ra*******@gmail.com wrote:

Currently using cosine function in math.h

Currently I get:

1 = cos(1e^-7)

Is there another way for cos to return value of high accuracy say:

0.999999 = cos(1e^-7)

That is a grossly inaccurate value. Higher precision is not high accuracy:

#include <stdio.h>

#include <math.h>

#include <float.h>

int main(void)

{

int i;

double x = 1.0e-7, y = cos(x);

printf("With default precisions, cos(%g) is shown as:\n"

" (%%f) %f, (%%g) %g, (%%e) %e\n\n", x, y, y, y);

printf("With various precision up to DBL_DIG (%d), cos(%g) is\n",

DBL_DIG, x);

for (i = 0; i <= DBL_DIG; i++)

printf(" precision = %d, %.*f, %.*g, %.*e\n",

i, i, y, i, y, i, y);

x = acos(0.999999);

y = cos(x);

printf("\nWith default precisions, cos(%g) is shown as:\n"

" (%%f) %f, (%%g) %g, (%%e) %e\n\n", x, y, y, y);

printf("With various precision up to DBL_DIG (%d), cos(%g) is\n",

DBL_DIG, x);

for (i = 0; i <= DBL_DIG; i++)

printf(" precision = %d, %.*f, %.*g, %.*e\n",

i, i, y, i, y, i, y);

return 0;

}

With default precisions, cos(1e-07) is shown as:

(%f) 1.000000, (%g) 1, (%e) 1.000000e+00

With various precision up to DBL_DIG (15), cos(1e-07) is

precision = 0, 1, 1, 1e+00

precision = 1, 1.0, 1, 1.0e+00

precision = 2, 1.00, 1, 1.00e+00

precision = 3, 1.000, 1, 1.000e+00

precision = 4, 1.0000, 1, 1.0000e+00

precision = 5, 1.00000, 1, 1.00000e+00

precision = 6, 1.000000, 1, 1.000000e+00

precision = 7, 1.0000000, 1, 1.0000000e+00

precision = 8, 1.00000000, 1, 1.00000000e+00

precision = 9, 1.000000000, 1, 1.000000000e+00

precision = 10, 1.0000000000, 1, 1.0000000000e+00

precision = 11, 1.00000000000, 1, 1.00000000000e+00

precision = 12, 1.000000000000, 1, 1.000000000000e+00

precision = 13, 1.0000000000000, 1, 1.0000000000000e+00

precision = 14, 1.00000000000000, 1, 9.99999999999995e-01

precision = 15, 0.999999999999995, 0.999999999999995,

9.999999999999950e-01

With default precisions, cos(0.00141421) is shown as:

(%f) 0.999999, (%g) 0.999999, (%e) 9.999990e-01

With various precision up to DBL_DIG (15), cos(0.00141421) is

precision = 0, 1, 1, 1e+00

precision = 1, 1.0, 1, 1.0e+00

precision = 2, 1.00, 1, 1.00e+00

precision = 3, 1.000, 1, 1.000e+00

precision = 4, 1.0000, 1, 1.0000e+00

precision = 5, 1.00000, 1, 9.99999e-01

precision = 6, 0.999999, 0.999999, 9.999990e-01

precision = 7, 0.9999990, 0.999999, 9.9999900e-01

precision = 8, 0.99999900, 0.999999, 9.99999000e-01

precision = 9, 0.999999000, 0.999999, 9.999990000e-01

precision = 10, 0.9999990000, 0.999999, 9.9999900000e-01

precision = 11, 0.99999900000, 0.999999, 9.99999000000e-01

precision = 12, 0.999999000000, 0.999999, 9.999990000000e-01

precision = 13, 0.9999990000000, 0.999999, 9.9999900000000e-01

precision = 14, 0.99999900000000, 0.999999, 9.99999000000000e-01

precision = 15, 0.999999000000000, 0.999999, 9.999990000000000e-01