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Data Structures
struct	cordic_cmpx

Macros
#define	PI_Q4_28 843314857 /* int32(pi * 2^28) */
#define	PI_MUL2_Q4_28 1686629713 /* int32(2 * pi * 2^28) */
#define	PI_DIV2_Q3_29 843314857 /* int32(pi / 2 * 2^29) */
#define	PI_Q3_29 1686629713 /* int32(pi * 2^29) */
#define	CORDIC_31B_TABLE_SIZE 31
#define	CORDIC_15B_TABLE_SIZE 15
#define	CORDIC_30B_ITABLE_SIZE 30
#define	CORDIC_16B_ITABLE_SIZE 16
#define	CORDIC_31B_ITERATIONS (CORDIC_31B_TABLE_SIZE - 1)
#define	CORDIC_16B_ITERATIONS (CORDIC_16B_ITABLE_SIZE - 1)

Enumerations
enum	cordic_cfg { EN_32B_CORDIC_SINE , EN_32B_CORDIC_COSINE , EN_32B_CORDIC_CEXP , EN_16B_CORDIC_SINE , EN_16B_CORDIC_COSINE , EN_16B_CORDIC_CEXP }

Functions
void	cordic_approx (int32_t th_rad_fxp, int32_t a_idx, int32_t sign, int32_t b_yn, int32_t xn, int32_t th_cdc_fxp)
	cordic_approx() - CORDIC-based approximation of sine and cosine
int32_t	is_scalar_cordic_acos (int32_t realvalue, int numiters_minus_one)
	is_scalar_cordic_acos() - CORDIC-based approximation for inverse cosine
int32_t	is_scalar_cordic_asin (int32_t realvalue, int numiters_minus_one)
	is_scalar_cordic_asin() - CORDIC-based approximation for inverse sine
void	cmpx_cexp (int32_t sign, int32_t b_yn, int32_t xn, cordic_cfg type, struct cordic_cmpx *cexp)
	cmpx_cexp() - CORDIC-based approximation of complex exponential e^(j*THETA)
static int32_t	sin_fixed_32b (int32_t th_rad_fxp)
	sin_fixed_32b() - Sine function using CORDIC algorithm
static int32_t	cos_fixed_32b (int32_t th_rad_fxp)
	cos_fixed_32b() - Cosine function using CORDIC algorithm
static int16_t	sin_fixed_16b (int32_t th_rad_fxp)
	sin_fixed_16b() - Sine function using CORDIC algorithm
static int16_t	cos_fixed_16b (int32_t th_rad_fxp)
	cos_fixed_16b() - Cosine function using CORDIC algorithm
static void	cmpx_exp_32b (int32_t th_rad_fxp, struct cordic_cmpx *cexp)
	cmpx_exp_32b() - CORDIC-based approximation of complex exponential e^(j*THETA).
static void	cmpx_exp_16b (int32_t th_rad_fxp, struct cordic_cmpx *cexp)
	cmpx_exp_16b() - CORDIC-based approximation of complex exponential e^(j*THETA).
static int32_t	asin_fixed_32b (int32_t cdc_asin_th)
	asin_fixed_32b() - CORDIC-based approximation of inverse sine
static int32_t	acos_fixed_32b (int32_t cdc_acos_th)
	acos_fixed_32b() - CORDIC-based approximation of inverse cosine
static int16_t	asin_fixed_16b (int32_t cdc_asin_th)
	asin_fixed_16b() - CORDIC-based approximation of inverse sine
static int16_t	acos_fixed_16b (int32_t cdc_acos_th)
	acos_fixed_16b() - CORDIC-based approximation of inverse cosine
int32_t	sofm_atan2_32b (int32_t y, int32_t x)
	sofm_atan2_32b() - Four-quadrant arctangent using degree-9 Remez minimax polynomial

