TMS320C64x+ DSP
Little-Endian DSP Library
Programmer’s Reference
Literature Number: SPRUEB8
February 2006
Preface
Read This First
About This Manual
This document describes the C64x+ digital signal processor little-endian
(DSP) Library, or DSPLIB for short.
Notational Conventions
This document uses the following conventions:
- Hexadecimal numbers are shown with the suffix h. For example, the
following number is 40 hexadecimal (decimal 64): 40h.
- Registers in this document are shown in figures and described in tables.
- Macro names are written in uppercase text; function names are written in
lowercase.
J
Each register figure shows a rectangle divded into fields that repre-
sent the fields of the register. Each field is labeled with its bit name, its
beginning and ending bit numbers above, and its read/write properties
below. A legend explains the notation used for the properties.
J
Reserved bits in a register figure designate a bit that is used for future
device expansion.
Related Documentation From Texas Instruments
The following books describe the C6000™ devices and related support tools.
Copies of these documents are available on the Internet at www.ti.com. Tip:
Enter the literature number in the search box provided at www.ti.com.
SPRU732 — TMS320C64x/C64x+ DSP CPU and Instruction Set
Reference Guide. Describes the CPU architecture, pipeline, instruction
set, and interrupts for the TMS320C64x and TMS320C64x+ digital
signal processors (DSPs) of the TMS320C6000 DSP family. The
C64x/C64x+ DSP generation comprises fixed-point devices in the
C6000 DSP platform. The C64x+ DSP is an enhancement of the C64x
DSP with added functionality and an expanded instruction set.
i
Trademarks
SPRAA84 — TMS320C64x to TMS320C64+ CPU Migration Guide.
Describes migrating from the Texas Instruments TMS320C64x digital
signal processor (DSP) to the TMS320C64x+ DSP. The objective of this
document is to indicate differences between the two cores. Functionality
in the devices that is identical is not included.
Trademarks
C6000, TMS320C64x+, TMS320C64x, C64x are trademarks of Texas
Instruments.
ii
Contents
1
2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
Provides a brief introduction to the TI C64x+ DSPLIBs, shows the organization of the routines
contained in the libraries, and lists the features and benefits of the DSPLIBs.
1.1
1.2
Introduction to the TI C64x+ DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Features and Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Installing and Using DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
Provides information on how to install and rebuild the TI C64x+ DSPLIB.
2.1
2.2
How to Install DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
Using DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
2.2.1 DSPLIB Arguments and Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
2.2.2 Calling a DSPLIB Function From C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
2.2.3 Calling a DSP Function From Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
2.2.4 DSPLIB Testing − Allowable Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
2.2.5 DSPLIB Overflow and Scaling Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
2.2.6 Interrupt Behavior of DSPLIB Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
How to Rebuild DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2.3
3
4
DSPLIB Function Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
Provides tables containing all DSPLIB functions, a brief description of each, and a page refer-
ence for more detailed information.
3.1
3.2
3.3
3.4
Arguments and Conventions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
DSPLIB Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
DSPLIB Function Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
Differences Between the C64x and C64x+ DSPLIBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8
DSPLIB Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
Provides a list of the functions within the DSPLIB organized into functional categories.
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Adaptive Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
Filtering and Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38
Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-58
Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-73
Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-76
Obsolete Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-90
4.8.1 FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-90
iii
Contents
A
Performance/Fractional Q Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
Describes performance considerations related to the C64x+ DSPLIB and provides information
about the Q format used by DSPLIB functions.
A.1 Performance Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2
A.2 Fractional Q Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
A.2.1 Q3.12 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
A.2.2 Q.15 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
A.2.3 Q.31 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4
B
C
Software Updates and Customer Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1
Provides information about warranty issues, software updates, and customer support.
B.1 DSPLIB Software Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2
B.2 DSPLIB Customer Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1
Defines terms and abbreviations used in this book.
iv
Tables
2−1
3−1
3−2
3−3
3−4
3−5
3−6
3−7
3−8
3−9
DSPLIB Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Argument Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
Adaptive Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
Filtering and Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
Obsolete Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
3−10 Functions Optimized in the C64x+ DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8
A−1
A−2
A−3
A−4
Q3.12 Bit Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
Q.15 Bit Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
Q.31 Low Memory Location Bit Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4
Q.31 High Memory Location Bit Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4
Contents
v
vi
Chapter 1
Introduction
This chapter provides a brief introduction to the TI C64x+ DSP Libraries
(DSPLIB), shows the organization of the routines contained in the library, and
lists the features and benefits of the DSPLIB.
Topic
Page
1.2 Features and Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
1-1
Introduction to the TI C64x+ DSPLIB
1.1 Introduction to the TI C64x+ DSPLIB
The TI C64x+ DSPLIB is an optimized DSP Function Library for C
programmers using devices that include the C64x+ megamodule. It includes
many C-callable, assembly-optimized, general-purpose signal-processing
routines. These routines are typically used in computationally intensive
real-time applications where optimal execution speed is critical. By using
these routines, you can achieve execution speeds considerably faster than
equivalent code written in standard ANSI C language. In addition, by providing
ready-to-use DSP functions, TI DSPLIB can significantly shorten your DSP
application development time.
The TI DSPLIB includes commonly used DSP routines. Source code is
provided that allows you to modify functions to match your specific needs.
The routines contained in the library are organized into the following seven
different functional categories:
- Adaptive filtering
J
DSP_firlms2
- Correlation
J
J
DSP_autocor
DSP_autocor_rA8
- FFT
J
J
J
J
J
J
J
J
J
J
J
J
J
J
J
DSP_fft16x16
DSP_fft16x16_imre
DSP_fft16x16r
DSP_fft16x32
DSP_fft32x32
DSP_fft32x32s
DSP_ifft16x16
DSP_ifft16x16_imre
DSP_ifft16x32
DSP_ifft32x32
DSP_fft16x16t (obolete, use DSP_fft16x16)
DSP_bitrev_cplx (obsolete, use DSP_fft16x16)
DSP_radix 2 (obsolete, use DSP_fft16x16)
DSP_r4fft (obsolete, use DSP_fft16x16)
DSP_fft (obsolete, use DSP_fft16x16)
1-2
Introduction to the TI C64x+ DSPLIB
- Filtering and convolution
J
J
J
J
J
J
J
J
J
DSP_fir_cplx
DSP_fir_cplx_hM4X4
DSP_fir_gen
DSP_fir_gen_hM17_rA8X8
DSP_fir_r4
DSP_fir_r8
DSP_fir_r8_hM16_rM8A8X8
DSP_fir_sym
DSP_iir
- Math
J
J
J
J
J
J
J
J
J
J
DSP_dotp_sqr
DSP_dotprod
DSP_maxval
DSP_maxidx
DSP_minval
DSP_mul32
DSP_neg32
DSP_recip16
DSP_vecsumsq
DSP_w_vec
- Matrix
J
DSP_mat_mul
DSP_mat_trans
J
- Miscellaneous
J
J
J
J
J
J
J
J
DSP_bexp
DSP_blk_eswap16
DSP_blk_eswap32
DSP_blk_eswap64
DSP_blk_move
DSP_fltoq15
DSP_minerror
DSP_q15tofl
Introduction
1-3
Features and Benefits
1.2 Features and Benefits
- Hand-coded assembly-optimized routines
- C and linear assembly source code
- C-callable routines, fully compatible with the TI C6x compiler
- Fractional Q.15-format operands supported on some benchmarks
- Benchmarks (time and code)
- Tested against C model
1-4
Chapter 2
Installing and Using DSPLIB
This chapter provides information on how to install and rebuild the TI C64x+
DSPLIB.
Topic
Page
2.1 How to Install DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
2.2 Using DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
2.3 How to Rebuild DSPLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2-1
How to Install DSPLIB
2.1 How to Install DSPLIB
Note:
You should read the README.txt file for specific details of the release.
The DSPLIB is provided in the file dsp64plus.zip. The file must be unzipped to
provide the following directory structure:
dsp
|
+−−README.txt
Top−level README file
|
+−−docs
library documentation
|
+−−examples
CCS project examples
|
|−−include
Required include files
library and source archives
fft twiddle generation functions
|
|−−lib
|
|−−support
|
Please install the contents of the lib directory in the default directory indicated
by your C_DIR environment. If you choose not to install the contents in the
default directory, update the C_DIR environment variable, for example, by
adding the following line in autoexec.bat file:
SET C_DIR=<install_dir>/lib;<install_dir>/include;%C_DIR%
or under Unix/csh:
setenv C_DIR ”<install_dir>/lib;<install_dir>/include;
$C_DIR”
or under Unix/Bourne Shell:
C_DIR=”<install_dir>/lib;<install_dir>/include;$C_DIR”;
export C_DIR
2-2
Using DSPLIB
2.2 Using DSPLIB
2.2.1 DSPLIB Arguments and Data Types
2.2.1.1 DSPLIB Types
Table 2−1. DSPLIB Data Types
Size
(bits)
Name
Type
Minimum
Maximum
short
16
integer
−32768
32767
int
32
40
32
16
32
32
64
integer
−2147483648
2147483647
long
integer
−549755813888
0000:0000h
549755813887
FFFF:FFFFh
pointer
Q.15
address
fraction
−0.9999694824...
−0.99999999953...
1.17549435e−38
2.2250738585072014e−308
0.9999694824...
0.99999999953...
3.40282347e+38
Q.31
fraction
IEEE float
IEEE double
floating point
floating point
1.7976931348623157e+308
Unless specifically noted, DSPLIB operates on Q.15-fractional data type
elements. Appendix A presents an overview of Fractional Q formats.
2.2.1.2 DSPLIB Arguments
TI DSPLIB functions typically operate over vector operands for greater
efficiency. Even though these routines can be used to process short arrays, or
even scalars (unless a minimum size requirement is noted), they will be slower
for those cases.
- Vector stride is always equal to 1: Vector operands are composed of vector
elements held in consecutive memory locations (vector stride equal to 1).
- Complex elements are assumed to be stored in consecutive memory
locations with Real data followed by Imaginary data.
- In-place computation is not allowed, unless specifically noted: Source
operand cannot be equal to destination operand.
Installing and Using DSPLIB
2-3
Using DSPLIB
2.2.2 Calling a DSPLIB Function From C
In addition to correctly installing the DSPLIB software, follow these steps to
include a DSPLIB function in the code:
- Include the function header file corresponding to the DSPLIB function
- Link the code with dsp64plus.lib
- Use a correct linker command file for the platform used.
The examples in the DSP\Examples folder show how to use the DSPLIB in a
Code Composer Studio C envirionment.
2.2.3 Calling a DSP Function From Assembly
The C64x+ DSPLIB functions were written to be used from C. Calling the
functions from assembly language source code is possible as long as the
calling function conforms to the Texas Instruments C64x+ C compiler calling
conventions. For more information, see Section 8 (Runtime Environment) of
TMS320C6000 Optimizing C Compiler User’s Guide (SPRU187).
2.2.4 DSPLIB Testing − Allowable Error
DSPLIB is tested under the Code Composer Studio environment against a
reference C implementation. You can expect identical results between
Reference C implementation and its Assembly implementation when using
test routines that focus on fixed-point type results. The test routines that deal
with floating points typically allow an error margin of 0.000001 when
comparing the results of reference C code and DSPLIB assembly code.
2.2.5 DSPLIB Overflow and Scaling Issues
The DSPLIB functions implement the same functionality of the reference C
code. You must conform to the range requirements specified in the API
function, and in addition, restrict the input range so that the outputs do not
overflow.
In FFT functions, twiddle factors are generated with a fixed scale factor; i.e.,
15−1
30−1
32767(=2
) for all 16-bit FFT functions, 1073741823(=2
) for
31−1
DSP_fft32x32s, 2147483647(=2
) for all other 32-bit FFT functions.
Twiddle factors cannot be scaled further to not scale input data. Because
DSP_fft16x16r and DSP_fft32x32s perform scaling by 2 at each radix-4 stage,
(log2(nx)−cei[log4(nx)−1])
the input data must be scaled by 2
to completely prevent
(log2(nx))
overflow. In all other FFT functions, the input data must be scaled by 2
because no scaling is done by the functions.
2-4
How to Rebuild DSPLIB
2.2.6 Interrupt Behavior of DSPLIB Functions
All of the functions in this library are designed to be used in systems with
interrupts. Thus, it is not necessary to disable interrupts when calling any of
these functions. The functions in the library will disable interrupts as needed to
protect the execution of code in tight loops and so on. Library functions have
three categories:
- Fully-interruptible: These functions do not disable interrupts. Interrupts
are blocked by at most 5 to 10 cycles at a time (not counting stalls) by
branch delay slots.
- Partially-interruptible: These functions disable interrupts for long
periods of time, with small windows of interruptibility. Examples include a
function with a nested loop, where the inner loop is non-interruptible and
the outer loop permits interrupts between executions of the inner loop.
- Non-interruptible: These functions disable interrupts for nearly their
entire duration. Interrupts may happen for a short time during the setup
and exit sequence.
Note that all three function categories tolerate interrupts. That is, an interrupt
can occur at any time without affecting the function correctness. The
interruptibility of the function only determines how long the kernel might delay
the processing of the interrupt.
