Nuprl Definition : near-arcsine

near-arcsine(a;N) ==
  eval b = a 4000 in
  if (4) < (b)
     then eval b = a 400 in
          if (588) < (b)
             then (π/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - a * a);2 * N)
             else if (b + 4) < (584)  then arcsine-approx(a;N)  else arcsine-approx(a;N)
     else if (b + 4) < (0)
             then -(eval b = -(a) 400 in
                    if (588) < (b)

                       then (π/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - -(a) * -(a));2 * N)

                       else if (b + 4) < (584)  then arcsine-approx(-(a);N)  else arcsine-approx(-(a);N))

             else eval m = 4 * (N + 1) in
                  eval a@0 = r0 m in
                  eval b = a m in
                    if (a@0 + 4) < (b)
                       then eval b = a 400 in
                            if (588) < (b)

                               then (π/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - a * a);2 * N)

                               else if (b + 4) < (584)  then arcsine-approx(a;N)  else arcsine-approx(a;N)

                       else if (b + 4) < (a@0)
                               then -(eval b = -(a) 400 in
                                      if (588) < (b)

                                         then (π/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - -(a) * -(a));2 * N)

else if (b + 4) < (584)

                                                 then arcsine-approx(-(a);N)

                                                 else arcsine-approx(-(a);N))

else r0

Definitions occuring in Statement : arcsine-approx: arcsine-approx(a;n), halfpi: π/2, rsqrt: rsqrt(x), rational-approx: (x within 1/n), rsub: x - y, rmul: a * b, rminus: -(x), int-to-real: r(n), callbyvalue: callbyvalue, less: if (a) < (b) then c else d, apply: f a, multiply: n * m, add: n + m, natural_number: $n
Definitions occuring in definition : rminus: -(x), callbyvalue: callbyvalue, apply: f a, rational-approx: (x within 1/n), halfpi: π/2, rsqrt: rsqrt(x), rsub: x - y, int-to-real: r(n), rmul: a * b, multiply: n * m, less: if (a) < (b) then c else d, add: n + m, natural_number: $n, arcsine-approx: arcsine-approx(a;n)
FDL editor aliases : near-arcsine

Latex:
near-arcsine(a;N) == eval b = a 4000 in if (4) < (b) then eval b = a 400 in if (588) < (b) then (\mpi{}/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - a * a);2 * N) else if (b + 4) < (584) then arcsine-approx(a;N) else arcsine-approx(a;N) else if (b + 4) < (0) then -(eval b = -(a) 400 in if (588) < (b) then (\mpi{}/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - -(a) * -(a));2 * N) else if (b + 4) < (584) then arcsine-approx(-(a);N) else arcsine-approx(-(a);N)) else eval m = 4 * (N + 1) in eval a@0 = r0 m in eval b = a m in if (a@0 + 4) < (b) then eval b = a 400 in if (588) < (b) then (\mpi{}/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - a * a);2 * N) else if (b + 4) < (584) then arcsine-approx(a;N) else arcsine-approx(a;N) else if (b + 4) < (a@0) then -(eval b = -(a) 400 in if (588) < (b) then (\mpi{}/2 within 1/2 * N) - arcsine-approx(rsqrt(r1 - -(a) * -(a));2 * N) else if (b + 4) < (584) then arcsine-approx(-(a);N) else arcsine-approx(-(a);N)) else r0 Date html generated: 2016_10_26-PM-00_49_51 Last ObjectModification: 2016_10_13-PM-03_16_26 Theory : reals_2 Home Index