-- --
-- B o d y --
-- --
--- Copyright (C) 1992-2002 Free Software Foundation, Inc. --
+-- Copyright (C) 1992-2004 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- --
pragma Inline ("+");
-- Length doubling additions
- function "-" (A : Uns64; B : Uns32) return Uns64;
- pragma Inline ("-");
- -- Length doubling subtraction
-
function "*" (A, B : Uns32) return Uns64;
pragma Inline ("*");
-- Length doubling multiplication
pragma Inline ("&");
-- Concatenate hi, lo values to form 64-bit result
+ function Le3 (X1, X2, X3 : Uns32; Y1, Y2, Y3 : Uns32) return Boolean;
+ -- Determines if 96 bit value X1&X2&X3 <= Y1&Y2&Y3
+
function Lo (A : Uns64) return Uns32;
pragma Inline (Lo);
-- Low order half of 64-bit value
pragma Inline (Hi);
-- High order half of 64-bit value
+ procedure Sub3 (X1, X2, X3 : in out Uns32; Y1, Y2, Y3 : in Uns32);
+ -- Computes X1&X2&X3 := X1&X2&X3 - Y1&Y1&Y3 with mod 2**96 wrap
+
function To_Neg_Int (A : Uns64) return Int64;
-- Convert to negative integer equivalent. If the input is in the range
-- 0 .. 2 ** 63, then the corresponding negative signed integer (obtained
return A + Uns64 (B);
end "+";
- ---------
- -- "-" --
- ---------
-
- function "-" (A : Uns64; B : Uns32) return Uns64 is
- begin
- return A - Uns64 (B);
- end "-";
-
---------
-- "/" --
---------
return Uns32 (Shift_Right (A, 32));
end Hi;
+ ---------
+ -- Le3 --
+ ---------
+
+ function Le3 (X1, X2, X3 : Uns32; Y1, Y2, Y3 : Uns32) return Boolean is
+ begin
+ if X1 < Y1 then
+ return True;
+ elsif X1 > Y1 then
+ return False;
+ elsif X2 < Y2 then
+ return True;
+ elsif X2 > Y2 then
+ return False;
+ else
+ return X3 <= Y3;
+ end if;
+ end Le3;
+
--------
-- Lo --
--------
Zhi : Uns32 := Hi (Zu);
Zlo : Uns32 := Lo (Zu);
- D1, D2, D3, D4 : Uns32;
- -- The dividend, four digits (D1 is high order)
+ D : array (1 .. 4) of Uns32;
+ -- The dividend, four digits (D(1) is high order)
- Q1, Q2 : Uns32;
- -- The quotient, two digits (Q1 is high order)
+ Qd : array (1 .. 2) of Uns32;
+ -- The quotient digits, two digits (Qd(1) is high order)
S1, S2, S3 : Uns32;
-- Value to subtract, three digits (S1 is high order)
-- First do the multiplication, giving the four digit dividend
T1 := Xlo * Ylo;
- D4 := Lo (T1);
- D3 := Hi (T1);
+ D (4) := Lo (T1);
+ D (3) := Hi (T1);
if Yhi /= 0 then
T1 := Xlo * Yhi;
- T2 := D3 + Lo (T1);
- D3 := Lo (T2);
- D2 := Hi (T1) + Hi (T2);
+ T2 := D (3) + Lo (T1);
+ D (3) := Lo (T2);
+ D (2) := Hi (T1) + Hi (T2);
if Xhi /= 0 then
T1 := Xhi * Ylo;
- T2 := D3 + Lo (T1);
- D3 := Lo (T2);
- T3 := D2 + Hi (T1);
+ T2 := D (3) + Lo (T1);
+ D (3) := Lo (T2);
+ T3 := D (2) + Hi (T1);
T3 := T3 + Hi (T2);
- D2 := Lo (T3);
- D1 := Hi (T3);
+ D (2) := Lo (T3);
+ D (1) := Hi (T3);
- T1 := (D1 & D2) + Uns64'(Xhi * Yhi);
- D1 := Hi (T1);
- D2 := Lo (T1);
+ T1 := (D (1) & D (2)) + Uns64'(Xhi * Yhi);
+ D (1) := Hi (T1);
+ D (2) := Lo (T1);
else
- D1 := 0;
+ D (1) := 0;
end if;
else
if Xhi /= 0 then
T1 := Xhi * Ylo;
- T2 := D3 + Lo (T1);
- D3 := Lo (T2);
- D2 := Hi (T1) + Hi (T2);
+ T2 := D (3) + Lo (T1);
+ D (3) := Lo (T2);
+ D (2) := Hi (T1) + Hi (T2);
else
- D2 := 0;
+ D (2) := 0;
end if;
- D1 := 0;
+ D (1) := 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
+ if D (1) /= 0 or else D (2) >= Zlo then
Raise_Error;
-- Here we are dividing at most three digits by one digit
else
- T1 := D2 & D3;
- T2 := Lo (T1 rem Zlo) & D4;
+ T1 := D (2) & D (3);
+ T2 := Lo (T1 rem Zlo) & D (4);
Qu := Lo (T1 / Zlo) & Lo (T2 / Zlo);
Ru := T2 rem Zlo;
-- If divisor is double digit and too large, raise error
- elsif (D1 & D2) >= Zu then
+ elsif (D (1) & D (2)) >= Zu then
Raise_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
+ -- multiple division algorithm (see section (4.3.1) of Knuth's "The Art
-- of Computer Programming", Vol. 2 for a description (algorithm D).
else
-- 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;
+ -- not change the invariant that (D (1) & D (2)) >= Zu.
