! TEST VECTORS FOR Annuity: ! ! 1 - (1+r)^-n ! x = -------------- ! r ! ! The following combinations occur in this file: ! ! |r| |n| ! ---------- --------- ! near 0 near 0 ! near E near E ! near 1u1 near 1u1 ! near 1 near 1 ! near 2 near 2 ! some integers some integers ! near H near H ! NaN NaN ! ! n = 0: ! FIRST THE ONLY VECTOR WHICH FAILS ! ! Commented out signaling NaN cases <JPO, 5/13/93> ! 3Z d Hm1 -2 x -Hm1 3Z d 0 0 OK 0 3Z d 0i1 0 OK 0 3Z d 0i2 0 OK 0 3Z d Em1 0 OK 0 3Z d Ed1 0 OK 0 3Z d E 0 OK 0 3Z d Ei1 0 OK 0 3Z d 1u1 0 OK 0 3Z d 1d1 0 OK 0 3Z d 1 0 OK 0 3Z d 1i1 0 OK 0 3Z d 2d1 0 OK 0 3Z d 2 0 OK 0 3Z d 2i1 0 OK 0 3Z d 255 0 OK 0 3Z d 256 0 OK 0 3Z d 257 0 OK 0 3Z d Hm1 0 OK 0 3Z d Hd1 0 OK 0 3Z d H 0 OK 0 3Z d Q 0 OK Q 3Z d -Q 0 OK -Q !3Z e S 0 i Q !3Z e -S 0 i -Q 3Z d -0 0 OK 0 3Z d -0i1 0 OK 0 3Z d -0i2 0 OK 0 3Z d -Em1 0 OK 0 3Z d -Ed1 0 OK 0 3Z d -E 0 OK 0 3Z d -Ei1 0 OK 0 3Z d -1u1 0 OK 0 3Z d -1d1 0 OK 0 3Z d -1 0 OK 0 3Z d -1i1 0 i Q 3Z d -2d1 0 i Q 3Z d -2 0 i Q 3Z d -2i1 0 i Q 3Z d -255 0 i Q 3Z d -256 0 i Q 3Z d -257 0 i Q 3Z d -Hm1 0 i Q 3Z d -Hd1 0 i Q 3Z d -H 0 i Q ! n = -0: 3Z d 0 -0 OK 0 3Z d 0i1 -0 OK 0 3Z d 0i2 -0 OK 0 3Z d Em1 -0 OK 0 3Z d Ed1 -0 OK 0 3Z d E -0 OK 0 3Z d Ei1 -0 OK 0 3Z d 1u1 -0 OK 0 3Z d 1d1 -0 OK 0 3Z d 1 -0 OK 0 3Z d 1i1 -0 OK 0 3Z d 2d1 -0 OK 0 3Z d 2 -0 OK 0 3Z d 2i1 -0 OK 0 3Z d 255 -0 OK 0 3Z d 256 -0 OK 0 3Z d 257 -0 OK 0 3Z d Hm1 -0 OK 0 3Z d Hd1 -0 OK 0 3Z d H -0 OK 0 3Z d Q -0 OK Q 3Z d -Q -0 OK -Q !3Z e S -0 i Q !3Z e -S -0 i -Q 3Z d -0 -0 OK 0 3Z d -0i1 -0 OK 0 3Z d -0i2 -0 OK 0 3Z d -Em1 -0 OK 0 3Z d -Ed1 -0 OK 0 3Z d -E -0 OK 0 3Z d -Ei1 -0 OK 0 3Z d -1u1 -0 OK 0 3Z d -1d1 -0 OK 0 3Z d -1 -0 OK 0 3Z d -1i1 -0 i Q 3Z d -2d1 -0 i Q 3Z d -2 -0 i Q 3Z d -2i1 -0 i Q 3Z d -255 -0 i Q 3Z d -256 -0 i Q 3Z d -257 -0 i Q 3Z d -Hm1 -0 i Q 3Z d -Hd1 -0 i Q 3Z d -H -0 i Q ! n = -0i1: 