επιστευσεν δε αβρααμ τω θεω και ελογισθη αυτω εις δικαιοσυνην
[Romans 4:3 - TR (undisputed) - Beza, Stephanus, Elzevir and Scrivener are all identical]
Logizomai Strong 3049 is a deponent verb, thus it is middle voice or responsive. It is a response to an action. Some call this 'reflexive'.
The word appears in the NT several times and also in the Septuagint in regard to Abraham. The words 'Abraham believed God and it was 'accounted'/'reckoned' to him unto righteousness' appear several times in exactly the same form.
Logizomai is God's response to Abraham's faith.
Logizomai is a matter of evaluation. This can be seen in Paul's use of the word in regard to 'treasuring up' weekly contributions so that there should be no gatherings of large numbers of small denomination coins when he arrives. They should add to their savings, then 'treasure up' to a small number of high denomination coins, easily transported on Paul's further journey, 1 Corinthians 16:2.
Concentration of value is the concept lying behind the word.
A value is concentrated, and an estimation of that value is made.
'Accounting' is useful but has too much association with finance and coinage. 'Logicate' would be useful and it is available in the English language but has not been used, 'reckoning' having developed but 'reckoning' has bad connotations, a 'reckoning' behind the 'reckoning' ; a hint of deviousness in the reckoning.
Logizomai, in the way in which it is used, particularly by Paul, is a matter of the logical assessment of real value.
God sees the faith of Abraham.
In that faith he sees his own righteousness, for that is what Abraham saw. Abram, as he then was, saw that God had promised and that God was true and that God would do what he had promised . . . . because God is righteous.
And Abram believed God.
And God saw that faith and saw the content of the faith.
And 'there was' (there is no subject) 'evaluated' (logizomai) 'to' (an indirect object) 'him' . . . 'unto' (another indirect object, a prepositional clause) 'righteousness'.
... there was evaluated to him unto righteousness
Abraham had, and has, no righteousness of his own. There is evaluated to him, unto (it is always eis) the righteousness of God (at the time not stated, because there was no full revelation, then, of the source of the righteousness ; for it was yet to be revealed in Paul's gospel).
That is to say, by faith, he is justified with the righteousness of God, for it is the righteousness of God that he believes and that is what is in his faith.
God sees it in his faith.
And attributes it to him.
It would be wrong not to attribute it to him.