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sem_prag.adb: Minor reformatting. 

2012-11-06  Robert Dewar  <dewar@adacore.com>

	* sem_prag.adb: Minor reformatting.

2012-11-06  Robert Dewar  <dewar@adacore.com>

	* s-bignum.adb (Div_Rem): Fix bug in step D3.
	* uintp.adb (UI_Div_Rem): Add comment on bug in step D3.

From-SVN: r193217
This commit is contained in:
Robert Dewar 2012-11-06 09:55:50 +00:00 committed by Arnaud Charlet
parent ed7b9d6ecf
commit 0ce1ec6465
4 changed files with 55 additions and 27 deletions
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9
gcc/ada/ChangeLog
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@ -1,3 +1,12 @@
2012-11-06 Robert Dewar <dewar@adacore.com>
* sem_prag.adb: Minor reformatting.
2012-11-06 Robert Dewar <dewar@adacore.com>
* s-bignum.adb (Div_Rem): Fix bug in step D3.
* uintp.adb (UI_Div_Rem): Add comment on bug in step D3.
2012-11-06 Hristian Kirtchev <kirtchev@adacore.com>
* exp_prag.adb (Expand_Pragma_Loop_Assertion): Update the comment

47
gcc/ada/s-bignum.adb
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@ -776,7 +776,9 @@ package body System.Bignums is
d : DD;
j : Length;
qhat : SD;
qhat : DD;
rhat : DD;
temp : DD;
begin
-- Initialize data of left and right operands
@ -847,26 +849,37 @@ package body System.Bignums is
-- Loop through digits
loop
-- Note: In the original printing, step D3 was as follows:
-- D3. [Calculate qhat.] If uj = v1, set qhat to b-l; otherwise
-- set qhat to (uj,uj+1)/v1.
-- set qhat to (uj,uj+1)/v1. Now test if v2 * qhat is greater than
-- (uj*b + uj+1 - qhat*v1)*b + uj+2. If so, decrease qhat by 1 and
-- repeat this test
if u (j) = v1 then
qhat := -1;
else
qhat := SD ((u (j) & u (j + 1)) / DD (v1));
end if;
-- This had a bug not discovered till 1995, see Vol 2 errata:
-- http://www-cs-faculty.stanford.edu/~uno/err2-2e.ps.gz. Under
-- rare circumstances the expression in the test could overflow.
-- The code below is the fixed version of this step.
-- D3 (continued). Now test if v2 * qhat is greater than (uj*b +
-- uj+1 - qhat*v1)*b + uj+2. If so, decrease qhat by 1 and repeat
-- this test, which determines at high speed most of the cases in
-- which the trial value qhat is one too large, and it eliminates
-- all cases where qhat is two too large.
-- D3. [Calculate qhat.] Set qhat to (uj,uj+1)/v1 and rhat to
-- to (uj,uj+1) mod v1.
while DD (v2) * DD (qhat) >
((u (j) & u (j + 1)) -
DD (qhat) * DD (v1)) * b + DD (u (j + 2))
temp := u (j) & u (j + 1);
qhat := temp / DD (v1);
rhat := temp mod DD (v1);
-- D3 (continued). Now test if qhat = b or v2*qhat > (rhat,uj+2):
-- if so, decrease qhat by 1, increase rhat by v1, and repeat this
-- test if rhat < b. [The test on v2 determines at at high speed
-- most of the cases in which the trial value qhat is one too
-- large, and eliminates all cases where qhat is two too large.]
while qhat = b
or else DD (v2) * qhat > LSD (rhat) & u (j + 2)
loop
qhat := qhat - 1;
rhat := rhat + DD (v1);
exit when rhat >= b;
end loop;
-- D4. [Multiply and subtract.] Replace (uj,uj+1..uj+n) by
@ -892,7 +905,7 @@ package body System.Bignums is
begin
Borrow := 0;
for K in reverse 1 .. n loop
Temp := DD (qhat) * DD (v (K)) + DD (Borrow);
Temp := qhat * DD (v (K)) + DD (Borrow);
Borrow := MSD (Temp);
if LSD (Temp) > u (j + K) then
@ -908,7 +921,7 @@ package body System.Bignums is
-- D5. [Test remainder.] Set qj = qhat. If the result of step
-- D4 was negative, we will do the add back step (step D6).
q (j) := qhat;
q (j) := LSD (qhat);
if Negative then

15
gcc/ada/sem_prag.adb
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@ -11289,16 +11289,13 @@ package body Sem_Prag is
--------------------
-- pragma Loop_Assertion
-- ( [Invariant =>] boolean_Expression
-- | [Invariant =>] boolean_Expression ,
-- Variant => TERMINATION_VARIANTS
-- | Variant => TERMINATION_VARIANTS );
--
-- TERMINATION_VARIANTS ::=
-- ( TERMINATION_VARIANT {, TERMINATION_VARIANT} )
--
-- ( [Invariant =>] boolean_Expression );
-- | ( [[Invariant =>] boolean_Expression ,]
-- Variant =>
-- ( TERMINATION_VARIANT {, TERMINATION_VARIANT ) );
-- TERMINATION_VARIANT ::= CHANGE_MODIFIER => discrete_EXPRESSION
--
-- CHANGE_MODIFIER ::= Increasing | Decreasing
when Pragma_Loop_Assertion => Loop_Assertion : declare

11
gcc/ada/uintp.adb
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@ -1216,6 +1216,15 @@ package body Uintp is
-- [ CALCULATE Q (hat) ] (step D3 in the algorithm)
-- Note: this version of step D3 is from the original published
-- algorithm, which is known to have a bug causing overflows.
-- See: http://www-cs-faculty.stanford.edu/~uno/err2-2e.ps.gz.
-- In this code we are safe since our representation of double
-- length numbers allows an expanded range.
-- We don't have a proof of this claim, but the only cases we
-- have found that show the bug in step D3 work fine here.
Tmp_Int := Dividend (J) * Base + Dividend (J + 1);
-- Initial guess
@ -1230,7 +1239,7 @@ package body Uintp is
while Divisor_Dig2 * Q_Guess >
(Tmp_Int - Q_Guess * Divisor_Dig1) * Base +
Dividend (J + 2)
Dividend (J + 2)
loop
Q_Guess := Q_Guess - 1;
end loop;