3Z d 0 -0i1 OK -0i1 3Z d -0 -0i1 OK -0i1 3Z d Hm1 -0i1 ux -0 3Z d Hd1 -0i1 ux -0 3Z d H -0i1 OK -0 3Z d Q -0i1 OK Q 3Z d -Q -0i1 OK -Q !3Z e S -0i1 i Q !3Z e -S -0i1 i -Q 3Z d -1 -0i1 OK -1 3Z d -6 -0i1 i Q 3Z d -Hm1 -0i1 i Q 3Z d -Hd1 -0i1 i Q 3Z d -H -0i1 i Q ! n = 0i1: 3Z d 0 0i1 OK 0i1 3Z d -0 0i1 OK 0i1 3Z d Hm1 0i1 ux 0 3Z d Hd1 0i1 ux 0 3Z d H 0i1 OK 0 3Z d Q 0i1 OK Q 3Z d -Q 0i1 OK -Q !3Z e S 0i1 i Q !3Z e -S 0i1 i -Q 3Z d -1 0i1 z H 3Z d -2 0i1 i Q 3Z d -Hm1 0i1 i Q 3Z d -Hd1 0i1 i Q 3Z d -H 0i1 i Q ! n near E: 3Z d 0 E OK E 3Z d 0 Em1 OK Em1 3Z d 0 Ep1 OK Ep1 3Z d -0 E OK E 3Z d -0 Em1 OK Em1 3Z d -0 Ep1 OK Ep1 3Z d Hm1 E ux 0 3Z d Hm1 Em1 ux 0 3Z d Hm1 Ep1 ux 0 3Z d Hd1 E ux 0 3Z d Hd1 Em1 ux 0 3Z d Hd1 Ep1 ux 0 3Z d H Em1 OK 0 3Z d H E OK 0 3Z d H Ep1 OK 0 3Z d Q Em1 OK Q 3Z d Q E OK Q 3Z d Q Ep1 OK Q !3Z e S Em1 i Q !3Z e S E i Q !3Z e S Ep1 i Q !3Z e -S Em1 i -Q !3Z e -S E i -Q !3Z e -S Ep1 i -Q 3Z d -Q Em1 OK -Q 3Z d -Q E OK -Q 3Z d -Q Ep1 OK -Q 3Z d -1 Em1 z H 3Z d -1 E z H 3Z d -1 Ep1 z H 3Z d -13 Em1 i Q 3Z d -13 E i Q 3Z d -13 Ep1 i Q 3Z d -Hm1 Em1 i Q 3Z d -Hm1 E i Q 3Z d -Hm1 Ep1 i Q 3Z d -Hd1 Em1 i Q 3Z d -Hd1 E i Q 3Z d -Hd1 Ep1 i Q 3Z d -H Em1 i Q 3Z d -H E i Q 3Z d -H Ep1 i Q ! n near -E: 3Z d 0 -E OK -E 3Z d 0 -Em1 OK -Em1 3Z d 0 -Ep1 OK -Ep1 3Z d -0 -E OK -E 3Z d -0 -Em1 OK -Em1 3Z d -0 -Ep1 OK -Ep1 3Z d Hm1 -E ux -0 3Z d Hm1 -Em1 ux -0 3Z d Hm1 -Ep1 ux -0 3Z d Hd1 -E ux -0 3Z d Hd1 -Em1 ux -0 3Z d Hd1 -Ep1 ux -0 3Z d H -Em1 OK -0 3Z d H -E OK -0 3Z d H -Ep1 OK -0 3Z d Q -Em1 OK Q 3Z d Q -E OK Q 3Z d Q -Ep1 OK Q !3Z e S -Em1 i Q !3Z e S -E i Q !3Z e S -Ep1 i Q !3Z e -S -Em1 i -Q !3Z e -S -E i -Q !3Z e -S -Ep1 i -Q 3Z d -Q -Em1 OK -Q 3Z d -Q -E OK -Q 3Z d -Q -Ep1 OK -Q 3Z d -1 -Em1 OK -1 3Z d -1 -E OK -1 3Z d -1 -Ep1 OK -1 3Z d -13 -Em1 i Q 3Z d -13 -E i Q 3Z d -13 -Ep1 i Q 3Z d -Hm1 -Em1 i Q 3Z d -Hm1 -E i Q 3Z d -Hm1 -Ep1 i Q 3Z d -Hd1 -Em1 i Q 3Z d -Hd1 -E i Q 3Z d -Hd1 -Ep1 i Q 3Z d -H -Em1 i Q 3Z d -H -E i Q 3Z d -H -Ep1 i Q ! n = 1u1: 3Z d 0 1u1 OK 1u1 3Z d -0 1u1 OK 1u1 3Z d H 1u1 OK 0 3Z d Q 1u1 OK Q 3Z d -Q 1u1 OK -Q !3Z e S 1u1 i Q !3Z e -S 1u1 i -Q 3Z d -1 1u1 z H 3Z d -Hm1 1u1 i Q 3Z d -Hd1 1u1 i Q 3Z d -H 1u1 i Q ! n = -1u1: 3Z d 0 -1u1 OK -1u1 3Z d -0 -1u1 OK -1u1 3Z d H -1u1 OK -0 3Z d Q -1u1 OK Q 3Z d -Q -1u1 OK -Q !3Z e S -1u1 i Q !3Z e -S -1u1 i -Q 3Z d -1 -1u1 OK -1 3Z d -13 -1u1 i Q 3Z d -Hm1 -1u1 i Q 3Z d -Hd1 -1u1 i Q 3Z d -H -1u1 i Q ! n = 1: 3Z d 0 1 OK 1 3Z d 0i1 1 x 1 3Z d E 1 x 1+1 3Z d 1u1 1 x 1d2+2 3Z d 1d1 1 x 1m1+1 3Z d 1 1 OK 1m1 3Z d 1i1 1 x 1m1d1-1 3Z d 3 1 OK 1m2 3Z d 255 1 OK 1m8 3Z d Hm1 1 x E 3Z d Hd1 1 ux Em1 3Z d H 1 OK 0 3Z d Q 1 OK Q 3Z d -Q 1 OK -Q !3Z e S 1 i Q !3Z e -S 1 i -Q 3Z d -0 1 OK 1 3Z d -0i1 1 x 1 3Z d -E 1 x 1+1 3Z d -1u1 1 x 1i1+1 3Z d -1d1 1 OK 1p64 3Z d -1 1 z H 3Z d -1i1 1 i Q 3Z d -3 1 i Q 3Z d -255 1 i Q 3Z d -Hm1 1 i Q 3Z d -Hd1 1 i Q 3Z d -H 1 i Q ! n = 1d1: 3Z d 0 1d1 OK 1d1 3Z d H 1d1 OK 0 3Z d Q 1d1 OK Q 3Z d -Q 1d1 OK -Q !3Z e S 1d1 i Q !3Z e -S 1d1 i -Q 3Z d -0 1d1 OK 1d1 3Z d -3 1d1 i Q 3Z d -Hm1 1d1 i Q 3Z d -H 1d1 i Q ! n = 1i1: 3Z d 0 1i1 OK 1i1 3Z d H 1i1 OK 0 3Z d Q 1i1 OK Q 3Z d -Q 1i1 OK -Q !3Z e S 1i1 i Q !3Z e -S 1i1 i -Q 3Z d -0 1i1 OK 1i1 3Z d -5 1i1 i Q 3Z d -Hm1 1i1 i Q 3Z d -H 1i1 i Q ! n = 2: 3Z d 0 2 OK 2 3Z d 0i1 2 x 2 3Z d 0i2 2 x 2 3Z d 0i22 2 x 2 3Z d Em2 2 x 2 3Z d E 2 x 2+1 3Z d 1u1 2 x 2d2+1 3Z d 1d1 2 x 3m2i1 3Z d 1 2 OK 3m2 3Z d 1i1 2 x 3m2d1 3Z d 3 2 OK 5m4 3Z d 7 2 OK 9m6 3Z d 255 2 OK 257m16 3Z d Hm1 2 x E 3Z d H 2 OK 0 3Z d Q 2 OK Q 3Z d -Q 2 OK -Q !3Z e S 2 i Q !3Z e -S 2 i -Q 3Z d -0 2 OK 2 3Z d -0i1 2 x 2 3Z d -0i2 2 x 2 3Z d -0i13 2 x 2 3Z d -Ed4 2 x 2+1 3Z d -E 2 x 2+1 3Z d -1u1 2 x 2i2 3Z d -1d2 2 x 1i1p126 Note: Result actually exact. 