Diagnosis resumes after milestone # 7, ... page 5 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. Closest relative separation found is 1.11022302E-16 Recalculating radix and precision confirms closest relative separation . Radix confirmed. The number of significant digits of radix 2. is 53.00 Test for extra-precise subexpressions: Subexpressions do not appear to be calculated with extra precision. To continue diagnosis, press return. Diagnosis resumes after milestone # 30, ... page 6 Subtraction appears to be normalized as it should. Checking for guard digits in multiply divide and subtract. These operations appear to have guard digits as they should. To continue diagnosis, press return. Diagnosis resumes after milestone # 40, ... page 7 Checking for rounding in multiply, divide and add/subtract: Multiplication appears to be correctly rounded. Division appears to be correctly rounded. Add/subtract appears to be correctly rounded. checking for sticky bit: Sticky bit appears to be used correctly. Does multiplication commute? Testing if x*y = y*x for 20 random pairs: No failure found in 20 randomly chosen pairs. Running tests of square root... Testing if sqrt(x*x) = x for 20 integers x. Found no discrepancies. Sqrt has passed a test for monotonicity. Testing whether sqrt is rounded or chopped: Square root appears to be correctly rounded. To continue diagnosis, press return. Diagnosis resumes after milestone # 90, ... page 8 Testing powers z^i for small integers z and i : Start with 0.**0 . No discrepancies found. Seeking underflow threshold and min positive number: Smallest strictly positive number found is minpos = 4.94065646-324 Since comparison denies MINPOS = 0, evaluating ( MINPOS + MINPOS ) / MINPOS should be safe; what the machine gets for ( MINPOS + MINPOS ) / MINPOS is 0.2000000E+01 This is O.K. provided over/underflow has not just been signaled. Underflow is gradual; it incurs absolute error = (roundoff in underflow threshold) < minpos. The underflow threshold is 0.22250739-307 , below which calculation may suffer larger relative error than merely roundoff. To continue diagnosis, press return. Diagnosis resumes after milestone # 130, ... page 9 since underflow occurs below the threshold = ( 2.00000000E+00)^( -1.02200000E+03) , only underflow should afflict the expression ( 2.00000000E+00)^( -2.04400000E+03) ; actually calculating it yields 0.00000000E+00 This computed value is O.K. Testing x^((x+1)/(x-1)) vs. exp(2) = 0.73890561E+01 as x -> 1. Accuracy seems adequate. Testing powers z^q at four nearly extreme values: No discrepancies found. To continue diagnosis, press return. Diagnosis resumes after milestone # 160, ... page 10 Searching for overflow threshold: Can " z = -y " overflow? trying it on y = -Infinity Seems O.K. Overflow threshold is v = 1.79769313+308 Overflow saturates at sat = Infinity No overflow should be signaled for v*1 = 1.79769313+308 nor for v/1 = 1.79769313+308 Any overflow signal separating this * from one above is a DEFECT. To continue diagnosis, press return. Diagnosis resumes after milestone # 190, ... page 11 What messages and/or values does division by zero produce? About to compute 1/0... Trying to compute 1/0 produces Infinity About to compute 0/0... Trying to compute 0/0 produces NaN To continue diagnosis, press return. Diagnosis resumes after milestone # 220, ... page 12 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.