Kahan's Floating Point Test "Paranoia"

[Michael Price <mprice at atl dot lmco dot com>]

The other day I ran Kahan's Floating Point Test "Paranoia" from
http://www.netlib.org/paranoia/index.html on two different platforms. One
was Linux 2.2.14 on a Pentium III with gcc version 3.0 20010526 (prerelease)
while the other was FreeBSD 4.3-STABLE on an AMD Thunderbird with gcc
version 3.0 20010526 (prerelease).

The FreeBSD machine passed but the Linux machine didn't. A diff of the
output from each test is shown below. Is this expected behavior?

*** freebsd.out	Wed May 30 10:11:36 2001
--- linux.out	Wed May 30 10:10:08 2001
***************
*** 96,101 ****
--- 96,105 ----
   confirms closest relative separation U1 .
  Radix confirmed.
  The number of significant digits of the Radix is 53.000000 .
+ Some subexpressions appear to be calculated extra
+ precisely with about 11 extra B-digits, i.e.
+ roughly 3.31133 extra significant decimals.
+ That feature is not tested further by this program.
  
  To continue, press RETURN
  Diagnosis resumes after milestone Number 30          Page: 5
***************
*** 108,118 ****
  Diagnosis resumes after milestone Number 40          Page: 6
  
  Checking rounding on multiply, divide and add/subtract.
! Multiplication appears to round correctly.
! Division appears to round correctly.
! Addition/Subtraction appears to round correctly.
! Checking for sticky bit.
! Sticky bit apparently used correctly.
  
  Does Multiplication commute?  Testing on 20 random pairs.
       No failures found in 20 integer pairs.
--- 112,123 ----
  Diagnosis resumes after milestone Number 40          Page: 6
  
  Checking rounding on multiply, divide and add/subtract.
! * is neither chopped nor correctly rounded.
! / is neither chopped nor correctly rounded.
! Addition/Subtraction neither rounds nor chops.
! Sticky bit used incorrectly or not at all.
! FLAW:  lack(s) of guard digits or failure(s) to correctly round or chop
! (noted above) count as one flaw in the final tally below.
  
  Does Multiplication commute?  Testing on 20 random pairs.
       No failures found in 20 integer pairs.
***************
*** 122,128 ****
  Test for sqrt monotonicity.
  sqrt has passed a test for Monotonicity.
  Testing whether sqrt is rounded or chopped.
! Square root appears to be correctly rounded.
  
  To continue, press RETURN
  Diagnosis resumes after milestone Number 90          Page: 7
--- 127,134 ----
  Test for sqrt monotonicity.
  sqrt has passed a test for Monotonicity.
  Testing whether sqrt is rounded or chopped.
! Square root is neither chopped nor correctly rounded.
! Observed errors run from -5.0000000e-01 to 5.0000000e-01 ulps.
  
  To continue, press RETURN
  Diagnosis resumes after milestone Number 90          Page: 7
***************
*** 147,153 ****
  This computed value is O.K.
  
  Testing X^((X + 1) / (X - 1)) vs. exp(2) = 7.38905609893065218e+00 as X -> 1.
! Accuracy seems adequate.
  Testing powers Z^Q at four nearly extreme values.
   ... no discrepancies found.
  
--- 153,163 ----
  This computed value is O.K.
  
  Testing X^((X + 1) / (X - 1)) vs. exp(2) = 7.38905609893065218e+00 as X -> 1.
! DEFECT:  Calculated 7.38905609548934539e+00 for
! 	(1 + (-1.11022302462515654e-16) ^ (-1.80143985094819840e+16);
! 	differs from correct value by -3.44130679508225512e-09 .
! 	This much error may spoil financial
! 	calculations involving tiny interest rates.
  Testing powers Z^Q at four nearly extreme values.
   ... no discrepancies found.
  
***************
*** 183,191 ****
  Diagnosis resumes after milestone Number 220          Page: 10
  
  
  
! No failures, defects nor flaws have been discovered.
! Rounding appears to conform to the proposed IEEE standard P754,
! except for possibly Double Rounding during Gradual Underflow.
! The arithmetic diagnosed appears to be Excellent!
  END OF TEST.
--- 193,201 ----
  Diagnosis resumes after milestone Number 220          Page: 10
  
  
+ The number of  DEFECTs  discovered =         1.
+ The number of  FLAWs  discovered =           1.
  
! The arithmetic diagnosed may be Acceptable
! despite inconvenient Defects.
  END OF TEST.

-- 
Michael Price
Distributed Processing Lab; Lockheed Martin Adv. Tech. Labs
A&E 3W; 1 Federal Street; Camden, NJ 08102
856-338-4021, fax 856-338-4144  email: mprice@atl.lmco.com