diff options
author | Franciszek Malinka <franciszek.malinka@gmail.com> | 2021-10-05 21:49:54 +0200 |
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committer | Franciszek Malinka <franciszek.malinka@gmail.com> | 2021-10-05 21:49:54 +0200 |
commit | c5fcf7179a83ef65c86c6a4a390029149e518649 (patch) | |
tree | d29ffc5b86a0d257453cedcf87d91a13d8bf3b0d /Semestr 3/anm/cordic | |
parent | f8a88b6a4aba1f66d04711a9330eaba49a50c463 (diff) |
Duzy commit ze smieciami
Diffstat (limited to 'Semestr 3/anm/cordic')
-rw-r--r-- | Semestr 3/anm/cordic/CORDICtable.c | 21 | ||||
-rw-r--r-- | Semestr 3/anm/cordic/cordic | bin | 17368 -> 0 bytes | |||
-rw-r--r-- | Semestr 3/anm/cordic/cordic.cpp | 189 | ||||
-rw-r--r-- | Semestr 3/anm/cordic/cordic.jl | 81 | ||||
-rw-r--r-- | Semestr 3/anm/cordic/csin | bin | 17576 -> 0 bytes | |||
-rw-r--r-- | Semestr 3/anm/cordic/csin.cpp | 49 | ||||
-rw-r--r-- | Semestr 3/anm/cordic/taylor.jl | 103 | ||||
-rw-r--r-- | Semestr 3/anm/cordic/trig.jl | 43 |
8 files changed, 0 insertions, 486 deletions
diff --git a/Semestr 3/anm/cordic/CORDICtable.c b/Semestr 3/anm/cordic/CORDICtable.c deleted file mode 100644 index f222d08..0000000 --- a/Semestr 3/anm/cordic/CORDICtable.c +++ /dev/null @@ -1,21 +0,0 @@ -//CORDIC, 21 bits, 18 iterations -// 1.0 = 262144.000000 multiplication factor -// A = 1.743279 convergence angle (limit is 1.7432866 = 99.9deg) -// F = 1.646760 gain (limit is 1.64676025812107) -// 1/F = 0.607253 inverse gain (limit is 0.607252935008881) -// pi = 3.141593 (3.1415926536897932384626) - -#define CORDIC_A 1.743279 // CORDIC convergence angle A -#define CORDIC_F 0x00069648 // CORDIC gain F -#define CORDIC_1F 0x00026DD4 // CORDIC inverse gain 1/F -#define CORDIC_HALFPI 0x0006487F -#define CORDIC_PI 0x000C90FE -#define CORDIC_TWOPI 0x001921FB -#define CORDIC_MUL 262144.000000 // CORDIC multiplication factor M = 2^18 -#define CORDIC_MAXITER 18 - -int CORDIC_ZTBL[] = { - 0x0003243F, 0x0001DAC6, 0x0000FADC, 0x00007F57, 0x00003FEB, 0x00001FFD, 0x00001000, 0x00000800, - 0x00000400, 0x00000200, 0x00000100, 0x00000080, 0x00000040, 0x00000020, 0x00000010, 0x00000008, - 0x00000004, 0x00000002 }; - diff --git a/Semestr 3/anm/cordic/cordic b/Semestr 3/anm/cordic/cordic Binary files differdeleted file mode 100644 index cb593c0..0000000 --- a/Semestr 3/anm/cordic/cordic +++ /dev/null diff --git a/Semestr 3/anm/cordic/cordic.cpp b/Semestr 3/anm/cordic/cordic.cpp deleted file mode 100644 index b0dfd39..0000000 --- a/Semestr 3/anm/cordic/cordic.cpp +++ /dev/null @@ -1,189 +0,0 @@ -#include <stdio.h>
-#include <math.h>
-//#define M_PI 3.1415926536897932384626
-int main(int argc, char **argv)
-{
- FILE *f;
- char tname[50], cname[10];
- int n, n2, mp2, niter, bits, t;
- double F, A, mul, tmul; // CORDIC gain, convergence angle, multiplication factor
- printf("0)circular, 1)linear, 2)hyperbolic? ");
- scanf("%d", &t);
- switch (t)
- {
- case 0:
- sprintf(cname, "%s", "");
- break;
- case 1:
- sprintf(cname, "%s", "_LIN");
- break;
- case 2:
- sprintf(cname, "%s", "_HYPER");
- break;
- }
- sprintf(tname, "CORDICtable%s.c", cname);
- if (NULL == (f = fopen(tname, "wt")))
- {
- printf("cannot write to %s\n", tname);
- return 0;
- }
-
- printf("number of bits for mantissa (e.g. 30)? ");
- scanf("%d", &bits);
- printf("0) mul factor is 2^n (easier output scaling), or\n"
- "1) 2pi is 2^n (easier implementation)\n ? ");
- scanf("%d", &mp2);
- printf("suggested multiplication factor ");
- if (mp2 == 0)
- {
- tmul = (double)(1 << (bits - 3));
- printf("2^%d = %f\n", bits - 3, tmul);
- }
- else
- {
- tmul = (double)(1 << (bits - 2)) / M_PI;
- printf("2^%d/pi = %f\n", bits - 2, tmul);
- }
- printf("multiplication factor (0 for suggested)? ");
- scanf("%lf", &mul);
- if (mul < 0.1)
- {
- mul = tmul;
- printf("%f\n", mul);
- }
- else
- mp2 = -1; // custom mul factor
- switch (t)
- {
- case 0:
- for (n = 0; n < bits; n++)
- if ((int)round(atan(pow(2.0, (double)(-n))) * mul) == 0)
- break;
- break;
- case 1:
- for (n = 0; n < bits; n++)
- if ((int)round((pow(2.0, (double)(-n))) * mul) == 0)
- break;
- break;
- case 2:
- for (n = 1, n2 = 4; n < bits;)
- {
- if ((int)round(atanh(pow(2.0, (double)(-n))) * mul) == 0)
- break;
- if (n == n2)
- n2 = 3 * n + 1;
- else
- n++;
- }
- break;
- }
- printf("iterations (up to %d)? ", n);
- scanf("%d", &niter);
-
- F = 1.0;
- A = 0.0;
- switch (t)
- {
- case 0:
- for (n = 0; n < niter; n++)
- {
- F = F * sqrt(1 + pow(2.0, -2.0 * n));
- A += atan(pow(2.0, (double)(-n)));
- }
- break;
- case 1:
- for (n = 0; n < niter; n++)
- {
- F = F * sqrt(1);
- A += (pow(2.0, (double)(-n)));
- }
- break;
- case 2:
- for (n = 1, n2 = 4; n < niter;)
- {
- F = F * sqrt(1 - pow(2.0, -2.0 * n));
- A += atanh(pow(2.0, (double)(-n)));
- if (n == n2)
- n2 = 3 * n + 1;
- else
- n++;
- }
- break;
- }
-
- fprintf(f, "//CORDIC%s, %d bits, %d iterations\n", cname, bits, niter);
- fprintf(f, "// 1.0 = %f multiplication factor\n", mul);
- switch (t)
- {
- case 0:
- fprintf(f, "// A = %lf convergence angle "
- "(limit is 1.7432866 = 99.9deg)\n",
- A);
- fprintf(f, "// F = %lf gain (limit is 1.64676025812107)\n", F);
- fprintf(f, "// 1/F = %lf inverse gain (limit is 0.607252935008881)\n", 1.0 / F);
- break;
- case 1:
- fprintf(f, "// A = %lf convergence angle (limit is 2)\n", A);
- fprintf(f, "// F = %lf gain (limit is 1.0)\n", F);
- fprintf(f, "// 1/F = %lf inverse gain (limit is 1.0)\n", 1.0 / F);
- break;
- case 2:
- fprintf(f, "// A = %lf convergence angle "
- "(limit is 1.1181730 = 64.0deg)\n",
- A);
- fprintf(f, "// F = %lf gain (limit is 0.82978162013890)\n", F);
- fprintf(f, "// 1/F = %lf inverse gain (limit is 1.20513635844646)\n", 1.0 / F);
- break;
- }
- fprintf(f, "// pi = %lf (3.1415926536897932384626)\n", M_PI);
- fprintf(f, "\n");
- fprintf(f, "#define CORDIC%s_A %f // CORDIC convergence angle A\n", cname, A);
- fprintf(f, "#define CORDIC%s_F 0x%08X // CORDIC gain F\n",
- cname, (int)round(mul * F));
- fprintf(f, "#define CORDIC%s_1F 0x%08X // CORDIC inverse gain 1/F\n",
- cname, (int)round(mul / F));
