Table of Contents
Cordic Calculations
Originating from the Cordic-based Sine Computer example in the cookbook this code here also calculates the magnitude and the phase of a vector given it's I- and Q-components. Also it works within the 306° range instead of 180° as in the cookbook.
The plotting is done using matplotlib. Matplotlib Plotter is a small script to monitor and plot the data.
Sine and Cosine Calculation
Cosine and sine values for the given input angle are calculated. The angle ranges from -180° to +180° which spans the full integer range for the given width.
Vector Calculation
Given the I- and Q-compenent of a vector the magnitude and phase is calculated.
Code
#!/usr/bin/env python INTWIDTH = 16 INTMAX = 2**(INTWIDTH-1)-1 INTMIN = -2**(INTWIDTH-1) TODO = """ - Tests - Scaling Optimisation - Iteration Optimisation """ import sys, os from os import system import plotter from math import atan, sqrt, ceil, floor, pi, sin, cos from myhdl import * class Plot: x=[] y=[] z=[] pl=Plot t_State = enum("WAITING", "CALCULATING") calcmode = enum("VECTOR","ROTATE") def Cordic(x_out, y_out, done, x0, y0, z0, start, clock, reset, mode=calcmode.VECTOR): """ General Cordic computer Ports: ----- x_out -- cosine of the input angle y_out -- sine of the input angle done -- output flag indicating completion of the computation z0 -- input angle; -pi/2 <= z0 <= pi/2 start -- input that starts the computation on a posedge clock -- clock input reset -- reset input """ M = 2 ** (INTWIDTH-1)/pi MpiH = 2 **(INTWIDTH-2) # nr of iterations equals nr of significant input bits N = INTWIDTH An = 1.0 for i in range(N): An *= (sqrt(1 + 2**(-2*i))) X0 = int(round(M*1/An)) # tuple with elementary angles angles = tuple([int(round(M*atan(2**(-i)))) for i in range(N)]) # iterative cordic processor @instance def processor(): x = intbv(0, min=x_out.min, max=x_out.max) y = intbv(0, min=y_out.min, max=y_out.max) z = intbv(0,min=x0.min, max=x0.max) dz = intbv(0, min=x0.min, max=x0.max) dx = intbv(0, min=x_out.min, max=x_out.max) dy = intbv(0, min=x_out.min, max=x_out.max) i = intbv(0, min=0, max=N) state = t_State.WAITING while True: yield clock.posedge, reset.posedge if reset: state = t_State.WAITING done.next = False x[:] = 0 y[:] = 0 z[:] = 0 i[:] = 0 else: if state == t_State.WAITING: if start: if mode == calcmode.ROTATE: if z0 > MpiH: z[:] = z0 - MpiH y[:] = X0 x[:] = 0 elif z0 < -MpiH: z[:] = z0 + MpiH y[:] = -X0 x[:] = 0 else: x[:] = X0 y[:] = 0 z[:] = z0 else: if x0>= 0: x[:] = x0 y[:] = y0 z[:] = z0 else: x[:] = -x0 y[:] = -y0 z[:] = -z0 # TODO: is this correct!? i[:] = 0 done.next = False state = t_State.CALCULATING elif state == t_State.CALCULATING: dx[:] = y >> i dy[:] = x >> i dz[:] = angles[int(i)] if mode == calcmode.ROTATE: if (z >= 0): x -= dx y += dy z -= dz else: x += dx y -= dy z += dz else: if (y < 0): x -= dx y += dy z -= dz else: x += dx y -= dy z += dz if i == N-1: if mode == calcmode.ROTATE: x_out.next = y y_out.next = x else: x_out.next = x y_out.next = z state = t_State.WAITING done.next = True else: i += 1 return processor def VectorCalc(mag,phase,done,i_input,q_input,start,clock,reset): """ calcuclate vector magnitude and vector angle from i and q component i -- inphase input q -- quadrature phase input mag -- magnitude output phase -- phase output """ return Cordic(mag,phase,done,i_input,q_input,0,start,clock,reset,mode=calcmode.VECTOR) def