2.3 How to Rebuild DSPLIB
If you would like to rebuild DSPLIB (for example, because you modified the
source file contained in the archive), you will have to use the mk6x utility as
follows:
mk6x dsp64plus.src −mv64plus −l dsp64plus.lib
Installing and Using DSPLIB
2-5
2-6
Chapter 3
DSPLIB Function Tables
This chapter provides tables containing all DSPLIB functions, a brief
description of each, and a page reference for more detailed information.
Topic
Page
3.2 DSPLIB Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
3.3 DSPLIB Function Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
3.4 Differences Between the C64x and C64x+ DSPLIBs
3-1
Arguments and Conventions Used
3.1 Arguments and Conventions Used
The following convention has been used when describing the arguments for
each individual function:
Table 3−1. Argument Conventions
Argument
Description
x,y
Argument reflecting input data vector
r
Argument reflecting output data vector
nx,ny,nr
Arguments reflecting the size of vectors x,y, and r, respectively. For
functions in the case nx = ny = nr, only nx has been used across.
h
Argument reflecting filter coefficient vector (filter routines only)
Argument reflecting the size of vector h
nh
w
Argument reflecting FFT coefficient vector (FFT routines only)
Some C64x+ functions have additional restrictions due to optimization using
new features such as higher multiply throughput. While these new functions
perform better, they can also lead to problems if not carefully used. For
example, DSP_autocor_rA8 is faster than DSP_autocor, but the output buffer
must be aligned to an 8−byte boundary. Therefore, the new functions are
named with any additional restrictions. Three types of restrictions are specified
to a pointer: minimum buffer size (M), buffer alignment (A), and the number of
elements in the buffer to be a multiple of an integer (X).The following
convention has been used when describing the arguments for each individual
function:
A kernel function foo with two parameters, m and n, with the following
restrictions:
m −> Minimum buffer size = 8, buffer alignment = double word, buffer
needs to be a multiple of 8 elements
n −> Minimum buffer size = 32, buffer alignment = word , buffer needs to be
a multiple of 16 elements
This function would be named: foo_mM8A8X8_nM32A4X16.
3-2
DSPLIB Functions
3.2 DSPLIB Functions
The routines included in the DSP library are organized into eight functional
categories and listed below in alphabetical order.
- Adaptive filtering
- Correlation
- FFT
- Filtering and convolution
- Math
- Matrix functions
- Miscellaneous
- Obsolete functions
DSPLIB Function Tables
3-3
DSPLIB Function Tables
3.3 DSPLIB Function Tables
Table 3−2. Adaptive Filtering
Functions
Description
Page
long DSP_firlms2(short *h, short *x, short b, int nh)
LMS FIR
Table 3−3. Correlation
Functions
Description
Page
void DSP_autocor(short *r,short *x, int nx, int nr)
Autocorrelation
void DSP_autocor_rA8(short *r,short *x, int nx, int nr)
Autocorrelation ( r[] must be
double word aligned)
Table 3−4. FFT
Functions
Description
Page
void DSP_fft16x16(short *w, int nx, short *x, short *y)
Complex out of place, Forward
FFT mixed radix with digit
reversal. Input/Output data in
Re/Im order.
4-8
void DSP_fft16x16_imre(short *w, int nx, short *x, short
*y)
Complex out of place, Forward
FFT mixed radix with digit
reversal. Input/Output data in
Im/Re order.
4-11
void DSP_fft16x16r(int nx, short *x, short *w, unsigned
char *brev, short *y, int radix, int offset, int n_max)
Cache-optimized mixed radix FFT
with scaling and rounding, digit
reversal, out of place. Input and
output: 16 bits, Twiddle factor: 16
bits.
void DSP_fft16x32(short *w, int nx, int *x, int *y)
void DSP_fft32x32(int *w, int nx, int *x, int *y)
void DSP_fft32x32s(int *w, int nx, int *x, int *y)
Extended precision, mixed radix
FFT, rounding, digit reversal, out
of place. Input and output: 32 bits,
Twiddle factor: 16 bits.
Extended precision, mixed radix
FFT, rounding, digit reversal, out
of place. Input and output: 32 bits,
Twiddle factor: 32 bits.
Extended precision, mixed radix
FFT, digit reversal, out of place.,
with scaling and rounding. Input
and output: 32 bits, Twiddle
factor: 32 bits.
3-4
DSPLIB Function Tables
Functions
Description
Page
void DSP_ifft16x16(short *w, int nx, short *x, short *y)
Complex out of place, Inverse
FFT mixed radix with digit
reversal. Input/Output data in
Re/Im order.
void DSP_ifft16x16_imre(short *w, int nx, short *x, short
*y)
Complex out of place, Inverse
FFT mixed radix with digit
reversal. Input/Output data in
Re/Im order.
void DSP_ifft16x32(short *w, int nx, int *x, int *y)
void DSP_ifft32x32(int *w, int nx, int *x, int *y)
Extended precision, mixed radix
IFFT, rounding, digit reversal, out
of place. Input and output: 32 bits,
Twiddle factor: 16 bits.
Extended precision, mixed radix
IFFT, digit reversal, out of place,
with scaling and rounding. Input
and output: 32 bits, Twiddle
factor: 32 bits.
Table 3−5. Filtering and Convolution
Functions
Description
Page
void DSP_fir_cplx (short *x, short *h, short *r, int nh, int
nx)
Complex FIR Filter (nh is a
multiple of 2)
void DSP_fir_cplx_hM4X4 (short *x, short *h, short *r, int
nh, int nx)
Complex FIR Filter (nh is a
multiple of 4)
void DSP_fir_gen (short *x, short *h, short *r, int nh, int nr) FIR Filter (any nh)
void DSP_fir_gen_hM17_rA8X8 (short *x, short *h, short
*r, int nh, int nr)
FIR Filter (r[] must be double
word aligned, nr must be multiple
of 8)
void DSP_fir_r4 (short *x, short *h, short *r, int nh, int nr)
void DSP_fir_r8 (short *x, short *h, short *r, int nh, int nr)
FIR Filter (nh is a multiple of 4)
FIR Filter (nh is a multiple of 8)
void DSP_fir_r8_hM16_rM8A8X8 (short *x, short *h, short FIR Filter (r[] must be double
*r, int nh, int nr) word aligned, nr is a multiple of 8)
void DSP_fir_sym (short *x, short *h, short *r, int nh, int nr, Symmetric FIR Filter (nh is a
int s) multiple of 8)
DSPLIB Function Tables
3-5
DSPLIB Function Tables
Functions
Description
Page
void DSP_iir(short *r1, short *x, short *r2, short *h2, short IIR with 5 Coefficients
*h1, int nr)
void DSP_iirlat(short *x, int nx, short *k, int nk, int *b,
short *r)
All−pole IIR Lattice Filter
Table 3−6. Math
Functions
Description
Page
int DSP_dotp_sqr(int G, short *x, short *y, int *r, int nx)
Vector Dot Product and Square
int DSP_dotprod(short *x, short *y, int nx)
short DSP_maxval (short *x, int nx)
int DSP_maxidx (short *x, int nx)
Vector Dot Product
Maximum Value of a Vector
Index of the Maximum Element of
a Vector
short DSP_minval (short *x, int nx)
Minimum Value of a Vector
32-bit Vector Multiply
32-bit Vector Negate
void DSP_mul32(int *x, int *y, int *r, short nx)
void DSP_neg32(int *x, int *r, short nx)
void DSP_recip16 (short *x, short *rfrac, short *rexp, short 16-bit Reciprocal
nx)
int DSP_vecsumsq (short *x, int nx)
Sum of Squares
void DSP_w_vec(short *x, short *y, short m, short *r, short Weighted Vector Sum
nr)
Table 3−7. Matrix
Functions
Description
Page
void DSP_mat_mul(short *x, int r1, int c1, short *y, int c2, Matrix Multiplication
short *r, int qs)
void DSP_mat_trans(short *x, short rows, short columns, Matrix Transpose
short *r)
3-6
DSPLIB Function Tables
Table 3−8. Miscellaneous
Functions
Description
Page
short DSP_bexp(int *x, short nx)
Max Exponent of a Vector (for
scaling)
void DSP_blk_eswap16(void *x, void *r, int nx)
void DSP_blk_eswap32(void *x, void *r, int nx)
void DSP_blk_eswap64(void *x, void *r, int nx)
Endian-swap a block of 16-bit
values
Endian-swap a block of 32-bit
values
Endian-swap a block of 64-bit
values
void DSP_blk_move(short *x, short *r, int nx)
void DSP_fltoq15 (float *x,short *r, short nx)
Move a Block of Memory
Float to Q15 Conversion
Minimum Energy Error Search
int DSP_minerror (short *GSP0_TABLE,short *errCoefs,
int *savePtr_ret)
void DSP_q15tofl (short *x, float *r, short nx)
Q15 to Float Conversion
Table 3−9. Obsolete Functions
Functions
Description
Page
void DSP_bitrev_cplx (int *x, short *index, int nx)
Use DSP_fft16x16() instead
4-88
void DSP_radix2 (int nx, short *x, short *w)
void DSP_r4fft (int nx, short *x, short *w)
Use DSP_fft16x16() instead
Use DSP_fft16x16() instead
Use DSP_fft16x16() instead
Use DSP_fft16x16() instead
4-91
4-93
void DSP_fft(short *w, int nx, short *x, short *y)
void DSP_fft16x16t(short *w, int nx, short *x, short *y)
4-96
DSPLIB Function Tables
3-7
Differences Between the C64x and C64x+ DSPLIBs
3.4 Differences Between the C64x and C64x+ DSPLIBs
The C64x+ DSPLIB was developed by optimizing some of the functions of the
C64x DSPLIB to take advantage of the C64x+ architecture.
There are two optimization types:
- SPLOOP conversion: Optimized code uses SPLOOP to provide
interruptibility and decrease power consumption. The new C64x+
instructions do not increase algorithm performance, and thus, are not
used.
- Kernel redesign, SPLOOP: Kernel of algorithm rewritten to take
advantage of the new C64x+ instructions and of the SPLOOP feature.
Table 3−10. Functions Optimized in the C64x+ DSPLIB
Function
C64x+ Optimized
Optimization Type
DSP_firlms2
No
DSP_autocor
No
DSP_autocor_rA8
Yes
Kernel re−design, SPLOOP
Optimization resulted in new
requirements. New name is used.
DSP_fft16x16
DSP_fft16x16_imre
DSP_fft16x16r
DSP_fft16x32
DSP_fft32x32
DSP_fft32x32s
DSP_ifft16x16
DSP_ifft16x16_imre
DSP_ifft16x32
DSP_ifft32x32
DSP_fir_cplx
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
New Function Optimized C64x+
New Function Optimized C64x+
Kernel re−design, SPLOOP
Kernel re−design, SPLOOP
Kernel re−design, SPLOOP
Kernel re−design, SPLOOP
New Function Optimized C64x+
New Function Optimized C64x+
Kernel re−design, SPLOOP
Kernel re−design, SPLOOP
3-8
Differences Between the C64x and C64x+ DSPLIBs
Function
C64x+ Optimized
Optimization Type
DSP_fir_cplx_hM4X4
Yes
Kernel re−design, SPLOOP
Optimization resulted in new
requirements. New name is used.
DSP_fir_gen
No
DSP_fir_gen_hM17_rA8X8
Yes
Kernel re−design, SPLOOP
Optimization resulted in new
requirements. New name is used.
DSP_fir_r4
No
No
DSP_fir_r8
DSP_fir_r8_hM16_rM8A8X8
Yes
Kernel re−design, SPLOOP
Optimization resulted in new
requirements. New name is used.
DSP_fir_sym
DSP_iir
No
No
No
No
Yes
No
No
No
No
No
No
No
No
No
No
No
DSP_iirlat
DSP_dotp_sqr
DSP_dotprod
DSP_maxval
DSP_maxidx
DSP_minval
DSP_mul32
DSP_neg32
DSP_recip16
DSP_vecsumsq
DSP_w_vec
DSP_mat_mu
DSP_mat_trans
DSP_bexp
SPLOOP conversion
DSPLIB Function Tables
3-9
Differences Between the C64x and C64x+ DSPLIBs
Function
C64x+ Optimized
Optimization Type
DSP_blk_eswap16
No
DSP_blk_eswap32
DSP_blk_move
DSP_fltoq15
No
Yes
No
No
No
SPLOOP conversion
DSP_minerror
DSP_q15tofl
DSP_bitrev_cplx
DSP_radix2
DSP_r4fft
No
No
No
No
No
Obsolete
Obsolete
Obsolete
Obsolete
Obsolete
DSP_fft
DSP_fft16x16t
Any functions which were not optimized for the C64x+ have the same
performance as on the C64x.
3-10
Chapter 4
DSPLIB Reference
This chapter provides a list of the functions within the DSP library (DSPLIB)
organized into functional categories. The functions within each category are
listed in alphabetical order and include arguments, descriptions, algorithms,
benchmarks, and special requirements.
Topic
Page
4.1 Adaptive Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
4.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4.3 FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
4.4 Filtering and Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38
4.5 Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-58
4.6 Matirx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-73
4.7 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-76
4.8 Obsolete Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-90
4-1
DSP_firlms2
4.1 Adaptive Filtering
LMS FIR
DSP_firlms2
Function
long DSP_firlms2(short * restrict h, const short * restrict x, short b, int nh)
Arguments
h[nh]
x[nh+1]
b
Coefficient Array
Input Array
Error from previous FIR
Number of coefficients. Must be multiple of 4.
