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