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*To*: gcc at gcc dot gnu dot org*Subject*: Kahan's Floating Point Test "Paranoia"*From*: Michael Price <mprice at atl dot lmco dot com>*Date*: Wed, 30 May 2001 10:17:00 -0400

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

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