Add trigonometry functions for calculations on MCU

getopt/cmdlnopts/parseargs.c

@@ -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

table_sincos/Makefile

@@ -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)

table_sincos/README

@@ -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
+

table_sincos/calcsin.c

@@ -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;
+}

table_sincos/gentab.c

@@ -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;
+}

table_sincos/sqrt.c

@@ -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;
+}
+