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using Printf
global C_ITERATIONS = 30
global CORDIC_MUL_POW = 30
global CORDIC_MUL = 2.0^CORDIC_MUL_POW
global CORDIC_ATANS = [843314857, 497837829, 263043837, 133525159, 67021687, 33543516, 16775851,
8388437, 4194283, 2097149, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096,
2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2]
global CORDIC_F = 1768195363
global CORDIC_F_INV = 652032874
global T_ITERATIONS = 15
global HYPERBOLIC_MAX = 1
# liczenie szeregu Taylora
function series(x, parity, change_sign, iterations)
res = zero(x)
elem = one(x)
if parity == 1
elem = x
end
i = parity + 1
while i <= 2*iterations + parity
res += elem
elem *= change_sign*x*x/(i*(i+1))
i += 2
end
return res
end
# generyczna funkcja stosująca wzory redukcyjne, licząca sinusa
function gen_sin(x, iterations, sin_fun, cos_fun)
if x < 0
return -gen_sin(-x, iterations, sin_fun, cos_fun)
end
x = mod2pi(x)
if x > pi
return -gen_sin(x-pi, iterations, sin_fun, cos_fun)
end
if x > pi/2
return gen_cos(x-pi/2, iterations, sin_fun, cos_fun)
end
if x > pi/4
return gen_cos(pi/2-x, iterations, sin_fun, cos_fun)
end
return sin_fun(x, iterations)
end
# generyczna funkcja stosująca wzory redukcyjne, licząca cosinusa
function gen_cos(x, iterations, sin_fun, cos_fun)
if x < 0
return gen_cos(-x, iterations, sin_fun, cos_fun)
end
x = mod2pi(x)
if x > pi
return -gen_cos(x-pi, iterations, sin_fun, cos_fun)
end
if x > pi/2
return -gen_sin(x-pi/2, iterations, sin_fun, cos_fun)
end
if x > pi/4
return gen_sin(pi/2-x, iterations, sin_fun, cos_fun)
end
return cos_fun(x, iterations)
end
# sin dla liczb rzeczywistych [taylor]
function real_sin(r, iterations)
return series(r, 1, -1, iterations)
end
# cos dla liczb rzeczywistych [taylor]
function real_cos(r, iterations)
return series(r, 0, -1, iterations)
end
# sinh [taylor]
function real_sinh(r, iterations)
if r > 1000
return Inf
end
if r < -1000
return -Inf
end
if r == 0
return Float64(0)
end
if abs(r) > HYPERBOLIC_MAX
return 2*real_sinh(r/2, iterations)*real_cosh(r/2, iterations)
end
return series(r, 1, 1, iterations)
end
# cosh [taylor]
function real_cosh(r, iterations)
if abs(r) > 1000
return Inf
end
if r == 1
return Float64(1)
end
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, 1, iterations)
end
# sin dla liczb zespolonych [taylor]
function complex_sin(a, b, iterations)
return (gen_sin(a, iterations, real_sin, real_cos)*real_cosh(b, iterations),
gen_cos(a, iterations, real_sin, real_cos)*real_sinh(b, iterations))
end
# cos dla liczb zespolonych [taylor]
function complex_cos(a, b, iterations)
return (real_cos(a, iterations)*real_cosh(b, iterations),
-real_sin(a, iterations)*real_sinh(b, iterations))
end
# funkcja dla użytkownika [taylor]
function taylor_sin(a, b)
return complex_sin(a, b, T_ITERATIONS)
end
# funkcja dla użytkownika [taylor]
function taylor_cos(a, b)
return complex_cos(a, b, T_ITERATIONS)
end
# funkcja dla użytkownika [taylor]
function taylor_sinh(r)
return real_sinh(r, T_ITERATIONS)
end
# funkcja dla użytkownika [taylor]
function taylor_cosh(r)
return real_cosh(r, T_ITERATIONS)
end
# preprocesing [cordic]
function preprocess_atan(iterations)
global CORDIC_MUL
atan2pow = Array{Float64}(undef, iterations)
@printf("CORDIC_ATANS = [")
for i in 1:iterations
atan2pow[i] = round(atan(1.0 / Float64(BigInt(2)^(i - 1))) * CORDIC_MUL)
@printf("%d", atan2pow[i])
if i < iterations
@printf(", ")
end
end
@printf("]\n")
end
# preprocesing [cordic]
function preprocess_scaling_factor(iterations)
CORDIC_F = 1.0
for i in 0:iterations
CORDIC_F *= sqrt(1. + 1. / Float64(BigInt(2)^(2 * i)))
end
@printf("CORDIC_F = %d\nCORDIC_F_INV = %d\n", round(CORDIC_F * CORDIC_MUL), round(CORDIC_MUL / CORDIC_F))
end
# funkcja licząca zarówno sin oraz cos [cordic]
function approx_trig(x, iterations)
global CORDIC_ATANS
global CORDIC_F_INV
X = CORDIC_F_INV
Y = 0
Z = round(x * CORDIC_MUL)
s = 1
for i in 0:(iterations - 1)
tempX = X
if Z == 0
break
end
if Z >= 0
X -= s * (Y >> i)
Y += s * (tempX >> i)
Z -= s * CORDIC_ATANS[i + 1]
else
X += s * (Y >> i)
Y -= s * (tempX >> i)
Z += s * CORDIC_ATANS[i + 1]
end
end
return (Float64(X) / CORDIC_MUL, Float64(Y) / CORDIC_MUL)
end
# wyciąganie sin z approx_trig [cordic]
function approx_sin(x, iterations)
return approx_trig(x, iterations)[2]
end
# wyciąganie cos z approx_trig [cordic]
function approx_cos(x, iterations)
return approx_trig(x, iterations)[1]
end
# funkcja dla użytkownika [cordic]
function cordic_sin(x)
return gen_sin(x, C_ITERATIONS, approx_sin, approx_cos)
end
# funkcja dla użytkownika [cordic]
function cordic_cos(x)
return gen_cos(x, C_ITERATIONS, approx_sin, approx_cos)
end
# uruchamianie preprocesingu [cordic]
function preprocess_cordic()
println("Preprocessing CORDIC constants.")
preprocess_atan(CORDIC_MUL_POW)
preprocess_scaling_factor(CORDIC_MUL_POW)
end
# sinh bez stosowania wzorów redukcyjnych [taylor]
function sinh_no_reduction(x, iterations)
return series(x, 1, 1, iterations)
end
# cosh bez stosowania wzorów redukcyjnych [taylor]
function cosh_no_reduction(x, iterations)
return series(x, 0, 1, iterations)
end
# sin bez stosowania wzorów redukcyjnych [taylor]
function taylor_sin_no_reduction(x, y)
return (real_sin(x, 10*round(x)+10) * cosh_no_reduction(y, 10*round(y)+10),
real_cos(x, 10*round(x)+10) * sinh_no_reduction(y, 10*round(x)+10))
end
# zmiana liczby iteracji [taylor]
function set_taylor_iterations(x)
global T_ITERATIONS = x
end
# zmiana liczby iteracji [cordic]
function set_cordic_iterations(x)
global C_ITERATIONS = x
end
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