perm filename MCLFLO.RES[TIM,LSP] blob
sn#864809 filedate 1984-12-21 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00002 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00002 00002 (fasload mclflo)
C00021 ENDMK
C⊗;
(fasload mclflo)
(fasload machar)
(timit)
Timing performed on Friday 12/21/84 at 16:24:27.
;-1.0 NEG ARG - SQRT
(show-results)
;OVERFLOW/UNDERFLOW IN ATAN
;OVERFLOW/UNDERFLOW IN ATAN
;OVERFLOW/UNDERFLOW IN ATAN
Cpu (- GC) Time = 11.026
Elapsed Time = 104.0
Wholine Time = 53.0
GC Time = 25.476
Load Average Before = 1.09154606
Load Average After = 1.47047102
Average Load Average = 1.28100854
(TEST OF SQRT (X * X) - X)
(8000 RANDOM ARGUMENTS WERE TESTED IN THE INTERVAL (0.70710678 1.0))
(SQRT (X) WAS LARGER 0 TIMES)
(IT AGREED 8000 TIMES)
(IT WAS SMALLER 0 TIMES)
(THERE ARE 27 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 0.0 = 2 ↑ -999.0 OCCURRED FOR X = 0.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0 = 2 ↑ -999.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(TEST OF SQRT (X * X) - X)
(8000 RANDOM ARGUMENTS WERE TESTED IN THE INTERVAL (1.0 1.41421357))
(SQRT (X) WAS LARGER 0 TIMES)
(IT AGREED 8000 TIMES)
(IT WAS SMALLER 0 TIMES)
(THERE ARE 27 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 0.0 = 2 ↑ -999.0 OCCURRED FOR X = 0.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0 = 2 ↑ -999.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(TEST OF SPECIAL ARGUMENTS)
(SQRT (*XMIN*) = SQRT (2.93873587E-39) = 5.42101085E-20)
(SQRT (1.0 - *EPSNEG*) = SQRT (1.0 - 7.4505806E-9) = 1.0)
(SQRT (1.0) = 1.0)
(SQRT (1.0 + *EPS*) = SQRT (1.0 + 7.4505806E-9) = 1.00000001)
(SQRT (*XMAX*) = SQRT (1.70141183E+38) = 1.30438177E+19)
(TEST OF ERROR RETURNS)
(SQRT WILL BE CALLED WITH AN ARGUMENT OF 0.0 THIS SHOULD NOT TRIGGER AN
ERROR)
(SQRT RETURNED THE VALUE 0.0)
(SQRT WILL BE CALLED WITH AN ARGUMENT OF -1.0 THIS SHOULD TRIGGER AN ERROR)
(SQRT RETURNED THE VALUE 0.0)
(THIS CONCLUDES THE TESTS)
(TEST OF ATAN (X) VS TRUNCATED TAYLOR SERIES)
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (-0.0625 0.0625))
(ATAN (X) WAS LARGER 6669 TIMES)
(IT AGREED 19 TIMES)
(IT WAS SMALLER 1312 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 1.0100327 = 2 ↑ 0.0144019946 OCCURRED FOR
X = -0.062492318)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 27.014402)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.71064784 = 2 ↑ -0.4927933)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 26.5072067)
(TEST OF ATAN (X) VS ATAN (1 // 16) + ATAN ((X - 1 // 16) // (1 + X //
16)))
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.0625 0.267949194))
(ATAN (X) WAS LARGER 3226 TIMES)
(IT AGREED 16 TIMES)
(IT WAS SMALLER 4758 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 8.5598472E-7 = 2 ↑ -20.1559117 OCCURRED
FOR X = 0.094940901)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 6.8440883)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 3.41086605E-7 = 2 ↑ -21.4833586)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 5.5166414)
(TEST OF 2 * ATAN (X) VS ATAN (2X // (1 - X * X)))
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.267949194 0.414213568))
(ATAN (X) WAS LARGER 4011 TIMES)
(IT AGREED 630 TIMES)
(IT WAS SMALLER 3359 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 1.07312274E-7 = 2 ↑ -23.151682 OCCURRED
FOR X = 0.401570223)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 3.8483181)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 4.9316151E-8 = 2 ↑ -24.2733648)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 2.72663522)
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.414213568 1.0))
