#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <time.h>

#define INPUT    "qcoeffs.dat"

#define DEGREES    360

typedef struct {double a, b, c;} QCOEFFS;

double normalize(double d)
{
    if (d < 0.0)
        d += ceil(d / -(double)DEGREES) * (double)DEGREES;

    if (d >= DEGREES)
        d -= floor(d / (double)DEGREES) * (double)DEGREES;

    return d;
}

int main()
{
    FILE *f;
    time_t tm;
    double d;
    QCOEFFS qc[DEGREES];

    if (!(f = fopen(INPUT, "rb")) || fread(qc, sizeof(QCOEFFS), DEGREES, f) < DEGREES)
    {
        fprintf(stderr, "Problem with %s - aborting.", INPUT);
        return EXIT_FAILURE;
    }
    fclose(f);

    tm = -clock();

    while (scanf("%lf", &d) > 0)
    {
        int i;
        double e, f;

        /* sin */
        d = normalize(d);
        i = (int)d;
        e = (qc[i].a * d + qc[i].b) * d + qc[i].c;

        /* cos */
        d = normalize((double)DEGREES / 4.0 - d);
        i = (int)d;
        f = (qc[i].a * d + qc[i].b) * d + qc[i].c;

        /* tan = sin / cos */

        /* output - format closest to specs, AFAICT */
        if (d != 0.0 && d != 180.0)
            printf("%.6e %.6e %.6e\n", e, f, e / f);
        else
            printf("%.6e %.6e n\n", e, f);
    }

    tm += clock();

    fprintf(stderr, "time: %.3fs\n", (double)tm/(double)CLOCKS_PER_SEC);    

    return EXIT_SUCCESS;
}

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <time.h>

#define INPUT    "qcoeffs.dat"

#define DEGREES    360

typedef struct {double a, b, c;} QCOEFFS;

double normalize(double d)
{
    if (d < 0.0)
        d += ceil(d / -(double)DEGREES) * (double)DEGREES;

    if (d >= (double)DEGREES)
        d -= floor(d / (double)DEGREES) * (double)DEGREES;

    return d;
}

int main()
{
    FILE *f;
    time_t tm;
    double d;
    QCOEFFS qc[DEGREES];

    if (!(f = fopen(INPUT, "rb")) || fread(qc, sizeof(QCOEFFS), DEGREES, f) < DEGREES)
    {
        fprintf(stderr, "Problem with %s - aborting.", INPUT);
        return EXIT_FAILURE;
    }
    fclose(f);

    tm = -clock();

    while (scanf("%lf", &d) > 0)
    {
        int i;
        double e, f;

        /* sin */
        d = normalize(d);
        i = (int)d;
        e = (qc[i].a * d + qc[i].b) * d + qc[i].c;

        /* cos */
        d = normalize((double)DEGREES / 4.0 - d);
        i = (int)d;
        f = (qc[i].a * d + qc[i].b) * d + qc[i].c;

        /* tan = sin / cos */

        /* output - format closest to specs, AFAICT */
        if (d != 0.0 && d != 180.0)
            printf("%.6e %.6e %.6e\n", e, f, e / f);
        else
            printf("%.6e %.6e n\n", e, f);
    }

    tm += clock();

    fprintf(stderr, "time: %.3fs\n", (double)tm/(double)CLOCKS_PER_SEC);    

    return EXIT_SUCCESS;
}

The approach is to generate approximating quadratic polynomial for each degree. So degree = [0, 1), degree = [1, 2), etc. degree = [359, 360) each have a different polynomial.

This determines the best fit quadratic curve for every degree.

The maximum absolute error for sin and cos was < 1e-08. For tan, because the result isn't limited to ± 1 and you can divide a relatively large number by a relatively small number, the absolute error could be larger. The maximum relative error, e.g. fabs((actual - result) / actual) was usually < 2e-08 until you get in the area of (90 ± 5) or (270 ± 5) degrees, then the error gets worse.

The approach is to generate approximating quadratic polynomials for each degree. So degree = [0, 1), degree = [1, 2), ..., degree = [359, 360) will each have a different polynomial.

This determines the best fit quadratic polynomial for every degree.

The maximum absolute error for sin and cos was ≤ 3e-07. For tan, because the result isn't limited to ± 1 and you can divide a relatively large number by a relatively small number, the absolute error could be larger. From -1 ≤ tan(x) ≤ +1, the maximum absolute error was ≤ 4e-07. For tan(x) > 1 and tan(x) < -1, the maximum relative error, e.g. fabs((actual - result) / actual) was usually < 1e-06 until you get in the area of (90 ± 5) or (270 ± 5) degrees, then the error gets worse.

Octave & C

The approach is to generate approximating quadratic polynomial for each degree. So degree = [0, 1), degree = [1, 2), etc. each have a different polynomial.

The maximum absolute error for sin and cos was < 1e-08. For tan, because the result isn't limited to ± 1, the absolute error could be larger, but the maximum relative error, e.g. fabs((actual - result) / actual) for |actual| > 1 was < 2e-08.

In testing, the average time per single input was (1.053 ± 0.007) µs, which on my machine was about 0.070 µs faster than native sin and cos.

Octave (or Matlab) & C

The approach is to generate approximating quadratic polynomial for each degree. So degree = [0, 1), degree = [1, 2), etc. degree = [359, 360) each have a different polynomial.

The maximum absolute error for sin and cos was < 1e-08. For tan, because the result isn't limited to ± 1 and you can divide a relatively large number by a relatively small number, the absolute error could be larger. The maximum relative error, e.g. fabs((actual - result) / actual) was usually < 2e-08 until you get in the area of (90 ± 5) or (270 ± 5) degrees, then the error gets worse.

In testing, the average time per single input was (1.053 ± 0.007) µs, which on my machine was about 0.070 µs faster than native sin and cos, tan being defined the same way.