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Wrap

Text File | 1995-10-17 | 16.7 KB | 667 lines

------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- S Y S T E M . A R I T H _ 6 4 -- -- -- -- B o d y -- -- -- -- $Revision: 1.2 $ -- -- -- -- The GNAT library is free software; you can redistribute it and/or modify -- -- it under terms of the GNU Library General Public License as published by -- -- the Free Software Foundation; either version 2, or (at your option) any -- -- later version. The GNAT library is distributed in the hope that it will -- -- be useful, but WITHOUT ANY WARRANTY; without even the implied warranty -- -- of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -- -- Library General Public License for more details. You should have -- -- received a copy of the GNU Library General Public License along with -- -- the GNAT library; see the file COPYING.LIB. If not, write to the Free -- -- Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. -- -- -- ------------------------------------------------------------------------------ with Text_IO; use Text_IO; with Interfaces; use Interfaces; with Unchecked_Conversion; package body System.Arith_64 is pragma Suppress (Overflow_Check); pragma Suppress (Range_Check); subtype Uns64 is Unsigned_64; function To_Uns is new Unchecked_Conversion (Int64, Uns64); function To_Int is new Unchecked_Conversion (Uns64, Int64); subtype Uns32 is Unsigned_32; ----------------------- -- Local Subprograms -- ----------------------- function "+" (A, B : Uns32) return Uns64; function "+" (A : Uns64; B : Uns32) return Uns64; pragma Inline ("+"); -- Length doubling additions function "-" (A : Uns64; B : Uns32) return Uns64; pragma Inline ("-"); -- Length doubling subtraction function "*" (A, B : Uns32) return Uns64; function "*" (A : Uns64; B : Uns32) return Uns64; pragma Inline ("*"); -- Length doubling multiplications function "/" (A : Uns64; B : Uns32) return Uns64; pragma Inline ("/"); -- Length doubling division function "rem" (A : Uns64; B : Uns32) return Uns64; pragma Inline ("rem"); -- Length doubling remainder function "&" (Hi, Lo : Uns32) return Uns64; pragma Inline ("&"); -- Concatenate hi, lo values to form 64-bit result function Lo (A : Uns64) return Uns32; pragma Inline (Lo); -- Low order half of 64-bit value function Hi (A : Uns64) return Uns32; pragma Inline (Hi); -- High order half of 64 bit value --------- -- "+" -- --------- function "+" (A, B : Uns32) return Uns64 is begin return Uns64 (A) + Uns64 (B); end "+"; function "+" (A : Uns64; B : Uns32) return Uns64 is begin return A + Uns64 (B); end "+"; --------- -- "-" -- --------- function "-" (A : Uns64; B : Uns32) return Uns64 is begin return A - Uns64 (B); end "-"; --------- -- "*" -- --------- function "*" (A, B : Uns32) return Uns64 is begin return Uns64 (A) * Uns64 (B); end "*"; function "*" (A : Uns64; B : Uns32) return Uns64 is begin return A * Uns64 (B); end "*"; --------- -- "/" -- --------- function "/" (A : Uns64; B : Uns32) return Uns64 is begin return A / Uns64 (B); end "/"; ----------- -- "rem" -- ----------- function "rem" (A : Uns64; B : Uns32) return Uns64 is begin return A rem Uns64 (B); end "rem"; --------- -- "&" -- --------- function "&" (Hi, Lo : Uns32) return Uns64 is begin return Shift_Left (Uns64 (Hi), 32) or Uns64 (Lo); end "&"; -------- -- Hi -- -------- function Hi (A : Uns64) return Uns32 is begin return Uns32 (Shift_Right (A, 32)); end Hi; -------- -- Lo -- -------- function Lo (A : Uns64) return Uns32 is begin return Uns32 (A and 16#FFFF_FFFF#); end Lo; -------------------------- -- Add_With_Ovflo_Check -- -------------------------- function Add_With_Ovflo_Check (X, Y : Int64) return Int64 is R : constant Int64 := To_Int (To_Uns (X) + To_Uns (Y)); begin if X >= 0 then if Y < 0 or else R >= 0 then return R; end if; else -- X < 0 if Y > 0 or else R < 0 then return R; end if; end if; raise Constraint_Error; end Add_With_Ovflo_Check; ----------------------------- -- Divide_With_Ovflo_Check -- ----------------------------- function Divide_With_Ovflo_Check (X, Y : Int64) return Int64 is begin if Y = 0 or else (Y = (-1) and then X = (-(2 ** 63))) then raise Constraint_Error; else return X / Y; end if; end Divide_With_Ovflo_Check; ------------------- -- Double_Divide -- ------------------- procedure Double_Divide (X, Y, Z : Int64; Q, R : out Int64; Round : Boolean) is Xu : constant Uns64 := To_Uns (abs X); Xhi : constant Uns32 := Hi (Xu); Xlo : constant Uns32 := Lo (Xu); Yu : constant Uns64 := To_Uns (abs Y); Yhi : constant Uns32 := Hi (Yu); Ylo : constant Uns32 := Lo (Yu); Zu : constant Uns64 := To_Uns (abs Z); Zhi : constant Uns32 := Hi (Zu); Zlo : constant Uns32 := Lo (Zu); T1, T2 : Uns64; Du, Qu, Ru : Uns64; Den_Pos : Boolean; begin if Yu = 0 or else Zu = 0 then raise Constraint_Error; end if; -- Compute Y * Z. Note that if the result overflows 64 bits unsigned, -- then the rounded result is clearly zero (since the dividend is at -- most 2**63 - 1, the extra bit of precision is nice here!) if Yhi /= 0 then if Zhi /= 0 then Q := 0; R := X; return; else T2 := Yhi * Zlo; end if; else if Zhi /= 0 then T2 := Ylo * Zhi; else T2 := 0; end if; end if; T1 := Xlo * Ylo; T2 := T2 + Hi (T1); if Hi (T2) /= 0 then Q := 0; R := X; return; end if; Du := Lo (T2) & Lo (T1); Qu := Xu / Du; Ru := Xu rem Du; -- Deal with rounding case if Round and then Ru > (Du - 1) / 2 then Qu := Qu + 1; end if; -- Set final signs (RM 4.5.5(27-30)) Den_Pos := (Y < 0) = (Z < 0); -- Case of dividend (X) sign positive if X >= 0 then R := To_Int (Ru); if Den_Pos then Q := To_Int (Qu); else Q := -To_Int (Qu); end if; -- Case of dividend (X) sign negative else R := -To_Int (Ru); if Den_Pos then Q := -To_Int (Qu); else Q := To_Int (Qu); end if; end if; end Double_Divide; ------------------------------- -- Multiply_With_Ovflo_Check -- ------------------------------- function Multiply_With_Ovflo_Check (X, Y : Int64) return Int64 is Xu : constant Uns64 := To_Uns (abs X); Xhi : constant Uns32 := Hi (Xu); Xlo : constant Uns32 := Lo (Xu); Yu : constant Uns64 := To_Uns (abs Y); Yhi : constant Uns32 := Hi (Yu); Ylo : constant Uns32 := Lo (Yu); T1, T2 : Uns64; begin if Xhi /= 0 then if Yhi /= 0 then raise Constraint_Error; else T2 := Xhi * Ylo; end if; else if Yhi /= 0 then T2 := Xlo * Yhi; else return X * Y; end if; end if; T1 := Xlo * Ylo; T2 := T2 + Hi (T1); if Hi (T2) /= 0 then raise Constraint_Error; end if; T2 := Lo (T2) & Lo (T1); if X >= 0 then if Y >= 0 then return To_Int (T2); else return -To_Int (T2); end if; else -- X < 0 if Y < 0 then return To_Int (T2); else return -To_Int (T2); end if; end if; end Multiply_With_Ovflo_Check; ------------------- -- Scaled_Divide -- ------------------- procedure Scaled_Divide (X, Y, Z : Int64; Q, R : out Int64; Round : Boolean) is Xu : constant Uns64 := To_Uns (abs X); Xhi : constant Uns32 := Hi (Xu); Xlo : constant Uns32 := Lo (Xu); Yu : constant Uns64 := To_Uns (abs Y); Yhi : constant Uns32 := Hi (Yu); Ylo : constant Uns32 := Lo (Yu); Zu : Uns64 := To_Uns (abs Z); Zhi : Uns32 := Hi (Zu); Zlo : Uns32 := Lo (Zu); D1, D2, D3, D4 : Uns32; -- The dividend, four digits (D1 is high order) Q1, Q2 : Uns32; -- The quotient, two digits (Q1 is high order) S1, S2, S3 : Uns32; -- Value to subtract, three digits (S1 is high order) Qu : Uns64; Ru : Uns64; -- Unsigned quotient and remainder Scale : Natural; -- Scaling factor used for multiple-precision divide. Dividend and -- Divisor are multiplied by 2 ** Scale, and the final remainder -- is divided by the scaling factor. The reason for this scaling -- is to allow more accurate estimation of quotient digits. T1, T2, T3 : Uns64; -- Temporary values begin -- First do the multiplication, giving the four digit dividend T1 := Xlo * Ylo; D4 := Lo (T1); D3 := Hi (T1); if Yhi /= 0 then T1 := Xlo * Yhi; T2 := D3 + Lo (T1); D3 := Lo (T2); D2 := Hi (T1) + Hi (T2); if Xhi /= 0 then T1 := Xhi * Ylo; T2 := D3 + Lo (T1); D3 := Lo (T2); T3 := D2 + Hi (T1); T3 := T3 + Hi (T2); D2 := Lo (T3); D1 := Hi (T3); T1 := (D1 & D2) + (Xhi * Yhi); D1 := Hi (T1); D2 := Lo (T1); else D1 := 0; end if; else if Xhi /= 0 then T1 := Xhi * Ylo; T2 := D3 + Lo (T1); D3 := Lo (T2); D2 := Hi (T1) + Hi (T2); else D2 := 0; end if; D1 := 0; end if; -- Now it is time for the dreaded multiple precision division. First -- an easy case, check for the simple case of a one digit divisor. if Zhi = 0 then if D1 /= 0 or else D2 >= Zlo then raise Constraint_Error; -- Here we are dividing at most three digits by one digit else T1 := D2 & D3; T2 := Lo (T1 rem Zlo) & D4; Qu := Lo (T1 / Zlo) & Lo (T2 / Zlo); Ru := T2 rem Zlo; end if; -- If divisor is double digit and too large, raise error elsif (D1 & D2) >= Zu then raise Constraint_Error; -- This is the complex case where we definitely have a double digit -- divisor and a dividend of at least three digits. We use the classical -- multiple division algorithm (see section (4.3.1) of Knuth's "The Art -- of Computer Programming", Vol. 2 for a description (algorithm D). else -- First normalize the divisor so that it has the leading bit on. -- We do this by finding the appropriate left shift amount. Scale := 0; if (Zhi and 16#FFFF0000#) = 0 then Scale := 16; Zu := Shift_Left (Zu, 16); end if; if (Hi (Zu) and 16#FF00_0000#) = 0 then Scale := Scale + 8; Zu := Shift_Left (Zu, 8); end if; if (Hi (Zu) and 16#F000_0000#) = 0 then Scale := Scale + 4; Zu := Shift_Left (Zu, 4); end if; if (Hi (Zu) and 16#C000_0000#) = 0 then Scale := Scale + 2; Zu := Shift_Left (Zu, 2); end if; if (Hi (Zu) and 