COMMENT ⊗   VALID 00003 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	 Test of Floating-point hardware
C00013 00003	 Builtin SQRT and ATAN tests
C00023 ENDMK
C⊗;
;;; Test of Floating-point hardware
(fasload machar)

*ibeta* = 2 
*it* = 27 
*irnd* = 1 
*ngrd* = 0 
*machep* = -26 
*epsneg* = 7.4505806E-9 
*maxexp* = 127 
*negep* = -26 
*iexp* = 8 
*minexp* = -128 
*eps* = 7.4505806E-9 
*xmin* = 2.93873587E-39 
*xmax* = 1.70141183E+38 

(fasload float)
(timit)
Timing performed on Monday 07/18/83 at 01:02:05.
Square-root of a negative number
arctan2 called with u = 0.0 and v = 0.0
Cpu (- GC) Time = 10.796
Elapsed Time = 105.816667
Wholine Time = 59.85
GC Time = 32.741
Load Average Before  = 0.69501066
Load Average After   = 1.30672002
Average Load Average = 1.00086534
(TEST OF SQRT (X * X) - X) 
(8000 RANDOM ARGUMENTS WERE TESTED IN THE INTERVAL (0.70710678 1.0)) 
(SQRT (X) WAS LARGER 618 TIMES) 
(IT AGREED 7382 TIMES) 
(IT WAS SMALLER 0 TIMES) 
(THERE ARE 27 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER) 
(THE MAXIMUM RELATIVE ERROR OF 1.05350655E-8 = 2 ↑ -26.5002255 OCCURRED 
FOR X = 0.707217306) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.499774456) 
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 2.61463252E-9 = 2 ↑ -28.5107443) 
(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 3928 TIMES) 
(IT AGREED 4072 TIMES) 
(IT WAS SMALLER 0 TIMES) 
(THERE ARE 27 BASE 2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER) 
(THE MAXIMUM RELATIVE ERROR OF 1.48971613E-8 = 2 ↑ -26.0003872 OCCURRED 
FOR X = 1.0002685) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99961281) 
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 8.7896637E-9 = 2 ↑ -26.761545) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.238455057) 
(TEST OF SPECIAL ARGUMENTS) 
(SQRT (*XMIN*) = SQRT (2.93873587E-39) = 5.421011E-20) 
(SQRT (1.0 - *EPSNEG*) = SQRT (1.0 - 7.4505806E-9) = 1.0) 
(SQRT (1.0) = 1.00000001) 
(SQRT (1.0 + *EPS*) = SQRT (1.0 + 7.4505806E-9) = 1.00000001) 
(SQRT (*XMAX*) = SQRT (1.70141183E+38) = 1.30438179E+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 ARCTAN (X) VS TRUNCATED TAYLOR SERIES) 
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (-0.0625 0.0625)) 
(ARCTAN (X) WAS LARGER 4 TIMES) 
(IT AGREED 7994 TIMES) 
(IT WAS SMALLER 2 TIMES) 
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER) 
(THE MAXIMUM RELATIVE ERROR OF 1.3543158E-8 = 2 ↑ -26.1378605 OCCURRED 
FOR X = -0.0343970642) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.86213946) 
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 2.63454574E-10 = 2 ↑ -31.8217268) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0) 
(TEST OF ARCTAN (X) VS ARCTAN (1 // 16) + ARCTAN ((X - 1 // 16) // (1 + 
X // 16))) 
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.0625 0.267949194)) 
(ARCTAN (X) WAS LARGER 1202 TIMES) 
(IT AGREED 5299 TIMES) 
(IT WAS SMALLER 1499 TIMES) 
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER) 
(THE MAXIMUM RELATIVE ERROR OF 1.48968492E-8 = 2 ↑ -26.0004175 OCCURRED 
FOR X = 0.12569189) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.99958253) 
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 5.965045E-9 = 2 ↑ -27.3208199) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.0) 
(TEST OF 2 * ARCTAN (X) VS ARCTAN (2X // (1 - X * X))) 
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.267949194 0.414213568)) 
(ARCTAN (X) WAS LARGER 2007 TIMES) 
(IT AGREED 4830 TIMES) 
(IT WAS SMALLER 1163 TIMES) 
(THERE ARE 27 SIGNIFICANT BASE 2 DIGITS IN A FLOATING-POINT NUMBER) 
(THE MAXIMUM RELATIVE ERROR OF 2.84573352E-8 = 2 ↑ -25.066624 OCCURRED 
FOR X = 0.26796681) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 1.93337607) 
(THE ROOT MEAN SQUARE RELATIVE ERROR WAS 7.6160271E-9 = 2 ↑ -26.9683142) 
(THE ESTIMATED LOSS OF BASE 2 SIGNIFICANT DIGITS IS 0.031685829) 
(8000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (0.414213568 1.0)) 
(ARCTAN (X) WAS LARGER 2971 TIMES) 
(IT AGREED 4932 TIMES) 
(IT WAS SMALLER 97 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: ARCTAN (-X) = -ARCTAN (X) WILL BE TESTED) 
(X : F (X) + F (-X)) 
(4.1264082 : 0.0) 
(0.80102554 : 0.0) 
(0.128191695 : 0.0) 
(1.02396178 : 0.0) 
(2.99522245 : 0.0) 
(THE IDENTITY ARCTAN (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 ARCTAN (X // Y) = ARCTAN2 (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 : 3.14159265) 
(-1.97689867 : 0.72191647 : 0.0 : 3.14159265) 
(-1.04176486 : 0.944848426 : 0.0 : 3.14159265) 
(TEST OF VERY SMALL ARGUMENT) 
(ARCTAN (1.2621776E-29) = 1.2621776E-29) 
(TEST OF ERROR RETURNS) 
(ARCTAN WILL BE CALLED WITH THE ARGUMENT 1.70141183E+38) 
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE) 
(ARCTAN (1.70141183E+38) = 1.57079633) 
(ARCTAN2 WILL BE CALLED WITH THE ARGUMENTS 1.0 0.0) 
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE) 
(ARCTAN2 (1.0 0.0) = 1.57079633) 
(ARCTAN2 WILL BE CALLED WITH THE ARGUMENTS 2.93873587E-39 1.70141183E+38) 
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE) 
(ARCTAN2 (2.93873587E-39 1.70141183E+38) = 1.57079633) 
(ARCTAN2 WILL BE CALLED WITH THE ARGUMENTS 1.70141183E+38 2.93873587E-39) 
(THIS SHOULD NOT TRIGGER AN ERROR MESSAGE) 
(ARCTAN2 (1.70141183E+38 2.93873587E-39) = 0.0) 
(ARCTAN2 WILL BE CALLED WITH THE ARGUMENTS 0.0 0.0) 
(THIS SHOULD TRIGGER AN ERROR MESSAGE) 
(ARCTAN2 (0.0 0.0) = 0.0) 
(THIS CONCLUDES THE TESTS) 
T 

;;; Builtin SQRT and ATAN tests
(fasload mclflo)

(timit)
Timing performed on Monday 07/18/83 at 18:36:00.
;-1.0 NEG ARG - SQRT
;OVERFLOW/UNDERFLOW IN ATAN
;OVERFLOW/UNDERFLOW IN ATAN
;OVERFLOW/UNDERFLOW IN ATAN
Cpu (- GC) Time = 11.012
Elapsed Time = 51.25
Wholine Time = 47.0333333
GC Time = 25.482
Load Average Before  = 0.358628273
Load Average After   = 0.57884002
Average Load Average = 0.468734145
(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