On Thursday 17 June 2010 11:48:46 Pavel Pisa wrote:
I should find time to run paranoia FP test probably.
I will report results, when i find time.
I have managed to run paranoia.c test on real
ARM920T hardware with updated newlib-1.18.0
and GCC-4.4.4 compiled with default soft-float
parameters passing for system less environment.
No problem has been detected.
Double precision run
====================
paranoia version 1.1 [cygnus]
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: 1
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: 2
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: 3
Testing powers Z^i for small Integers Z and i.
... no discrepancies found.
Seeking Underflow thresholds UfThold and E0.
Smallest strictly positive number found is E0 = 4.94066e-324 .
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.
Underflow is gradual; it incurs Absolute Error =
(roundoff in UfThold)< E0.
The Underflow threshold is 2.22507385850720188e-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) ^ (-2.04400000000000000e+03);
actually calculating yields: 0.00000000000000000e+00 .
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.
Diagnosis resumes after milestone Number 160 Page: 4
Searching for Overflow threshold:
This may generate an error.
Can `Z = -Y' overflow?
Trying it on Y = -inf .
Seems O.K.
Overflow threshold is V = 1.79769313486231571e+308 .
Overflow saturates at V0 = inf .
No Overflow should be signaled for V * 1 = 1.79769313486231571e+308
nor for V / 1 = 1.79769313486231571e+308 .
Any overflow signal separating this * from the one
above is a DEFECT.
Diagnosis resumes after milestone Number 190 Page: 5
What message and/or values does Division by Zero produce?
Trying to compute 1 / 0 produces ... inf .
Trying to compute 0 / 0 produces ... nan .
Diagnosis resumes after milestone Number 220 Page: 6
No failures, defects nor flaws have been discovered.
Rounding appears to conform to the proposed IEEE standard P754.
The arithmetic diagnosed appears to be Excellent!
END OF TEST.
Single precision run
====================
paranoia version 1.1 [cygnus]
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 = 5.9604645e-08 .
Recalculating radix and precision
confirms closest relative separation U1 .
Radix confirmed.
The number of significant digits of the Radix is 24.000000 .
Diagnosis resumes after milestone Number 30 Page: 1
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: 2
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: 3
Testing powers Z^i for small Integers Z and i.
... no discrepancies found.
Seeking Underflow thresholds UfThold and E0.
Smallest strictly positive number found is E0 = 1.4013e-45 .
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.
Underflow is gradual; it incurs Absolute Error =
(roundoff in UfThold)< E0.
The Underflow threshold is 1.17549449095213394e-38, below which
calculation may suffer larger Relative error than merely roundoff.
Since underflow occurs below the threshold
UfThold = (2.00000000000000000e+00) ^ (-1.26000000000000000e+02)
only underflow should afflict the expression
(2.00000000000000000e+00) ^ (-2.52000000000000000e+02);
actually calculating yields: 0.00000000000000000e+00 .
This computed value is O.K.
Testing X^((X + 1) / (X - 1)) vs. exp(2) = 7.38905572891235352e+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: 4
Searching for Overflow threshold:
This may generate an error.
Can `Z = -Y' overflow?
Trying it on Y = -inf .
Seems O.K.
Overflow threshold is V = 3.40282346638528860e+38 .
Overflow saturates at V0 = inf .
No Overflow should be signaled for V * 1 = 3.40282346638528860e+38
nor for V / 1 = 3.40282346638528860e+38 .
Any overflow signal separating this * from the one
above is a DEFECT.
Diagnosis resumes after milestone Number 190 Page: 5
What message and/or values does Division by Zero produce?
Trying to compute 1 / 0 produces ... inf .
Trying to compute 0 / 0 produces ... nan .
Diagnosis resumes after milestone Number 220 Page: 6
No failures, defects nor flaws have been discovered.
Rounding appears to conform to the proposed IEEE standard P754.
The arithmetic diagnosed appears to be Excellent!
END OF TEST.
Best wishes,
Pavel Pisa
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