Macro Definition Documentation

◆ CORDIC_15B_TABLE_SIZE

#define CORDIC_15B_TABLE_SIZE 15

◆ CORDIC_16B_ITABLE_SIZE

#define CORDIC_16B_ITABLE_SIZE 16

◆ CORDIC_16B_ITERATIONS

#define CORDIC_16B_ITERATIONS (CORDIC_16B_ITABLE_SIZE - 1)

◆ CORDIC_30B_ITABLE_SIZE

#define CORDIC_30B_ITABLE_SIZE 30

◆ CORDIC_31B_ITERATIONS

#define CORDIC_31B_ITERATIONS (CORDIC_31B_TABLE_SIZE - 1)

◆ CORDIC_31B_TABLE_SIZE

#define CORDIC_31B_TABLE_SIZE 31

◆ PI_DIV2_Q3_29

#define PI_DIV2_Q3_29 843314857 /* int32(pi / 2 * 2^29) */

◆ PI_MUL2_Q4_28

#define PI_MUL2_Q4_28 1686629713 /* int32(2 * pi * 2^28) */

◆ PI_Q3_29

#define PI_Q3_29 1686629713 /* int32(pi * 2^29) */

◆ PI_Q4_28

#define PI_Q4_28 843314857 /* int32(pi * 2^28) */

Enumeration Type Documentation

◆ cordic_cfg

enum cordic_cfg

Enumerator
EN_32B_CORDIC_SINE
EN_32B_CORDIC_COSINE
EN_32B_CORDIC_CEXP
EN_16B_CORDIC_SINE
EN_16B_CORDIC_COSINE
EN_16B_CORDIC_CEXP

Function Documentation

◆ acos_fixed_16b()

int16_t acos_fixed_16b ( int32_t cdc_acos_th )

inlinestatic

acos_fixed_16b() - CORDIC-based approximation of inverse cosine

Parameters

cdc_acos_th Input value in Q2.30 format.

Returns: Inverse cosine angle in Q3.13 format.

inverse cosine of cdc_acos_theta based on a CORDIC approximation acos(cdc_acos_th) inverse cosine angle values in radian produces using the DCORDIC (Double CORDIC) algorithm. Q2.30 cdc_acos_th , input value range [-1 to 1] Q3.13 th_acos_fxp, output value range [3.14159265346825 to 0] LUT size set type 31 number of iteration 15 Error (max = 0.000059799232976), THD+N = -89.824298401466635 (dBc)

◆ acos_fixed_32b()

int32_t acos_fixed_32b ( int32_t cdc_acos_th )

inlinestatic

acos_fixed_32b() - CORDIC-based approximation of inverse cosine

Parameters

cdc_acos_th Input value in Q2.30 format.

Returns: Inverse cosine angle in Q3.29 format.

inverse cosine of cdc_acos_theta based on a CORDIC approximation acos(cdc_acos_th) inverse cosine angle values in radian produces using the DCORDIC (Double CORDIC) algorithm. Q2.30 cdc_acos_th , input value range [-1 to 1] Q3.29 th_acos_fxp, output value range [3.14159265346825 to 0] LUT size set type 31 Error (max = 0.000000026077032), THD+N = -157.948952635422842 (dBc)

◆ asin_fixed_16b()

int16_t asin_fixed_16b ( int32_t cdc_asin_th )

inlinestatic

asin_fixed_16b() - CORDIC-based approximation of inverse sine

Parameters

cdc_asin_th Input value in Q2.30 format.

Returns: Inverse sine angle in Q2.14 format.

inverse sine of cdc_asin_theta based on a CORDIC approximation. asin(cdc_asin_th) inverse sine angle values in radian produces using the DCORDIC (Double CORDIC) algorithm. Inverse sine angle values in rad Q2.30 cdc_asin_th, value in between range of [-1 to 1] Q2.14 th_asin_fxp, output value range [-1.5707963258028 to 1.5707963258028] LUT size set type 31 number of iteration 15 Error (max = 0.000059800222516), THD+N = -89.824282520774048 (dBc)

◆ asin_fixed_32b()

int32_t asin_fixed_32b ( int32_t cdc_asin_th )

inlinestatic

asin_fixed_32b() - CORDIC-based approximation of inverse sine

Parameters

cdc_asin_th Input value in Q2.30 format.

