From 952c5c128f9efaea89d41d882c4ea3ade7df4591 Mon Sep 17 00:00:00 2001 From: zakk Date: Fri, 26 Aug 2005 04:48:05 +0000 Subject: Itsa me, quake3io! git-svn-id: svn://svn.icculus.org/quake3/trunk@2 edf5b092-35ff-0310-97b2-ce42778d08ea --- lcc/alpha/osf/tst/paranoia.1bk | 195 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 195 insertions(+) create mode 100755 lcc/alpha/osf/tst/paranoia.1bk (limited to 'lcc/alpha/osf/tst/paranoia.1bk') diff --git a/lcc/alpha/osf/tst/paranoia.1bk b/lcc/alpha/osf/tst/paranoia.1bk new file mode 100755 index 0000000..c74a883 --- /dev/null +++ b/lcc/alpha/osf/tst/paranoia.1bk @@ -0,0 +1,195 @@ +Lest this program stop prematurely, i.e. before displaying + + `END OF TEST', + +try to persuade the computer NOT to terminate execution when an +error like Over/Underflow or Division by Zero occurs, but rather +to persevere with a surrogate value after, perhaps, displaying some +warning. If persuasion avails naught, don't despair but run this +program anyway to see how many milestones it passes, and then +amend it to make further progress. + +Answer questions with Y, y, N or n (unless otherwise indicated). + + +Diagnosis resumes after milestone Number 0 Page: 1 + +Users are invited to help debug and augment this program so it will +cope with unanticipated and newly uncovered arithmetic pathologies. + +Please send suggestions and interesting results to + Richard Karpinski + Computer Center U-76 + University of California + San Francisco, CA 94143-0704, USA + +In doing so, please include the following information: + Precision: double; + Version: 10 February 1989; + Computer: + + Compiler: + + Optimization level: + + Other relevant compiler options: + +Diagnosis resumes after milestone Number 1 Page: 2 + +Running this program should reveal these characteristics: + Radix = 1, 2, 4, 8, 10, 16, 100, 256 ... + Precision = number of significant digits carried. + U2 = Radix/Radix^Precision = One Ulp + (OneUlpnit in the Last Place) of 1.000xxx . + U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 . + Adequacy of guard digits for Mult., Div. and Subt. + Whether arithmetic is chopped, correctly rounded, or something else + for Mult., Div., Add/Subt. and Sqrt. + Whether a Sticky Bit used correctly for rounding. + UnderflowThreshold = an underflow threshold. + E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy. + V = an overflow threshold, roughly. + V0 tells, roughly, whether Infinity is represented. + Comparisions are checked for consistency with subtraction + and for contamination with pseudo-zeros. + Sqrt is tested. Y^X is not tested. + Extra-precise subexpressions are revealed but NOT YET tested. + Decimal-Binary conversion is NOT YET tested for accuracy. + +Diagnosis resumes after milestone Number 2 Page: 3 + +The program attempts to discriminate among + FLAWs, like lack of a sticky bit, + Serious DEFECTs, like lack of a guard digit, and + FAILUREs, like 2+2 == 5 . +Failures may confound subsequent diagnoses. + +The diagnostic capabilities of this program go beyond an earlier +program called `MACHAR', which can be found at the end of the +book `Software Manual for the Elementary Functions' (1980) by +W. J. Cody and W. Waite. Although both programs try to discover +the Radix, Precision and range (over/underflow thresholds) +of the arithmetic, this program tries to cope with a wider variety +of pathologies, and to say how well the arithmetic is implemented. + +The program is based upon a conventional radix representation for +floating-point numbers, but also allows logarithmic encoding +as used by certain early WANG machines. + +BASIC version of this program (C) 1983 by Prof. W. M. Kahan; +see source comments for more history. + +Diagnosis resumes after milestone Number 3 Page: 4 + +Program is now RUNNING tests on small integers: +-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K. + +Searching for Radix and Precision. +Radix = 2.000000 . +Closest relative separation found is U1 = 1.1102230e-16 . + +Recalculating radix and precision + confirms closest relative separation U1 . +Radix confirmed. +The number of significant digits of the Radix is 53.000000 . + +Diagnosis resumes after milestone Number 30 Page: 5 + +Subtraction appears to be normalized, as it should be. +Checking for guard digit in *, /, and -. + *, /, and - appear to have guard digits, as they should. + +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. + +Running test of square root(x). +Testing if sqrt(X * X) == X for 20 Integers X. +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. + +Diagnosis resumes after milestone Number 90 Page: 7 + +Testing powers Z^i for small Integers Z and i. +... no discrepancis found. + +Seeking Underflow thresholds UfThold and E0. +Smallest strictly positive number found is E0 = 2.22507e-308 . +Since comparison denies Z = 0, evaluating (Z + Z) / Z should be safe. +What the machine gets for (Z + Z) / Z is 2.00000000000000000e+00 . +This is O.K., provided Over/Underflow has NOT just been signaled. + +Diagnosis resumes after milestone Number 120 Page: 8 + + +FLAW: X = 3.05947655544740190e-308 + is not equal to Z = 2.22507385850720140e-308 . +yet X - Z yields 0.00000000000000000e+00 . + Should this NOT signal Underflow, this is a SERIOUS DEFECT +that causes confusion when innocent statements like + if (X == Z) ... else ... (f(X) - f(Z)) / (X - Z) ... +encounter Division by Zero although actually +X / Z = 1 + 0.375 . +The Underflow threshold is 2.22507385850720140e-308, below which +calculation may suffer larger Relative error than merely roundoff. +Since underflow occurs below the threshold +UfThold = (2.00000000000000000e+00) ^ (-1.02200000000000000e+03) +only underflow should afflict the expression + (2.00000000000000000e+00) ^ (-1.02200000000000000e+03); +actually calculating yields: 0.00000000000000000e+00 . +This computed value is O.K. + +Testing X^((X + 1) / (X - 1)) vs. exp(2) = 7.38905609893065220e+00 as X -> 1. +Accuracy seems adequate. +Testing powers Z^Q at four nearly extreme values. + ... no discrepancies found. + + +Diagnosis resumes after milestone Number 160 Page: 9 + +Searching for Overflow threshold: +This may generate an error. + +* * * FLOATING-POINT ERROR * * * +Can `Z = -Y' overflow? +Trying it on Y = -8.98846567431157950e+307 . +Seems O.K. +Overflow threshold is V = 1.79769313486231570e+308 . +There is no saturation value because the system traps on overflow. +No Overflow should be signaled for V * 1 = 1.79769313486231570e+308 + nor for V / 1 = 1.79769313486231570e+308 . +Any overflow signal separating this * from the one +above is a DEFECT. + + +Diagnosis resumes after milestone Number 190 Page: 10 + + +What message and/or values does Division by Zero produce? + Trying to compute 1 / 0 produces ... +* * * FLOATING-POINT ERROR * * * + + Trying to compute 0 / 0 produces ... +* * * FLOATING-POINT ERROR * * * + +Diagnosis resumes after milestone Number 220 Page: 11 + + + +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! + +A total of 3 floating point exceptions were registered. +END OF TEST. -- cgit v1.2.3