(ATAN (X) WAS LARGER 5446 TIMES)
(IT AGREED 302 TIMES)
(IT WAS SMALLER 2252 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 1.99999665 = 2 ↑ 0.99999757 OCCURRED FOR
X = 1.00000264)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 27.9999976)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0223606422 = 2 ↑ -5.4828946)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 21.5171053)
(SPECIAL TESTS)
(THE IDENTITY: ATAN (-X) = -ATAN (X) WILL BE TESTED)
(X : F (X) + F (-X))
(4.1264082 : 6.2831853)
(0.80102554 : 6.2831853)
(0.128191695 : 6.2831853)
(1.02396178 : 6.28318536)
(2.99522245 : 6.2831853)
(THE IDENTITY ATAN (X) = X FOR X SMALL WILL BE TESTED)
(X : X - F (X))
(6.56069255E-9 : 0.0)
(3.28034627E-9 : 0.0)
(1.64017314E-9 : 0.0)
(8.2008656E-10 : 0.0)
(4.1004328E-10 : 0.0)
(THE IDENTITY ATAN (X // Y) = ATAN2 (X Y) WILL BE TESTED)
(THE FIRST COLUMN OF RESULTS SHOULD BE 0 AND THE SECOND SHOULD BE +-π)
(X : Y : F1 (X // Y) - F2 (X Y) : F1 (X // Y) - F2 (X // -Y))
(-1.7193766 : 0.76948133 : 0.0 : -3.14159265)
(-1.2593356 : 0.145762308 : 0.0 : -3.14159265)
(-1.11884652 : 0.5360462 : 0.0 : -3.14159268)
(-1.97689867 : 0.72191647 : 5.9604645E-8 : -3.14159265)
(-1.04176486 : 0.944848426 : 0.0 : -3.14159265)
(TEST OF VERY SMALL ARGUMENT)
(ATAN (1.2621776E-29) = 1.2621776E-29)
(TEST OF ERROR RETURNS)
(ATAN WILL BE CALLED WITH THE ARGUMENT 1.70141183E+38)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN (1.70141183E+38) = 1.57079633)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 1.0 0.0)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN2 (1.0 0.0) = 1.57079633)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 2.93873587E-39 1.70141183E+38)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN2 (2.93873587E-39 1.70141183E+38) = 0.0)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 1.70141183E+38 2.93873587E-39)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN2 (1.70141183E+38 2.93873587E-39) = 0.0)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 0.0 0.0)
(THIS SHOULD TRIGGER AN ERROR MESSAGE)
(ATAN2 (0.0 0.0) = 0.0)
(THIS CONCLUDES THE TESTS)
T
(TEST OF SQRT (X * X) - X)
(8000 RANDOM ARGUMENTS WERE TESTED IN THE INTERVAL (0.70710678 1.0))
(SQRT (X) WAS LARGER 0 TIMES)
(IT AGREED 8000 TIMES)
(IT WAS SMALLER 0 TIMES)
(THERE ARE 27 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 0.0 = 2 ↑ -999.0 OCCURRED FOR X = 0.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0 = 2 ↑ -999.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(TEST OF SQRT (X * X) - X)
(8000 RANDOM ARGUMENTS WERE TESTED IN THE INTERVAL (1.0 1.41421357))
(SQRT (X) WAS LARGER 0 TIMES)
(IT AGREED 8000 TIMES)
(IT WAS SMALLER 0 TIMES)
(THERE ARE 27 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 0.0 = 2 ↑ -999.0 OCCURRED FOR X = 0.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0 = 2 ↑ -999.0)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0)
(TEST OF SPECIAL ARGUMENTS)
(SQRT (*XMIN*) = SQRT (2.93873587E-39) = 5.42101085E-20)
(SQRT (1.0 - *EPSNEG*) = SQRT (1.0 - 7.4505806E-9) = 1.0)
(SQRT (1.0) = 1.0)
(SQRT (1.0 + *EPS*) = SQRT (1.0 + 7.4505806E-9) = 1.00000001)
(SQRT (*XMAX*) = SQRT (1.70141183E+38) = 1.30438177E+19)
(TEST OF ERROR RETURNS)
(SQRT WILL BE CALLED WITH AN ARGUMENT OF 0.0 THIS SHOULD NOT TRIGGER AN
ERROR)
(SQRT RETURNED THE VALUE 0.0)
(SQRT WILL BE CALLED WITH AN ARGUMENT OF -1.0 THIS SHOULD TRIGGER AN ERROR)
(SQRT RETURNED THE VALUE 0.0)
(THIS CONCLUDES THE TESTS)
(TEST OF ATAN (X) VS TRUNCATED TAYLOR SERIES)
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (-0.0625 0.0625))
(ATAN (X) WAS LARGER 6669 TIMES)
(IT AGREED 19 TIMES)
