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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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4
getopt/cmdlnopts/parseargs.c
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@ -233,7 +233,7 @@ void parseargs(int *argc, char ***argv, myoption *options){
loptr->flag = opts->flag;
loptr->val = opts->val;
// fill short options if they are:
if(!opts->flag){
if(!opts->flag && opts->val){
#ifdef EBUG
shortlist[i] = (char) opts->val;
#endif
@ -396,7 +396,7 @@ void showhelp(int oindex, myoption *options){
qsort(opts, N, sizeof(myoption), argsort);
do{
int p = sprintf(buf, " "); // a little indent
if(!opts->flag) // .val is short argument
if(!opts->flag && opts->val) // .val is short argument
p += snprintf(buf+p, bufsz-p, "-%c, ", opts->val);
p += snprintf(buf+p, bufsz-p, "--%s", opts->name);
if(opts->has_arg == 1) // required argument

22
table_sincos/Makefile Normal file
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@ -0,0 +1,22 @@
PROGRAM = gentab
LDFLAGS = -lm
SRCS = gentab.c
CC = gcc
DEFINES = -D_XOPEN_SOURCE=1111
CXX = gcc
CFLAGS = -Wall -Werror -Wextra $(DEFINES)
OBJS = $(SRCS:.c=.o)
all : $(PROGRAM)
$(PROGRAM) : $(OBJS)
$(CC) $(CFLAGS) $(OBJS) $(LDFLAGS) -o $(PROGRAM)
# some addition dependencies
# %.o: %.c
# $(CC) $(LDFLAGS) $(CFLAGS) $< -o $@
#$(SRCS) : %.c : %.h $(INDEPENDENT_HEADERS)
# @touch $@
clean:
/bin/rm -f *.o *~
depend:
$(CXX) -MM $(CXX.SRCS)

13
table_sincos/README Normal file
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@ -0,0 +1,13 @@
Generate table and functions for calculation of sin and cos on MCU (in integers)
compile: make
defines:
-DMAX_LEN=val - maximal length of generated array (128 by default)
-DDATATYPE=\"type\" - type of data (\"int32_t\" by default)
run:
gentab number
where 'number' is desired precision - step of sin/cos (for example, 0.001)
sin is integer, for "1" if precision is 0.001 would be 1000

87
table_sincos/calcsin.c Normal file
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@ -0,0 +1,87 @@
/*
* calcsin.c
*
* 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>
#include <limits.h>
#define ONE_FIXPT (10000)
#define SZ (61)
typedef int32_t TYPE;
#define _PI (31415)
#define _2PI (62831)
#define _PI_2 (15707)
TYPE angles[61] = {0, 966, 1700, 2025, 2331, 2622, 2898, 3163, 3418, 3663, 3900, 4129, 4351, 4566, 4982, 5375, 5747, 6102, 6441, 6764, 7073, 7369, 7652, 7925, 8186, 8438, 8680, 8912, 9136, 9352, 9560, 9761, 9954, 10141, 10321, 10495, 10663, 10825, 10982, 11133, 11425, 11698, 11953, 12191, 12414, 12622, 12817, 12999, 13170, 13329, 13479, 13759, 14003, 14217, 14404, 14567, 14710, 14959, 15147, 15427, 15708};
TYPE sinuses[61] = {0, 965, 1692, 2011, 2310, 2592, 2858, 3111, 3352, 3582, 3802, 4013, 4215, 4409, 4778, 5119, 5436, 5731, 6004, 6260, 6498, 6720, 6927, 7121, 7302, 7472, 7630, 7778, 7917, 8047, 8169, 8283, 8390, 8490, 8584, 8672, 8754, 8831, 8904, 8972, 9097, 9207, 9303, 9388, 9462, 9528, 9585, 9635, 9680, 9718, 9753, 9811, 9855, 9889, 9915, 9935, 9950, 9972, 9984, 9996, 10000};
TYPE calcsin(TYPE rad){
rad %= _2PI;
if(rad < 0) rad += _2PI;
TYPE sign = 1;
if(rad > _PI){
rad -= _PI;
sign = -1;
}
if(rad > _PI_2) rad = _PI - rad;
// find interval for given angle
int ind = 0, half = SZ/2, end = SZ - 1, iter=0;
do{
++iter;
if(angles[half] > rad){ // left half
end = half;
}else{ // right half
ind = half;
}
half = ind + (end - ind) / 2;
}while(angles[ind] > rad || angles[ind+1] < rad);
//printf("%d iterations, ind=%d, ang[ind]=%d, ang[ind+1]=%d\n", iter, ind, angles[ind], angles[ind+1]);
TYPE ai = angles[ind], si = sinuses[ind];
if(ai == rad) return si;
++ind;
if(angles[ind] == rad) return sinuses[ind];
return sign*(si + (sinuses[ind] - si)*(rad - ai)/(angles[ind] - ai));
}
TYPE calccos(TYPE rad){
return calcsin(_PI_2 - rad);
}
TYPE calctan(TYPE rad){
TYPE s = calcsin(rad) * ONE_FIXPT, c = calccos(rad);
if(c) return s/calccos(rad);
else return INT_MAX;
}
int main(int argc, char **argv){
if(argc != 2) return 1;
double ang = strtod(argv[1], NULL), drad = ang * M_PI/180.;
//printf("rad: %g\n", drad);
TYPE rad = (TYPE)(drad * ONE_FIXPT);
printf("Approximate sin of %g (%d) = %g, exact = %g\n",
drad, rad, calcsin(rad)/((double)ONE_FIXPT), sin(drad));
printf("Approximate cos of %g (%d) = %g, exact = %g\n",
drad, rad, calccos(rad)/((double)ONE_FIXPT), cos(drad));
printf("Approximate tan of %g (%d) = %g, exact = %g\n",
drad, rad, calctan(rad)/((double)ONE_FIXPT), tan(drad));
return 0;
}

109
table_sincos/gentab.c Normal file
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@ -0,0 +1,109 @@
/*
* 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;
}

43
table_sincos/sqrt.c Normal file
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@ -0,0 +1,43 @@
/*
* sqrt.c - Newton sqrt
*
* 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.
*/
#define _XOPEN_SOURCE 1111
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
float SQRT(float x, int iter){
float Result;
int i = 0;
Result = x;
for (i; i < iter; i++)
Result = (Result + x / Result) / 2;
return Result;
}
int main(int argc, char **argv){
if(argc != 2) return 1;
float x = strtof(argv[1], NULL);
if(x < 0) return 2;
printf("sqr(%f) = %f, by 6iter: %f, by 8iter: %f, by 16iter: %f\n", x, sqrtf(x),
SQRT(x, 6), SQRT(x, 8), SQRT(x, 16));
return 0;
}