C66x DSP优化技巧：循环提升与内存性能策略

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SPRABG7

—

November 2010 Optimizing Loops on the C66x DSP Application Report Page 9 of 48

Submit Documentation Feedback

3 C66x Floating-Point and Vector/Matrix Operations and Optimizations

www.ti.com

To check the results, compute the normalized error magnitude:

for abs_a[i] and ejalpha[i] of each implementation against generic C outputs. For fixed

point implementation, abs_a[i] is converted directly to floating-point, while ejalpha[i]

is converted to float, divided by 32768 because the number is represented in Q15

format, and then calculate the error magnitude compare to generic C output of abs_a[i]

and ejalpha[i]. Maximum of error magnitude is collected for the input test vector.

Cycle measurements and implementation errors for each optimization step is

summarized.

Tools used:

•CCSv4.1.0

• Compiler 7.2.0A10232

– General compiler options: -o3 –k –os. For C66x, using –mv6600.

• TCI6482 Cycle accurate Simulator Little Endian

• Nyquist Device Cycle Approximate Simulator, Little Endian

Here, Little Endian only is used, and code can be easily expanded to Big Endian case.

For cycle measurement, the cycle number is measured by calling the function twice and

measure the cycles for the second call. The first call of the function will access all the

data and program causing it to be loaded into the L1 cache. And the cycle measurement

for the second call is defined as warm cache cycles or warm cycles. TSCL is used for cycle

measurements.

3.1.3 A Quick Start

First, directly compile the generic C code on the C64x+ platform, which is fixed-point

only, and on the C66x platform, which is mixed fixed-floating-point. Table 2 shows the

benchmark comparison:

Both versions have the loop disqualified for pipeline because of function calls inside the

loop. That is the reason why these two cycle counts are very high. Particularly for direct

compilation on C64x+ platform, not only 1/sqrt(x) functions is a call to runtime

support library, but all the floating-point arithmetic are function calls using fixed-point

to mimic floating-point.

For direct compilation on C66x platform, only 1/sqrt(x) is a function call and other

operations are using floating-point instructions offered by C66x. This is why a 6.8× lift

ia seen by simply going to the combined fixed-floating-point platform.

If, for example, this routine is called sporadically and 70 k cycles is acceptable for the

first phase optimization, it can stop at this point. This offers a quick start and shorter

development cycles for this type of optimization problems.

iii

refrefoutput /−

Table 2 Benchmark Comparison

Generic C Code Directly Compiled For Warm Cycles (with division) Warm Cycles (without division)

C64x+ platform 473483 473483

C66x platform 69644 69644

Page 10 of 48 Optimizing Loops on the C66x DSP Application Report SPRABG7

—

November 2010

Submit Documentation Feedback

3 C66x Floating-Point and Vector/Matrix Operations and Optimizations

www.ti.com

If the number of cycle counts need to be reduced further, the generic C code must be

optimized.

For C64x+ platform, the following are needed:

• Have a function that can quickly calculate 1/sqrt(x). This is the key to reducing

the most cycles.

• Do necessary scaling and Q adjustment accordingly.

• Perform wider data read and write, as suggested in Chapter 4.

• Perform SIMD fixed-point complex multiplication.

For the C66x platform, the single-cycle instruction RSQRSP can be used to do 1/sqrt(x).

Complex multiplication must be optimized if further cycle reduction is needed.

In the following sections, one optimized implementation of C64x+ is discussed. Then

the optimization of C66x floating-point is covered in detail, including the usage of

RSQRSP, floating-point SIMD, and fixed-floating-point conversion.

3.1.4 One C64x+ Optimization

First is the 1/sqrt(x) calculation problem in fixed-point. There are many different ways

to implement this function. There are well optimized assembly functions for this

purpose, but they cannot be used because calling an assembly function disables the loop

pipeline. One better choice is to have a look-up-table-based implementation that can

be inlined. The one selected for this example is a 16-bit precision 1/sqrt(x) that uses

four tables, each with 256 elements.

Note that the fixed-point implementation is considered from the aspects of complexity

of the work. This may not be the state-of-art and best-optimized code in this section.

How 1/sqrt(x) is implemented is not explained in detail, either. The refinement is left

as an exercise for the reader.

_nassert(n % 4 == 0);

_nassert((int) a % 8 == 0);

_nassert((int) ejalpha % 8 == 0);

_nassert((int) abs_a % 8 == 0);

#pragma MUST_ITERATE(4,100, 4);

#pragma UNROLL(2);

for ( i = 0; i < n; i++)

{

temp1 = _amem4(&a[i]);

a_sqr = _dotp2(temp1, temp1);

/* 1/sqrt(a_sqr) */

normal = _norm(a_sqr);

normal = normal & 0xFFFFFFFE;

x_norm = _sshvl(a_sqr, normal);

normal = normal >> 1;

Index = _sshvr(_sadd(x_norm,0x800000),24);

oneOverAbs_a=_mpylir( xcbia[Index], x_norm );

oneOverAbs_a=_sadd((int)x3sa[Index]<<16,

_sshvr(oneOverAbs_a,ShiftValDifp1a[Index]));

normal =15 - ShiftVala[Index] + normal;

ejbeta_re =_sadd(_sshvl(_mpyhir(temp1, oneOverAbs_a), normal - 1), 0x8000);

ejbeta_im =_sadd(_sshvl(_mpylir(temp1, oneOverAbs_a), normal - 1), 0x8000);

_amem4(&ejalpha[i])= _packh2(ejbeta_re, ejbeta_im);

abs_a[i] = sshvr(_sadd(_mpyhir(oneOverAbs_a, a_sqr), 1<<(15 - normal)),

16-normal) ;

}

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