac : T; + X_Exp : UI; + Emin : constant UI := Machine_Emin_Value (RT); + + begin + Decompose (RT, X, X_Frac, X_Exp, Mode); + + -- Case of denormalized number or (gradual) underflow + + -- A denormalized number is one with the minimum exponent Emin, but that + -- breaks the assumption that the first digit of the mantissa is a one. + -- This allows the first non-zero digit to be in any of the remaining + -- Mant - 1 spots. The gap between subsequent denormalized numbers is + -- the same as for the smallest normalized numbers. However, the number + -- of significant digits left decreases as a result of the mantissa now + -- having leading seros. + + if X_Exp < Emin then + declare + Emin_Den : constant UI := Machine_Emin_Value (RT) + - Machine_Mantissa_Value (RT) + Uint_1; + begin + if X_Exp < Emin_Den or not Denorm_On_Target then + if UR_Is_Negative (X) then + Error_Msg_N + ("floating-point value underflows to -0.0?", Enode); + return Ureal_M_0; + + else + Error_Msg_N + ("floating-point value underflows to 0.0?", Enode); + return Ureal_0; + end if; + + elsif Denorm_On_Target then + + -- Emin - Mant <= X_Exp < Emin, so result is denormal. Handle + -- gradual underflow by first computing the number of + -- significant bits still available for the mantissa and + -- then truncating the fraction to this number of bits. + + -- If this value is different from the original fraction, + -- precision is lost due to gradual underflow. + + -- We probably should round here and prevent double rounding as + -- a result of first rounding to a model number and then to a + -- machine number. However, this is an extremely rare case that + -- is not worth the extra complexity. In any case, a warning is + -- issued in cases where gradual underflow occurs. + + declare + Denorm_Sig_Bits : constant UI := X_Exp - Emin_Den + 1; + + X_Frac_Denorm : constant T := UR_From_Components + (UR_Trunc (Scaling (RT, abs X_Frac, Denorm_Sig_Bits)), + Denorm_Sig_Bits, + Radix, + UR_Is_Negative (X)); + + begin + if X_Frac_Denorm /= X_Frac then + Error_Msg_N + ("gradual underflow causes loss of precision?", + Enode); + X_Frac := X_Frac_Denorm; + end if; + end; + end if; + end; + end if; + + return Scaling (RT, X_Frac, X_Exp); + end Machine; + + ----------- + -- Model -- + ----------- + + function Model (RT : R; X : T) return T is + X_Frac : T; + X_Exp : UI; + begin + Decompose (RT, X, X_Frac, X_Exp); + return Compose (RT, X_Frac, X_Exp); + end Model; + + ---------- + -- Pred -- + ---------- + + function Pred (RT : R; X : T) return T is + begin + return -Succ (RT, -X); + end Pred; + + --------------- + -- Remainder -- + --------------- + + function Remainder (RT : R; X, Y : T) return T is + A : T; + B : T; + Arg : T; + P : T; + Arg_Frac : T; + P_Frac : T; + Sign_X : T; + IEEE_Rem : T; + Arg_Exp : UI; + P_Exp : UI; + K : UI; + P_Even : Boolean; + + pragma Warnings (Off, Arg_Frac); + + begin + if UR_Is_Positive (X) then + Sign_X := Ureal_1; + else + Sign_X := -Ureal_1; + end if; + + Arg := abs X; + P := abs Y; + + if Arg < P then + P_Even := True; + IEEE_Rem := Arg; + P_Exp := Exponent (RT, P); + + else + -- ??? what about zero cases? + Decompose (RT, Arg, Arg_Frac, Arg_Exp); + Decompose (RT, P, P_Frac, P_Exp); + + P := Compose (RT, P_Frac, Arg_Exp); + K := Arg_Exp - P_Exp; + P_Even := True; + IEEE_Rem := Arg; + + for Cnt in reverse 0 .. UI_To_Int (K) loop + if IEEE_Rem >= P then + P_Even := False; + IEEE_Rem := IEEE_Rem - P; + else + P_Even := True; + end if; + + P := P * Ureal_Half; + end loop; + end if; + + -- That completes the calculation of modulus remainder. The final step + -- is get the IEEE remainder. Here we compare Rem with (abs Y) / 2. + + if P_Exp >= 0 then + A := IEEE_Rem; + B := abs Y * Ureal_Half; + + else + A := IEEE_Rem * Ureal_2; + B := abs Y; + end if; + + if A > B or else (A = B and then not P_Even) then + IEEE_Rem := IEEE_Rem - abs Y; + end if; + + return Sign_X * IEEE_Rem; + end Remainder; + + -------------- + -- Rounding -- + -------------- + + function Rounding (RT : R; X : T) return T is + Result : T; + Tail : T; + + begin + Result := Truncation (RT, abs X); + Tail := abs X - Result; + + if Tail >= Ureal_Half then + Result := Result + Ureal_1; + end if; + + if UR_Is_Negative (X) then + return -Result; + else + return Result; + end if; + end Rounding; + + ------------- + -- Scaling -- + ------------- + + function Scaling (RT : R; X : T; Adjustment : UI) return T is + pragma Warnings (Off, RT); + + begin + if Rbase (X) = Radix then + return UR_From_Components + (Num => Numerator (X), + Den => Denominator (X) - Adjustment, + Rbase => Radix, + Negative => UR_Is_Negative (X)); + + elsif Adjustment >= 0 then + return X * Radix ** Adjustment; + else + return X / Radix ** (-Adjustment); + end if; + end Scaling; + + ---------- + -- Succ -- + ---------- + + function Succ (RT : R; X : T) return T is + Emin : constant UI := Machine_Emin_Value (RT); + Mantissa : constant UI := Machine_Mantissa_Value (RT); + Exp : UI := UI_Max (Emin, Exponent (RT, X)); + Frac : T; + New_Frac : T; + + begin + if UR_Is_Zero (X) then + Exp := Emin; + end if; + + -- Set exponent such that the radix point will be directly following the + -- mantissa after scaling. + + if Denorm_On_Target or Exp /= Emin then + Exp := Exp - Mantissa; + else + Exp := Exp - 1; + end if; + + Frac := Scaling (RT, X, -Exp); + New_Frac := Ceiling (RT, Frac); + + if New_Frac = Frac then + if New_Frac = Scaling (RT, -Ureal_1, Mantissa - 1) then + New_Frac := New_Frac + Scaling (RT, Ureal_1, Uint_Minus_1); + else + New_Frac := New_Frac + Ureal_1; + end if; + end if; + + return Scaling (RT, New_Frac, Exp); + end Succ; + + ---------------- + -- Truncation -- + ---------------- + + function Truncation (RT : R; X : T) return T is + pragma Warnings (Off, RT); + begin + return UR_From_Uint (UR_Trunc (X)); + end Truncation; + + ----------------------- + -- Unbiased_Rounding -- + ----------------------- + + function Unbiased_Rounding (RT : R; X : T) return T is + Abs_X : constant T := abs X; + Result : T; + Tail : T; + + begin + Result := Truncation (RT, Abs_X); + Tail := Abs_X - Result; + + if Tail > Ureal_Half then + Result := Result + Ureal_1; + + elsif Tail = Ureal_Half then + Result := Ureal_2 * + Truncation (RT, (Result / Ureal_2) + Ureal_Half); + end if; + + if UR_Is_Negative (X) then + return -Result; + elsif UR_Is_Positive (X) then + return Result; + + -- For zero case, make sure sign of zero is preserved + + else + return X; + end if; + end Unbiased_Rounding; + +end Eval_Fat; -- cgit v1.2.3