Returns: Inverse sine angle in Q2.30 format.

inverse sine of cdc_asin_theta based on a CORDIC approximation. asin(cdc_asin_th) inverse sine angle values in radian produces using the DCORDIC (Double CORDIC) algorithm. Inverse sine angle values in rad Q2.30 cdc_asin_th, value in between range of [-1 to 1] Q2.30 th_asin_fxp, output value range [-1.5707963258028 to 1.5707963258028] LUT size set type 15 Error (max = 0.000000027939677), THD+N = -157.454534077921551 (dBc)

◆ cmpx_cexp()

void cmpx_cexp	(	int32_t	sign,
		int32_t	b_yn,
		int32_t	xn,
		cordic_cfg	type,
		struct cordic_cmpx *	cexp )

cmpx_cexp() - CORDIC-based approximation of complex exponential e^(j*THETA)

Parameters

sign	Sine sign
b_yn	Sine value in Q2.30 format
xn	Cosine value in Q2.30 format
type	CORDIC type
cexp	Output pointer to complex result in struct cordic_cmpx

◆ cmpx_exp_16b()

void cmpx_exp_16b	(	int32_t	th_rad_fxp,
		struct cordic_cmpx *	cexp )

inlinestatic

cmpx_exp_16b() - CORDIC-based approximation of complex exponential e^(j*THETA).

Parameters

th_rad_fxp	Input angle in radian Q4.28 format.
cexp	Output pointer to complex result in struct cordic_cmpx in Q1.15 format.

computes COS(THETA) + j*SIN(THETA) using CORDIC algorithm approximation and returns the complex result. THETA values must be in the range [-2*pi, 2*pi). The cordic exponential algorithm converges, when the angle is in the range [-pi/2, pi/2).If an angle is outside of this range, then a multiple of pi/2 is added or subtracted from the angle until it is within the range [-pi/2,pi/2).Start with the angle in the range [-2*pi, 2*pi) and output has range in [-1.0 to 1.0] Error (max = 0.000060862861574), THD+N = -89.049303454077403 +---------------—+--------------—+-----—+---------—+ | thRadFxp |cdccexpth |thRadFxp| cdccexpth| +-—+--—+----—+-—+-—+----—+-----—+---------—+ |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat | +-—+--—+----—+-—+-—+----—+-----—+---------—+ | 32 | 28 | 1 | 32 | 15 | 1 | 4.28 | 1.15 | +---------------—+--------------—+-----—+---------—+

◆ cmpx_exp_32b()

void cmpx_exp_32b	(	int32_t	th_rad_fxp,
		struct cordic_cmpx *	cexp )

inlinestatic

cmpx_exp_32b() - CORDIC-based approximation of complex exponential e^(j*THETA).

Parameters

th_rad_fxp	Input angle in radian Q4.28 format.
cexp	Output pointer to complex result in struct cordic_cmpx in Q2.30 format.

computes COS(THETA) + j*SIN(THETA) using CORDIC algorithm approximation and returns the complex result. THETA values must be in the range [-2*pi, 2*pi). The cordic exponential algorithm converges, when the angle is in the range [-pi/2, pi/2).If an angle is outside of this range, then a multiple of pi/2 is added or subtracted from the angle until it is within the range [-pi/2,pi/2).Start with the angle in the range [-2*pi, 2*pi) and output has range in [-1.0 to 1.0] Error (max = 0.000000015832484), THD+N = -167.082852232808847 +---------------—+--------------—+-----—+---------—+ | thRadFxp |cdccexpth |thRadFxp| cdccexpth| +-—+--—+----—+-—+-—+----—+-----—+---------—+ |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat | +-—+--—+----—+-—+-—+----—+-----—+---------—+ | 32 | 28 | 1 | 32 | 15 | 1 | 4.28 | 2.30 | +---------------—+--------------—+-----—+---------—+

