#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include <unistd.h>
#include <libgen.h>

Macros
#define	Cordic_T_Bits (int)(sizeof(Cordic_T) << 3)

#define	FCordic_T_Bits (int)(sizeof(FCordic_T) << 3)

#define	Cordic_T_FractionBits (int)(Cordic_T_Bits - 3 - 1)

#define	Cordic_T_STR "typedef int Cordic_T;"

#define	UCordic_T_STR "typedef unsigned int UCordic_T;"

#define	FCordic_T_STR "typedef double FCordic_T;"

#define	Cordic_One (1UL << Cordic_T_FractionBits)

#define	Cordic_K (Cordic_One * 0.6072529350088812561694)

#define	Cordic_INVK (Cordic_One / 0.6072529350088812561694)

#define	Cordic_KP (Cordic_One * 1.20749706776307212887772)

#define	Cordic_INVKP (Cordic_One * 1/1.20749706776307212887772)

#define	Cordic_HalfPI ((UCordic_T) (Cordic_One * M_PI_2) )

#define	Cordic2FP(a) ( (double) (a) / (double) (Cordic_One))

#define	FP2Cordic(a) ((Cordic_T) (Cordic_One * (a)))

Typedefs
typedef int	Cordic_T
	cordicC.c – J. Pitts Jarvis, III cordicC.c computes CORDIC constants and exercises the basic algorithms. Represents all numbers in fixed point notation. 1 bit sign, Cordic_T_Bits-1-n bit integral part, and n bit fractional part. n=29 lets us represent numbers in the interval [-4, 4) in 32 bit Cordic_T. Two's complement arithmetic is operative here. More...

typedef unsigned int	UCordic_T

typedef double	FCordic_T

Functions
char *	get_date ()
	Get the current date in a string. More...

void	dump_tables (FILE *FO)
	Create Cordic tables Normalize base number system to 1.0 == Cordic_One == PI/2 (90 degrees) Example .5 is 50 gradians or PI/4 This value as great advantages: More...

void	PrintXYZ (char *str)
	Display X,Y,Z as floating point. More...

void	Circular (Cordic_T x, Cordic_T y, Cordic_T z)
	Main Cordic routine - used for basic trig and vector rotations. More...

void	cordit1 (Cordic_T x, Cordic_T y, Cordic_T z, Cordic_T vecmode)
	This is the circular method. One slight change from the other methods is the y < vecmode test. this is to implement arcsin, otherwise it can be y < 0 and you can compute arcsin from arctan using trig identities, so it is not essential. More...

Cordic_T	asinCordic (Cordic_T a)
	Compute ArcSine (a) Only works for \|a\| < 0.98. More...

int	main (int argc, char *argv[])
	Create C Cordic Tables and test the results. More...

Variables
static Cordic_T	v_atan [Cordic_T_Bits+1]

static Cordic_T	X

static Cordic_T	Y

static Cordic_T	Z

Macro Definition Documentation

#define Cordic2FP ( a ) ( (double) (a) / (double) (Cordic_One))

Definition at line 123 of file cordic2c.c.

Referenced by get_date(), and PrintXYZ().

#define Cordic_HalfPI ((UCordic_T) (Cordic_One * M_PI_2) )

Definition at line 122 of file cordic2c.c.

Referenced by get_date().

#define Cordic_INVK (Cordic_One / 0.6072529350088812561694)

Definition at line 119 of file cordic2c.c.

Referenced by get_date().

#define Cordic_INVKP (Cordic_One * 1/1.20749706776307212887772)

Definition at line 121 of file cordic2c.c.

Referenced by get_date().

#define Cordic_K (Cordic_One * 0.6072529350088812561694)

Definition at line 118 of file cordic2c.c.

Referenced by asinCordic(), get_date(), and main().

#define Cordic_KP (Cordic_One * 1.20749706776307212887772)

Definition at line 120 of file cordic2c.c.

Referenced by get_date().

#define Cordic_One (1UL << Cordic_T_FractionBits)

Definition at line 117 of file cordic2c.c.

Referenced by get_date().

#define Cordic_T_Bits (int)(sizeof(Cordic_T) << 3)

Definition at line 102 of file cordic2c.c.

Referenced by get_date().

#define Cordic_T_FractionBits (int)(Cordic_T_Bits - 3 - 1)

Definition at line 105 of file cordic2c.c.

Referenced by Circular(), cordit1(), and get_date().

#define Cordic_T_STR "typedef int Cordic_T;"

Definition at line 107 of file cordic2c.c.

Referenced by get_date().

#define FCordic_T_Bits (int)(sizeof(FCordic_T) << 3)

Definition at line 103 of file cordic2c.c.

Referenced by get_date().

#define FCordic_T_STR "typedef double FCordic_T;"

Definition at line 109 of file cordic2c.c.

Referenced by get_date().

#define FP2Cordic ( a ) ((Cordic_T) (Cordic_One * (a)))

Definition at line 124 of file cordic2c.c.

Referenced by main().

#define UCordic_T_STR "typedef unsigned int UCordic_T;"

Definition at line 108 of file cordic2c.c.

