! First some easy integer cases. 3C ALL 1 1 OK = 3C ALL 1 2 OK < 3C ALL 2 1 OK > 3C ALL 2 2 OK = 3C ALL 2 -2 OK > 3C ALL 5 -5 OK > 3C ALL 1 7 OK < 3C ALL 5 -1 OK > 3C ALL 2 -5 OK > 3C ALL 5 5 OK = 3C ALL 5 -0 OK > 3C ALL 5 +0 OK > ! Infinity vs Infinity. 3C ALL H H OK = always equal 3C ALL -H -H OK = always equal 3C ALL H -H OK > 3C ALL -H H OK < ! Infinity vs huge. 3C ALL H Hm1 OK > 3C ALL H -Hm1 OK > 3C ALL -H Hm1 OK < 3C ALL -H -Hm1 OK < 3C ALL H Hd1 OK > 3C ALL H -Hd1 OK > 3C ALL -H Hd1 OK < 3C ALL -H -Hd1 OK < 3C ALL Hm1 H OK < 3C ALL Hm1 -H OK > 3C ALL -Hm1 H OK < 3C ALL -Hm1 -H OK > ! Infinity vs 0. 3C ALL H 0 OK > 3C ALL H -0 OK > 3C ALL -H 0 OK < 3C ALL -H -0 OK < 3C ALL 0 H OK < 3C ALL -0 H OK < 3C ALL 0 -H OK > 3C ALL -0 -H OK > ! Infinity vs denormalized. 3C ALL H Ed1 OK > 3C ALL -H Ed1 OK < 3C ALL H -Ed1 OK > 3C ALL -H -Ed1 OK < 3C ALL H 0i1 OK > 3C ALL -H 0i1 OK < 3C ALL H -0i1 OK > 3C ALL -H -0i1 OK < 3C ALL Ed1 H OK < 3C ALL Ed1 -H OK > 3C ALL -Ed1 H OK < 3C ALL -Ed1 -H OK > ! Zero vs finite -- watch that sign of 0 is meaningless. 3C ALL 0 Hm1 OK < 3C ALL -0 Hm1 OK < 3C ALL -Hm1 0 OK < 3C ALL -Hm1 -0 OK < 3C ALL 1 -0 OK > 3C ALL -1 -0 OK < 3C ALL 0 1 OK < 3C ALL -0 -1 OK > ! Zero vs denormalized. 3C ALL 0 Ed1 OK < 3C ALL -0 Ed1 OK < 3C ALL 0 -Ed1 OK > 3C ALL -0 -Ed1 OK > 3C ALL 0 0i1 OK < 3C ALL -0 0i1 OK < 3C ALL 0 -0i1 OK > 3C ALL -0 -0i1 OK > 3C ALL Ed1 0 OK > 3C ALL Ed1 -0 OK > 3C ALL -Ed1 0 OK < 3C ALL -Ed1 -0 OK < ! Zero vs tiny -- just in case. 3C ALL -0 -E OK > 3C ALL E 0 OK > 3C ALL 0 -E OK > 3C ALL -E 0 OK < ! Zero vs Zero -- watch signs and rounding modes. 3C ALL 0 -0 OK = 3C ALL -0 0 OK = 3C ALL 0 -0 OK = 3C ALL -0 0 OK = ! Big cancellations. 3C ALL Hm1 Hm1 OK = 3C ALL -Hm1 -Hm1 OK = 3C ALL Hm1d2 Hm1d2 OK = 3C ALL -Hm1d2 -Hm1d2 OK = 3C ALL Hd1 Hd1 OK = 3C ALL -Hd1 -Hd1 OK = ! Medium cancellations. 3C ALL 1 1 OK = 3C ALL 1m1 1m1 OK = 3C ALL 3 3 OK = 3C ALL E E OK = 3C ALL Hm2 Hm2 OK = ! Tiny cancellations -- might have underflowed. 3C ALL Ed1 Ed1 OK = 3C ALL -Ed1 -Ed1 OK = 3C ALL 0i4 0i4 OK = 3C ALL -0i4 -0i4 OK = 3C ALL 0i1 0i1 OK = 3C ALL -0i1 -0i1 OK = ! Doublings. 