CORDIC
Approximation of Elementary Functions

CORDIC is a MATLAB library which uses the CORDIC algorithm to evaluate certain functions, in particular the sine and cosine.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

CORDIC is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FN, a MATLAB library which approximates elementary and special functions using Chebyshev polynomials, by Wayne Fullerton.

POLPAK, a MATLAB library which evaluates a variety of mathematical functions.

SPECFUN, a FORTRAN90 library which evaluates certain special functions using fitted data.

TEST_VALUES, a MATLAB library which returns some tabulated values of various functions.

Reference:

1. Pitts Jarvis,
   Implementing CORDIC Algorithms,
   Dr. Dobb's Journal,
   October 1990.
2. Jean-Michel Muller,
   Elementary Functions: Algorithms and Implementation,
   Second Edition,
   Birkhaeuser, 2006,
   ISBN13: 978-0-8176-4372-0,
   LC: QA331.M866.
3. Allan Sultan,
   CORDIC: How Hand Calculators Calculate,
   The College Mathematics Journal,
   Volume 40, Number 2, March 2009, pages 87-92.
4. Jack Volder,
   The CORDIC Computing Technique,
   IRE Transactions on Electronic Computers,
   Volume 8, Number 3, pages 330-334, 1959.
5. Jack Volder,
   The Birth of CORDIC,
   Journal of VLSI Signal Processing Systems,
   Volume 25, Number 2, pages 101-105, June 2000.
6. Anthony Williams,
   Optimizing Math-Intensive Applications with Fixed-Point Arithmetic,
   Dr Dobb's Journal,
   Volume 33, Number 4, April 2008, pages 38-43.

Source Code:

• angle_shift.m, shifts an angle so it lies between BETA and BETA+2*PI.
• arccos_cordic.m, computes the arccosine, using the CORDIC method.
• arccos_values.m, returns some tabulated values of the arccosine function.
• arcsin_cordic.m, computes the arcsine, using the CORDIC method.
• arcsin_values.m, returns some tabulated values of the arcsine function.
• arctan_cordic.m, computes the arctangent, using the CORDIC method.
• arctan_values.m, returns some tabulated values of the arctangent function.
• cbrt_cordic.m, estimates the cube root function using the CORDIC algorithm.
• cbrt_values.m, returns some tabulated values of the cube root function.
• cos_values.m, returns some tabulated values of the cosine function.
• cossin_cordic.m, computes the cosine and sine of an angle, using the CORDIC method.
• exp_cordic.m, computes the exponential function, using the CORDIC method.
• exp_values.m, returns some tabulated values of the exponential function.
• ln_cordic.m, computes the natural logarithm function, using the CORDIC method.
• ln_values.m, returns some tabulated values of the natural logarithm function.
• r8_uniform_01.m, returns a unit pseudorandom value.
• sin_values.m, returns some tabulated values of the sine function.
• sqrt_cordic.m, estimates the square root function using the CORDIC algorithm.
• sqrt_values.m, returns some tabulated values of the square root function.
• tan_cordic.m, computes the tangent of an angle, using the CORDIC method.
• tan_values.m, returns some tabulated values of the tangent function.
• timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• cordic_test.m, calls all the tests;
• cordic_test_output.txt, the sample output.
• cordic_test001.m, tests COSSIN_CORDIC for calculating the cosine;
• cordic_test002.m, tests COSSIN_CORDIC for calculating the sine;
• cordic_test003.m, tests ARCTAN_CORDIC;
• cordic_test004.m, tests ARCCOS_CORDIC;
• cordic_test005.m, tests ARCSIN_CORDIC;
• cordic_test006.m, tests TAN_CORDIC;
• cordic_test007.m, tests EXP_CORDIC;
• cordic_test008.m, tests LN_CORDIC;
• cordic_test009.m, tests SQRT_CORDIC;
• cordic_test010.m, tests CBRT_CORDIC;

You can go up one level to the MATLAB source codes.