Return value
nh
return long
Description
Algorithm
The Least Mean Square Adaptive Filter computes an update of all nh
coefficients by adding the weighted error times the inputs to the original
coefficients. The input array includes the last nh inputs followed by a new
single sample input. The coefficient array includes nh coefficients.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
long DSP_firlms2(short h[ ],short x[ ], short b,
int nh)
{
int
i;
long
r = 0;
for (i = 0; i < nh; i++) {
h[i] += (x[i] * b) >> 15;
r += x[i + 1] * h[i];
}
return r;
}
Special Requirements
- This routine assumes 16-bit input and output.
- The number of coefficients nh must be a multiple of 4.
4-2
DSP_firlms2
Implementation Notes
Benchmarks
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The loop is unrolled 4 times.
Cycles
Codesize
3 * nh/4 + 17
148 bytes
C64x+ DSPLIB Reference
4-3
DSP_autocor
4.2 Correlation
AutoCorrelation
DSP_autocor
Function
void DSP_autocor(short * restrict r, const short * restrict x, int nx, int nr)
Arguments
r[nr]
x[nx+nr]
nx
Output array
Input array. Must be double-word aligned.
Length of autocorrelation. Must be a multiple of 8.
Number of lags. Must be a multiple of 4.
nr
Description
Algorithm
This routine accepts an input array of length nx + nr and performs nr
autocorrelations each of length nx producing nr output results. This is typically
used in VSELP code.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_autocor(short r[ ],short x[ ], int nx, int nr)
{
int i,k,sum;
for (i = 0; i < nr; i++){
sum = 0;
for (k = nr; k < nx+nr; k++)
sum += x[k] * x[k−i];
r[i] = (sum >> 15);
}
}
Special Requirements
- nx must be a multiple of 8.
- nr must be a multiple of 4.
- x[ ] must be double-word aligned.
4-4
DSP_autocor
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The inner loop is unrolled 8 times.
- The outer loop is unrolled 4 times.
- The outer loop is conditionally executed in parallel with the inner loop. This
allows for a zero overhead outer loop.
Benchmarks
Cycles
nx<40:
6*nr*nr/4 + 20
nx>=40: nx*nr/8 + 2*nr + 20
304 bytes
Codesize
C64x+ DSPLIB Reference
4-5
DSP_autocor_rA8
AutoCorrelation
DSP_autocor_rA8
Function
void DSP_autocor_rA8(short * restrict r, const short * restrict x, int nx, int nr)
Arguments
r[nr]
x[nx+nr]
nx
Output array, Must be double word aligned.
Input array. Must be double-word aligned.
Length of autocorrelation. Must be a multiple of 8.
Number of lags. Must be a multiple of 4.
nr
Description
Algorithm
This routine accepts an input array of length nx + nr and performs nr
autocorrelations each of length nx producing nr output results. This is typically
used in VSELP code.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_autocor(short r[ ],short x[ ], int nx, int nr)
{
int i,k,sum;
for (i = 0; i < nr; i++){
sum = 0;
for (k = nr; k < nx+nr; k++)
sum += x[k] * x[k−i];
r[i] = (sum >> 15);
}
}
Special Requirements
Implementation Notes
- nx must be a multiple of 8.
- nr must be a multiple of 4.
- x[ ] must be double-word aligned.
- r[ ] must be double-word aligned.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The inner loop is unrolled 8 times.
- The outer loop is unrolled 4 times.
4-6
DSP_autocor_rA8
Benchmarks
Cycles
nx<40:
6*nr+ 20
nx>=40: nx*nr/8 + 2*nr + 20
304 bytes
Codesize
C64x+ DSPLIB Reference
4-7
DSP_fft16x16
4.3 FFT
Complex Forward Mixed Radix 16 x 16-bit FFT
DSP_fft16x16
Function
void DSP_fft16x16(const short * restrict w, int nx, short * restrict x, short *
restrict y)
Arguments
w[2*nx]
nx
Pointer to complex Q.15 FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4
, and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 16-bit data input.
Pointer to complex 16-bit data output.
Description
This routine computes a complex forward mixed radix FFT with rounding and
digit reversal. Input data x[ ], output data y[ ], and coefficients w[ ] are 16-bit.
The output is returned in the separate array y[ ] in normal order. Each complex
value is stored with interleaved real and imaginary parts. The code uses a
special ordering of FFT coefficients (also called twiddle factors) and memory
accesses to improve performance in the presence of cache.
Algorithm
All stages are radix-4 except the last one, which can be radix-2 or radix-4,
depending on the size of the FFT. All stages except the last one scale by two
the stage output data.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be power of 2 or 4, and 16 ≤ nx ≤ 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices. All data are in short precision
or Q.15 format.
4-8
DSP_fft16x16
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
The routine uses log (nx) − 1 stages of radix-4 transform and performs either
4
a radix-2 or radix-4 transform on the last stage depending on nx. If nx is a
power of 4, then this last stage is also a radix-4 transform, otherwise it is a
radix-2 transform. The conventional Cooley Tukey FFT is written using three
loops. The outermost loop “k” cycles through the stages. There are log N to
the base 4 stages in all. The loop “j” cycles through the groups of butterflies
with different twiddle factors, and loop “i” reuses the twiddle factors for the
different butterflies within a stage. Note the following:
Butterflies With Common
Twiddle Factors
Stage
Groups
Groups*Butterflies
1
N/4
1
4
N/4
2
..
N/16
N/4
..
..
1
..
logN
N/4
N/4
The following statements can be made based on above observations:
1) Inner loop “i0” iterates a variable number of times. In particular, the number
of iterations quadruples every time from 1..N/4. Hence, software pipelining
a loop that iterates a variable number of times is not profitable.
2) Outer loop “j” iterates a variable number of times as well. However, the
number of iterations is quartered every time from N/4 ..1. Hence, the
behavior in (a) and (b) are exactly opposite to each other.
3) If the two loops “i” and “j” are coalesced together then they will iterate for
a fixed number of times, namely N/4. This allows us to combine the “i” and
“j” loops into one loop. Optimized implementations will make use of this
fact.
In addition,, the Cooley Tukey FFT accesses three twiddle factors per iteration
of the inner loop, as the butterflies that reuse twiddle factors are lumped
together. This leads to accessing the twiddle factor array at three points, each
separated by “ie”. Note that “ie” is initially 1, and is quadrupled with every
iteration. Therefore, these three twiddle factors are not even contiguous in the
array.
C64x+ DSPLIB Reference
4-9
DSP_fft16x16
To vectorize the FFT, it is desirable to access the twiddle factor array using
double word wide loads and fetch the twiddle factors needed. To do this, a
modified twiddle factor array is created, in which the factors WN/4, WN/2,
W3N/4 are arranged to be contiguous. This eliminates the separation between
twiddle factors within a butterfly. However, this implies that we maintain a
redundant version of the twiddle factor array as the loop is traversed from one
stage to another. Hence, the size of the twiddle factor array increases as
compared to the normal Cooley Tukey FFT. The modified twiddle factor array
is of size “2 * N” where the conventional Cooley Tukey FFT is of size “3N/4”
where N is the number of complex points to be transformed. The routine that
generates the modified twiddle factor array was presented earlier. With the
above transformation of the FFT, both the input data and the twiddle factor
array can be accessed using double-word wide loads to enable packed data
processing.
The final stage is optimized to remove the multiplication as w0 = 1. This stage
also performs digit reversal on the data, so the final output is in natural order.
In addition, if the number of points to be transformed is a power of 2, the final
stage applies a radix-2 pass instead of a radix-4. In any case, the outputs are
returned in normal order.
The code performs the bulk of the computation in place. However, because
digit-reversal cannot be performed in-place, the final result is written to a
separate array, y[].
Benchmarks
Cycles
(6 * nx/8 + 19) * ceil[log (nx) − 1] + 8*nx/8 + 30
4
Codesize 864 bytes
4-10
DSP_fft16x16_imre
Complex Forward Mixed Radix 16 x 16-bit FFT, With Im/Re Order
DSP_fft16x16_imre
Function
void DSP_fft16x16_imre(const short * restrict w, int nx, short * restrict x, short
* restrict y)
Arguments
w[2*nx]
nx
Pointer to complex Q.15 FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4
, and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 16-bit data input.
Pointer to complex 16-bit data output.
Description
This routine computes a complex forward mixed radix FFT with truncation and
digit reversal. Input data x[ ], output data y[ ], and coefficients w[ ] are 16-bit.
The output is returned in the separate array y[ ] in normal order. Each complex
value is stored with interleaved imaginary and real parts. The code uses a
special ordering of FFT coefficients (also called twiddle factors) and memory
accesses to improve performance in the presence of cache.
Algorithm
All stages are radix-4 except the last one, which can be radix-2 or radix-4,
depending on the size of the FFT. All stages except the last one scale by two
the stage output data.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be power of 2 or 4, and 16 ≤ nx ≤ 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the imaginary/real
components stored in adjacent locations in the array. The imaginary
components are stored at even array indices, and the real components are
stored at odd array indices. All data are in short precision or Q.15 format.
Implementation Notes
- Bank Conflicts: no conflicts occur.
- Interruptibility: The code is interruptible.
C64x+ DSPLIB Reference
4-11
DSP_fft16x16_imre
The routine uses log (nx) − 1 stages of radix-4 transform and performs either
4
a radix-2 or radix-4 transform on the last stage depending on nx. If nx is a
power of 4, then this last stage is also a radix-4 transform, otherwise it is a
radix-2 transform. The conventional Cooley Tukey FFT is written using three
loops. The outermost loop “k” cycles through the stages. There are log N to
the base 4 stages in all. The loop “j” cycles through the groups of butterflies
with different twiddle factors, and loop “i” reuses the twiddle factors for the
different butterflies within a stage. Note the following:
Butterflies With Common
Twiddle Factors
Stage
Groups
Groups*Butterflies
1
N/4
1
4
N/4
2
..
N/16
N/4
..
..
1
..
logN
N/4
N/4
The following statements can be made based on above observations:
1) Inner loop “i0” iterates a variable number of times. In particular, the number
of iterations quadruples every time from 1..N/4. Hence, software pipelining
a loop that iterates a variable number of times is not profitable.
2) Outer loop “j” iterates a variable number of times as well. However, the
number of iterations is quartered every time from N/4 ..1. Hence, the
behavior in (a) and (b) are exactly opposite to each other.
3) If the two loops “i” and “j” are coalesced together then they will iterate for
a fixed number of times, namely N/4. This allows us to combine the “i” and
“j” loops into one loop. Optimized implementations will make use of this
fact.
In addition, the Cooley Tukey FFT accesses three twiddle factors per iteration
of the inner loop, as the butterflies that reuse twiddle factors are lumped
together. This leads to accessing the twiddle factor array at three points, each
separated by “ie”. Note that “ie” is initially 1, and is quadrupled with every
iteration. Therefore these three twiddle factors are not even contiguous in the
array.
4-12
DSP_fft16x16_imre
To vectorize the FFT, it is desirable to access twiddle factor array using double
word wide loads and fetch the twiddle factors needed. To do this, a modified
twiddle factor array is created, in which the factors WN/4, WN/2, W3N/4 are
arranged to be contiguous. This eliminates the separation between twiddle
factors within a butterfly. However, this implies that we maintain a redundant
version of the twiddle factor array as the loop is traversed from one stage to
another. Hence, the size of the twiddle factor array increases as compared to
the normal Cooley Tukey FFT. The modified twiddle factor array is of size
“2 * N”, where the conventional Cooley Tukey FFT is of size “3N/4”, where N
is the number of complex points to be transformed. The routine that generates
the modified twiddle factor array was presented earlier. With the above
transformation of the FFT, both the input data and the twiddle factor array can
be accessed using double-word wide loads to enable packed data processing.
The final stage is optimized to remove the multiplication as w0 = 1. This stage
also performs digit reversal on the data, so the final output is in natural order.
In addition, if the number of points to be transformed is a power of 2, the final
stage applies a DSP_radix2 pass instead of a radix 4. In any case, the outputs
are returned in normal order.
The code performs the bulk of the computation in place. However, because
digit-reversal cannot be performed in-place, the final result is written to a
separate array, y[].
Benchmarks
Cycles
(6 * nx/8 + 19) * ceil[log (nx) − 1] + 8*nx/8 + 30
4
Codesize 864 bytes
C64x+ DSPLIB Reference
4-13
DSP_fft16x16r
Complex Forward Mixed Radix 16 x 16-bit FFT With Rounding
DSP_fft16x16r
Function
void DSP_fft16x16r(int nx, short * restrict x, const short * restrict w, const un-
signed char * restrict brev, short * restrict y, int radix, int offset, int nmax)
Arguments
nx
Length of FFT in complex samples. Must be power of 2 or 4, and
≤16384
x[2*nx]
w[2*nx]
brev[64]
Pointer to complex 16-bit data input
Pointer to complex FFT coefficients
Pointer to bit reverse table containing 64 entries. Only required for
C code. Use NULL for assembly code since BITR instruction
is used instead.
y[2*nx]
radix
Pointer to complex 16-bit data output
Smallest FFT butterfly used in computation used for
decomposing FFT into sub-FFTs. See notes.
offset
nmax
Index in complex samples of sub-FFT from start of main FFT.
Size of main FFT in complex samples.