3C ALL Hm1 -Hm1 OK > 3C ALL -Hm1d2 Hm1d2 OK < 3C ALL 1 -1 OK > 3C ALL -3 3 OK < 3C ALL E -E OK > 3C ALL -E E OK < 3C ALL Ed4 -Ed4 OK > 3C ALL -Ed1 Ed1 OK < 3C ALL 0i1 -0i1 OK > 3C ALL -0i1 0i1 OK < ! Cancellation with diff in LSB ! Difference is in last place of larger number. ! Medium numbers... 3C ALL 1i1 1 OK > 3C ALL -1i1 -1 OK < 3C ALL 1i1 1i2 OK < 3C ALL -1i1 -1i2 OK > 3C ALL 2 2i1 OK < 3C ALL -2 -2i1 OK > 3C ALL 2i4 2i3 OK > 3C ALL -2i4 -2i3 OK < 3C ALL 4d1 4d2 OK > 3C ALL -4d1 -4d2 OK < 3C ALL 2d4 2d3 OK < 3C ALL -2d4 -2d3 OK > ! Huge numbers... 3C ALL Hm1i1 Hm1 OK > 3C ALL -Hm1i1 -Hm1 OK < 3C ALL Hm1i1 Hm1i2 OK < 3C ALL -Hm1i1 -Hm1i2 OK > 3C ALL Hm2 Hm2i1 OK < 3C ALL -Hm2 -Hm2i1 OK > 3C ALL Hm2i4 Hm2i3 OK > 3C ALL -Hm2i4 -Hm2i3 OK < 3C ALL Hm2d1 Hm2d2 OK > 3C ALL -Hm2d1 -Hm2d2 OK < 3C ALL -Hd2 -Hd1 OK > 3C ALL Hd2 Hd1 OK < ! Tiny numbers... 3C ALL -Ei1 -E OK < 3C ALL Ei1 E OK > 3C ALL -Ed1 -E OK > 3C ALL Ed1 E OK < 3C ALL Ei1 Ei2 OK < 3C ALL -Ei1 -Ei2 OK > 3C ALL Ed1 Ed2 OK > 3C ALL -Ed1 -Ed2 OK < 3C ALL Ed3 Ed2 OK < 3C ALL -Ed3 -Ed2 OK > 3C ALL 0i2 0i1 OK > 3C ALL -0i2 -0i1 OK < 3C ALL 0i3 0i2 OK > 3C ALL -0i3 -0i2 OK < ! Normalize from round bit -- set up tests so that operands have ! exponents differing by 1 unit. ! Medium numbers... 3C ALL 2 2d1 OK > 3C ALL -2 -2d1 OK < 3C ALL -2d1 -2 OK > 3C ALL 2d1 2 OK < 3C ALL 4i1 4d1 OK > 3C ALL -4i1 -4d1 OK < 3C ALL 4d1 4i2 OK < 3C ALL -4d1 -4i2 OK > 3C ALL 2i1 1i1 OK > 3C ALL -2i1 -1i1 OK < 3C ALL 2i2 1i1 OK > 3C ALL -2i2 -1i1 OK < 3C ALL 2i2 1i3 OK > 3C ALL -2i2 -1i3 OK < ! Huge numbers... 3C ALL Hm2 Hm2d1 OK > 3C ALL -Hm2 -Hm2d1 OK < 3C ALL -Hm1d1 -Hm1 OK > 3C ALL Hm1d1 Hm1 OK < 3C ALL Hm4i1 Hm4d1 OK > 3C ALL -Hm4i1 -Hm4d1 OK < 3C ALL Hm2d1 Hm2i2 OK < 3C ALL -Hm2d1 -Hm2i2 OK > 3C ALL Hm2i1 Hm1i1 OK < 3C ALL -Hm2i1 -Hm1i1 OK > 3C ALL Hm1i2 Hm2i1 OK > 3C ALL -Hm1i2 -Hm2i1 OK < 3C ALL Hm2i2 Hm3i3 OK > 3C ALL -Hm2i2 -Hm3i3 OK < ! Tiny numbers... 