acos.py

import math

def fma(a, b, c):
    return a * b + c

def asin_core(a):
    s = a * a
    q = s * s
    r = 5.5579749017470502e-2
    t = -6.2027913464120114e-2
    r = fma(r, q, 5.4224464349245036e-2)
    t = fma(t, q, -1.1326992890324464e-2)
    r = fma(r, q, 1.5268872539397656e-2)
    t = fma(t, q, 1.0493798473372081e-2)
    r = fma(r, q, 1.4106045900607047e-2)
    t = fma(t, q, 1.7339776384962050e-2)
    r = fma(r, q, 2.2372961589651054e-2)
    t = fma(t, q, 3.0381912707941005e-2)
    r = fma(r, q, 4.4642857881094775e-2)
    t = fma(t, q, 7.4999999991367292e-2)
    r = fma(r, s, t)
    r = fma(r, s, 1.6666666666670193e-1)
    t = a * s
    r = fma(r, t, a)
    return r

def my_acos(a):
    r = -a if a > 0.0 else a
    if r > -0.5625:
        r = fma(9.3282184640716537e-1, 1.6839188885261840e+0, asin_core(r))
    else:
        r = 2.0 * asin_core(math.sqrt(fma(0.5, r, 0.5)))
    if not (a > 0.0) and (a >= -1.0):
        r = fma(1.8656436928143307e+0, 1.6839188885261840e+0, -r)
    return r

# Test with values in [-9/16, 9/16]
for a in [-9/16, -3/8, -1/4, 0, 1/4, 3/8, 9/16]:
    print(f"Actual: {math.acos(a)}, Approximation: {my_acos(a)}")