atan.md

atan

Table of Contents:

Functions

atan_rational

atan_cordic

Examples

Examples

Quality of Results

Error Graph

Resource Usage

Function atan_rational

template <unsigned int W_OUT, int IW_OUT, unsigned int W_IN, int IW_IN>
ap_fixpt<unsigned int W_OUT, int IW_OUT> atan_rational(ap_fixpt<unsigned int W_IN, int IW_IN> num)

A rational function approximation of arctan.

Template Parameters:

• unsigned int W_OUT: width of the output
• int IW_OUT: width of integer portion of the output
• unsigned int W_IN: width of the input (automatically inferred)
• int IW_IN: width of integer portion of the input (automatically inferred)

Function Arguments:

• ap_fixpt<unsigned int W_IN, int IW_IN> num: input

Returns:

• ap_fixpt<unsigned int W_OUT, int IW_OUT>: arctangent of input value (in radians)

Function atan_cordic

template <unsigned int W_OUT, int IW_OUT, int N_ITERATIONS, unsigned int W_IN, int IW_IN>
ap_fixpt<unsigned int W_OUT, int IW_OUT> atan_cordic(ap_fixpt<unsigned int W_IN, int IW_IN> num)

CORDIC implementation of arctan.

Template Parameters:

• unsigned int W_OUT: width of the output
• int IW_OUT: width of integer portion of the output
• int N_ITERATIONS: number of CORDIC iterations
• unsigned int W_IN: width of the input (automatically inferred)
• int IW_IN: width of integer portion of the input (automatically inferred)

Function Arguments:

• ap_fixpt<unsigned int W_IN, int IW_IN> num: input

Returns:

• ap_fixpt<unsigned int W_OUT, int IW_OUT>: arctangent of input value (in radians)

Examples

  hls::ap_fixpt<10, 2> y = 1;

  auto x = hls::math::atan_rational<10, 2>(y); // x will be an ap_fixpt number with the value 0.785398163

  hls::ap_fixpt<10, 2> y = 1;

  auto x = hls::math::atan_cordic<10, 2, 16>(y); // x will be an ap_fixpt number with the value 0.785398163

The example used to gather the following graph and resource report can be found here.

Error Graph

Resource Usage

Using MPF300

Input Plot Range: [-2.00, 2.00] Using N_ITER = 16 Using W = 32, IW = 8, Q_M = AP_TRN, O_M = AP_WRAP

Name	Latency [cycles] (min/max/avg)	II [cycles] (min/max/avg)	Avg Error	Max Error	LUTs	DFFs	DSPs	LSRAM	uSRAM	Estimated Frequency
atan_cmath	308 / 308 / 308.00	17 / 17 / 17.00	0	0	15136	23146	9	0	6	277.932 MHz
atan_cordic	39 / 40 / 39.00	1 / 2 / 1.00	0.00012	0.000244	3048	9644	0	0	3	446.030 MHz
atan_rational	80 / 81 / 80.00	1 / 2 / 1.00	0.001957	0.002828	9865	13451	14	0	0	307.882 MHz

Input Plot Range: [-20.00, 20.00] Using N_ITER = 16 Using W = 32, IW = 16, Q_M = AP_TRN, O_M = AP_WRAP

Name	Latency [cycles] (min/max/avg)	II [cycles] (min/max/avg)	Avg Error	Max Error	LUTs	DFFs	DSPs	LSRAM	uSRAM	Estimated Frequency
atan_cmath	308 / 308 / 308.00	17 / 17 / 17.00	0	0	15136	23146	9	0	6	277.932 MHz
atan_cordic	43 / 44 / 43.01	1 / 2 / 1.01	0.000134	0.000348	3393	11224	0	0	6	435.161 MHz
atan_rational	77 / 78 / 77.01	1 / 2 / 1.01	0.002222	0.0028	9298	12936	10	0	0	345.185 MHz

Notes:

• The standard C math library uses floating point numbers.
• Targeted FMax was 400MHz.

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