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eomnment ellint computes the value of the incomplete elliptic integrals of the first and second kinds, F(phi, k) and E (phi, k), where phi is in radians. If [ k I > 1 or [ phi I > Ir/2, E and F will be set equal to 100,000,000, otherwise they will contain the computed integrals. For the formulation of this procedure, see n := 0; sinphi : = sin (phi) ; if abs (k X sinphi) < tanh (1) then go to small else if abs (k) _< 1 A abs(phi) < r/2 then go to large; A [2] := E X A [1]-sinphi T (2 × n-l) X cosphi/(2 X n); del [1] := H [2] X A [2]; del [2] :=-k1`2 > H [1] X A [2]/(2 X n); sigma [1] := sigma [1] + del [1]; sigma [2] := sigma [2] + del [2]; H [1] := H [2]; h [1] := A [2]; if abs ((sigma [1] + del [1])-sigma [1]) > 0 /k phi X sinphi 1" (2 X n) > A [2] then go to step 1; F := phi + sigma [1]; E := phi + sigma [2]; go to stop; large: kp := sqrt (1-kT2); + del [1])-sigma [1]) > 0 then go to step 2; T [1] := In (4/(sqrt (1-kT2 × sinphi 1`2) + abs (k) X sqrt(1-sinphi T 2))); T [2] := abs (k) × sqrt ((1-sinphi 1`2)/(1-k~2 × sinphi T2)); F := T [1] X (1+sigma [3]) + T [2] X In (.5 + .5 × abs (k X sinphi)) + sigma [1]; E := (.5 + sigma [4]) X kp~2 X T [1] + 1-T [2] X (1-abs (k × sinphi)) + sigma [2]; stop : end Contributions to this department must be in the form stated in the Algorithms Department policy statement (Communications , February, 1960) except that ALGOL 60 notation should be used (see Communications, May 1960). Contributions should be sent in duplicate to J. D. C. Algorithms should be in the Publication form of ALGOL 60 and written in a style patterned after the most recent algorithms appearing in this department. For the convenience of the printer, please underline words that are delimiters to appear in boldface type. Although each algorithm has been tested by its contributor, no warranty, express or implied, is made by the contributor, the editor, or the Association for Computing …

Remark on algorithm 28: least-squares fit by orthogonal polynomials