Description
This routine implements a cache-optimized complex forward mixed radix FFT
with scaling, rounding and digit reversal. Input data x[ ], output data y[ ], and
coefficients w[ ] are 16-bit. The output is returned in the separate array y[ ] in
normal order. Each complex value is stored as interleaved 16-bit real and
imaginary parts. The code uses a special ordering of FFT coefficients (also
called twiddle factors).
This redundant set of twiddle factors is size 2*N short samples. As pointed out
in subsequent sections, dividing these twiddle factors by 2 will give an effective
divide by 4 at each stage to guarantee no overflow. The function is accurate
to about 68dB of signal to noise ratio to the DFT function as follows.
4-14
DSP_fft16x16r
void dft(int n, short x[], short y[])
{
int k,i, index;
const double PI = 3.14159654;
short * p_x;
double arg, fx_0, fx_1, fy_0, fy_1, co, si;
for(k = 0; k<n; k++)
{
p_x = x;
fy_0 = 0;
fy_1 = 0;
for(i=0; i<n; i++)
{
fx_0 = (double)p_x[0];
fx_1 = (double)p_x[1];
p_x += 2;
index = (i*k) % n;
arg = 2*PI*index/n;
co = cos(arg);
si = −sin(arg);
fy_0 += ((fx_0 * co) − (fx_1 * si));
fy_1 += ((fx_1 * co) + (fx_0 * si));
}
y[2*k] = (short)2*fy_0/sqrt(n);
y[2*k+1] = (short)2*fy_1/sqrt(n);
}
}
Scaling by 2 (i.e., >>1) takes place at each radix-4 stage except the last one.
A radix-4 stage could give a maximum bit-growth of 2 bits, which would require
scaling by 4. To completely prevent overflow, the input data must be scaled by
(BT−BS)
2
, where BT (total number of bit growth) = log (nx) and BS (number of
2
scales by the functions) = ceil[log (nx)−1]. All shifts are rounded to reduce
4
truncation noise power by 3dB.
C64x+ DSPLIB Reference
4-15
DSP_fft16x16r
The function takes the twiddle factors and input data, and calculates the FFT
producing the frequency domain data in the y[ ] array. As the FFT allows every
input point to affect every output point, which causes cache thrashing in a
cache based system. This is mitigated by allowing the main FFT of size N to
be divided into several steps, allowing as much data reuse as possible. For
example, see the following function:
DSP_fft16x16r(1024,&x[0],
&w[0],
y,brev,4,
0,1024);
is equivalent to:
DSP_fft16x16r(1024,&x[2*0], &w[0]
,y,brev,256, 0,1024);
0,1024);
DSP_fft16x16r(256, &x[2*0], &w[2*768],y,brev,4,
DSP_fft16x16r(256, &x[2*256],&w[2*768],y,brev,4, 256,1024);
DSP_fft16x16r(256, &x[2*512],&w[2*768],y,brev,4, 512,1024);
DSP_fft16x16r(256, &x[2*768],&w[2*768],y,brev,4, 768,1024);
Notice how the first FFT function is called on the entire 1K data set. It covers
the first pass of the FFT until the butterfly size is 256.
The following 4 FFTs do 256-point FFTs 25% of the size. These continue down
to the end when the butterfly is of size 4. They use an index to the main twiddle
factor array of 0.75*2*N. This is because the twiddle factor array is composed
of successively decimated versions of the main array.
N not equal to a power of 4 can be used; i.e. 512. In this case, the following
would be needed to decompose the FFT:
DSP_fft16x16r(512, &x[0],
is equivalent to:
&w[0],
&w[0],
y,brev,2,
0,512);
DSP_fft16x16r(512, &x[0],
y,brev,128, 0,512);
0,512);
DSP_fft16x16r(128, &x[2*0], &w[2*384],y,brev,2,
DSP_fft16x16r(128, &x[2*128],&w[2*384],y,brev,2, 128,512);
DSP_fft16x16r(128, &x[2*256],&w[2*384],y,brev,2, 256,512);
DSP_fft16x16r(128, &x[2*384],&w[2*384],y,brev,2, 384,512);
The twiddle factor array is composed of log (N) sets of twiddle factors, (3/4)*N,
4
(3/16)*N, (3/64)*N, etc. The index into this array for each stage of the FFT is
calculated by summing these indices up appropriately. For multiple FFTs, they
can share the same table by calling the small FFTs from further down in the
twiddle factor array, in the same way as the decomposition works for more data
reuse.
Thus, the above decomposition can be summarized for a general N, radix “rad”
as follows.
4-16
DSP_fft16x16r
DSP_fft16x16r(N, &x[0],
DSP_fft16x16r(N/4,&x[0],
&w[0],
brev,y,N/4,0,
N)
N)
&w[2*3*N/4],brev,y,rad,0,
DSP_fft16x16r(N/4,&x[2*N/4], &w[2*3*N/4],brev,y,rad,N/4, N)
DSP_fft16x16r(N/4,&x[2*N/2], &w[2*3*N/4],brev,y,rad,N/2, N)
DSP_fft16x16r(N/4,&x[2*3*N/4],&w[2*3*N/4],brev,y,rad,3*N/4,N)
As discussed previously, N can be either a power of 4 or 2. If N is a power of
4, then rad = 4, and if N is a power of 2 and not a power of 4, then rad = 2. “rad”
controls how many stages of decomposition are performed. It also determines
whether a radix4 or DSP_radix2 decomposition should be performed at the
last stage. Hence, when “rad” is set to “N/4”, the first stage of the transform
alone is performed and the code exits. To complete the FFT, four other calls
are required to perform N/4 size FFTs. In fact, the ordering of these 4 FFTs
amongst themselves does not matter and, thus, from a cache perspective, it
helps to go through the remaining 4 FFTs in exactly the opposite order to the
first. This is illustrated as follows:
DSP_fft16x16r(N, &x[0],
&w[0],
brev,y,N/4,0,
N)
DSP_fft16x16r(N/4,&x[2*3*N/4],&w[2*3*N/4],brev,y,rad,3*N/4, N)
DSP_fft16x16r(N/4,&x[2*N/2], &w[2*3*N/4],brev,y,rad,N/2, N)
DSP_fft16x16r(N/4,&x[2*N/4], &w[2*3*N/4],brev,y,rad,N/4, N)
DSP_fft16x16r(N/4,&x[0],
&w[2*3*N/4],brev,y,rad,0,
N)
In addition, this function can be used to minimize call overhead by completing
the FFT with one function call invocation as shown below:
DSP_fft16x16r(N, &x[0], &w[0], y, brev, rad, 0, N)
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void fft16x16r
(
int
n,
short
short
*ptr_x,
*ptr_w,
unsigned char *brev,
short
*y,
int
int
radix,
offset,
nmax
int
)
C64x+ DSPLIB Reference
4-17
DSP_fft16x16r
{
int i, l0, l1, l2, h2, predj;
int l1p1,l2p1,h2p1, tw_offset, stride, fft_jmp;
short xt0, yt0, xt1, yt1, xt2, yt2;
short si1,si2,si3,co1,co2,co3;
short xh0,xh1,xh20,xh21,xl0,xl1,xl20,xl21;
short x_0, x_1, x_l1, x_l1p1, x_h2 , x_h2p1, x_l2, x_l2p1;
short *x,*w;
short *ptr_x0, *ptr_x2, *y0;
unsigned int j, k, j0, j1, k0, k1;
short x0, x1, x2, x3, x4, x5, x6, x7;
short xh0_0, xh1_0, xh0_1, xh1_1;
short xl0_0, xl1_0, xl0_1, xl1_1;
short yt3, yt4, yt5, yt6, yt7;
unsigned a, num;
stride = n;
/* n is the number of complex samples */
tw_offset = 0;
while (stride > radix)
{
j = 0;
fft_jmp = stride + (stride>>1);
h2 = stride>>1;
l1 = stride;
l2 = stride + (stride>>1);
x = ptr_x;
w = ptr_w + tw_offset;
for (i = 0; i < n>>1; i += 2)
{
co1 = w[j+0];
si1 = w[j+1];
co2 = w[j+2];
si2 = w[j+3];
co3 = w[j+4];
si3 = w[j+5];
j += 6;
x_0
= x[0];
4-18
DSP_fft16x16r
x_1
= x[1];
x_h2 = x[h2];
x_h2p1 = x[h2+1];
x_l1 = x[l1];
x_l1p1 = x[l1+1];
x_l2 = x[l2];
x_l2p1 = x[l2+1];
xh0 = x_0
xh1 = x_1
xl0 = x_0
xl1 = x_1
+ x_l1;
+ x_l1p1;
− x_l1;
− x_l1p1;
xh20 = x_h2 + x_l2;
xh21 = x_h2p1 + x_l2p1;
xl20 = x_h2 − x_l2;
xl21 = x_h2p1 − x_l2p1;
ptr_x0 = x;
ptr_x0[0] = ((short)(xh0 + xh20))>>1;
ptr_x0[1] = ((short)(xh1 + xh21))>>1;
ptr_x2 = ptr_x0;
x += 2;
predj = (j − fft_jmp);
if (!predj) x += fft_jmp;
if (!predj) j = 0;
xt0 = xh0 − xh20;
yt0 = xh1 − xh21;
xt1 = xl0 + xl21;
yt2 = xl1 + xl20;
xt2 = xl0 − xl21;
yt1 = xl1 − xl20;
l1p1 = l1+1;
h2p1 = h2+1;
l2p1 = l2+1;
ptr_x2[l1 ] = (xt1 * co1 + yt1 * si1 + 0x00008000) >> 16;
ptr_x2[l1p1] = (yt1 * co1 − xt1 * si1 + 0x00008000) >> 16;
ptr_x2[h2 ] = (xt0 * co2 + yt0 * si2 + 0x00008000) >> 16;
C64x+ DSPLIB Reference
4-19
DSP_fft16x16r
ptr_x2[h2p1] = (yt0 * co2 − xt0 * si2 + 0x00008000) >> 16;
ptr_x2[l2 ] = (xt2 * co3 + yt2 * si3 + 0x00008000) >> 16;
ptr_x2[l2p1] = (yt2 * co3 − xt2 * si3 + 0x00008000) >> 16;
}
tw_offset += fft_jmp;
stride = stride>>2;
} /* end while */
j = offset>>2;
ptr_x0 = ptr_x;
y0 = y;
/* determine _norm(nmax) − 17 */
l0 = 31;
if (((nmax>>31)&1)==1)
num = ~nmax;
else
num = nmax;
if (!num)
l0 = 32;
else
{
a=num&0xFFFF0000; if (a) { l0−=16; num=a; }
a=num&0xFF00FF00; if (a) { l0−= 8; num=a; }
a=num&0xF0F0F0F0; if (a) { l0−= 4; num=a; }
a=num&0xCCCCCCCC; if (a) { l0−= 2; num=a; }
a=num&0xAAAAAAAA; if (a) { l0−= 1; }
}
l0 −= 1;
l0 −= 17;
if(radix == 2 || radix == 4)
for (i = 0; i < n; i += 4)
{
/* reversal computation */
j0 = (j
) & 0x3F;
j1 = (j >> 6) & 0x3F;
k0 = brev[j0];
k1 = brev[j1];
4-20
DSP_fft16x16r
k = (k0 << 6) | k1;
if (l0 < 0)
k = k << −l0;
else
k = k >> l0;
j++;
/* multiple of 4 index */
x0 = ptr_x0[0]; x1 = ptr_x0[1];
x2 = ptr_x0[2]; x3 = ptr_x0[3];
x4 = ptr_x0[4]; x5 = ptr_x0[5];
x6 = ptr_x0[6]; x7 = ptr_x0[7];
ptr_x0 += 8;
xh0_0 = x0 + x4;
xh1_0 = x1 + x5;
xh0_1 = x2 + x6;
xh1_1 = x3 + x7;
if (radix == 2)
{
xh0_0 = x0;
xh1_0 = x1;
xh0_1 = x2;
xh1_1 = x3;
}
yt0 = xh0_0 + xh0_1;
yt1 = xh1_0 + xh1_1;
yt4 = xh0_0 − xh0_1;
yt5 = xh1_0 − xh1_1;
xl0_0 = x0 − x4;
xl1_0 = x1 − x5;
xl0_1 = x2 − x6;
xl1_1 = x3 − x7;
if (radix == 2)
{
xl0_0 = x4;
xl1_0 = x5;
C64x+ DSPLIB Reference
4-21
DSP_fft16x16r
xl1_1 = x6;
xl0_1 = x7;
}
yt2 = xl0_0 + xl1_1;
yt3 = xl1_0 − xl0_1;
yt6 = xl0_0 − xl1_1;
yt7 = xl1_0 + xl0_1;
if (radix == 2)
{
yt7 = xl1_0 − xl0_1;
yt3 = xl1_0 + xl0_1;
}
y0[k] = yt0; y0[k+1] = yt1;
k += n>>1;
y0[k] = yt2; y0[k+1] = yt3;
k += n>>1;
y0[k] = yt4; y0[k+1] = yt5;
k += n>>1;
y0[k] = yt6; y0[k+1] = yt7;
}
}
Special Requirements
- In-place computation is not allowed.
- nx must be a power of 2 or 4.
- Complex input data x[ ], twiddle factors w[ ], and output array y[ ] must be
double-word aligned.
- Real values are stored in even word, imaginary in odd.