◆ cordic_approx()

void cordic_approx	(	int32_t	th_rad_fxp,
		int32_t	a_idx,
		int32_t *	sign,
		int32_t *	b_yn,
		int32_t *	xn,
		int32_t *	th_cdc_fxp )

cordic_approx() - CORDIC-based approximation of sine and cosine

Parameters

th_rad_fxp	Input angle in radian Q4.28 format.
a_idx	Used LUT size.
sign	Output pointer to sine/cosine sign.
b_yn	Output pointer to sine value in Q2.30 format.
xn	Output pointer to cosine value in Q2.30 format.
th_cdc_fxp	Output pointer to the residual angle in Q2.30 format.

◆ cos_fixed_16b()

int16_t cos_fixed_16b ( int32_t th_rad_fxp )

inlinestatic

cos_fixed_16b() - Cosine function using CORDIC algorithm

Parameters

th_rad_fxp Input angle in radian Q4.28 format.

Returns: Cosine value in Q1.15 format.

Compute fixed point cordic cosine with table lookup and interpolation The cordic cos algorithm converges, when the angle is in the range [-pi/2, pi/2).If an angle is outside of this range, then a multiple of pi/2 is added or subtracted from the angle until it is within the range [-pi/2,pi/2).Start with the angle in the range [-2*pi, 2*pi) and output has range in [-1.0 to 1.0] +---------------—+--------------—+-----—+---------—+ | thRadFxp | cdccosth |thRadFxp| cdccosth| +-—+--—+----—+-—+-—+----—+-----—+---------—+ |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat | +-—+--—+----—+-—+-—+----—+-----—+---------—+ | 32 | 28 | 1 | 32 | 15 | 1 | 4.28 | 1.15 | +---------------—+--------------—+-----—+---------—+

◆ cos_fixed_32b()

int32_t cos_fixed_32b ( int32_t th_rad_fxp )

inlinestatic

cos_fixed_32b() - Cosine function using CORDIC algorithm

Parameters

th_rad_fxp Input angle in radian Q4.28 format.

Returns: Cosine value in Q1.31 format.

Compute fixed point cordicsine with table lookup and interpolation The cordic cosine algorithm converges, when the angle is in the range [-pi/2, pi/2).If an angle is outside of this range, then a multiple of pi/2 is added or subtracted from the angle until it is within the range [-pi/2,pi/2).Start with the angle in the range [-2*pi, 2*pi) and output has range in [-1.0 to 1.0] +---------------—+--------------—+-----—+-----—+ | thRadFxp | cdccosth |thRadFxp|cdccosth| +-—+--—+----—+-—+-—+----—+-----—+-----—+ |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat| +-—+--—+----—+-—+-—+----—+-----—+-----—+ | 32 | 28 | 1 | 32 | 31 | 1 | 4.28 | 1.31 | +---------------—+--------------—+-----—+-----—+

◆ is_scalar_cordic_acos()

int32_t is_scalar_cordic_acos	(	int32_t	realvalue,
		int	numiters_minus_one )

is_scalar_cordic_acos() - CORDIC-based approximation for inverse cosine

Parameters

realvalue	Input cosine value in Q2.30 format.
numiters_minus_one	Number of iterations minus one.

Returns: Inverse cosine angle in Q3.29 format.

◆ is_scalar_cordic_asin()

int32_t is_scalar_cordic_asin	(	int32_t	realvalue,
		int	numiters_minus_one )

is_scalar_cordic_asin() - CORDIC-based approximation for inverse sine

Parameters

realvalue	Input sine value in Q2.30 format.
numiters_minus_one	Number of iterations minus one.

Returns: Inverse sine angle in Q2.30 format.