16#8000_0000#) = 0 then Scale := Scale + 1; Zu := Shift_Left (Zu, 1); end if; Zhi := Hi (Zu); Zlo := Lo (Zu); -- Note that when we scale up the dividend, it still fits in four -- digits, since we already tested for overflow, and scaling does -- not change the invariant that (D1 & D2) >= Zu. T1 := Shift_Left (D1 & D2, Scale); D1 := Hi (T1); T2 := Shift_Left (0 & D3, Scale); D2 := Lo (T1) or Hi (T2); T3 := Shift_Left (0 & D4, Scale); D3 := Lo (T2) or Hi (T3); D4 := Lo (T3); -- Compute first quotient digit. We have to divide three digits by -- two digits, and we estimate the quotient by dividing the leading -- two digits by the leading digit. Given the scaling we did above -- which ensured the first bit of the divisor is set, this gives an -- estimate of the quotient that is at most two too high. if D1 = Zhi then Q1 := 2 ** 32 - 1; else Q1 := Lo ((D1 & D2) / Zhi); end if; -- Compute amount to subtract T1 := Q1 * Zlo; T2 := Q1 * Zhi; S3 := Lo (T1); T1 := Hi (T1) + Lo (T2); S2 := Lo (T1); S1 := Hi (T1) + Hi (T2); -- Adjust quotient digit if it was too high loop exit when S1 < D1; if S1 = D1 then exit when S2 < D2; if S2 = D2 then exit when S3 <= D3; end if; end if; Q1 := Q1 - 1; T1 := (S2 & S3) - Zlo; S3 := Lo (T1); T1 := (S1 & S2) - Zhi; S2 := Lo (T1); S1 := Hi (T1); end loop; -- Subtract from dividend (note: do not bother to set D1 to -- zero, since it is no longer needed in the calculation). T1 := (D2 & D3) - S3; D3 := Lo (T1); T1 := (D1 & Hi (T1)) - S2; D2 := Lo (T1); -- Compute second quotient digit in same manner if D2 = Zhi then Q2 := 2 ** 32 - 1; else Q2 := Lo ((D2 & D3) / Zhi); end if; T1 := Q2 * Zlo; T2 := Q2 * Zhi; S3 := Lo (T1); T1 := Hi (T1) + Lo (T2); S2 := Lo (T1); S1 := Hi (T1) + Hi (T2); loop exit when S1 < D2; if S1 = D2 then exit when S2 < D3; if S2 = D3 then exit when S3 <= D4; end if; end if; Q2 := Q2 - 1; T1 := (S2 & S3) - Zlo; S3 := Lo (T1); T1 := (S1 & S2) - Zhi; S2 := Lo (T1); S1 := Hi (T1); end loop; T1 := (D3 & D4) - S3; D4 := Lo (T1); T1 := (D2 & Hi (T1)) - S2; D3 := Lo (T1); -- The two quotient digits are now set, and the remainder of the -- scaled division is in (D3 & D4). To get the remainder for the -- original unscaled division, we rescale this dividend. Qu := Q1 & Q2; Ru := Shift_Right (D3 & D4, Scale); end if; -- Deal with rounding case if Round and then Ru > (Zu - 1) / 2 then Qu := Qu + 1; end if; -- Set final signs (RM 4.5.5(27-30)) -- Case of dividend (X * Y) sign positive if (X >= 0 and then Y >= 0) or else (X < 0 and then Y < 0) then R := To_Int (Ru); if Z > 0 then Q := To_Int (Qu); else Q := -To_Int (Qu); end if; -- Case of dividend (X * Y) sign negative else R := -To_Int (Ru); if Z > 0 then Q := -To_Int (Qu); else Q := To_Int (Qu); end if; end if; end Scaled_Divide; ------------------------------- -- Subtract_With_Ovflo_Check -- ------------------------------- function Subtract_With_Ovflo_Check (X, Y : Int64) return Int64 is R : constant Int64 := To_Int (To_Uns (X) - To_Uns (Y)); begin if X >= 0 then if Y > 0 or else R >= 0 then return R; end if; else -- X < 0 if Y <= 0 or else R < 0 then return R; end if; end if; raise Constraint_Error; end Subtract_With_Ovflo_Check; end System.Arith_64;