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 To continue, press any key and newline: 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. To continue, press any key and newline: 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. To continue, press any key and newline: 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. To continue, press any key and newline: 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. To continue, press any key and newline: 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. To continue, press any key and newline: Diagnosis resumes after milestone no 150 Page: 9 To continue, press any key and newline: 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. To continue, press any key and newline: 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. To continue, press any key and newline: 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.