%%%off % Copyright: This file is part of the MMIX Supplement package (c) Martin Ruckert 2014 % File: 1.3.2/ex14opt.mms % Author: M.Ruckert % Title: Exercise 14, The Date of Easter Sunday PREFIX :Easter: y IS $0 g IS$1 c IS $2 x IS$3 z IS $4 d IS$5 e IS $6 n IS$7 t IS $9 %%%on 1H GREG 970881267037344822$2^{64}\!/19+2/19$:Easter MULU t,y,1B; GET t,:rH \ut E1. Golden number.\\^{Golden number}^{rH+rH (himult register)}^{Himult register} MUL t,t,19 SUB g,y,t ADD g,g,1$G\is Y\mod 19 +1$. %%% 1H GREG 184467440737095517$2^{64}\!/100+84/100$MULU t,y,1B; GET t,:rH \ut E2. Century.\\ ADD c,t,1$C\is \lfloor Y/100\rfloor+1$. 2ADDU x,c,c \ut E3. Corrections.\\^{2ADDU+<2ADDU> (times 2 and add unsigned)} SRU x,x,2 SUB x,x,12$X\is \lfloor 3C/4\rfloor-12$. 8ADDU z,c,5 1H GREG 737869762948382065$2^{64}\!/25-9/25$^{GREG+ (allocate global register)} MULU t,z,1B; GET z,:rH SUB z,z,5$Z\is \lfloor (8C+5)/25\rfloor-5$. 4ADDU d,y,y \ut E4. Find Sunday.\\^{4ADDU+<4ADDU> (times 4 and add unsigned)} SRU d,d,2 SUB d,d,x SUB d,d,10$D\is \lfloor 5Y/4\rfloor-X-10$. 2ADDU e,g,g \ut E5. Epact.\\^{2ADDU+<2ADDU> (times 2 and add unsigned)} 8ADDU e,g,e ADD e,e,20 ADD e,e,z SUB e,e,x 1H GREG 614891469123651721$2^{64}\!/30-14/30$MULU t,e,1B; GET t,:rH MUL t,t,30 SUB e,e,t$E\is (11G+20+Z-X) \mod 30$. %%% CMP t,e,25 BNZ t,1F CMP t,g,11 ZSP t,t,1$\.t.\is G>11$. JMP 2F %%% 1H CMP t,e,24 ZSZ t,t,1$\.t.\is E=24$. 2H ADD e,e,t Increase$E$if needed. %%% NEG n,44,e \ut E6. Find full moon.\\$N\is 44-E$. CMP t,n,21 ZSN t,t,30 ADD n,n,t$N\is N+30$if$N<21$. %%% ADD t,d,n \ut E7. Advance to Sunday.\\ 1H GREG 2635249153387078803$2^{64}\!/7+5/7$MULU t+1,t,1B; GET t+1,:rH MUL t+1,t+1,7 SUB t,t,t+1 ADD n,n,7 SUB n,n,t$N\is N+7-(D+N)\mod 7$. %%% CMP t,n,31 \ut E8. Get month.\\ BNP t,1F If$N>31$, SUB$1,n,31 \quad return $N-31$ SET $0,4 \quad and April. POP 2,0 %%% 1H SET$1,n Else return $N$ SET \$0,3 \quad and March. %%% POP 2,0 \slug %%%off PREFIX :