[Bug middle-end/33780] different results between O3 and O0

["dominiq at lps dot ens dot fr" <gcc-bugzilla@gcc.gnu.org>]

------- Comment #4 from dominiq at lps dot ens dot fr  2007-10-18 15:23 -------
> while we expand a constant integral power to an optimal (as of the count of
> multiplications / additions) series of multiplications and additions.

It seems the difference is coming from something else. I'll bet that with -O3
the powers are computed at compile time with some extra precision. At least it
is what I conclude from the following code:

  integer :: ia(16) = (/ 1, 1, 2, 2, 3, 3, 4, 4, 6, 5, 6, 6, 10, 7, 9, 8 /)
  real(8) :: a(16), b(16), c(16), d(16)
  real(16) :: e(16)
  real(8), parameter :: r=4.51556282882533D0
  a(1) = r
  a(2) = a(1)*a(1)
  a(3:4) = a(2)*a(1:2)
  a(5:8) = a(4)*a(1:4)
  a(9:16) = a(8)*a(1:8)
  b(1) = r
  do i = 2, 16
     b(i) = b(ia(i))*b(i-ia(i))
  end do
  e(1) = r
  e(2) = e(1)*e(1)
  e(3:4) = e(2)*e(1:2)
  e(5:8) = e(4)*e(1:4)
  e(9:16) = e(8)*e(1:8)
  d = real(e,8)
  do i=1, 16
     c(i) = r**i
  end do
  do i=1, 16
     print *, a(i)/d(i)-1.0d0, b(i)/d(i)-1.0d0, c(i)/d(i)-1.0d0
  end do
  print *
  print *, sum(abs(a/d-1.0d0)), sum(abs(b/d-1.0d0)), sum(abs(c/d-1.0d0)),
epsilon(r)
end

a stores the powers computed from the usual shift, b those computed from the
"optimal" tree (from gcc/builtins.c, c those computed from the power, and d the
values rounded from values with higher precision. At -O2 the output is:

   0.0000000000000000        0.0000000000000000        0.0000000000000000     
   0.0000000000000000        0.0000000000000000        0.0000000000000000     
   0.0000000000000000        0.0000000000000000        0.0000000000000000     
  2.22044604925031308E-016  2.22044604925031308E-016  2.22044604925031308E-016
  2.22044604925031308E-016  2.22044604925031308E-016  2.22044604925031308E-016
  2.22044604925031308E-016   0.0000000000000000       2.22044604925031308E-016
  2.22044604925031308E-016  2.22044604925031308E-016  2.22044604925031308E-016
  4.44089209850062616E-016  4.44089209850062616E-016  4.44089209850062616E-016
  2.22044604925031308E-016   0.0000000000000000       2.22044604925031308E-016
  4.44089209850062616E-016  2.22044604925031308E-016  4.44089209850062616E-016
  4.44089209850062616E-016  2.22044604925031308E-016  4.44089209850062616E-016
  4.44089209850062616E-016   0.0000000000000000       4.44089209850062616E-016
  4.44089209850062616E-016  4.44089209850062616E-016  4.44089209850062616E-016
  4.44089209850062616E-016  2.22044604925031308E-016  4.44089209850062616E-016
  6.66133814775093924E-016   0.0000000000000000       6.66133814775093924E-016
  6.66133814775093924E-016  6.66133814775093924E-016  6.66133814775093924E-016

  5.10702591327572009E-015  2.88657986402540701E-015  5.10702591327572009E-015 
2.22044604925031308E-016

a and c are equal, while at -O3 the output is

   0.0000000000000000        0.0000000000000000        0.0000000000000000     
   0.0000000000000000        0.0000000000000000        0.0000000000000000     
   0.0000000000000000        0.0000000000000000        0.0000000000000000     
  2.22044604925031308E-016  2.22044604925031308E-016   0.0000000000000000     
  2.22044604925031308E-016  2.22044604925031308E-016   0.0000000000000000     
  2.22044604925031308E-016   0.0000000000000000        0.0000000000000000     
  2.22044604925031308E-016  2.22044604925031308E-016   0.0000000000000000     
  4.44089209850062616E-016  4.44089209850062616E-016   0.0000000000000000     
  2.22044604925031308E-016   0.0000000000000000        0.0000000000000000     
  4.44089209850062616E-016  2.22044604925031308E-016   0.0000000000000000     
  4.44089209850062616E-016  2.22044604925031308E-016   0.0000000000000000     
  4.44089209850062616E-016   0.0000000000000000        0.0000000000000000     
  4.44089209850062616E-016  4.44089209850062616E-016   0.0000000000000000     
  4.44089209850062616E-016  2.22044604925031308E-016   0.0000000000000000     
  6.66133814775093924E-016   0.0000000000000000        0.0000000000000000     
  6.66133814775093924E-016  6.66133814775093924E-016   0.0000000000000000     

  5.10702591327572009E-015  2.88657986402540701E-015   0.0000000000000000      
2.22044604925031308E-016

c and d are equal. If the difference were coming only from the "optimal" tree,
c should be equal to b.


-- 


http://gcc.gnu.org/bugzilla/show_bug.cgi?id=33780