LARGESUM

[Xlambda]

LARGESUM sums 2 large numbers
On Fibonacci post this site was pointed to me Lambda for large numbers . This is my take using recursion. Uses this tools:
T_2RH(a,b)=LAMBDA(a,b,LET(ca,COLUMNS(a),cb,COLUMNS(b),c,ca+cb,s,SEQUENCE(,c),rs,IF(s<=ca,IF(a="","",a),INDEX(IF(b="","",b),s-ca)),rs))
!! recursive !! T_LSUM(a,i)=LAMBDA(a,i,LET(n,COLUMNS(a),x,INDEX(a,n),c,SEQUENCE(,COLUMNS(i)),y,T_2RH(x+INT(INDEX(i,1)/10),i),IF(n=1,INDEX(y,c),T_LSUM(INDEX(a,SEQUENCE(,n-1)),y))))

=LAMBDA(a,b,
    LET(ab,CHOOSE({1;2},a,b),l,LEN(ab),ml,MAX(l),x,IF(LEN(ab)<ml,REPLACE(ab,1,0,REPT(0,ml-LEN(ab))),ab),
       mx,--MID(x,SEQUENCE(,ml),1),y,MMULT({1,1},mx),t,T_LSUM(y,0),
       INDEX(t,1)&CONCAT(RIGHT(INDEX(t,SEQUENCE(,ml-1,2)),1))
    )
)

LAMBDA 6.0.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L
1	FIB	1	2	3	4	5	6	7	8	9	10
2	1	1	1	2	3	5	8	13	21	34	55
3	2	89	144	233	377	610	987	1597	2584	4181	6765
4	3	10946	17711	28657	46368	75025	121393	196418	317811	514229	832040
5	4	1346269	2178309	3524578	5702887	9227465	14930352	24157817	39088169	63245986	102334155
6	5	165580141	267914296	433494437	701408733	1134903170	1836311903	2971215073	4807526976	7778742049	12586269025
7	6	20365011074	32951280099	53316291173	86267571272	139583862445	225851433717	365435296162	591286729879	956722026041	1548008755920
8	7	2504730781961	4052739537881	6557470319842	10610209857723	17167680177565	27777890035288	44945570212853	72723460248141	117669030460994	190392490709135
9	8	308061521170129	498454011879264	806515533049393	1304969544928660	2111485077978050	3416454622906710	5527939700884760	8944394323791460	14472334024676200	23416728348467700
10					excel sum fails
11	8	308061521170129	498454011879264	806515533049393	1304969544928657	2111485077978050	3416454622906707	5527939700884757	8944394323791464	14472334024676221	23416728348467685
12	9	37889062373143906	61305790721611591	99194853094755497	160500643816367088	259695496911122585	420196140727489673	679891637638612258	1100087778366101931	1779979416004714189	2880067194370816120
13	10	4660046610375530309	7540113804746346429	12200160415121876738	19740274219868223167	31940434634990099905	51680708854858323072	83621143489848422977	135301852344706746049	218922995834555169026	354224848179261915075
14	11	573147844013817084101	927372692193078999176	1500520536206896083277	2427893228399975082453	3928413764606871165730	6356306993006846248183	10284720757613717413913	16641027750620563662096	26925748508234281076009	43566776258854844738105
15	12	70492524767089125814114	114059301025943970552219	184551825793033096366333	298611126818977066918552	483162952612010163284885	781774079430987230203437	1264937032042997393488322	2046711111473984623691759	3311648143516982017180081	5358359254990966640871840
16	13	8670007398507948658051921	14028366653498915298923761	22698374052006863956975682	36726740705505779255899443	59425114757512643212875125	96151855463018422468774568	155576970220531065681649693	251728825683549488150424261	407305795904080553832073954	659034621587630041982498215
17
18
19			LEN
20			100	7987623457654123456787654234512340987345612345987651234523451234587650987653456787654345678765434567
21			100	9088776876651234453436465475476576588585758757555412365098785650987665544332312465189081893873262367
22			=LARGESUM(D20,D21)	17076400334305357910224119709988917575931371103543063599622236885575316531985769252843427572638696934
23
LARGESUM post

Cell Formulas
Range	Formula
B1:K1	B1	=SEQUENCE(,10)
A2:A9	A2	=SEQUENCE(8)
D2:K9	D2	=B2+C2
B3:B9	B3	=J2+K2
C3:C9	C3	=B3+K2
E11:K11,D12:K16	E11	=LARGESUM(C11,D11)
B12:B16	B12	=LARGESUM(J11,K11)
C12:C16	C12	=LARGESUM(B12,K11)
C20:C21	C20	=LEN(D20)
C22	C22	=FORMULATEXT(D22)
D22	D22	=LARGESUM(D20,D21)
Dynamic array formulas.

 

[Xlambda]

Checking latest excel update recursion limits on a different type of recursive function.
Before the nr. of digits limit was 100, now is 255.

CM Lambda helper functions.xlsx
	A	B	C
1	nr chars:
2	255
3
4	=REPT("1",A2)		111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
5
6	=REPT("9",A2)		999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
7
8	lenghts check		=LARGESUM(C4,C6)
9	256		1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110
10	=LEN(C9)
11
12	nr chars:
13	256
14
15	=REPT("1",A13)		1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
16
17	=REPT("9",A13)		9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
18
19			=LARGESUM(C15,C17)
20			#VALUE!
21
22	nr chars:
23	255
24
25	=REPT("9",A23)		999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
26
27	=REPT("8",A23)		888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888
28
29	lenghts check		=LARGESUM(C25,C27)
30	256		1888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
31	=LEN(C30)
32
33	last 2 digit check		Note:
34	to prove the sum		To "hack" excel displaying numbers with so many digits, these are the string representations of the respective numbers.
35	is correct
36	=RIGHT(C9,2)
37	10
38	=RIGHT(C30,2)
39	87
40
LARGESUM

Cell Formulas
Range	Formula
A4,A27,A25,A17,A15,A6	A4	=FORMULATEXT(C4)
C4,C15	C4	=REPT("1",A2)
C6,C17	C6	=REPT("9",A2)
C8,A36,A38,C29,C19	C8	=FORMULATEXT(C9)
C9,C30,C20	C9	=LARGESUM(C4,C6)
A9,A30	A9	=LEN(C9)
A10,A31	A10	=FORMULATEXT(A9)
C25	C25	=REPT("9",A23)
C27	C27	=REPT("8",A23)
A37	A37	=RIGHT(C9,2)
A39	A39	=RIGHT(C30,2)