The real problem is that fib(399) results in a 84 algarisms number:
108788617463475645289761992289049744844995705477812699099751202749393926359816304226
Therefor, I use in my code this :
SECTION .bss
f1array : resb 80
f2array : resb 80
f3array : resb 80
Each digit is stored in a separate byte inside this array. So I can add for example f1array[5] + f2array[5] and store it in f3array[5] . If I do this for all array-elements, then I can afterwards calculate with DIV and MOD that the f3array-elements are not bigger than 9, and in this way I get in f3array the new fibonacci with every digit in one byte stored. The size of the array by now 80 bytes is hardcoded, but can easily made bigger. I tested numbers with up to 160 digits, and I am sure, there can be calculated even bigger ones.
/edit :
Just for the fun of it, I modified the arrays to 10000 and the fibonaccis to 5000 and found out, that fibonacci around 5000 is :
6276302800488957086035253108349684055478528702736457439025824448927937256811663264475883711527806250329984690249846819800648580083040107584710332687596562185073640422286799239932615797105974710857095487342820351307477141875012176874307156016229965832589137779724973854362777629878229505500260477136108363709090010421536915488632339240756987974122598603591920306874926755600361865354330444681915154695741851960071089944015319300128574107662757054790648152751366475529121877212785489665101733755898580317984402963873738187000120737824193162011399200547424034440836239726275765901190914513013217132050988064832024783370583789324109052449717186857327239783000020791777804503930439875068662687670678802914269784817022567088069496231111407908953313902398529655056082228598715882365779469902465675715699187225655878240668599547496218159297881601061923195562143932693324644219266564617042934227893371179832389642895285401263875342640468017378925921483580111278055044254198382265567395946431803304304326865077742925818757370691726168228648841319231470626
(I'm not sure if my indexing is totally correct.maybe it is fib(4999) or fib(5001).