The Biquad revisited

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ECE6580 Lecture 13

• The Biquad revisited

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Rules of Engagement

• Develop and test algorithm in C
• Register allocation
• Write non-parallel assembly code
• Create dependency graph
• Create Scheduling Chart
• Write parallel assembly code

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Biquad in C
include "ctypes.h" float BiquadC(float x,float
states,float pm coefs,U32 sections) float
y U32 i,j float xxx for(i0,j0iltsections
i5,j4) y coefsixx
coefsi1statesi coefsi2statesj1 -
coefsj3statesj2 - coefsj4statesj
3 statesi3 statesi2 statesi2y
statesi1statesi statesixx xx
y return(y)
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Register Allocation

• f0 states and return value
• f2 states
• f4 x and coefs
• f8 product
• f12 accumulator
• i4 pointer to states
• i12 pointer to coefs

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Non-parallel Assembly
include ltasm_sprt.hgt include ltdef21161.hgt //floa
t BiquadAsm(float x, // input, f4 //
float states, // pointer to states, r8 //
float pm coefs, // pointer to coefs,
r12 // U32 sections) // number of
biquad sections .segment /pm seg_pmco .global
_BiquadLinear _BiquadLinear entry b4 r8
// pointer to states b12 r12 // pointer to
coefs r1reads(1) // read number of
sections r12 r12 xor r12 // clear the
accumulator f2 f4 // save f4 in f2 lcntr
r1,do BiquadLinearEnd until lce f4
pm(i12,m14) // fetch b0 f12f2f4 //
b0x f4 pm(i12,m14) // fetch b1 f0
dm(i4,m5) // fetch x(n-1) dm(i4,m6) f2 //
x(n-1)x f8 f0f4 // b1x(n-1) f12
f8f12 // b0x b1x(n-1) f4
pm(i12,m14) // fetch b2 f4 dm(i4,m5) //
fetch x(n-2) dm(i4,m6) f0 //
x(n-2)x(n-1) f8 f4f1 // b2x(n-2) f12
f8f12 // b0x b1x(n-1) b2x(n-2) f4
pm(i12,m14) // fetch a1 f0 dm(i4,m6) //
fetch y(n-1) f8 f0f1 // a1y(n-1) f12
f8f12 // b0x b1x(n-1) b2x(n-2) -
a1y(n-1) f4 pm(i12,m14) // fetch a2 f4
dm(i4,m5) // fetch y(n-2) dm(i4,m7) f0 //
y(n-2)y(n-1) f8 f4f1 // a2y(n-2) f2
f8f12 // yb0xb1x(n-1)b2x(n-2)-a1y(n-1)-a2
y(n-2) r12 r12 xor r12 // clear the
accumulator BiquadLinearEnd dm(i4,2) f2 //
y(n-1)y f0 f4 exit
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f2f4
end
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Rules for Creating Scheduling Chart

• All parent nodes become first parallel
  instruction. If not enough resources use 2
  intructions
• Identify next instructions that can be executed.
  Create a parallel instruction with them.
• Repeat until done.

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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x
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f2f4
end
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Scheduling Table
f4f2x