3Z d -1d1 2 x 1p128+1 3Z d -1 2 z H 3Z d -3 2 i Q 3Z d -255 2 i Q 3Z d -Hm1 2 i Q 3Z d -H 2 i Q ! n = 3: 3Z d 0 3 OK 3 3Z d 0i1 3 x 3 3Z d 0i2 3 x 3 3Z d 0i8 3 x 3 3Z d Em3 3 x 3-4 3Z d E 3 x 3 3Z d 1u1 3 x 3d3+1 3Z d 1d1 3 x 7m3i1 3Z d 1 3 OK 7m3 3Z d 1i1 3 x 7m3d1-1 3Z d 3 3 OK 21m6 3Z d 7 3 OK 73m9 3Z d 127 3 OK 16513m21 3Z d Hm1 3 x E 3Z d H 3 OK 0 3Z d Q 3 OK Q 3Z d -Q 3 OK -Q !3Z e S 3 i Q !3Z e -S 3 i -Q 3Z d -0 3 OK 3 3Z d -0i1 3 x 3 3Z d -0i2 3 x 3 3Z d -0i3 3 x 3 3Z d -Ed7 3 x 3+1 3Z d -E 3 x 3 3Z d -1u1 3 x 3i3+1 3Z d -1d1 3 x 1i1p192 3Z d -1 3 z H 3Z d -1i1 3 i Q 3Z d -3 3 i Q 3Z d -7 3 i Q 3Z d -127 3 i Q 3Z d -Hm1 3 i Q 3Z d -H 3 i Q ! n = 4: 3Z d 0 4 OK 4 3Z d 0i1 4 x 4 3Z d 0i2 4 x 4 3Z d 0i17 4 x 4 3Z d Ed5 4 x 4 3Z d E 4 x 4+1 3Z d 1u1 4 x 4d5+2 3Z d 1d1 4 x 15m4i1 3Z d 1 4 OK 15m4 3Z d 1i1 4 x 15m4d2 3Z d 3 4 OK 85m8 3Z d 7 4 OK 585m12 3Z d Hm1 4 x E 3Z d H 4 OK 0 3Z d Q 4 OK Q 3Z d -Q 4 OK -Q !3Z e S 4 i Q !3Z e -S 4 i -Q 3Z d -0 4 OK 4 3Z d -0i1 4 x 4 3Z d -0i2 4 x 4 3Z d -0i18 4 x 4 3Z d -Em4 4 x 4+4 3Z d -E 4 x 4+1 3Z d -1u1 4 x 4i3 3Z d -1d1 4 x 1i1p256 3Z d -1 4 z H 3Z d -1i1 4 i Q 3Z d -3 4 i Q 3Z d -7 4 i Q 3Z d -Hm1 4 i Q 3Z d -H 4 i Q ! n = 64: 3Z d 0 64 OK 64 3Z d 0i1 64 x 64 3Z d 0i2 64 x 64 3Z d 0i21 64 x 64 3Z d Ed7 64 x 64 3Z d E 64 x 64+1 3Z d 1u1 64 x 1d65p6+2 3Z d 1 64 OK 1d1 3Z d 4 64 x 1m2 3Z d Hm1 64 x E 3Z d H 64 OK 0 3Z d Q 64 OK Q 3Z d -Q 64 OK -Q !3Z e S 64 i Q !3Z e -S 64 i -Q 3Z d -0 64 OK 64 3Z d -0i1 64 x 64 3Z d -0i2 64 x 64 3Z d -Em7 64 x 64 3Z d -Ed2 64 x 64+1 3Z d -E 64 x 64+1 3Z d -1u1 64 x 1i33p6 3Z d -1 64 z H 3Z d -3 64 i Q 3Z d -Hm1 64 i Q 3Z d -H 64 i Q ! n = 1024: 3Z d 0 1024 OK 1024 3Z d 0i1 1024 x 1024 3Z d 0i2 1024 x 1024 3Z d 0i7 1024 x 1024 3Z d Ed5 1024 x 1024 3Z d E 1024 x 1024+1 3Z d 1u1 1024 x 1024d1025+2 3Z d 1 1024 x 1 3Z d 4 1024 x 1m2 3Z d Hm1 1024 