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 . To continue, press RETURN 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. To continue, press RETURN 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. To continue, press RETURN Diagnosis resumes after milestone Number 90 Page: 7 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 = 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. To continue, press RETURN 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) ^ (-2.04400000000000000e+03); actually calculating yields: 0.00000000000000000e+00 . This computed value is O.K. Testing X^((X + 1) / (X - 1)) vs. exp(2) = 7.38905609893065220e+00 as X -> 1. Accuracy seems adequate. Testing powers Z^Q at four nearly extreme values. ... no discrepancies found. To continue, press RETURN Diagnosis resumes after milestone Number 160 Page: 9 Searching for Overflow threshold: This may generate an error. * * * FLOATING-POINT ERROR 8 * * * 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. To continue, press RETURN Diagnosis resumes after milestone Number 190 Page: 10 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? Trying to compute 1 / 0 produces ... * * * FLOATING-POINT ERROR 8 * * * Do you wish to compute 0 / 0? Trying to compute 0 / 0 produces ... * * * FLOATING-POINT ERROR 8 * * * To continue, press RETURN Diagnosis resumes after milestone Number 220 Page: 11 The number of FLAWs discovered = 1. The arithmetic diagnosed seems Satisfactory though flawed. A total of 3 floating point exceptions were registered. END OF TEST.