Script started on Mon Mar 27 14:01:52 1995 [~]: telnet dalph1 Trying 134.30.15.12... Connected to dalph1. Escape character is '^]'. Welcome on HMI node DALPH1, a VAX ALPH with VMS V6.1 dalph1_cbu:>set def [.paranoia] dalph1_cbu:>show cpu DALPH1, a DEC 3000 Model 400 Multiprocessing is DISABLED. Uniprocessing synchronization image loaded. Minimum multiprocessing revision levels: CPU = 1 PRIMARY CPU = 00 Active CPUs: 00 Configured CPUs: 00 dalph1_cbu:>run dpara 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 used incorrectly or not at all. 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 . %MTH-F-INVARGMAT, invalid argument to math library user PC 80550B1C %TRACE-F-TRACEBACK, symbolic stack dump follows Image Name Module Name Routine Name Line Number rel PC abs PC 0 80550B1C 80550B1C 0 80550C10 80550C10 0 80552DA8 80552DA8 DPARA DPARA$MAIN POWER 986 00004AD4 00034AD4 DPARA DPARA$MAIN DPARA$MAIN 266 00000B00 00030B00 0 846B9A50 846B9A50 dalph1_cbu:>run dpara Is this a program restart after failure (1) or a start from scratch (0) ? 1 Restarting from milestone 90. To continue diagnosis, press return. Diagnosis resumes after milestone # 90, ... page 9 Testing powers z^i for small integers z and i : No discrepancies found. Seeking underflow threshold and min positive number: Smallest strictly positive number found is minpos = 5.56268465-309 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. FLAW: x = 0.76486914-308 is unequal to z = 0.55626846-308 , yet x-z yields 0.0000000E+00 Should this not signal underflow, this is a SERIOUS DEFECT that causes confusion when innocent statements like if (x.eq.z) then ... else ... ( f(x)-f(z) )/(x-z) ... encounter division by zero although actually x/z = 1 + 0.37500000E+00 The underflow threshold is 0.55626846-308 , below which calculation may suffer larger relative error than merely roundoff. To continue diagnosis, press return. Diagnosis resumes after milestone # 130, ... page 10 since underflow occurs below the threshold = ( 2.00000000E+00)^( -1.02400000E+03) , only underflow should afflict the expression ( 2.00000000E+00)^( -2.04800000E+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 11 Searching for overflow threshold: %SYSTEM-F-HPARITH, high performance arithmetic trap, Imask=00000000, Fmask=00000 020, summary=08, PC=000333B8, PS=0000001B -SYSTEM-F-FLTOVF, arithmetic trap, floating overflow at PC=000333B8, PS=0000001B %TRACE-F-TRACEBACK, symbolic stack dump follows Image Name Module Name Routine Name Line Number rel PC abs PC DPARA DPARA$MAIN OVERF 1150 000033B8 000333B8 DPARA DPARA$MAIN DPARA$MAIN 278 00000B50 00030B50 0 846B9A50 846B9A50 dalph1_cbu:>run dpara Is this a program restart after failure (1) or a start from scratch (0) ? 1 Restarting from milestone 161. Can " z = -y " overflow? trying it on y = -4.49423284+307 Seems O.K. Overflow threshold is v = 8.98846567+307 There is no saturation value because the system traps on overflow. No overflow should be signaled for v*1 = 8.98846567+307 nor for v/1 = 8.98846567+307 Any overflow signal separating this * from one above is a DEFECT. To continue diagnosis, press return. Diagnosis resumes after milestone # 190, ... page 12 What messages and/or values does division by zero produce? About to compute 1/0... %SYSTEM-F-HPARITH, high performance arithmetic trap, Imask=00000000, Fmask=00000 001, summary=04, PC=0003BA58, PS=0000001B -SYSTEM-F-FLTDIV, arithmetic trap, floating/decimal divide by zero at PC=0003BA5 8, PS=0000001B %TRACE-F-TRACEBACK, symbolic stack dump follows Image Name Module Name Routine Name Line Number rel PC abs PC DPARA DPARA$MAIN ZEROS 3343 0000BA58 0003BA58 DPARA DPARA$MAIN DPARA$MAIN 284 00000B74 00030B74 0 846B9A50 846B9A50 dalph1_cbu:>run dpara Is this a program restart after failure (1) or a start from scratch (0) ? 1 Restarting from milestone 211. About to compute 0/0... %SYSTEM-F-HPARITH, high performance arithmetic trap, Imask=00000000, Fmask=00000 001, summary=04, PC=0003BAE8, PS=0000001B -SYSTEM-F-FLTDIV, arithmetic trap, floating/decimal divide by zero at PC=0003BAE 8, PS=0000001B %TRACE-F-TRACEBACK, symbolic stack dump follows Image Name Module Name Routine Name Line Number rel PC abs PC DPARA DPARA$MAIN ZEROS 3350 0000BAE8 0003BAE8 DPARA DPARA$MAIN DPARA$MAIN 284 00000B74 00030B74 0 846B9A50 846B9A50 dalph1_cbu:>run dpara Is this a program restart after failure (1) or a start from scratch (0) ? 1 Restarting from milestone 212. To continue diagnosis, press return. Diagnosis resumes after milestone # 220, ... page 13 The number of FLAWs discovered = 1 The arithmetic diagnosed seems Satisfactory though flawed. End of Test.

Tue Aug 8 13:05:00 GMT+0200 1995