x E 3Z d H 1024 OK 0 3Z d Q 1024 OK Q 3Z d -Q 1024 OK -Q !3Z e S 1024 i Q !3Z e -S 1024 i -Q 3Z d -0 1024 OK 1024 3Z d -0i1 1024 x 1024 3Z d -0i2 1024 x 1024 3Z d -Em3 1024 x 1024+1 3Z d -Ed1 1024 x 1024 3Z d -E 1024 x 1024+1 3Z d -1u1 1024 x 1024i513 3Z d -1 1024 z H 3Z d -3 1024 i Q 3Z d -Hm1 1024 i Q 3Z d -H 1024 i Q ! n = Hd1: 3Z d 0 Hd1 OK Hd1 3Z d 1 Hd1 x 1 3Z d 4 Hd1 x 1m2 3Z d Hm1 Hd1 x E 3Z d H Hd1 OK 0 3Z d Q Hd1 OK Q 3Z d -Q Hd1 OK -Q !3Z e S Hd1 i Q !3Z e -S Hd1 i -Q 3Z d -0 Hd1 OK Hd1 3Z d -1 Hd1 z H 3Z d -3 Hd1 i Q 3Z d -Hm1 Hd1 i Q 3Z d -H Hd1 i Q ! n = H: 3Z d 0 H OK H 3Z d 0i1 H ox H 3Z d E H OK Hm1 3Z d 1 H OK 1 3Z d 4 H OK 1m2 3Z d Hm1 H OK E 3Z d H H OK 0 3Z d Q H OK Q 3Z d -Q H OK -Q !3Z e S H i Q !3Z e -S H i -Q 3Z d -0 H OK H 3Z d -0i1 H OK H 3Z d -E H OK H 3Z d -1 H z H 3Z d -3 H i Q 3Z d -Hm1 H i Q 3Z d -H H i Q ! n = -H: 3Z d 0 -H OK -H 3Z d 0i1 -H OK -H 3Z d E -H OK -H 3Z d 1 -H OK -H 3Z d 4 -H OK -H 3Z d Hm1 -H OK -H 3Z d H -H OK -H 3Z d Q -H OK Q 3Z d -Q -H OK -Q !3Z e S -H i Q !3Z e -S -H i -Q 3Z d -0 -H OK -H 3Z d -0i1 -H ox -H 3Z d -E -H OK -Hm1 3Z d -1 -H OK -1 3Z d -3 -H i Q 3Z d -Hm1 -H i Q 3Z d -H -H i Q ! n = -Hd1: 3Z d 0 -Hd1 OK -Hd1 3Z d 1 -Hd1 ox -H 3Z d 4 -Hd1 ox -H 3Z d Hm1 -Hd1 ox -H 3Z d H -Hd1 OK -H 3Z d Q -Hd1 OK Q 3Z d -Q -Hd1 OK -Q !3Z e S -Hd1 i Q !3Z e -S -Hd1 i -Q 3Z d -0 -Hd1 OK -Hd1 3Z d -1 -Hd1 OK -1 3Z d -4 -Hd1 i Q 3Z d -Hm1 -Hd1 i Q 3Z d -H -Hd1 i Q ! n = NaN: 3Z d 0 -Q OK -Q 3Z d 0i1 -Q OK -Q 3Z d 1u1 -Q OK -Q 3Z d 1d1 -Q OK -Q 3Z d 1 -Q OK -Q 3Z d 1i1 -Q OK -Q 3Z d 3 -Q OK -Q 3Z d 255 -Q OK -Q 3Z d 257 -Q OK -Q 3Z d Hm1 -Q OK -Q 3Z d Hd1 -Q OK -Q 3Z d H -Q OK -Q 3Z d Q -Q OK -Q 3Z d -Q -Q OK -Q !3Z e S -Q i Q !3Z e -S -Q i -Q 3Z d -0 -Q OK -Q 3Z d -0i1 -Q OK -Q 3Z d -E -Q OK -Q 3Z d -1u1 -Q OK -Q 3Z d -1d1 -Q OK -Q 3Z d -1 -Q OK -Q 3Z d -1i1 -Q OK -Q 3Z d -3 -Q OK -Q 3Z d -255 -Q OK -Q 3Z d -Hm1 -Q OK -Q 3Z d -Hd1 -Q OK -Q 3Z d -H -Q OK -Q !3Z e 0 S i Q !3Z e 0i1 S i Q !3Z e 1u1 S i Q !3Z e 1d1 S i Q !3Z e 1 S i Q !3Z e 1i1 S i Q !3Z e 3 S i Q !3Z e 255 S i Q !3Z e 257 S i Q !3Z e Hm1 S i Q !3Z e Hd1 S i Q !3Z e H S i Q !3Z e Q S i Q !3Z e -Q S i -Q !3Z e S S i Q !3Z e -S S i -Q !3Z e -0 S i Q !3Z e -0i1 S i Q !3Z e -E S i Q !3Z e -1u1 S i Q !3Z e -1d1 S i Q !3Z e -1 S i Q !3Z e -1i1 S i Q !3Z e -3 S i Q !3Z e -255 S i Q !3Z e -Hm1 S i Q !3Z e -Hd1 S i Q !3Z e -H S i Q 3Z d 0 Q OK Q 3Z d 0i1 Q OK Q 3Z d 1u1 Q OK Q 3Z d 1d1 Q OK Q 3Z d 1 Q OK Q 3Z d 1i1 Q OK Q 3Z d 3 Q OK Q 3Z d 255 Q OK Q 3Z d 257 Q OK Q 3Z d Hm1 Q OK Q 3Z d Hd1 Q OK Q 3Z d H Q OK Q 3Z d Q Q OK Q 3Z d -Q Q OK -Q !3Z e S Q i Q !3Z e -S Q i -Q 3Z d -0 Q OK Q 3Z d -0i1 Q OK Q 3Z d -E Q OK Q 3Z d -1u1 Q OK Q 3Z d -1d1 Q OK Q 3Z d -1 Q OK Q 3Z d -1i1 Q OK Q 3Z d -3 Q OK Q 3Z d -255 Q OK Q 3Z d -Hm1 Q OK Q 3Z d -Hd1 Q OK Q 3Z d -H Q OK Q !3Z e 0i1 -S i -Q !3Z e 1u1 -S i -Q !3Z e 1d1 -S i -Q !3Z e 1 -S i -Q !3Z e 1i1 -S i -Q !3Z e 3 -S i -Q !3Z e 255 -S i -Q !3Z e 257 -S i -Q !3Z e Hm1 -S i -Q !3Z e Hd1 -S i -Q !3Z e H -S i -Q !3Z e Q -S i Q !3Z e -Q -S i -Q !3Z e S -S i Q !3Z e -S -S i -Q !3Z e -0 -S i -Q !3Z e -0i1 -S i -Q !3Z e -E -S i -Q !3Z e -1u1 -S i -Q !3Z e -1d1 -S i -Q !3Z e -1 -S i -Q !3Z e -1i1 -S i -Q !3Z e -3 -S i -Q !3Z e -255 -S i -Q !3Z e -Hm1 -S i -Q !3Z e -Hd1 -S i -Q !3Z e -H -S i -Q ! n = -1: NOTE: Annuity formula reduces to EXACTLY -1 for -1 < r < H. 3Z d 0 -1 OK -1 3Z d 0i1 -1 x -1 Note: Result exact. 3Z d E -1 x -1+1 Note: Result exact. 3Z d 1u1 -1 x -1+1 Note: Result exact. 3Z d 1d1 -1 x -1+1 Note: Result exact. 3Z d 1 -1 OK -1 3Z d 1i1 -1 x -1-2 Note: Result exact. 3Z d 2 -1 x -1 Note: Result exact. 3Z d 255 -1 OK -1 3Z d 257 -1 x -1 Note: Result exact. 3Z d Hm1 -1 x -1 Note: Result exact. 