- All data are in short precision or Q.15 format. Allowed input dynamic range
is 16 − (log (nx)−ceil[log (nx)−1]).
2
4
- Output results are returned in normal order.
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft16x16 provided in the directory ‘support\fft’. The scale factor must be
(log2(nx)−ceil[log4(nx)−1])
32767.5. The input data must be scaled by 2
completely prevent overflow.
to
4-22
DSP_fft16x16r
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- A special sequence of coefficients used as generated above produces the
FFT. This collapses the inner 2 loops in the traditional Burrus and Parks
implementation.
- The revised FFT uses a redundant sequence of twiddle factors to allow a
linear access through the data. This linear access enables data and
instruction level parallelism.
- The butterfly is bit reversed; i.e. the inner 2 points of the butterfly are
crossed over. This makes the data come out in bit reversed rather than in
radix 4 digit reversed order. This simplifies the last pass of the loop. The
BITR instruction does the bit reversal out of place.
Benchmarks
Cycles
ceil[log (nx) − 1] * (8 * nx/8 + 24) + 5.25 * nx/4 + 31
4
Codesize 640 bytes
C64x+ DSPLIB Reference
4-23
DSP_fft16x32
DSP_fft16x32
Complex Forward Mixed Radix 16 x 32-bit FFT With Rounding
Function
void DSP_fft16x32(const short * restrict w, int nx, int * restrict x, int * restrict y)
Arguments
w[2*nx]
nx
Pointer to complex Q.15 FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4,
and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 32-bit data input.
Pointer to complex 32-bit data output.
Description
This routine computes an extended precision complex forward mixed radix
FFT with rounding and digit reversal. Input data x[ ] and output data y[ ] are
32-bit, coefficients w[ ] are 16-bit. The output is returned in the separate array
y[ ] in normal order. Each complex value is stored with interleaved real and
imaginary parts. The code uses a special ordering of FFT coefficients (also
called twiddle factors) and memory accesses to improve performance in the
presence of cache. The C code to generate the twiddle factors is the same as
the one used for the DSP_fft16x16r routine.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
shown for the DSP_fft16x16t routine. For further details, see the source code
of the C version of this function, which is provided with this library. Note that
the assembly code is hand optimized and restrictions may apply.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices.
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft16x32 provided in the directory ‘support\fft’. The scale factor must be
32767.5. No scaling is done with the function; thus, the input data must be
log2(nx)
scaled by 2
to completely prevent overflow.
4-24
DSP_fft16x32
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16t implementation notes, as similar ideas are used.
Benchmarks
Cycles
(10.25 * nx/8 + 10) * ceil[log (nx) − 1] + 6 * nx/4 + 81
4
Codesize 1056 bytes
C64x+ DSPLIB Reference
4-25
DSP_fft32x32
DSP_fft32x32
Complex Forward Mixed Radix 32 x 32-bit FFT With Rounding
Function
void DSP_fft32x32(const int * restrict w, int nx, int * restrict x, int * restrict y)
Arguments
w[2*nx]
nx
Pointer to complex 32-bit FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4,
and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 32-bit data input.
Pointer to complex 32-bit data output.
Description
This routine computes an extended precision complex forward mixed radix
FFT with rounding and digit reversal. Input data x[ ], output data y[ ], and
coefficients w[ ] are 32-bit. The output is returned in the separate array y[ ] in
normal order. Each complex value is stored with interleaved real and
imaginary parts. The code uses a special ordering of FFT coefficients (also
called twiddle factors) and memory accesses to improve performance in the
presence of cache. The C code to generate the twiddle factors is similar to the
one used for the DSP_fft16x16r routine, except that the factors are maintained
at 32-bit precision.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
shown for the DSP_fft16x16t routine. For further details, see the source code
of the C version of this function, which is provided with this library. Note that
the assembly code is hand optimized and restrictions may apply.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices.
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft32x32 provided in the directory ‘support\fft’. The scale factor must be
2147483647.5. No scaling is done with the function; thus, the input data
log2(nx)
must be scaled by 2
to completely prevent overflow.
4-26
DSP_fft32x32
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16t implementation notes, as similar ideas are used.
Benchmarks
Cycles
(12 * nx/8 + 12) * ceil[log (nx) − 1] + 6 * nx/4 + 79
4
Codesize 1056 bytes
C64x+ DSPLIB Reference
4-27
DSP_fft32x32s
DSP_fft32x32s
Complex Forward Mixed Radix 32 x 32-bit FFT With Scaling
Function
void DSP_fft32x32s(const int * restrict w, int nx, int * restrict x, int * restrict y)
Arguments
w[2*nx]
nx
Pointer to complex 32-bit FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4,
and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 32-bit data input.
Pointer to complex 32-bit data output.
Description
This routine computes an extended precision complex forward mixed radix
FFT with scaling, rounding and digit reversal. Input data x[ ], output data y[ ],
and coefficients w[ ] are 32-bit. The output is returned in the separate array y[ ]
in normal order. Each complex value is stored with interleaved real and
imaginary parts. The code uses a special ordering of FFT coefficients (also
called twiddle factors) and memory accesses to improve performance in the
presence of cache. The C code to generate the twiddle factors is the same one
used for the DSP_fft32x32 routine.
Scaling by 2 (i.e., >>1) takes place at each radix-4 stage except for the last
one. A radix-4 stage can add a maximum of 2 bits, which would require scaling
by 4 to completely prevent overflow. Thus, the input data must be scaled by
log2(nx)−ceil[log4(nx)−1])
2
.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
shown for the fft16x16t routine. For further details, see the source code of the
C version of this function, which is provided with this library. Note that the
assembly code is hand optimized and restrictions may apply.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices.
4-28
DSP_fft32x32s
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft32x32 provided in the directory ‘support\fft’. The scale factor must be
(log2(nx) − ceil[ log4(nx)−1
1073741823.5. The input data must be scaled by 2
to completely prevent overflow.
])
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- Scaling is performed at each stage by shifting the results right by 1,
preventing overflow.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16t implementation notes, as similar ideas are used.
Benchmarks
Cycles
(13 * nx/8 + 36) * ceil[log (nx) − 1] + 6 * nx/4 + 36
4
Codesize 928 bytes
C64x+ DSPLIB Reference
4-29
DSP_ifft16x16
Complex Inverse Mixed Radix 16 x 16-bit FFT With Rounding
DSP_ifft16x16
Function
void DSP_ifft16x16(const short * restrict w, int nx, short * restrict x, short *
restrict y)
Arguments
w[2*nx]
nx
Pointer to complex Q.15 FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4,
and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 16-bit data input.
Pointer to complex 16-bit data output.
Description
This routine computes a complex inverse mixed radix IFFT with rounding and
digit reversal. Input data x[ ], output data y[ ], and coefficients w[ ] are 16-bit.
The output is returned in the separate array y[ ] in normal order. Each complex
value is stored with interleaved real and imaginary parts. The code uses a
special ordering of IFFT coefficients (also called twiddle factors) and memory
accesses to improve performance in the presence of cache.
The fft16x16 can be used to perform IFFT, by first conjugating the input,
performing the FFT, and conjugating again. This allows fft16x16 to perform the
IFFT as well. However, if the double conjugation needs to be avoided, then this
routine uses the same twiddle factors as the FFT and performs an IFFT. The
change in the sign of the twiddle factors is adjusted for in the routine. Hence,
this routine uses the same twiddle factors as the fft16x16 routine.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
of the fft16x16 routine. For further details, see the source code of the C version
of this function which is provided with this library.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices.
- Scaling by two is performed after each radix-4 stage except the last one.
4-30
DSP_ifft16x16
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16 implementation notes, as similar ideas are used.
Benchmarks
Cycles
(6 * nx/8 + 19) * ceil[log (nx) − 1] + 8 * nx/8 + 30
4
Codesize 864 bytes
C64x+ DSPLIB Reference
4-31
DSP_ifft16x16_imre
Complex Inverse Mixed Radix 16 x 16-bit FFT With Im/Re Order
DSP_ifft16x16_imre
Function
void DSP_ifft16x16_imre(const short * restrict w, int nx, short * restrict x, short
* restrict y)
Arguments
w[2*nx]
Pointer to complex Q.15 FFT coefficients.
nx
Length of FFT in complex samples. Must be power of 2 or 4,
and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex data input.
Pointer to complex data output.
Description
This routine computes a complex inverse mixed radix IFFT with rounding and
digit reversal. Input data x[ ], output data y[ ], and coefficients w[ ] are 16-bit.
The output is returned in the separate array y[ ] in normal order. Each complex
value is stored with interleaved imaginary and real parts. The code uses a
special ordering of IFFT coefficients (also called twiddle factors) and memory
accesses to improve performance in the presence of cache.
The fft16x16_imre can be used to perform IFFT, by first conjugating the input,
performing the FFT, and conjugating again. This allows fft16x16_imre to
perform the IFFT as well. However, if the double conjugation needs to be
avoided, then this routine uses the same twiddle factors as the FFT and
performs an IFFT. The change in the sign of the twiddle factors is adjusted for
in the routine. Hence, this routine uses the same twiddle factors as the
fft16x16_imre routine.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
of the ifft16x16 routine. For further details, see the source code of the C version
of this function which is provided with this library.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the imaginary/real
components stored in adjacent locations in the array. The imaginary
components are stored at even array indices, and the real components are
stored at odd array indices.
- Scaling by two is performed after each radix-4 stage except the last one.
4-32
DSP_ifft16x16_imre
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16 implementation notes, as similar ideas are used.
Benchmarks
Cycles
(6 * nx/8 + 19) * ceil[log (nx) − 1] + 8 * nx/8 + 30
4
Codesize 864 bytes
C64x+ DSPLIB Reference
4-33
DSP_ifft16x32
Complex Inverse Mixed Radix 16 x 32-bit FFT With Rounding
DSP_ifft16x32
Function
void DSP_ifft16x32(const short * restrict w, int nx, int * restrict x, int * restrict
y)
Arguments
w[2*nx]
nx
Pointer to complex Q.15 FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4,
and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 32-bit data input.
Pointer to complex 32-bit data output.
Description
This routine computes an extended precision complex inverse mixed radix
FFT with rounding and digit reversal. Input data x[ ] and output data y[ ] are
32-bit, coefficients w[ ] are 16-bit. The output is returned in the separate array
y[ ] in normal order. Each complex value is stored with interleaved real and
imaginary parts. The code uses a special ordering of FFT coefficients (also
called twiddle factors) and memory accesses to improve performance in the
presence of cache.
fft16x32 can be reused to perform IFFT, by first conjugating the input,
performing the FFT, and conjugating again. This allows fft16x32 to perform the
IFFT as well. However, if the double conjugation needs to be avoided, then this
routine uses the same twiddle factors as the FFT and performs an IFFT. The
change in the sign of the twiddle factors is adjusted for in the routine. Hence,
this routine uses the same twiddle factors as the fft16x32 routine.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
shown for the fft16x16t routine. For further details, see the source code of the
C version of this function which is provided with this library. Note that the
assembly code is hand optimized and restrictions may apply.
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices.
4-34
DSP_ifft16x32
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft16x32 provided in the directory ‘support\fft’. The scale factor must be
32767.5. No scaling is done with the function; thus the input data must be
log2(nx)
scaled by 2
to completely prevent overflow.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16t implementation notes, as similar ideas are used.
Benchmarks
Cycles
(12.5 * nx/8 + 30) * ceil[log (nx) − 1] + 6 * nx/4 + 32
4
Codesize 864 bytes
C64x+ DSPLIB Reference
4-35
DSP_ifft32x32
DSP_ifft32x32
Complex Inverse Mixed Radix 32 x 32-bit FFT With Rounding
Function
void DSP_ifft32x32(const int * restrict w, int nx, int * restrict x, int * restrict y)
Arguments
w[2*nx]
nx
Pointer to complex 32-bit FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4, and
16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 32-bit data input.
Pointer to complex 32-bit data output.
Description
This routine computes an extended precision complex inverse mixed radix
FFT with rounding and digit reversal. Input data x[ ], output data y[ ], and
coefficients w[ ] are 32-bit. The output is returned in the separate array y[ ] in
normal order. Each complex value is stored with interleaved real and
imaginary parts. The code uses a special ordering of FFT coefficients (also
called twiddle factors) and memory accesses to improve performance in the
presence of cache.
fft32x32 can be reused to perform IFFT, by first conjugating the input,
performing the FFT, and conjugating again. This allows fft32x32 to perform the
IFFT as well. However, if the double conjugation needs to be avoided, then this
routine uses the same twiddle factors as the FFT and performs an IFFT. The
change in the sign of the twiddle factors is adjusted for in the routine. Hence,
this routine uses the same twiddle factors as the fft32x32 routine.
Algorithm
The C equivalent of the assembly code without restrictions is similar to the one
shown for the fft16x16t routine. For further details, see the source code of the
C version of this function which is provided with this library. Note that the
assembly code is hand optimized and restrictions may apply.
Special Requirements
- In-place computation is not allowed.
- The size of the IFFT, nx, must be a power of 4 or 2 and greater than or equal
to 16 and less than 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices.
4-36
DSP_ifft32x32
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft32x32 provided in the directory ‘support\fft’. The scale factor must be
2147483647.5. No scaling is done with the function; thus the input data
log2(nx)
must be scaled by 2
to completely prevent overflow.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The routine uses log (nx) − 1 stages of radix-4 transform and performs
4
either a radix-2 or radix-4 transform on the last stage depending on nx. If
nx is a power of 4, then this last stage is also a radix-4 transform, otherwise
it is a radix-2 transform.
