CORDIC
Approximation of Elementary Functions

CORDIC is a FORTRAN77 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 FORTRAN77 library which evaluates elementary and special functions, by Wayne Fullerton.

POLPAK, a FORTRAN77 library which evaluates recursively defined polynomials and other special functions.

SPECFUN, a FORTRAN77 library which evaluates certain special functions using fitted data.

SPECIAL_FUNCTIONS, a FORTRAN77 library which computes special functions, by Shanjie Zhang, Jianming Jin;

TEST_VALUES, a FORTRAN77 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. Frederick Ruckdeschel,
   BASIC Scientific Subroutines,
   Volume II,
   McGraw-Hill, 1980,
   ISBN: 0-07-054202-3,
   LC: QA76.95.R82.
4. Allan Sultan,
   CORDIC: How Hand Calculators Calculate,
   The College Mathematics Journal,
   Volume 40, Number 2, March 2009, pages 87-92.
5. Jack Volder,
   The CORDIC Computing Technique,
   IRE Transactions on Electronic Computers,
   Volume 8, Number 3, pages 330-334, 1959.
6. Jack Volder,
   The Birth of CORDIC,
   Journal of VLSI Signal Processing Systems,
   Volume 25, Number 2, pages 101-105, June 2000.
7. 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:

• cordic.f, the source code.
• cordic.sh, commands to compile the source code.

Examples and Tests:

• cordic_prb.f, a sample calling program.
• cordic_prb.sh, commands to compile and run the sample program.
• cordic_prb_output.txt, the output file.

List of Routines:

• ANGLE_SHIFT shifts angle ALPHA to lie between BETA and BETA+2PI.
• ARCCOS_CORDIC returns the arccosine of an angle using the CORDIC method.
• ARCCOS_VALUES returns some values of the arc cosine function.
• ARCSIN_CORDIC returns the arcsine of an angle using the CORDIC method.
• ARCSIN_VALUES returns some values of the arc sine function.
• ARCTAN_CORDIC returns the arctangent of an angle using the CORDIC method.
• ARCTAN_VALUES returns some values of the arc tangent function.
• COS_VALUES returns some values of the cosine function.
• COSSIN_CORDIC returns the sine and cosine using the CORDIC method.
• EXP_CORDIC evaluates the exponential function using the CORDIC method.
• EXP_VALUES returns some values of the exponential function.
• I4_HUGE returns a "huge" I4.
• LN_CORDIC evaluates the natural logarithm using the CORDIC method.
• LN_VALUES returns some values of the natural logarithm function.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• SIN_VALUES returns some values of the sine function.
• SQRT_CORDIC returns the square root of a value using the CORDIC method.
• SQRT_VALUES returns some values of the square root function.
• TAN_CORDIC returns the tangent of an angle using the CORDIC method.
• TAN_VALUES returns some values of the tangent function.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.