'Calculate atan2 without std functions or C99

I am calculating angles from a 3-axis accelerometer, but my compiler doesn't have a atan or atan2 function. It has a reserved memory slot, but it calls a function i can't find in any files.

My compiler is Keil µVision 4 running the ARMCC compiler. The compiles has the file math.h, but the function is extern and doesn't exist:

  extern _ARMABI double atan2(double /*y*/, double /*x*/);

Is there a lib or function I can include that has the function arctan implemented? Or is there an alternative function to calculate angles from accelerometer? I need full 3-axis calibration of the angles.

Edit: I was hoping to avoid a table full of pre-calculated values.

Solution 1:^[1]

The following code uses a rational approximation to get the arctangent normalized to the [0 1) interval (you can multiply the result by Pi/2 to get the real arctangent)

normalized_atan(x) ~ (b x + x^2) / (1 + 2 b x + x^2)

where b = 0.596227

The maximum error is 0.1620º

#include <stdint.h>
#include <math.h>

// Approximates atan(x) normalized to the [-1,1] range
// with a maximum error of 0.1620 degrees.

float normalized_atan( float x )
{
    static const uint32_t sign_mask = 0x80000000;
    static const float b = 0.596227f;

    // Extract the sign bit
    uint32_t ux_s  = sign_mask & (uint32_t &)x;

    // Calculate the arctangent in the first quadrant
    float bx_a = ::fabs( b * x );
    float num = bx_a + x * x;
    float atan_1q = num / ( 1.f + bx_a + num );

    // Restore the sign bit
    uint32_t atan_2q = ux_s | (uint32_t &)atan_1q;
    return (float &)atan_2q;
}

// Approximates atan2(y, x) normalized to the [0,4) range
// with a maximum error of 0.1620 degrees

float normalized_atan2( float y, float x )
{
    static const uint32_t sign_mask = 0x80000000;
    static const float b = 0.596227f;

    // Extract the sign bits
    uint32_t ux_s  = sign_mask & (uint32_t &)x;
    uint32_t uy_s  = sign_mask & (uint32_t &)y;

    // Determine the quadrant offset
    float q = (float)( ( ~ux_s & uy_s ) >> 29 | ux_s >> 30 ); 

    // Calculate the arctangent in the first quadrant
    float bxy_a = ::fabs( b * x * y );
    float num = bxy_a + y * y;
    float atan_1q =  num / ( x * x + bxy_a + num );

    // Translate it to the proper quadrant
    uint32_t uatan_2q = (ux_s ^ uy_s) | (uint32_t &)atan_1q;
    return q + (float &)uatan_2q;
}

In case you need more precision, there is a 3rd order rational function:

normalized_atan(x) ~ ( c x + x^2 + x^3) / ( 1 + (c + 1) x + (c + 1) x^2 + x^3)

where c = (1 + sqrt(17)) / 8

which has a maximum approximation error of 0.00811º

Solution 2:^[2]

There is an open source atan implementation here.

Solution 3:^[3]

The actual implementations of the math functions (or stubs to the HWFPU if one exists) should be in libm. With GCC this is indicated by passing -lm to the compiler, but I don't know how it is done with your specific tools.

Sources

This article follows the attribution requirements of Stack Overflow and is licensed under CC BY-SA 3.0.

Source: Stack Overflow

Solution	Source
Solution 1	Glorfindel
Solution 2	Eric Postpischil
Solution 3	Ignacio Vazquez-Abrams

'Calculate atan2 without std functions or C99

Solution 1:[1]

Solution 2:[2]

Solution 3:[3]

Sources

Related Questions

Solution 1:^[1]

Solution 2:^[2]

Solution 3:^[3]