- See the fft16x16t implementation notes, as similar ideas are used.
Benchmarks
Cycles
(13*nx/8 + 28) * ceil(log (nx) − 1) + 6 * nx/4 + 39
4
Codesize 960 bytes
C64x+ DSPLIB Reference
4-37
DSP_fir_cplx
4.4 Filtering and Convolution
Complex FIR Filter
DSP_fir_cplx
Function
void DSP_fir_cplx (const short * restrict x, const short * restrict h, short * restrict
r, int nh, int nr)
Arguments
x[2*(nr+nh−1)] Complex input data. x must point to x[2*(nh−1)].
h[2*nh]
r[2*nr]
nh
Complex coefficients (in normal order).
Complex output data.
Number of complex coefficients. Must be a multiple of 2.
Number of complex output samples. Must be a multiple of 4.
nr
Description
Algorithm
This function implements the FIR filter for complex input data. The filter has
nr output samples and nh coefficients. Each array consists of an even and odd
term with even terms representing the real part and the odd terms the
imaginary part of the element. The pointer to input array x must point to the
(nh)th complex sample; i.e., element 2*(nh−1), upon entry to the function. The
coefficients are expected in normal order.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_cplx(short *x, short *h, short *r,short nh, short
nr)
{
short i,j;
int imag, real;
for (i = 0; i < 2*nr; i += 2){
imag = 0;
real = 0;
for (j = 0; j < 2*nh; j += 2){
real += h[j] * x[i−j] − h[j+1] * x[i+1−j];
imag += h[j] * x[i+1−j] + h[j+1] * x[i−j];
}
r[i] = (real >> 15);
r[i+1] = (imag >> 15);
}
}
4-38
DSP_fir_cplx
Special Requirements
Implementation Notes
- The number of coefficients nh must be a multiple of 2.
- The number of output samples nr must be a multiple of 4.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The outer loop is unrolled 4 times while the inner loop is not unrolled.
- Both inner and outer loops are collapsed in one loop.
- ADDAH and SUBAH are used along with PACKH2 to perform
accumulation, shift, and data packing.
- Collapsed one stage of epilog and prolog each.
Benchmarks
Cycles
nr * nh/2 + 7
Codesize 448 bytes
C64x+ DSPLIB Reference
4-39
DSP_fir_cplx_hM4X4
Complex FIR Filter
DSP_fir_cplx_hM4X4
Function
void DSP_fir_cplx _hM4X4(const short * restrict x, const short * restrict h, short
* restrict r, int nh, int nr)
Arguments
x[2*(nr+nh−1)] Complex input data. x must point to x[2*(nh−1)].
h[2*nh]
Complex coefficients (in normal order).
r[2*nr]
nh
Complex output data.
Number of complex coefficients. Must be a multiple of 4.
Number of complex output samples. Must be a multiple of 4.
nr
Description
Algorithm
This function implements the FIR filter for complex input data. The filter has
nr output samples and nh coefficients. Each array consists of an even and odd
term with even terms representing the real part and the odd terms the
imaginary part of the element. The pointer to input array x must point to the
(nh)th complex sample; i.e., element 2*(nh−1), upon entry to the function. The
coefficients are expected in normal order.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_cplx(short *x, short *h, short *r,short nh, short
nr)
{
short i,j;
int imag, real;
for (i = 0; i < 2*nr; i += 2){
imag = 0;
real = 0;
for (j = 0; j < 2*nh; j += 2){
real += h[j] * x[i−j] − h[j+1] * x[i+1−j];
imag += h[j] * x[i+1−j] + h[j+1] * x[i−j];
}
r[i] = (real >> 15);
r[i+1] = (imag >> 15);
}
}
4-40
DSP_fir_cplx_hM4X4
Special Requirements
Implementation Notes
- The number of coefficients nh must be larger or equal to 4 and a multiple
of 4.
- The number of output samples nr must be a multiple of 4.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is fully interruptible.
- The outer loop is unrolled 4 times while the inner loop is not unrolled.
- Both inner and outer loops are collapsed in one loop.
- ADDAH and SUBAH are used along with PACKH2 to perform
accumulation, shift and data packing.
- Collapsed one stage of epilog and prolog each.
Benchmarks
Cycles
nr * nh*9/16 + 40
Codesize 384 bytes
C64x+ DSPLIB Reference
4-41
DSP_fir_gen
FIR Filter
DSP_fir_gen
Function
void DSP_fir_gen (const short * restrict x, const short * restrict h, short * restrict
r, int nh, int nr)
Arguments
x[nr+nh−1]
h[nh]
Pointer to input array of size nr + nh − 1.
Pointer to coefficient array of size nh (coefficients must be in
reverse order).
r[nr]
nh
Pointer to output array of size nr. Must be word aligned.
Number of coefficients. Must be ≥5.
nr
Number of samples to calculate. Must be a multiple of 4.
Description
Algorithm
Computes a real FIR filter (direct-form) using coefficients stored in vector h[ ].
The real data input is stored in vector x[ ]. The filter output result is stored in
vector r[ ]. It operates on 16-bit data with a 32-bit accumulate. The filter
calculates nr output samples using nh coefficients.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_gen(short *x, short *h, short *r, int nh, int nr)
{
int i, j, sum;
for (j = 0; j < nr; j++) {
sum = 0;
for (i = 0; i < nh; i++)
sum += x[i + j] * h[i];
r[j] = sum >> 15;
}
}
4-42
DSP_fir_gen
Special Requirements
- The number of coefficients, nh, must be greater than or equal to 5.
Coefficients must be in reverse order.
- The number of outputs computed, nr, must be a multiple of 4 and greater
than or equal to 4.
- Array r[ ] must be word aligned.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Load double-word instruction is used to simultaneously load four values
in a single clock cycle.
- The inner loop is unrolled four times and will always compute a multiple
of 4 of nh and nr. If nh is not a multiple of 4, the code will fill in zeros to make
nh a multiple of 4.
- This code yields best performance when the ratio of outer loop to inner
loop is less than or equal to 4.
Benchmarks
Cycles: Not available
Codesize: Not available
C64x+ DSPLIB Reference
4-43
DSP_fir_gen_hM17_rA8X8
DSP_fir_gen_hM17_rA8X8
FIR Filter
Function
void DSP_fir_gen_hM17_rA8X8 (const short * restrict x, const short * restrict
h, short * restrict r, int nh, int nr)
Arguments
x[nr+nh−1]
h[nh]
Pointer to input array of size nr + nh − 1.
Pointer to coefficient array of size nh (coefficients must be in
reverse order).
r[nr]
Pointer to output array of size nr. Must be double word
aligned.
nh
nr
Number of coefficients. Must be ≥17.
Number of samples to calculate. Must be a multiple of 8.
Description
Algorithm
Computes a real FIR filter (direct-form) using coefficients stored in vector h[ ].
The real data input is stored in vector x[ ]. The filter output result is stored in
vector r[ ]. It operates on 16-bit data with a 32-bit accumulate. The filter
calculates nr output samples using nh coefficients.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_gen(short *x, short *h, short *r, int nh, int nr)
{
int i, j, sum;
for (j = 0; j < nr; j++) {
sum = 0;
for (i = 0; i < nh; i++)
sum += x[i + j] * h[i];
r[j] = sum >> 15;
}
}
4-44
DSP_fir_gen_hM17_rA8X8
Special Requirements
- The number of coefficients, nh, must be greater than or equal to 17.
Coefficients must be in reverse order.
- The number of outputs computed, nr, must be a multiple of 8 and greater
than or equal to 8.
- Array r[ ] must be word aligned.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is fully interruptible.
- Load double-word instruction is used to simultaneously load four values
in a single clock cycle.
- The inner loop is unrolled four times and will always compute a multiple
of 4 of nh and nr. If nh is not a multiple of 4, the code will fill in zeros to make
nh a multiple of 4.
- This code yields best performance when the ratio of outer loop to inner
loop is less than or equal to 4.
Benchmarks
Cycles: 3*ceil(nh/4)*nr/4+39
Codesize: 416 bytes
C64x+ DSPLIB Reference
4-45
DSP_fir_r4
FIR Filter (when the number of coefficients is a multiple of 4)
DSP_fir_r4
Function
void DSP_fir_r4 (const short * restrict x, const short * restrict h, short * restrict
r, int nh, int nr)
Arguments
x[nr+nh−1]
h[nh]
Pointer to input array of size nr + nh – 1.
Pointer to coefficient array of size nh (coefficients must be in
reverse order).
r[nr]
nh
Pointer to output array of size nr.
Number of coefficients. Must be multiple of 4 and ≥8.
Number of samples to calculate. Must be multiple of 4.
nr
Description
Algorithm
Computes a real FIR filter (direct-form) using coefficients stored in vector h[ ].
The real data input is stored in vector x[ ]. The filter output result is stored in
vector r[ ]. This FIR operates on 16-bit data with a 32-bit accumulate. The filter
calculates nr output samples using nh coefficients.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_r4(short *x, short *h, short *r, int nh, int nr)
{
int i, j, sum;
for (j = 0; j < nr; j++) {
sum = 0;
for (i = 0; i < nh; i++)
sum += x[i + j] * h[i];
r[j] = sum >> 15;
}
}
4-46
DSP_fir_r4
Special Requirements
Implementation Notes
- The number of coefficients, nh, must be a multiple of 4 and greater than
or equal to 8. Coefficients must be in reverse order.
- The number of outputs computed, nr, must be a multiple of 4 and greater
than or equal to 4.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The load double-word instruction is used to simultaneously load four
values in a single clock cycle.
- The inner loop is unrolled four times and will always compute a multiple
of 4 output samples.
Benchmarks
Cycles
(8 + nh) * nr/4 + 9
Codesize 308 bytes
C64x+ DSPLIB Reference
4-47
DSP_fir_r8
DSP_fir_r8
FIR Filter (when the number of coefficients is a multiple of 8)
Function
void DSP_fir_r8_hM16_rM8A8X8 (short *x, short *h, short *r, int nh, int nr)
Arguments
x[nr+nh−1]
h[nh]
Pointer to input array of size nr + nh – 1.
Pointer to coefficient array of size nh (coefficients must be in
reverse order).
r[nr]
nh
Pointer to output array of size nr. Must be word aligned.
Number of coefficients. Must be multiple of 8, ≥ 8.
Number of samples to calculate. Must be multiple of 4.
nr
Description
Algorithm
Computes a real FIR filter (direct-form) using coefficients stored in vector h[ ].
The real data input is stored in vector x[ ]. The filter output result is stored in
vector r[ ]. This FIR operates on 16-bit data with a 32-bit accumulate. The filter
calculates nr output samples using nh coefficients.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_r8 (short *x, short *h, short *r, int nh, int nr)
{
int i, j, sum;
for (j = 0; j < nr; j++) {
sum = 0;
for (i = 0; i < nh; i++)
sum += x[i + j] * h[i];
r[j] = sum >> 15;
}
}
Special Requirements
- The number of coefficients, nh, must be a multiple of 8 and greater than
or equal to 8. Coefficients must be in reverse order.
- The number of outputs computed, nr, must be a multiple of 4 and greater
than or equal to 4.
- Array r[ ] must be word aligned.
4-48
DSP_fir_r8
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The load double-word instruction is used to simultaneously load four
values in a single clock cycle.
- The inner loop is unrolled 4 times and will always compute a multiple of
4 output samples.
- The outer loop is conditionally executed in parallel with the inner loop. This
allows for a zero overhead outer loop.
Benchmarks
Cycles
nh*nr/4 + 17
Codesize 336 bytes
C64x+ DSPLIB Reference
4-49
DSP_fir_r8_hM16_rM8A8X8
DSP_fir_r8_hM16_rM8A8X8
FIR Filter (the number of coefficients is a multiple of 8)
Function
void DSP_fir_r8_hM16_rM8A8X8 (short *x, short *h, short *r, int nh, int nr)
Arguments
x[nr+nh−1]
h[nh]
Pointer to input array of size nr + nh – 1.
Pointer to coefficient array of size nh (coefficients must be in
reverse order).
r[nr]
Pointer to output array of size nr. Must be double word
aligned.
nh
nr
Number of coefficients. Must be multiple of 8, ≥ 16.
Number of samples to calculate. Must be multiple of 8, ≥.8.
Description
Algorithm
Computes a real FIR filter (direct-form) using coefficients stored in vector h[ ].
The real data input is stored in vector x[ ]. The filter output result is stored in
vector r[ ]. This FIR operates on 16-bit data with a 32-bit accumulate. The filter
calculates nr output samples using nh coefficients.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_r8 (short *x, short *h, short *r, int nh, int nr)
{
int i, j, sum;
for (j = 0; j < nr; j++) {
sum = 0;
for (i = 0; i < nh; i++)
sum += x[i + j] * h[i];
r[j] = sum >> 15;
}
}
4-50
DSP_fir_r8_hM16_rM8A8X8
Special Requirements
- The number of coefficients, nh, must be a multiple of 8 and greater than
or equal to 16. Coefficients must be in reverse order.
- The number of outputs computed, nr, must be a multiple of 8 and greater
than or equal to 8.
