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Add trigonometry functions for calculations on MCU

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eddyem
2016-06-20 14:40:26 +03:00
parent be1cbe0956
commit d826925162
6 changed files with 276 additions and 2 deletions
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109
table_sincos/gentab.c Normal file
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/*
* gentab.c - generate sin/cos table
*
* Copyright 2016 Edward V. Emelianov <eddy@sao.ru, edward.emelianoff@gmail.com>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02110-1301, USA.
*/
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <stdint.h>
#define MAX_LEN (256)
#define DATATYPE "int32_t"
/**
* Calculate angle \alpha_{i+1} for given precision
* @param ai - \alpha_i
* @param prec - precision
* @return calculated angle
*/
double get_next_angle(double ai, double prec){
double anxt, amid = M_PI_2, diff = 1.;
int i = 0;
do{
anxt = amid;
double si = sin(ai), snxt = sin(anxt);
/*
* We have: sin(a[i]+a) \approx sin(a[i]) + (sin(a[i+1])-sin(a[i]))/(a[i+1]-a[i])*a
* so maximal deviation from real sin(a) would be at point
* amax = acos((sin(a[i+1]) - sin(a[i]))/(a[i+1] - a[i]))
* to calculate a[i+1] we always start from pi/2
*/
amid = acos((snxt - si)/(anxt - ai));
double sinapp = si + (snxt - si)/(anxt - ai)*(amid - ai);
diff = fabs(sinapp - sin(amid));
++i;
}while(diff > prec);
return anxt;
}
/**
* calculate sin/cos table
* sin(a) = s1 + (s2 - s1)*(a - a1)/(a2 - a1)
* @param ang - NULL (to calculate tabular length only) or array of angles
* @param sin - NULL (-//-) or array of sinuses from 0 to 1
*/
int calc_table(double prec, uint64_t *ang, uint64_t *sinuses){
int L = 1; // points 0 and pi/2 included!
double ai = 0.;
if(ang) *ang++ = 0;
if(sinuses) *sinuses++ = 0;
while(M_PI_2 > ai){
ai = get_next_angle(ai, prec);
if(ang) *ang++ = (uint64_t)round(ai/prec);
if(sinuses) *sinuses++ = (uint64_t)round(sin(ai)/prec);
++L;
}
return L;
}
int main(int argc, char **argv){
if(argc != 2){
fprintf(stderr, "Usage: %s prec\n\twhere 'prec' is desired precision\n", argv[0]);
return 1;
}
char *eptr;
double prec = strtod(argv[1], &eptr);
if(*eptr || eptr == argv[1]){
fprintf(stderr, "Bad number: %s\n", argv[1]);
return 2;
}
uint64_t *angles = malloc(sizeof(uint64_t)*MAX_LEN);
uint64_t *sinuses = malloc(sizeof(uint64_t)*MAX_LEN);
int L = calc_table(prec, NULL, NULL), i;
if(L > MAX_LEN){
fprintf(stderr, "Error! Get vector of length %d instead of %d\n", L, MAX_LEN);
return 3;
}
calc_table(prec, angles, sinuses);
printf("#define ONE_FIXPT (%d)\n#define SZ (%d)\ntypedef %s TYPE;\n", (int)(1./prec), L, DATATYPE);
printf("#define _PI (%ld)\n#define 2_PI (%ld)\n#define _PI_2 (%ld)\n\n", (int64_t)(M_PI/prec), (int64_t)(2*M_PI/prec),
(int64_t)(M_PI/2/prec));
printf("TYPE angles[%d] = {", L);
for(i = 0; i < L; ++i){
printf("%ld, ", *angles++);
}
printf("\b\b");
printf("};\nTYPE sinuses[%d] = {", L);
for(i = 0; i < L; ++i){
printf("%ld, ", *sinuses++);
}
printf("\b\b");
printf("};\n");
return 0;
}