Referenced by get_date().

Typedef Documentation

typedef int Cordic_T

cordicC.c – J. Pitts Jarvis, III cordicC.c computes CORDIC constants and exercises the basic algorithms. Represents all numbers in fixed point notation. 1 bit sign, Cordic_T_Bits-1-n bit integral part, and n bit fractional part. n=29 lets us represent numbers in the interval [-4, 4) in 32 bit Cordic_T. Two's complement arithmetic is operative here.

IMPLEMENTING CORDIC ALGORITHMS by Pitts Jarvis Cordic algorithm identities for circular functions starting with [x, y, z] and then driving z to 0 gives: [P*(x*cos(z)-y*sin(z)), P*(y*cos(z)+x*sin(z)), 0] driving y to 0 gives: [P*sqrt(x^2+y^2), 0, z+atan(y/x)] where K = 1/P = sqrt(1+1)* . . . sqrt(1+(2^(-2*i))) special cases which compute interesting functions sin, cos [K, 0, a] -> [cos(a), sin(a), 0] atan [1, a, 0] -> [sqrt(1+a^2)/K, 0, atan(a)] [x, y, 0] -> [sqrt(x^2+y^2)/K, 0, atan(y/x)] for hyperbolic functions, starting with [x, y, z] and then driving z to 0 gives: [P(x*cosh(z)+y*sinh(z)), P*(y*cosh(z)+x*sinh(z)), 0] driving y to 0 gives: [P*sqrt(x^2-y^2), 0, z+atanh(y/x)] where K = 1/P = sqrt(1-(1/2)^2)* . . . sqrt(1-(2^(-2*i))) sinh, cosh [K, 0, a] -> [cosh(a), sinh(a), 0] exponential [K, K, a] -> [e^a, e^a, 0] atanh [1, a, 0] -> [sqrt(1-a^2)/K, 0, atanh(a)] [x, y, 0] -> [sqrt(x^2-y^2)/K, 0, atanh(y/x)] ln [a+1, a-1, 0] -> [2*sqrt(a)/K, 0, ln(a)/2] sqrt [a+(K/2)^2, a-(K/2)^2, 0] -> [sqrt(a), 0, ln(a(2/K)^2)/2] sqrt, ln [a+(K/2)^2, a-(K/2)^2, -ln(K/2)] -> [sqrt(a), 0, ln(a)/2] for linear functions, starting with [x, y, z] and then driving z to 0 gives: [x, y+x*z, 0] driving y to 0 gives: [x, 0, z+y/x] compute atan(x) and atanh(x) using infinite series atan(x) = x - x^3/3 + x^5/5 - x^7/7 + . . . for x^2 < 1 atanh(x) = x + x^3/3 + x^5/5 + x^7/7 + . . . for x^2 < 1 To calculate these functions to 32 bits of precision, pick terms[i] s.t. ((2^-i)^(terms[i]))/(terms[i]) < 2^-32 For x <= 2^(-11), atan(x) = atanh(x) = x with 32 bits of accuracy

Definition at line 97 of file cordic2c.c.

typedef double FCordic_T

Definition at line 99 of file cordic2c.c.

typedef unsigned int UCordic_T

Definition at line 98 of file cordic2c.c.

Function Documentation

Cordic_T asinCordic ( Cordic_T a )

Compute ArcSine (a) Only works for |a| < 0.98.

Parameters

[in] a Sine

Returns: ArcSine (a)

Definition at line 292 of file cordic2c.c.

void Circular	(	Cordic_T	x,
		Cordic_T	y,
		Cordic_T	z
	)

Main Cordic routine - used for basic trig and vector rotations.

See also: http://en.wikipedia.org/wiki/CORDIC

Parameters

[in,out]	x	Cordik_K, out: Cos of z
[in,out]	y	0, out: Sin of z
[in,out]	z	fixed point version of angle

Returns: void

Definition at line 216 of file cordic2c.c.

Referenced by main().

void cordit1	(	Cordic_T	x,
		Cordic_T	y,
		Cordic_T	z,
		Cordic_T	vecmode
	)

This is the circular method. One slight change from the other methods is the y < vecmode test. this is to implement arcsin, otherwise it can be y < 0 and you can compute arcsin from arctan using trig identities, so it is not essential.

See also: http://en.wikipedia.org/wiki/CORDIC

Parameters

[in,out]	x	in: Cordik_K, out: Cos of z
[in,out]	y	in: 0
[in,out]	z	in: 0
[in]	vecmode	arcsize value

Returns: void

Definition at line 259 of file cordic2c.c.

Referenced by asinCordic().

void dump_tables ( FILE * FO )

Create Cordic tables Normalize base number system to 1.0 == Cordic_One == PI/2 (90 degrees) Example .5 is 50 gradians or PI/4 This value as great advantages:

integer part is small on the unit circle
integer part is the circle quadrant number (think range reductions)Dump Cordic C structure
Parameters

[in] *FO File handle to write tables to

Returns
void

Definition at line 153 of file cordic2c.c.

Referenced by get_date(), and main().

char* get_date ( )

Get the current date in a string.