3Z d H -1 OK -1 3Z d Q -1 OK Q 3Z d -Q -1 OK -Q !3Z e S -1 i Q !3Z e -S -1 i -Q 3Z d -0 -1 OK -1 3Z d -0i1 -1 x -1 Note: Result exact. 3Z d -E -1 x -1+1 Note: Result exact. 3Z d -1u1 -1 x -1+1 Note: Result exact. 3Z d -1d1 -1 OK -1 3Z d -1 -1 OK -1 3Z d -1i1 -1 i Q 3Z d -2 -1 i Q 3Z d -255 -1 i Q 3Z d -257 -1 i Q 3Z d -Hm1 -1 i Q 3Z d -H -1 i Q ! n = -2: 3Z d 0 -2 OK -2 3Z d 0i1 -2 x -2 3Z d 0i3 -2 x -2 3Z d E -2 x -2+1 3Z d 1u1 -2 x -2+2 3Z d 1d1 -2 x -3+1 3Z d 1 -2 OK -3 3Z d 1i1 -2 x -3-1 3Z d 2 -2 x -4 Note: Result exact. 3Z d 255 -2 OK -257 3Z d 257 -2 x -259 Note: Result exact. 3Z d Hm1 -2 x -Hm1 3Z d H -2 OK -H 3Z d Q -2 OK Q 3Z d -Q -2 OK -Q !3Z e S -2 i Q !3Z e -S -2 i -Q 3Z d -0 -2 OK -2 3Z d -0i1 -2 x -2 3Z d -Em5 -2 x -2 3Z d -E -2 x -2+1 3Z d -1u1 -2 x -2 3Z d -1d1 -2 x -1d1+2 3Z d -1 -2 OK -1 3Z d -1i1 -2 i Q 3Z d -2 -2 i Q 3Z d -255 -2 i Q 3Z d -257 -2 i Q 3Z d -Hm1 -2 i Q 3Z d -H -2 i Q ! n = -4: 3Z d 0 -4 OK -4 3Z d 0i1 -4 x -4 3Z d Ed4 -4 x -4+1 3Z d E -4 x -4+1 3Z d 1u1 -4 x -4i2+1 3Z d 1d1 -4 x -15d1+2 3Z d 1 -4 OK -15 3Z d 1i1 -4 x -15i1-3 3Z d 2 -4 x -40+1 Note: Result exact. 3Z d Hm1 -4 ox -H 3Z d H -4 OK -H 3Z d Q -4 OK Q 3Z d -Q -4 OK -Q !3Z e S -4 i Q !3Z e -S -4 i -Q 3Z d -0 -4 OK -4 3Z d -0i1 -4 x -4 3Z d -0i7 -4 x -4 3Z d -E -4 x -4+1 3Z d -1u1 -4 x -4d2 3Z d -1d1 -4 x -1i1 3Z d -1 -4 OK -1 3Z d -1i1 -4 i Q 3Z d -2 -4 i Q 3Z d -255 -4 i Q 3Z d -257 -4 i Q 3Z d -Hm1 -4 i Q 3Z d -H -4 i Q ! n = -64: 3Z d 0 -64 OK -64 3Z d 0i1 -64 x -64 3Z d 0i7 -64 x -64 3Z d E -64 x -64+1 3Z d 1u1 -64 x -1i32p6+1 3Z d 1 -64 OK -1d1p64 3Z d Hm1 -64 ox -H 3Z d H -64 OK -H 3Z d Q -64 OK Q 3Z d -Q -64 OK -Q !3Z e S -64 i Q !3Z e -S -64 i -Q 3Z d -0 -64 OK -64 3Z d -0i1 -64 x -64 3Z d -Em6 -64 x -64+3 3Z d -E -64 x -64+1 3Z d -1u1 -64 x -64d63+1 3Z d -1 -64 OK -1 3Z d -1i1 -64 i Q 3Z d -2 -64 i Q 3Z d -255 -64 i Q 3Z d -Hm1 -64 i Q 3Z d -H -64 i Q