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module taylor
using Base
using Printf
ITER = 12
HYPERBOLIC_MAX = 0.2
function series(x, parity, change_sign, iterations)
elements = ones(Float64, 2 * iterations)
res = 0.0
i = 2
while i <= 2 * iterations + parity - 2
elements[i + 1] = elements[i] / i
if change_sign && (i % 2 == parity)
elements[i + 1] = -elements[i + 1]
end -
i += 1
end
i = 2 * iterations + parity - 2
while i >= parity
res *= x * x
res += elements[i + 1]
i -= 2
end
if parity == 1
res *= x
end
return res
end
function real_sin(r, iterations)
r = r - floor(r / (2 * pi)) * 2 * pi
if r > pi
return -real_sin(r - pi, iterations)
end
if r > pi / 2
return real_cos(r - pi / 2, iterations)
end
if r > pi / 4
return real_cos(pi / 2 - r, iterations)
end
return series(r, 1, true, iterations)
end
function real_cos(r, iterations)
r = r - floor(r / (2 * pi)) * 2 * pi
if r > pi
return -real_cos(r - pi, iterations)
end
if r > pi / 2
return -real_sin(r - pi / 2, iterations)
end
if r > pi / 4
return real_sin(pi / 2 - r, iterations)
end
return series(r, 0, true, iterations)
end
function real_sinh(r, iterations)
if abs(r) > HYPERBOLIC_MAX
return 2 * real_sinh(r / 2, iterations) * real_cosh(r / 2, iterations)
end
return series(r, 1, false, iterations)
end
function real_cosh(r, iterations)
if abs(r) > HYPERBOLIC_MAX
s = real_sinh(r / 2, iterations)
c = real_cosh(r / 2, iterations)
return s * s + c * c
end
return series(r, 0, false, iterations)
end
function complex_sin(a, b, iterations)
return (real_sin(a, iterations) * real_cosh(b, iterations),
real_cos(a, iterations) * real_sinh(b, iterations))
end
function complex_cos(a, b, iterations)
return (real_cos(a, iterations) * real_cosh(b, iterations),
-real_sin(a, iterations) * real_sinh(b, iterations))
end
# c = a + bi
function csin(a, b)
return complex_sin(a, b, ITER)
end
function ccos(a, b)
return complex_cos(a, b, ITER)
end
function rsinh(r)
return real_sinh(r, ITER)
end
function rcosh(r)
return real_cosh(r, ITER)
end
end
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