- fprintf(f, "#define CORDIC%s_HALFPI 0x%08X\n", cname, (int)round(mul * (M_PI / 2.0)));
- fprintf(f, "#define CORDIC%s_PI 0x%08X\n", cname, (int)round(mul * (M_PI)));
- fprintf(f, "#define CORDIC%s_TWOPI 0x%08X\n", cname, (int)round(mul * (2.0 * M_PI)));
- fprintf(f, "#define CORDIC%s_MUL %f // CORDIC multiplication factor M", cname, mul);
- switch (mp2)
- {
- case 0:
- fprintf(f, " = 2^%d\n", bits - 3);
- break;
- case 1:
- fprintf(f, " = 2^%d/pi\n", bits - 2);
- break;
- default:
- fprintf(f, "\n");
- break;
- }
- fprintf(f, "#define CORDIC%s_MAXITER %d\n\n", cname, niter);
- fprintf(f, "int CORDIC%s_ZTBL[] = {", cname);
- for (n = 0; n < niter; n++)
- {
- if ((n % 8) == 0)
- fprintf(f, "\n ");
- switch (t)
- {
- case 0:
- fprintf(f, "0x%08X", (int)round(atan(pow(2.0, (double)(-n))) * mul));
- break;
- case 1:
- fprintf(f, "0x%08X", (int)round((pow(2.0, (double)(-n))) * mul));
- break;
- case 2:
- n = n == 0 ? 1 : n;
- fprintf(f, "0x%08X", (int)round(atanh(pow(2.0, (double)(-n))) * mul));
- break;
- }
- if (n < (niter - 1))
- fprintf(f, ", ");
- else
- fprintf(f, " ");
- }
- fprintf(f, "};\n\n");
- fclose(f);
- printf("table written to %s\n", tname);
- return 0;
-}
diff --git a/Semestr 3/anm/cordic/cordic.jl b/Semestr 3/anm/cordic/cordic.jl deleted file mode 100644 index 9509fb2..0000000 --- a/Semestr 3/anm/cordic/cordic.jl +++ /dev/null @@ -1,81 +0,0 @@ -using Printf - -global ITERATIONS = 30 -global CORDIC_MUL_POW = 30 -global CORDIC_MUL = 2.0^CORDIC_MUL_POW -global CORDIC_ATANS -global CORDIC_F -global CORDIC_F_INV - -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] -CORDIC_F = 1768195363 -CORDIC_F_INV = 652032874 - -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 - -function preprocess_scaling_factor(iterations) - # @printf("Preprocessing scaling factor, %d iterations\n", iterations) - CORDIC_F = 1.0 - for i in 0:iterations - CORDIC_F *= sqrt(1. + 1. / Float64(BigInt(2)^(2 * i))) - end - # @printf("Scaling factor: %.16f\n", F) - @printf("CORDIC_F = %d\nCORDIC_F_INV = %d\n", round(CORDIC_F * CORDIC_MUL), round(CORDIC_MUL / CORDIC_F)) -end - -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) - println(X, " ", Y) - - 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 - - println(X, " ", Y) - return (Float64(X) / CORDIC_MUL, Float64(Y) / CORDIC_MUL) -end - -# works only for real numbers -function approx_sin(x, y) - return (approx_trig(x, ITERATIONS)[2], 0) -end - -# works only for real numbers -function approx_cos(x, y) - return (approx_trig(x, ITERATIONS)[1], 0) -end - -function main() - println("Preprocessing CORDIC constants.") - preprocess_atan(CORDIC_MUL_POW) - preprocess_scaling_factor(CORDIC_MUL_POW) -end diff --git a/Semestr 3/anm/cordic/csin b/Semestr 3/anm/cordic/csin Binary files differdeleted file mode 100644 index 49d3cfb..0000000 --- a/Semestr 3/anm/cordic/csin +++ /dev/null diff --git a/Semestr 3/anm/cordic/csin.cpp b/Semestr 3/anm/cordic/csin.cpp deleted file mode 100644 index bcc9af4..0000000 --- a/Semestr 3/anm/cordic/csin.cpp +++ /dev/null @@ -1,49 +0,0 @@ -#include "CORDICtable.c"