+
+ T1 := Shift_Left (D (1) & D (2), Scale);
+ D (1) := Hi (T1);
+ T2 := Shift_Left (0 & D (3), Scale);
+ D (2) := Lo (T1) or Hi (T2);
+ T3 := Shift_Left (0 & D (4), Scale);
+ D (3) := Lo (T2) or Hi (T3);
+ D (4) := Lo (T3);
+
+ -- Loop to compute quotient digits, runs twice for Qd(1) and Qd(2).
+
+ for J in 0 .. 1 loop
+
+ -- Compute next quotient digit. We have to divide three digits by
+ -- two digits. 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 D (J + 1) = Zhi then
+ Qd (J + 1) := 2 ** 32 - 1;
+ else
+ Qd (J + 1) := Lo ((D (J + 1) & D (J + 2)) / Zhi);
end if;
- Q1 := Q1 - 1;
+ -- Compute amount to subtract
- T1 := (S2 & S3) - Zlo;
+ T1 := Qd (J + 1) * Zlo;
+ T2 := Qd (J + 1) * Zhi;
S3 := Lo (T1);
- T1 := (S1 & S2) - Zhi;
+ T1 := Hi (T1) + Lo (T2);
S2 := Lo (T1);
- S1 := Hi (T1);
- end loop;
+ S1 := Hi (T1) + Hi (T2);
- -- Subtract from dividend (note: do not bother to set D1 to
- -- zero, since it is no longer needed in the calculation).
+ -- Adjust quotient digit if it was too high
- T1 := (D2 & D3) - S3;
- D3 := Lo (T1);
- T1 := (D1 & Hi (T1)) - S2;
- D2 := Lo (T1);
+ loop
+ exit when Le3 (S1, S2, S3, D (J + 1), D (J + 2), D (J + 3));
+ Qd (J + 1) := Qd (J + 1) - 1;
+ Sub3 (S1, S2, S3, 0, Zhi, Zlo);
+ end loop;
- -- Compute second quotient digit in same manner
+ -- Now subtract S1&S2&S3 from D1&D2&D3 ready for next step
- 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);
+ Sub3 (D (J + 1), D (J + 2), D (J + 3), S1, S2, S3);
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
+ -- scaled division is in D3&D4. To get the remainder for the
-- original unscaled division, we rescale this dividend.
+
-- We rescale the divisor as well, to make the proper comparison
-- for rounding below.
- Qu := Q1 & Q2;
- Ru := Shift_Right (D3 & D4, Scale);
+ Qu := Qd (1) & Qd (2);
+ Ru := Shift_Right (D (3) & D (4), Scale);
Zu := Shift_Right (Zu, Scale);
end if;
Q := To_Pos_Int (Qu);
end if;
end if;
-
end Scaled_Divide;
+ ----------
+ -- Sub3 --
+ ----------
+
+ procedure Sub3 (X1, X2, X3 : in out Uns32; Y1, Y2, Y3 : in Uns32) is
+ begin
+ if Y3 > X3 then
+ if X2 = 0 then
+ X1 := X1 - 1;
+ end if;
+
+ X2 := X2 - 1;
+ end if;
+
+ X3 := X3 - Y3;
+
+ if Y2 > X2 then
+ X1 := X1 - 1;
+ end if;
+
+ X2 := X2 - Y2;
+ X1 := X1 - Y1;
+ end Sub3;
+
-------------------------------
-- Subtract_With_Ovflo_Check --
-------------------------------
-- --
-- S p e c --
-- --
--- Copyright (C) 1994,1995,1996 Free Software Foundation, Inc. --
+-- Copyright (C) 1992-2004, 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- --
function Multiply_With_Ovflo_Check (X, Y : Int64) return Int64;
-- Raises Constraint_Error if product of operands overflows 64
- -- bits, otherwise returns the 64-bit signed integer difference.
+ -- bits, otherwise returns the 64-bit signed integer product.
procedure Scaled_Divide
(X, Y, Z : Int64;
Q, R : out Int64;
Round : Boolean);
-- Performs the division X / (Y * Z), storing the quotient in Q and
- -- the remainder in R. Constraint_Error is raised if Y or Z is zero.
- -- Round indicates if the result should be rounded. If Round is False,
- -- then Q, R are the normal quotient and remainder from a truncating
- -- division. If Round is True, then Q is the rounded quotient. The
- -- remainder R is not affected by the setting of the Round flag. The
- -- result is known to be in range except for the noted possibility of
- -- Y or Z being zero, so no other overflow checks are required.
+ -- the remainder in R. Constraint_Error is raised if Y or Z is zero,
+ -- or if the quotient does not fit in 64-bits. Round indicates if the
+ -- result should be rounded. If Round is False, then Q, R are the normal
+ -- quotient and remainder from a truncating division. If Round is True,
+ -- then Q is the rounded quotient. The remainder R is not affected by the
+ -- setting of the Round flag.
end System.Arith_64;
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