3C ALL Ep1 Ep1d1 OK > 3C ALL -Ep1 -Ep1d1 OK < 3C ALL -Ep1d1 -Ep1 OK > 3C ALL Ep1d1 Ep1 OK < 3C ALL Ep1i1 Ep1d1 OK > 3C ALL -Ep1i1 -Ep1d1 OK < 3C ALL Ep2 Ep2d1 OK > 3C ALL -Ep2 -Ep2d1 OK < 3C ALL -Ep2d1 -Ep2 OK > 3C ALL Ep2d1 Ep2 OK < 3C ALL Ep2i1 Ep2d1 OK > 3C ALL -Ep2i1 -Ep2d1 OK < 3C ALL Ep1d1 Ep1i2 OK < 3C ALL -Ep1d1 -Ep1i2 OK > 3C ALL Ep1d1 Ep1i4 OK < 3C ALL -Ep1d1 -Ep1i4 OK > 3C ALL Ep1i1 Ei1 OK > 3C ALL -Ep1i1 -Ei1 OK < 3C ALL Ep1i2 Ei1 OK > 3C ALL -Ep1i2 -Ei1 OK < 3C ALL Ep2i2 Ep1i3 OK > 3C ALL -Ep2i2 -Ep1i3 OK < ! ! Add magnitude ! cases where one operand is off in sticky -- rounding ! perhaps to an overflow. ! Huge vs medium 3C ALL Hm1 1 OK > 3C ALL -Hm1 -1 OK < 3C ALL Hm1d1 -1 OK > 3C ALL Hm1d1 1 OK > 3C ALL -Hm1d1 1 OK < 3C ALL -Hm1d1 -1 OK < 3C ALL Hd1 1 OK > 3C ALL Hd1 -1 OK > 3C ALL -Hd1 1 OK < 3C ALL -Hd1 -1 OK < 3C ALL Hd2 -1 OK > 3C ALL Hd2 1 OK > 3C ALL -Hd2 1 OK < 3C ALL -Hd2 -1 OK < ! Huge vs tiny. 3C ALL 0i1 Hm1 OK < 3C ALL 0i1 -Hm1 OK > 3C ALL -0i1 Hm1 OK < 3C ALL -0i1 -Hm1 OK > 3C ALL 0i1 Hm1d1 OK < 3C ALL 0i1 -Hm1d1 OK > 3C ALL -0i1 Hm1d1 OK < 3C ALL -0i1 -Hm1d1 OK > 3C ALL 0i1 Hd1 OK < 3C ALL 0i1 -Hd1 OK > 3C ALL -0i1 Hd1 OK < 3C ALL -0i1 -Hd1 OK > 3C ALL 0i1 Hd2 OK < 3C ALL 0i1 -Hd2 OK > 3C ALL -0i1 Hd2 OK < 3C ALL -0i1 -Hd2 OK > ! Medium vs tiny. 3C ALL 0i1 1 OK < 3C ALL 0i1 -1 OK > 3C ALL -0i1 1 OK < 3C ALL -0i1 -1 OK > 3C ALL 0i1 1d1 OK < 3C ALL 0i1 -1d1 OK > 3C ALL -0i1 1d1 OK < 3C ALL -0i1 -1d1 OK > 3C ALL 0i1 2d1 OK < 3C ALL 0i1 -2d1 OK > 3C ALL -0i1 2d1 OK < 3C ALL -0i1 -2d1 OK > 3C ALL 0i1 2d2 OK < 3C ALL 0i1 -2d2 OK > 3C ALL -0i1 2d2 OK < 3C ALL -0i1 -2d2 OK > ! ! Magnitude subtract when an operand is in the sticky bit. ! The interesting cases will arise when directed rounding ! forces a nonzero cancellation. ! Huge and medium. 3C ALL Hm1 1 OK > 3C ALL Hm1 -1 OK > 3C ALL -Hm1 1 OK < 3C ALL -Hm1 -1 OK < 3C ALL Hm1d1 1 OK > 3C ALL Hm1d1 -1 OK > 3C ALL -Hm1d1 1 OK < 3C ALL -Hm1d1 -1 OK < 3C ALL Hd1 1 OK > 3C ALL Hd1 -1 OK > 3C ALL -Hd1 1 OK < 3C ALL -Hd1 -1 OK < 3C ALL Hd2 1 OK > 3C ALL Hd2 -1 OK > 3C ALL -Hd2 1 OK < 3C ALL -Hd2 -1 OK < ! Huge and tiny. 3C ALL Hd1 0i1 OK > 3C ALL Hd1 -0i1 OK > 3C ALL -Hd1 0i1 OK < 3C ALL -Hd1 -0i1 OK < 3C ALL 0i3 Hm1 OK < 3C ALL -0i3 Hm1 OK < 3C ALL 0i3 -Hm1 OK > 3C ALL -0i3 -Hm1 OK > ! Medium and tiny. 3C ALL 1d1 0i1 OK > 3C ALL 1d1 -0i1 OK > 3C ALL 2d1 0i1 OK > 3C ALL -2d1 0i1 OK < 3C ALL 0i3 3 OK < 3C ALL -0i3 3 OK < 3C ALL 0i3 5 OK < 3C ALL 0i3 -5 OK > ! ! Add magnitude with difference in LSB so, except for denorms, ! round bit is crucial. Half-way cases arise. ! Medium cases. 3C ALL 1i1 1 OK > 3C ALL 1i1 -1 OK > 3C ALL -1i1 1 OK < 3C ALL -1i1 -1 OK < 3C ALL -2 2i1 OK < 3C ALL -2 -2i1 OK > 3C ALL 2 -2i1 OK > 3C ALL 2 2i1 OK < 3C ALL 1 1i3 OK < 3C ALL 1 -1i3 OK > 3C ALL -1 1i3 OK < 3C ALL -1 -1i3 OK > 3C ALL -2i1 -2i2 OK > 3C ALL -2i1 2i2 OK < 3C ALL 2i1 -2i2 OK > 3C ALL 2i1 2i2 OK < ! Huge cases. 3C ALL Hd2 Hd1 OK < 3C ALL Hd2 -Hd1 OK > 3C ALL -Hd2 Hd1 OK < 3C ALL -Hd2 -Hd1 OK > 3C ALL Hm1d1 Hm1 OK < 3C ALL Hm1d1 -Hm1 OK > 3C ALL -Hm1d1 Hm1 OK < 3C ALL -Hm1d1 -Hm1 OK > 3C ALL Hm1i1 Hm1 OK > 3C ALL Hm1i1 -Hm1 OK > 3C ALL -Hm1i1 Hm1 OK < 3C ALL -Hm1i1 -Hm1 OK < 3C ALL Hm2i1 Hm2 OK > 3C ALL Hm2i1 -Hm2 OK > 3C ALL -Hm2i1 Hm2 OK < 3C ALL -Hm2i1 -Hm2 OK < 3C ALL Hm1d2 Hm1d1 OK < 3C ALL Hm1d2 -Hm1d1 OK > 3C ALL -Hm1d2 Hm1d1 OK < 3C ALL -Hm1d2 -Hm1d1 OK > ! NaN operands. Signaling NaN cases commented out <JPO, 4/30/93>. 3C ALL Q 0 OK ? 3C ALL Q -0 OK ? 3C ALL 0 Q OK ? 3C ALL -0 Q OK ? 3C ALL Q 1 OK ? 3C ALL Q -1 OK ? 3C ALL 1 Q OK ? 3C ALL -1 Q OK ? 3C ALL Ed1 Q OK ? 3C ALL -Ed1 Q OK ? 3C ALL Q Ed1 OK ? 3C ALL Q -Ed1 OK ? 3C ALL Q 0i1 OK ? 3C ALL Q -0i1 OK ? 3C ALL 0i1 Q OK ? 3C ALL -0i1 Q OK ? 3C ALL Q Hd1 OK ? 3C ALL Q -Hd1 OK ? 3C ALL Hd1 Q OK ? 3C ALL -Hd1 Q OK ? 3C ALL Q H OK ? 3C ALL Q -H OK ? 3C ALL H Q OK ? 3C ALL -H Q OK ? 3C ALL Q Q OK ? !3C ALL S 0 i ? !3C ALL S -0 i ? !3C ALL 0 S i ? !3C ALL -0 S i ? !3C ALL S 1 i ? !3C ALL S -1 i ? !3C ALL 1 S i ? !3C ALL -1 S i ? !3C ALL Ed1 S i ? !3C ALL -Ed1 S i ? !3C ALL S Ed1 i ? !3C ALL S -Ed1 i ? !3C ALL S 0i1 i ? !3C ALL S -0i1 i ? !3C ALL 0i1 S i ? !3C ALL -0i1 S i ? !3C ALL S Hd1 i ? !3C ALL S -Hd1 i ? !3C ALL Hd1 S i ? !3C ALL -Hd1 S i ? !3C ALL S H i ? !3C ALL S -H i ? !3C ALL H S i ? !3C ALL -H S i ? !3C ALL Q S i ? !3C ALL S Q i ? !3C ALL S S i ?