◆ sin_fixed_16b()

int16_t sin_fixed_16b ( int32_t th_rad_fxp )

inlinestatic

sin_fixed_16b() - Sine function using CORDIC algorithm

Parameters

th_rad_fxp Input angle in radian Q4.28 format.

Returns: Sine value in Q1.15 format

Compute fixed point cordic sine with table lookup and interpolation The cordic sine algorithm converges, when the angle is in the range [-pi/2, pi/2).If an angle is outside of this range, then a multiple of pi/2 is added or subtracted from the angle until it is within the range [-pi/2,pi/2).Start with the angle in the range [-2*pi, 2*pi) and output has range in [-1.0 to 1.0] +---------------—+--------------—+-----—+---------—+ | thRadFxp | cdcsinth |thRadFxp| cdcsinth| +-—+--—+----—+-—+-—+----—+-----—+---------—+ |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat | +-—+--—+----—+-—+-—+----—+-----—+---------—+ | 32 | 28 | 1 | 32 | 15 | 1 | 4.28 | 1.15 | +---------------—+--------------—+-----—+---------—+

◆ sin_fixed_32b()

int32_t sin_fixed_32b ( int32_t th_rad_fxp )

inlinestatic

sin_fixed_32b() - Sine function using CORDIC algorithm

Parameters

th_rad_fxp Input angle in radian Q4.28 format.

Returns: Sine value in Q1.31 format.

Compute fixed point cordicsine with table lookup and interpolation The cordic sine algorithm converges, when the angle is in the range [-pi/2, pi/2).If an angle is outside of this range, then a multiple of pi/2 is added or subtracted from the angle until it is within the range [-pi/2,pi/2).Start with the angle in the range [-2*pi, 2*pi) and output has range in [-1.0 to 1.0] +---------------—+--------------—+-----—+-----—+ | thRadFxp | cdcsinth |thRadFxp|cdcsinth| +-—+--—+----—+-—+-—+----—+-----—+-----—+ |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat| +-—+--—+----—+-—+-—+----—+-----—+-----—+ | 32 | 28 | 1 | 32 | 31 | 1 | 4.28 | 1.31 | +---------------—+--------------—+-----—+-----—+

◆ sofm_atan2_32b()

int32_t sofm_atan2_32b	(	int32_t	y,
		int32_t	x )

sofm_atan2_32b() - Four-quadrant arctangent using degree-9 Remez minimax polynomial

Parameters

y	Imaginary component (sine) in Q1.31 format.
x	Real component (cosine) in Q1.31 format.

Returns: Angle in Q3.29 radians, range [-pi, +pi].

Uses the Horner-form polynomial: atan(z) = z * (C0 + z^2 * (C1 + z^2 * (C2 + z^2 * (C3 + z^2 * C4))))

with Remez minimax coefficients on [0, 1]. Maximum error ~0.001 degrees (1.94e-5 radians).

Data Structures

Macros

Enumerations

Functions

Macro Definition Documentation

◆ CORDIC_15B_TABLE_SIZE

◆ CORDIC_16B_ITABLE_SIZE

◆ CORDIC_16B_ITERATIONS

◆ CORDIC_30B_ITABLE_SIZE

◆ CORDIC_31B_ITERATIONS

◆ CORDIC_31B_TABLE_SIZE

◆ PI_DIV2_Q3_29

◆ PI_MUL2_Q4_28

◆ PI_Q3_29

◆ PI_Q4_28

Enumeration Type Documentation

◆ cordic_cfg

Function Documentation

◆ acos_fixed_16b()

◆ acos_fixed_32b()

◆ asin_fixed_16b()

◆ asin_fixed_32b()

◆ cmpx_cexp()

◆ cmpx_exp_16b()

◆ cmpx_exp_32b()

◆ cordic_approx()

◆ cos_fixed_16b()

◆ cos_fixed_32b()

◆ is_scalar_cordic_acos()

◆ is_scalar_cordic_asin()

◆ sin_fixed_16b()

◆ sin_fixed_32b()

◆ sofm_atan2_32b()