- Array r[ ] must be double word aligned.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The load double-word instruction is used to simultaneously load four
values in a single clock cycle.
- The inner loop is unrolled 4 times and will always compute a multiple of
4 output samples.
- The outer loop is conditionally executed in parallel with the inner loop. This
allows for a zero overhead outer loop.
Benchmarks
Cycles
When nh>32, nh*nr/8+22
Otherwise, 32*nr/8+22
Codesize 640 bytes
C64x+ DSPLIB Reference
4-51
DSP_fir_sym
Symmetric FIR Filter
DSP_fir_sym
Function
void DSP_fir_sym (const short * restrict x, const short * restrict h, short * re-
strict r, int nh, int nr, int s)
Arguments
x[nr+2*nh]
Pointer to input array of size nr + 2*nh. Must be double-word
aligned.
h[nh+1]
Pointer to coefficient array of size nh + 1. Coefficients are in
normal order and only half (nh+1 out of 2*nh+1) are required.
Must be double-word aligned.
r[nr]
nh
Pointer to output array of size nr. Must be word aligned.
Number of coefficients. Must be multiple of 8. The number of
original symmetric coefficients is 2*nh+1.
nr
s
Number of samples to calculate. Must be multiple of 4.
Number of insignificant digits to truncate; e.g., 15 for Q.15
input data and coefficients.
Description
This function applies a symmetric filter to the input samples. The filter tap array
h[] provides ‘nh+1’ total filter taps. The filter tap at h[nh] forms the center point
of the filter. The taps at h[nh − 1] through h[0] form a symmetric filter about this
central tap. The effective filter length is thus 2*nh+1 taps.
The filter is performed on 16-bit data with 16-bit coefficients, accumulating
intermediate results to 40-bit precision. The accumulator is rounded and
truncated according to the value provided in ‘s’. This allows a variety of
Q-points to be used.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_fir_sym(short *x, short *h, short *r, int nh, int nr,
int s)
{
int
i, j;
long
long
y0;
round = (long) 1 << (s − 1);
for (j = 0; j < nr; j++) {
y0 = round;
for (i = 0; i < nh; i++)
4-52
DSP_fir_sym
y0 += (short) (x[j + i] + x[j + 2 * nh − i]) * h[i];
y0 += x[j + nh] * h[nh];
r[j] = (int) (y0 >> s);
}
}
Special Requirements
Implementation Notes
Benchmarks
- nh must be a multiple of 8. The number of original symmetric coefficients
is 2*nh+1. Only half (nh+1) are required.
- nr must be a multiple of 4.
- x[ ] and h[ ] must be double-word aligned.
- r[ ] must be word aligned.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The load double-word instruction is used to simultaneously load four
values in a single clock cycle.
- The inner loop is unrolled eight times.
Cycles
(10 * nh/8 + 15) * nr/4 + 26
Codesize 664 bytes
C64x+ DSPLIB Reference
4-53
DSP_iir
IIR With 5 Coefficients
DSP_iir
Function
void DSP_iir (short * restrict r1, const short * restrict x, short * restrict r2, const
short * restrict h2, const short * restrict h1, int nr)
Arguments
r1[nr+4]
must
Output array (used in actual computation. First four elements
have the previous outputs.)
x[nr+4]
r2[nr]
h2[5]
h1[5]
nr
Input array
Output array (stored)
Moving-average filter coefficients
Auto-regressive filter coefficients. h1[0] is not used.
Number of output samples. Must be ≥ 8.
Description
Algorithm
The IIR performs an auto-regressive moving-average (ARMA) filter with 4
auto-regressive filter coefficients and 5 moving-average filter coefficients for
nr output samples.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_iir(short *r1, short *x, short *r2, short *h2,
short *h1, int nr)
{
int j,i;
int sum;
for (i=0; i<nr; i++){
sum = h2[0] * x[4+i];
for (j = 1; j <= 4; j++)
sum += h2[j]*x[4+i−j]−h1[j]*r1[4+i−j];
r1[4+i] = (sum >> 15);
r2[i] = r1[4+i];
}
}
4-54
DSP_iir
Special Requirements
Implementation Notes
- nr is greater than or equal to 8.
- Input data array x[ ] contains nr + 4 input samples to produce nr output
samples.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Output array r1[ ] contains nr + 4 locations, r2[ ] contains nr locations for
storing nr output samples. The output samples are stored with an offset
of 4 into the r1[ ] array.
- The inner loop that iterated through the filter coefficients is completely
unrolled.
Benchmarks
Cycles
4 * nr + 21
Codesize 276 bytes
C64x+ DSPLIB Reference
4-55
DSP_iirlat
All-Pole IIR Lattice Filter
DSP_iirlat
Function
void DSP_iirlat(const short * restrict x, int nx, const short * restrict k, int nk, int
* restrict b, short * restrict r)
Arguments
x[nx]
nx
Input vector (16-bit).
Length of input vector.
k[nk]
nk
Reflection coefficients in Q.15 format.
Number of reflection coefficients/lattice stages. Must be >=4.
Make multiple of 2 to avoid bank conflicts.
b[nk+1]
r[nx]
Delay line elements from previous call. Should be initialized to
all zeros prior to the first call.
Output vector (16-bit).
Description
This routine implements a real all-pole IIR filter in lattice structure (AR lattice).
The filter consists of nk lattice stages. Each stage requires one reflection
coefficient k and one delay element b. The routine takes an input vector x[] and
returns the filter output in r[]. Prior to the first call of the routine, the delay
elements in b[] should be set to zero. The input data may have to be pre-scaled
to avoid overflow or achieve better SNR. The reflections coefficients lie in the
range −1.0 < k < 1.0. The order of the coefficients is such that k[nk−1]
corresponds to the first lattice stage after the input and k[0] corresponds to the
last stage.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void iirlat(short *x, int nx, short *k, int nk, int *b,
short *r)
{
int rt;
/* output
*/
int i, j;
for (j=0; j<nx; j++)
{
rt = x[j] << 15;
for (i = nk − 1; i >= 0; i−−)
{
4-56
DSP_iirlat
rt
= rt − (short)(b[i] >> 15) * k[i];
b[i + 1] = b[i] + (short)(rt >> 15) * k[i];
}
b[0] = rt;
r[j] = rt >> 15;
}
}
Special Requirements
Implementation Notes
- nk must be >= 4.
- No special alignment requirements
- See Bank Conflicts for avoiding bank conflicts
- Bank Conflicts: nk should be a multiple of 2, otherwise bank conflicts
occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Prolog and epilog of the inner loop are partially collapsed and overlapped
to reduce outer loop overhead.
Benchmarks
Cycles
(2 * nk + 7) * nx + 9
(without bank conflicts)
Codesize 352 bytes
C64x+ DSPLIB Reference
4-57
DSP_dotp_sqr
4.5 Math
Vector Dot Product and Square
DSP_dotp_sqr
Function
int DSP_dotp_sqr(int G, const short * restrict x, const short * restrict y, int *
restrict r, int nx)
Arguments
G
Calculated value of G (used in the VSELP coder).
First vector array
x[nx]
y[nx]
r
Second vector array
Result of vector dot product of x and y.
Number of elements. Must be multiple of 4, and ≥12.
nx
return int New value of G.
Description
Algorithm
This routine performs an nx element dot product of x[ ] and y[ ] and stores it
in r. It also squares each element of y[ ] and accumulates it in G. G is passed
back to the calling function in register A4. This computation of G is used in the
VSELP coder.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
int DSP_dotp_sqr (int G,short *x,short *y,int *r,
int nx)
{
short *y2;
short *endPtr2;
y2 = x;
for (endPtr2 = y2 + nx; y2 < endPtr2; y2++){
*r += *y * *y2;
G += *y * *y;
y++;
}
return(G);
}
4-58
DSP_dotp_sqr
Special Requirements nx must be a multiple of 4 and greater than or equal to 12.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Benchmarks
Cycles
nx/2 + 21
Codesize 128
C64x+ DSPLIB Reference
4-59
DSP_dotprod
DSP_dotprod
Vector Dot Product
Function
int DSP_dotprod(const short * restrict x, const short * restrict y, int nx)
Arguments
x[nx]
y[nx]
nx
First vector array. Must be double-word aligned.
Second vector array. Must be double word-aligned.
Number of elements of vector. Must be multiple of 4.
return int Dot product of x and y.
Description
Algorithm
This routine takes two vectors and calculates their dot product. The inputs are
16-bit short data and the output is a 32-bit number.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
int DSP_dotprod(short x[ ],short y[ ], int nx)
{
int sum;
int i;
sum = 0;
for(i=0; i<nx; i++){
sum += (x[i] * y[i]);
}
return (sum);
}
Special Requirements
- The input length must be a multiple of 4.
- The input data x[ ] and y[ ] are stored on double-word aligned boundaries.
- To avoid bank conflicts, the input arrays x[ ] and y[ ] must be offset by 4
half-words (8 bytes).
4-60
DSP_dotprod
Implementation Notes
- Bank Conflicts: No bank conflicts occur if the input arrays x[ ] and y[ ] are
offset by 4 half-words (8 bytes).
- Interruptibility: The code is fully interruptible.
- The code is unrolled 4 times to enable full memory and multiplier
bandwidth to be utilized.
- Interrupts are masked by branch delay slots only.
- Prolog collapsing has been performed to reduce codesize.
Benchmarks
Cycles
nx / 4 + 14
Codesize 64 bytes
C64x+ DSPLIB Reference
4-61
DSP_maxval
DSP_maxval
Maximum Value of Vector
Function
short DSP_maxval (const short *x, int nx)
Arguments
x[nx]
Pointer to input vector of size nx.
nx
Length of input data vector. Must be multiple of 8 and ≥32.
Maximum value of a vector.
return short
Description
Algorithm
This routine finds the element with maximum value in the input vector and
returns that value.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
short DSP_maxval(short x[ ], int nx)
{
int i, max;
max = −32768;
for (i = 0; i < nx; i++)
if (x[i] > max)
max = x[i];
return max;
}
Special Requirements nx is a multiple of 8 and greater than or equal to 32.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Benchmarks
Cycles nx / 4 + 10
Codesize 116 bytes
4-62
DSP_maxidx
Index of Maximum Element of Vector
DSP_maxidx
Function
int DSP_maxidx (const short *x, int nx)
Arguments
x[nx]
nx
Pointer to input vector of size nx. Must be double-word aligned.
Length of input data vector. Must be multiple of 16 and ≥ 48.
return int Index for vector element with maximum value.
Description
This routine finds the max value of a vector and returns the index of that value.
The input array is treated as 16 separate columns that are interleaved
throughout the array. If values in different columns are equal to the maximum
value, then the element in the leftmost column is returned. If two values within
a column are equal to the maximum, then the one with the lower index is
returned. Column takes precedence over index.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
int DSP_maxidx(short x[ ], int nx)
{
int max, index, i;
max = −32768;
for (i = 0; i < nx; i++)
if (x[i] > max) {
max = x[i];
index = i;
}
return index;
}
Special Requirements
- nx must be a multiple of 16 and greater than or equal to 48.
- The input vector x[ ] must be double-word aligned.
C64x+ DSPLIB Reference
4-63
DSP_maxidx
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The code is unrolled 16 times to enable the full bandwidth of LDDW and
MAX2 instructions to be utilized. This splits the search into 16 sub-ranges.
The global maximum is then found from the list of maximums of the
sub-ranges. Then, using this offset from the sub-ranges, the global
maximum and the index of it are found using a simple match. For common
maximums in multiple ranges, the index will be different to the above C
code.
- This code requires 40 bytes of stack space for a temporary buffer.
Benchmarks
Cycles
5 * nx / 16 + 42
Codesize 388 bytes
4-64
DSP_minval
Minimum Value of Vector
DSP_minval
Function
short DSP_minval (const short *x, int nx)
Arguments
x [nx]
Pointer to input vector of size nx.
nx
Length of input data vector. Must be multiple of 4 and ≥20.
return short
Maximum value of a vector.
Description
Algorithm
This routine finds the minimum value of a vector and returns the value.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
short DSP_minval(short x[ ], int nx)
{
int i, min;
min = 32767;
for (i = 0; i < nx; i++)
if (x[i] < min)
min = x[i];
return min;
}
Special Requirements nx is a multiple of 4 and greater than or equal to 20.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The input data is loaded using double word wide loads, and the MIN2
instruction is used to get to the minimum.
Benchmarks
Cycles
nx / 4 +10
Codesize 116 bytes
C64x+ DSPLIB Reference
4-65
DSP_mul32
32-Bit Vector Multiply
DSP_mul32
Function
void DSP_mul32(const int * restrict x, const int * restrict y, int * restrict r, short
nx)
Arguments
x[nx]
y[nx]
r[nx]
nx
Pointer to input data vector 1 of size nx. Must be double-word
aligned.
Pointer to input data vector 2 of size nx. Must be double-word
aligned.
Pointer to output data vector of size nx. Must be double-word
aligned.
Number of elements in input and output vectors. Must be multiple
of 8 and ≥16.
Description
Algorithm
The function performs a Q.31 x Q.31 multiply and returns the upper 32 bits of
the result. The result of the intermediate multiplies are accumulated into a
40-bit long register pair, as there could be potential overflow. The contribution
of the multiplication of the two lower 16-bit halves are not considered. The
output is in Q.30 format. Results are accurate to least significant bit.