(IT WAS SMALLER 1312 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 1.0100327 = 2 ↑ 0.0144019946 OCCURRED FOR
X = -0.062492318)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 27.014402)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.71064784 = 2 ↑ -0.4927933)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 26.5072067)
(TEST OF ATAN (X) VS ATAN (1 // 16) + ATAN ((X - 1 // 16) // (1 + X //
16)))
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.0625 0.267949194))
(ATAN (X) WAS LARGER 3226 TIMES)
(IT AGREED 16 TIMES)
(IT WAS SMALLER 4758 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 8.5598472E-7 = 2 ↑ -20.1559117 OCCURRED
FOR X = 0.094940901)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 6.8440883)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 3.41086605E-7 = 2 ↑ -21.4833586)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 5.5166414)
(TEST OF 2 * ATAN (X) VS ATAN (2X // (1 - X * X)))
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.267949194 0.414213568))
(ATAN (X) WAS LARGER 4011 TIMES)
(IT AGREED 630 TIMES)
(IT WAS SMALLER 3359 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 1.07312274E-7 = 2 ↑ -23.151682 OCCURRED
FOR X = 0.401570223)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 3.8483181)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 4.9316151E-8 = 2 ↑ -24.2733648)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 2.72663522)
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.414213568 1.0))
(ATAN (X) WAS LARGER 5446 TIMES)
(IT AGREED 302 TIMES)
(IT WAS SMALLER 2252 TIMES)
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER)
(THE MAXIMUM RELATIVE ERROR OF 1.99999665 = 2 ↑ 0.99999757 OCCURRED FOR
X = 1.00000264)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 27.9999976)
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0223606422 = 2 ↑ -5.4828946)
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 21.5171053)
(SPECIAL TESTS)
(THE IDENTITY: ATAN (-X) = -ATAN (X) WILL BE TESTED)
(X : F (X) + F (-X))
(4.1264082 : 6.2831853)
(0.80102554 : 6.2831853)
(0.128191695 : 6.2831853)
(1.02396178 : 6.28318536)
(2.99522245 : 6.2831853)
(THE IDENTITY ATAN (X) = X FOR X SMALL WILL BE TESTED)
(X : X - F (X))
(6.56069255E-9 : 0.0)
(3.28034627E-9 : 0.0)
(1.64017314E-9 : 0.0)
(8.2008656E-10 : 0.0)
(4.1004328E-10 : 0.0)
(THE IDENTITY ATAN (X // Y) = ATAN2 (X Y) WILL BE TESTED)
(THE FIRST COLUMN OF RESULTS SHOULD BE 0 AND THE SECOND SHOULD BE +-π)
(X : Y : F1 (X // Y) - F2 (X Y) : F1 (X // Y) - F2 (X // -Y))
(-1.7193766 : 0.76948133 : 0.0 : -3.14159265)
(-1.2593356 : 0.145762308 : 0.0 : -3.14159265)
(-1.11884652 : 0.5360462 : 0.0 : -3.14159268)
(-1.97689867 : 0.72191647 : 5.9604645E-8 : -3.14159265)
(-1.04176486 : 0.944848426 : 0.0 : -3.14159265)
(TEST OF VERY SMALL ARGUMENT)
(ATAN (1.2621776E-29) = 1.2621776E-29)
(TEST OF ERROR RETURNS)
(ATAN WILL BE CALLED WITH THE ARGUMENT 1.70141183E+38)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN (1.70141183E+38) = 1.57079633)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 1.0 0.0)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN2 (1.0 0.0) = 1.57079633)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 2.93873587E-39 1.70141183E+38)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN2 (2.93873587E-39 1.70141183E+38) = 0.0)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 1.70141183E+38 2.93873587E-39)
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE)
(ATAN2 (1.70141183E+38 2.93873587E-39) = 0.0)
(ATAN2 WILL BE CALLED WITH THE ARGUMENTS 0.0 0.0)
(THIS SHOULD TRIGGER AN ERROR MESSAGE)
(ATAN2 (0.0 0.0) = 0.0)
(THIS CONCLUDES THE TESTS)
T