**The Oxford English Dictionary on “have to” construction **
b. Hence to have to do: see DO v. 33c, d.
c. With infinitive: To be under obligation, to be obliged; to be necessitated to do something. It forms a kind of Future of obligation or duty.
[Cf. the Future tense of the Romanic langs, e.g. je parler-ai, je finir-ai, I have to speak, to finish.]
1579 FENTON Guicciard. (1618) 6 He told him, he had not to beleeue, that the couetousnesse of Virginio…had moued Ferdinand. 1594 HOOKER Eccl. Pol. I. i. §1 We have…to strive with a number of heavy prejudices. 1596 SPENSER State Irel. Wks. (Globe) 657/2 This is the manner of the Spanyardes captaynes, whoe never hath to meddle with his souldiours paye. 1765 H. WALPOLE Otranto v. (1798) 80 Having to talk with him on urgent affairs. 1831 F. TROLLOPE Dom. Manners Amer. (1894) II. 271 But ‘we had to do it’ as the Americans say. 1848 MRS. GASKELL Mary Barton ix, Mary had to change some clothes after her walk home. 1883 Manch. Exam. 29 Oct. 5/4 In 1831 the firm had to suspend payment. 1892 LOPES in Law Times Rep. LXVII. 144/1, I regret to have to say that I do not believe that evidence. Mod. I have to go to London to-morrow.
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On -S ending, as in “must needs”:**
forming adverbs, was originally -es, identical with the suffix of the genitive singular of many neuter and masculine ns. and adjs. Several of the adverbs in -es that existed in OE. are genitives either of ns. (neut. or masc.) as dæes by day, nédes NEEDS, ances voluntarily, or of neuter adjs., as sóes truly; on the analogy of these, -es was added, with adv.-forming function, to feminine nouns, as in nihtes by night, endebyrdes in order. OE. had also advs. compounded of tó prep. and a genitive governed by it, as tó-enes (see TO-GAINS), tó-middes (see TO-MIDS); side by side with these there existed parallel and synonymous advs. like on-en AGAIN, on-middan AMID, in which the dat. or accus. was governed by a prep. Hence there arose in early ME. mixed forms such as aeines, amiddes; and the frequent coexistence of the two forms of the same adv., one with and the other without s, led to the addition of s to many advs. as a sign of their function. In some instances the extended form prevailed, as in eftsoons; in others it survived only in dialects, as in oftens, gaylies (Sc.). See also the articles -LING2, -LI(N)GS, -WARD, -WARDS, -WAY, -WAYS.
In once, twice, thrice, hence, since, etc., the suffix is written differently. In AGAINST, ALONGST, AMONGST, AMIDST, and the dialectal onst (see ONCE), the original -es, -s has become -st.
(Note to mods: I realize that the wholesale offering of such posts would be an abuse of my privilege to access the OED online, and promise not to set myself as an etymological guru on the strength of it. But I don’t see the harm in answering an occasional question of this type).