PASCAL Version

Diagnosis resumes after milestone no          7               Page:          3

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 =  2.00000e+00
Closest relative separation found is U1 =  5.96046e-08

Recalculating radix and precision
 confirms closest relative separation U1 .
Radix confirmed.
The number of significant digits of the Radix is  2.40000e+01
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Diagnosis resumes after milestone no         30               Page:          4

Subtraction appears to be normalized, as it should be.

Checking for guard digit on *, /, and -.
 *, /, and - have guard digits, as they should.
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Diagnosis resumes after milestone no         40               Page:          5

Checking rounding on multiply, divide and add/subtract.
Multiplication appears to round correctly.
/ is neither chopped nor correctly rounded.
Addition/Subtraction appears to round correctly.
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.

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.
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Diagnosis resumes after milestone no         90               Page:          6

Testing powers Z^i for small integers Z and i.
DEFECT:  computed ( 2.00000e+00) ^ ( 1.30000e+01) = 
 8.19200e+03, which compares unequal to correct  8.19200e+03;
 they differ by  3.90625e-03
Error like this may invalidate financial 
calculations involving interest rates.
Similar discrepancies have occurred  9.00000e+01 times.

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Diagnosis resumes after milestone no        100               Page:          7

Seeking Underflow thresholds UnderflowThreshold and E0
Smallest strictly positive number found is E0 = 1.17549e-38
Since comparison denies Z = 0, evaluating
(Z + Z) / Z should be safe.
What the machine gets for (Z + Z) / Z is:  2.00000e+00
This is O.K., provided Over/Underflow has NOT just been signaled.
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Diagnosis resumes after milestone no        120               Page:          8


FLAW:  X =  1.61630e-38 is unequal to Z =  1.17549e-38
yet X - Z yields  0.00000e+00.  Should this NOT signal Underflow,
this is a SERIOUS DEFECT that causes
confusion when innocent statements like
    if X = Z then  ...  else  ...  (f(X) - f(Z)) / (X - Z) ...
encounter Division by Zero although actually
X / Z = 1 +  3.75000e-01
The Underflow threshold is  1.17549e-38 below which
calculation may suffer larger Relative error then merely roundoff.

Testing X^((X + 1) / (X - 1)) vs. exp(2) =  7.38906e+00 as X -> 1.
Accuracy seems adequate.
Testing powers Z^Q at four nearly extreme values.
DEFECT:  computed ( 2.00000e+00) ^ ( 9.60000e+01) = 
 7.92282e+28, which compares unequal to correct  7.92282e+28;
 they differ by  1.88895e+22
Similar discrepancies have occurred  4.00000e+00 times.

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Diagnosis resumes after milestone no        150               Page:          9

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Diagnosis resumes after milestone no        160               Page:         10

Searching for Overflow threshold:  This may generate an error.
Try a few values for N, starting with a large one,
and take the one that just does not stop the machine.
Did you find the correct value for N yet?
N = 
O.K.
Can "Z = -Y" overflow?  Trying it on Y = -1.70141e+38
Seems O.K.
Overflow threshold is V =  3.40282e+38
There is no saturation value because
the system traps on overflow.
No Overflow should get signaled for V * 1 =  3.40282e+38
                            nor for V / 1 =  3.40282e+38
Any overflow signal separating this * from the one
above is a DEFECT.

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Diagnosis resumes after milestone no        190               Page:         11


What message and/or values does Division by Zero produce?
This can interupt your program. You can skip this part if you wish.
Do you wish to compute 1 / 0? 
O.K.
Do you wish to compute 0 / 0?
O.K.
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Diagnosis resumes after milestone no        220               Page:         12


The number of  DEFECTs  encountered =                  2
The number of  FLAWs  encountered =                    2

The arithmetic diagnosed may be Acceptable
despite inconvenient Defects.
END OF TEST.