atan.md

atan

Table of Contents:

Functions

atan_cordic

atan_rational

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
  

Limitations:

No limitations.

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
  

Limitations:

No limitations.

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_cordic	28 / 29 / 28.00	1 / 2 / 1.00	0.00012	0.000244	2157	6059	0	0	0	362.845 MHz
atan_rational	80 / 81 / 80.00	1 / 2 / 1.00	0.001957	0.002828	9978	13612	12	0	0	317.561 MHz
atan_cmath	309 / 309 / 309.00	18 / 18 / 18.00	0	0	14800	22753	9	0	6	304.414 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_cordic	28 / 29 / 28.01	1 / 2 / 1.01	0.000134	0.000348	2135	5967	0	0	0	398.089 MHz
atan_rational	78 / 79 / 78.01	1 / 2 / 1.01	0.002222	0.0028	9405	13279	11	0	0	327.332 MHz
atan_cmath	309 / 309 / 309.00	18 / 18 / 18.00	0	0	14800	22753	9	0	6	307.503 MHz

Notes:

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

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