sincos_add

.gitignore

*.eps
*.pdf
*.png
*.dat

conv.sh

#!/bin/sh
for f in `ls *.eps`
do
	pstopdf $f
	base=`basename $f .eps`
	pdffile=$base.pdf
	outfile=$base.png
	sips -s format png $pdffile -o $outfile
done

main.cpp

#include <cmath>
#include <cstdio>
#include <cstdlib>

inline double rad(double degree)
{   return degree*M_PI/180; }

inline double sin_addition(double s1, double c1, double s2, double c2)
{   return s1*c2 + c1*s2;   }

inline double cos_addition(double s1, double c1, double s2, double c2)
{   return c1*c2 - s1*s2;   }

void sincos_by_addition(const int times, const int dr)
{
    if (times < 0) { throw; } 
    double sin_dr = std::sin( rad(static_cast<double>(dr)) );
    double cos_dr = std::cos( rad(static_cast<double>(dr)) );

    int r = 0;
    double sinr = 0.;
    double cosr = 1.;

    std::printf("#%s \t%20s \t%20s \t%20s \t%20s\n", "r", "sin", "cos", "std::sin", "std::cos");
    for(int i = 0; i < times; i++){
        std::printf("%d \t%.16f \t%.16f \t%.16f \t%.16f\n", r, sinr, cosr, 
                std::sin(rad(static_cast<double>(r))), 
                std::cos(rad(static_cast<double>(r))) );

        // next value
        double sinr_ = sin_addition(sinr, cosr, sin_dr, cos_dr);
        cosr = cos_addition(sinr, cosr, sin_dr, cos_dr);
        sinr = sinr_;
        r += dr;
    }

    std::printf("%d \t%.16f \t%.16f \t%.16f \t%.16f\n", r, sinr, cosr, 
            std::sin(rad(static_cast<double>(r))), 
            std::cos(rad(static_cast<double>(r))) );
    return;
}


int main(int argc, char **argv)
{
    // 第一引数は角度の刻み、第二引数は360*n°まで計算
    int dr = 3;
    int n = 6;
    if (1 < argc) {
        dr = std::atoi(argv[1]);
        if (2 < argc) {
            n = std::atoi(argv[2]);
        }
    }
    std::printf("# dr: %d, n: %d\n", dr, n);

    int r = 360 * n / dr;
    sincos_by_addition(r, dr);
    return 0;
}

makefile

all:
	g++ main.cpp -o main.x 

run:
	./main.x 1  10 > dr1.dat
	./main.x 2  10 > dr2.dat
	./main.x 3  10 > dr3.dat
	./main.x 10 10 > dr10.dat
	gnuplot plot.in
	gnuplot plot_diff.in
	sh conv.sh

plot.in

set yrange [-1.2:1.2]
set xtics 360
set mxtics 3
set ytics 0.2
set grid xtics ytics

i = 1;
ofile = sprintf("r%d.eps",  i)
ifile = sprintf("dr%d.dat", i)
set terminal postscript enhanced color
set output ofile
plot \
ifile using 1:2 with linespoints pt 7 ps 0.5 title "sin",\
ifile using 1:3 with linespoints pt 7 ps 0.5 title "cos",\
ifile using 1:4 with linespoints pt 7 ps 0.3 title "std::sin",\
ifile using 1:5 with linespoints pt 7 ps 0.3 title "std::cos",\


i = 3;
ofile = sprintf("r%d.eps",  i)
ifile = sprintf("dr%d.dat", i)
set terminal postscript enhanced color
set output ofile
plot \
ifile using 1:2 with linespoints pt 7 ps 0.5 title "sin",\
ifile using 1:3 with linespoints pt 7 ps 0.5 title "cos",\
ifile using 1:4 with linespoints pt 7 ps 0.3 title "std::sin",\
ifile using 1:5 with linespoints pt 7 ps 0.3 title "std::cos",\


i = 10;
ofile = sprintf("r%d.eps",  i)
ifile = sprintf("dr%d.dat", i)
set terminal postscript enhanced color
set output ofile
plot \
ifile using 1:2 with linespoints pt 7 ps 0.5 title "sin",\
ifile using 1:3 with linespoints pt 7 ps 0.5 title "cos",\
ifile using 1:4 with linespoints pt 7 ps 0.3 title "std::sin",\
ifile using 1:5 with linespoints pt 7 ps 0.3 title "std::cos",\

plot_diff.in

set terminal postscript enhanced color
set output "diff.eps"

set xtics 360
set mxtics 3
set grid xtics ytics

plot \
"dr1.dat"  using 1:(abs($4-$2)) with linespoints ps 0.5 title "dr=1  abs(sin(x)-std::sin(x))",\
"dr3.dat"  using 1:(abs($4-$2)) with linespoints ps 0.5 title "dr=3  abs(sin(x)-std::sin(x))",\
"dr10.dat" using 1:(abs($4-$2)) with linespoints ps 0.5 title "dr=10 abs(sin(x)-std::sin(x))",\