-#include <iostream>
-// angle is radians multiplied by CORDIC multiplication factor M
-// modulus can be set to CORDIC inverse gain 1/F to avoid post-division
-void CORDICsincos(int a, int m, int *s, int *c)
-{
- int k, tx, x = m, y = 0, z = a, fl = 0;
- if (z > +CORDIC_HALFPI)
- {
- fl = +1;
- z = (+CORDIC_PI) - z;
- }
- else if (z < -CORDIC_HALFPI)
- {
- fl = +1;
- z = (-CORDIC_PI) - z;
- }
- for (k = 0; k < CORDIC_MAXITER; k++)
- {
- std::cout << x << " " << y << " " << z << "\n";
- tx = x;
- if (z >= 0)
- {
- x -= (y >> k);
- y += (tx >> k);
- z -= CORDIC_ZTBL[k];
- }
- else
- {
- x += (y >> k);
- y -= (tx >> k);
- z += CORDIC_ZTBL[k];
- }
- }
- if (fl)
- x = -x;
- *c = x; // m*cos(a) multiplied by gain F and factor M
- *s = y; // m*sin(a) multiplied by gain F and factor M
-}
-
-int main()
-{
- double x;
- std::cin >> x;
- int sinus, cosinus;
- CORDICsincos(x * CORDIC_MUL, CORDIC_1F, &sinus, &cosinus);
- std::cout << sinus << " " << cosinus << "\n";
- std::cout << (double)sinus / (double)CORDIC_MUL << " " << (double)cosinus / (double)CORDIC_MUL << "\n";
-}
\ No newline at end of file diff --git a/Semestr 3/anm/cordic/taylor.jl b/Semestr 3/anm/cordic/taylor.jl deleted file mode 100644 index 5d2d26d..0000000 --- a/Semestr 3/anm/cordic/taylor.jl +++ /dev/null @@ -1,103 +0,0 @@ -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
\ No newline at end of file diff --git a/Semestr 3/anm/cordic/trig.jl b/Semestr 3/anm/cordic/trig.jl deleted file mode 100644 index bf1dc2c..0000000 --- a/Semestr 3/anm/cordic/trig.jl +++ /dev/null @@ -1,43 +0,0 @@ -include("cordic.jl") -include("taylor.jl") -using Printf - -# preprocessing -cordic.main() - -function rel_error(x, y) - return abs((x - y) / y) -end - -function test_real_sin(arg, trig_func) - @printf("Testing relative error for function %s and argument %f.\n", String(Symbol(trig_func)), arg) - res = trig_func(arg, 0) - real_res = sin(arg) - @printf("Result: %.50f\n", res[1]) - @printf("LibRes: %.50F\n", real_res) - @printf("Relative error: %e\n", rel_error(res[1], real_res)) -end - -function test_complex_sin(arg_real, arg_imag, trig_func) - @printf("Testing relative error for function %s and argument %f + %f i.\n", String(Symbol(trig_func)), arg_real, arg_imag) - res = trig_func(arg_real, arg_imag) - real_res = sin(arg_real + arg_imag * im) - @printf("Result: %.50f + %.50f i\n", res[1], res[2]) - @printf("LibRes: %.50f + %.50f i\n", real(real_res), imag(real_res)) - @printf("Relative error: %e, %e\n", rel_error(res[1], real(real_res)), rel_error(res[2], imag(real_res))) -end - -test_real_sin(0.5, taylor.csin) -test_real_sin(0.5, cordic.approx_sin) - - -test_real_sin(0.001, taylor.csin) -test_real_sin(0.001, cordic.approx_sin) - - -test_real_sin(0.1, taylor.csin) -test_real_sin(0.1, cordic.approx_sin) - - -# test_complex_sin(0.5 + 2pi, 0.5, taylor.csin) -# test_complex_sin(100, 0.5, taylor.csin)
\ No newline at end of file |