VectorCalc_v(mag,phase,done,i_input,q_input,start,clock,reset): toVerilog(VectorCalc,mag,phase,done,i_input,q_input,start,clock,reset) #conversion.analyze(VectorCalc,mag,phase,done,i_input,q_input,start,clock,reset) cmd = "cver -q +loadvpi=./myhdl_vpi:vpi_compat_bootstrap VectorCalc.v tb_VectorCalc.v" os.system ("iverilog -o tb_VectorCalc.vvp VectorCalc.v tb_VectorCalc.v") cmd = "vvp -v -m ./myhdl tb_VectorCalc.vvp" return Cosimulation(cmd,**locals()) def SinCos(sin_out, cos_out,done,amplitude,angle,start,clock,reset): """ calculate sine and cosine multiplied by amplitude """ return Cordic(sin_out, cos_out, done, amplitude, 0, angle, start, clock, reset, mode=calcmode.ROTATE) def SinCos_v(sin_out, cos_out,done,amplitude,angle,start,clock,reset): """ calculate sine and cosine multiplied by amplitude """ toVerilog(SinCos,sin_out,cos_out,done,amplitude,angle,start,clock,reset) #cmd = "cver -q +loadvpi=./myhdl_vpi:vpi_compat_bootstrap SinCos.v tb_SinCos.v" os.system("iverilog -o tb_SinCos.vvp SinCos.v tb_SinCos.v") cmd = "vvp -v -m ./myhdl tb_SinCos.vvp" return Cosimulation(cmd,**locals()) def normalize(f): return int(f * (INTMAX/2-1)) def _test_vectorcalc(): print "test_vectorcalc" clock = Signal(bool(0)) reset = Signal(bool(1)) start = Signal(bool(0)) done = Signal(bool(0)) i = Signal(intbv(0,min=INTMIN,max=INTMAX)) q = Signal(intbv(0,min=INTMIN,max=INTMAX)) mag = Signal(intbv(0,min=INTMIN,max=INTMAX)) phase = Signal(intbv(0,min=INTMIN,max=INTMAX)) vcalc = VectorCalc_v(mag,phase,done,i,q,start,clock,reset) #vcalc = VectorCalc(mag,phase,done,i,q,start,clock,reset) @always(delay(1)) def clockgen(): clock.next = not clock @instance def check(): yield clock.negedge reset.next = 0 for angle in range(0,360,5): yield clock.negedge angle=float(angle) i.next = normalize(sin(angle/180*pi)) q.next = normalize(cos(angle/180*pi)) start.next=1 yield clock.posedge start.next=0 yield done.posedge print "i=",i,"\tq=",q,"\tMag=",sqrt(i*i + q*q),"\tmag=",mag,"\tphase=",phase yield clock.negedge raise StopSimulation moni=plotter.monitor(I_Voltage=i,Q_Voltage=q,Magnitude=mag,Phase=phase) return instances() def test_vectorcalc(n=None): Simulation(_test_vectorcalc()).run(n) #plotter.show() plotter.saveplot("test_vectorcalc.png") def trace_vectorcalc(n=None): tb = traceSignals(_test_vectorcalc) Simulation(tb).run(n) def _test_sincos(): print "test_sincos" clock = Signal(bool(0)) reset = Signal(bool(1)) start = Signal(bool(0)) done = Signal(bool(0)) amplitude = Signal(intbv(0,min=-2**15,max=2**15 -1)) angle = Signal(intbv(0,min=-2**15,max=2**15 -1)) sin_out = Signal(intbv(0,min=-2**15,max=2**15 -1)) cos_out = Signal(intbv(0,min=-2**15,max=2**15 -1)) sincos = SinCos(sin_out, cos_out,done,amplitude,angle,start,clock,reset) #sincos = SinCos_v(sin_out, cos_out,done,amplitude,angle,start,clock,reset) @always(delay(1)) def clockgen(): clock.next = not clock @instance def check(): yield clock.negedge reset.next = 0 for iangle in range(-180,180,1): yield clock.negedge angle.next=int((iangle*1.0/180*2**(INTWIDTH-1))) start.next=1 yield clock.posedge start.next=0 yield done.posedge raise StopSimulation moni = plotter.monitor(Angle=angle,Sinus=sin_out,Cosinus=cos_out) return instances() def test_sincos(): Simulation(_test_sincos()).run() #plotter.show() plotter.saveplot("test_sincos.png") def trace_sincos(): tb = traceSignals(_test_sincos) Simulation(tb).run(1000) if __name__=="__main__": test_vectorcalc() #trace_vectorcalc() #trace_sincos() #test_sincos()