In the comments below, X and Y are the two input values. Xhigh and Xlow
represent the upper and lower 16 bits of X. This is the C equivalent of the
assembly code without restrictions. Note that the assembly code is hand
optimized and restrictions may apply.
void DSP_mul32(const int *x, const int *y, int *r,
short nx)
{
short
int
i;
a,b,c,d,e;
for(i=nx;i>0;i−−)
{
a=*(x++);
b=*(y++);
c=_mpyluhs(a,b); /* Xlow*Yhigh */
d=_mpyhslu(a,b); /* Xhigh*Ylow */
e=_mpyh(a,b); /* Xhigh*Yhigh */
d+=c;
/* Xhigh*Ylow+Xlow*Yhigh */
/* (Xhigh*Ylow+Xlow*Yhigh)>>16 */
d=d>>16;
4-66
DSP_mul32
e+=d;
/* Xhigh*Yhigh + */
/* (Xhigh*Ylow+Xlow*Yhigh)>>16 */
*(r++)=e;
}
}
Special Requirements
Implementation Notes
- nx must be a multiple of 8 and greater than or equal to 16.
- Input and output vectors must be double-word aligned.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The MPYHI instruction is used to perform 16 x 32 multiplies to form 48-bit
intermediate results.
Benchmarks
Cycles
9 * nx/8 + 18
Codesize 512 bytes
C64x+ DSPLIB Reference
4-67
DSP_neg32
DSP_neg32
32-Bit Vector Negate
Function
void DSP_neg32(int *x, int *r, short nx)
Arguments
x[nx]
r[nx]
nx
Pointer to input data vector 1 of size nx with 32-bit elements.
Must be double-word aligned.
Pointer to output data vector of size nx with 32-bit elements.
Must be double-word aligned.
Number of elements of input and output vectors. Must be a
multiple of 4 and ≥8.
Description
Algorithm
This function negates the elements of a vector (32-bit elements). The input and
output arrays must not be overlapped except for where the input and output
pointers are exactly equal.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_neg32(int *x, int *r, short nx)
{
short i;
for(i=nx; i>0; i−−)
*(r++)=−*(x++);
}
Special Requirements
Implementation Notes
- nx must be a multiple of 4 and greater than or equal to 8.
- The arrays x[ ] and r[ ] must be double-word aligned.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The loop is unrolled twice and pipelined.
Benchmarks
Cycles
nx/2 + 19
Codesize 124 bytes
4-68
DSP_recip16
16-Bit Reciprocal
DSP_recip16
Function
void DSP_recip16 (short *x, short *rfrac, short *rexp, short nx)
Arguments
x[nx]
Pointer to Q.15 input data vector of size nx.
rfrac[nx]
rexp[nx]
nx
Pointer to Q.15 output data vector for fractional values.
Pointer to output data vector for exponent values.
Number of elements of input and output vectors.
Description
This routine returns the fractional and exponential portion of the reciprocal of
an array x[ ] of Q.15 numbers. The fractional portion rfrac is returned in Q.15
format. Since the reciprocal is always greater than 1, it returns an exponent
such that:
(rfrac[i] * 2rexp[i]) = true reciprocal
The output is accurate up to the least significant bit of rfrac, but note that this
bit could carry over and change rexp. For a reciprocal of 0, the procedure will
return a fractional part of 7FFFh and an exponent of 16.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_recip16(short *x, short *rfrac, short *rexp, short
nx)
{
int i,j,a,b;
short neg, normal;
for(i=nx; i>0; i−−)
{
a=*(x++);
if(a<0)
{
/* take absolute value */
a=−a;
neg=1;
}
else neg=0;
normal=_norm(a);
a=a<<normal;
/* normalize number */
C64x+ DSPLIB Reference
4-69
DSP_recip16
*(rexp++)=normal−15;
/* store exponent */
/* dividend = 1 */
b=0x80000000;
for(j=15;j>0;j−−)
b=_subc(b,a);
/* divide */
b=b&0x7FFF;
/* clear remainder
/* (clear upper half) */
if(neg) b=−b;
*(rfrac++)=b;
/* if originally
/* negative, negate */
/* store fraction */
}
}
Special Requirements None
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interruptible.
- The conditional subtract instruction, SUBC, is used for division. SUBC is
used once for every bit of quotient needed (15).
Benchmarks
Cycles
8 * nx + 14
Codesize 196 bytes
4-70
DSP_vecsumsq
Sum of Squares
DSP_vecsumsq
Function
int DSP_vecsumsq (const short *x, int nx)
Arguments
x[nx]
nx
Input vector
Number of elements in x. Must be multiple of 4 and ≥8.
return int Sum of the squares
Description
Algorithm
This routine returns the sum of squares of the elements contained in the vector
x[ ].
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
int DSP_vecsumsq(short x[ ], int nx)
{
int i, sum=0;
for(i=0; i<nx; i++)
{
sum += x[i]*x[i];
}
return(sum);
}
Special Requirements nx must be a multiple of 4 and greater than or equal to 32.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The code is unrolled 4 times to enable full memory and multiplier
bandwidth to be utilized.
Benchmarks
Cycles
nx/4 + 11
Codesize 188 bytes
C64x+ DSPLIB Reference
4-71
DSP_w_vec
Weighted Vector Sum
DSP_w_vec
Function
void DSP_w_vec(const short * restrict x, const short * restrict y, short m, short
* restrict r, short nr)
Arguments
x[nr]
y[nr]
m
Vector being weighted. Must be double-word aligned.
Summation vector. Must be double-word aligned.
Weighting factor
r[nr]
nr
Output vector
Dimensions of the vectors. Must be multiple of 8 and ≥8.
Description
Algorithm
This routine is used to obtain the weighted vector sum. Both the inputs and
output are 16-bit numbers.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_w_vec(short x[ ],short y[ ],short m,
short r[ ],short nr)
{
short i;
for (i=0; i<nr; i++) {
r[i] = ((m * x[i]) >> 15) + y[i];
}
}
Special Requirements
Implementation Notes
- nr must be a multiple of 8 and ≥ 8.
- Vectors x[ ] and y[ ] must be double-word aligned.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Input is loaded in double-words.
- Use of packed data processing to sustain throughput.
Benchmarks
Cycles
3 * nr/8 + 18
Codesize 144 bytes
4-72
DSP_mat_mul
4.6 Matrix
Matrix Multiplication
DSP_mat_mul
Function
void DSP_mat_mul(const short * restrict x, int r1, int c1, const short * restrict
y, int c2, short * restrict r, int qs)
Arguments
x [r1*c1]
r1
Pointer to input matrix of size r1*c1.
Number of rows in matrix x.
c1
Number of columns in matrix x. Also number of rows in y.
Pointer to input matrix of size c1*c2.
Number of columns in matrix y.
y [c1*c2]
c2
r [r1*c2]
qs
Pointer to output matrix of size r1*c2.
Final right−shift to apply to the result.
Description
This function computes the expression “r = x * y” for the matrices x and y. The
columnar dimension of x must match the row dimension of y. The resulting
matrix has the same number of rows as x and the same number of columns as
y.
The values stored in the matrices are assumed to be fixed-point or integer
values. All intermediate sums are retained to 32-bit precision, and no overflow
checking is performed. The results are right-shifted by a user-specified
amount, and then truncated to 16 bits.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that the
assembly code is hand optimized and restrictions may apply.
void DSP_mat_mul(short *x, int r1, int c1, short *y, int c2,
short *r, int qs)
{
int i, j, k;
int sum;
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Multiply each row in x by each column in y. The */
/* product of row m in x and column n in y is placed */
/* in position (m,n) in the result.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
C64x+ DSPLIB Reference
4-73
DSP_mat_mul
for (i = 0; i < r1; i++)
for (j = 0; j < c2; j++)
{
sum = 0;
for (k = 0; k < c1; k++)
sum += x[k + i*c1] * y[j + k*c2];
r[j + i*c2] = sum >> qs;
}
}
Special Requirements
Implementation Notes
- The arrays x[], y[], and r[] are stored in distinct arrays. That is, in-place
processing is not allowed.
- The input matrices have minimum dimensions of at least 1 row and 1
column, and maximum dimensions of 32767 rows and 32767 columns.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: This code blocks interrupts during its innermost loop.
Interrupts are not blocked otherwise. As a result, interrupts can be blocked
for up to 0.25*c1’ + 16 cycles at a time.
- The ‘i’ loop and ‘k’ loops are unrolled 2x. The ’j’ loop is unrolled 4x. For
dimensions that are not multiples of the various loops’ unroll factors, this
code calculates extra results beyond the edges of the matrix. These extra
results are ultimately discarded. This allows the loops to be unrolled for
efficient operation on large matrices while not losing flexibility.
Benchmarks
Cycles
0.25 * ( r1’ * c2’ * c1’ ) + 2.25 * ( r1’ * c2’ ) + 11, where:
r1’ = 2 * ceil(r1/2.0) (r1 rounded up to next even)
c1’ = 2 * ceil(c1/2.0) (c1 rounded up to next even)
c2’ = 4 * ceil(c2/4.0) (c2 rounded up to next mult of 4)
For r1= 1, c1= 1, c2= 1: 33 cycles
For r1= 8, c1=20, c2= 8: 475 cycles
Codesize 416 bytes
4-74
DSP_mat_trans
Matrix Transpose
DSP_mat_trans
Function
void DSP_mat_trans (const short *x, short rows, short columns, short *r)
Arguments
x[rows*columns]
rows
Pointer to input matrix.
Number of rows in the input matrix. Must be a multiple
of 4.
columns
Number of columns in the input matrix. Must be a multiple
of 4.
r[columns*rows]
Pointer to output data vector of size rows*columns.
Description
Algorithm
This function transposes the input matrix x[ ] and writes the result to matrix r[ ].
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_mat_trans(short *x, short rows, short columns, short
*r)
{
short i,j;
for(i=0; i<columns; i++)
for(j=0; j<rows; j++)
*(r+i*rows+j)=*(x+i+columns*j);
}
Special Requirements
Implementation Notes
- Rows and columns must be a multiple of 4.
- Matrices are assumed to have 16-bit elements.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Data from four adjacent rows, spaced “columns” apart are read, and a
local 4x4 transpose is performed in the register file. This leads to four
double words, that are “rows” apart. These loads and stores can cause
bank conflicts; hence, non-aligned loads and stores are used.
Benchmarks
Cycles
(2 * rows + 9) * columns/4 + 3
Codesize 224 bytes
C64x+ DSPLIB Reference
4-75
DSP_bexp
4.7 Miscellaneous
Block Exponent Implementation
DSP_bexp
Function
short DSP_bexp(const int *x, short nx)
Arguments
x[nx]
Pointer to input vector of size nx. Must be double-word
aligned.
nx
Number of elements in input vector. Must be multiple of 8.
return short
Return value is the maximum exponent that may be used in
scaling.
Description
Algorithm
Computes the exponents (number of extra sign bits) of all values in the input
vector x[ ] and returns the minimum exponent. This will be useful in
determining the maximum shift value that may be used in scaling a block of
data.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
short DSP_bexp(const int *x, short nx)
{
int
min_val =_norm(x[0]);
short
int
n;
i;
for(i=1;i<nx;i++)
{
n =_norm(x[i]); /* _norm(x) = number of */
/* redundant sign bits */
if(n<min_val) min_val=n;
}
return min_val;
}
Special Requirements
- nx must be a multiple of 8.
- The input vector x[ ] must be double-word aligned.
4-76
DSP_bexp
Implementation Notes
Benchmarks
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Cycles
nx/2 + 21
Codesize 216 bytes
C64x+ DSPLIB Reference
4-77
DSP_blk_eswap16
DSP_blk_eswap16
Endian-Swap a Block of 16-Bit Values
Function
void blk_eswap16(void * restrict x, void * restrict r, int nx)
Arguments
x [nx]
r [nx]
nx
Source data. Must be double-word aligned.
Destination array. Must be double-word aligned.
Number of 16-bit values to swap. Must be multiple of 8.
Description
Algorithm
The data in the x[] array is endian swapped, meaning that the byte-order of the
bytes within each half-word of the r[] array is reversed. This facilitates moving
big-endian data to a little-endian system or vice-versa.
When the r pointer is non-NULL, the endian-swap occurs out-of-place, similar
to a block move. When the r pointer is NULL, the endian-swap occurs in-place,
allowing the swap to occur without using any additional storage.
This is the C equivalent of the assembly code without restrictions. Note that the
assembly code is hand optimized and restrictions may apply.
void DSP_blk_eswap16(void *x, void *r, int nx)
{
int i;
char *_x, *_r;
if (r)
{
_x = (char *)x;
_r = (char *)r;
} else
{
_x = (char *)x;
_r = (char *)r;
}
for (i = 0; i < nx; i++)
{
char t0, t1;
t0 = _x[i*2 + 1];
t1 = _x[i*2 + 0];
_r[i*2 + 0] = t0;
_r[i*2 + 1] = t1;
}
}
4-78
DSP_blk_eswap16
Special Requirements
- Input and output arrays do not overlap, except when “r == NULL” so that
the operation occurs in-place.
- The input array and output array are expected to be double-word aligned,
and a multiple of 8 half-words must be processed.
Implementation Notes
Benchmarks
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Cycles
nx/8 + 18
Codesize 104 bytes
C64x+ DSPLIB Reference
4-79
DSP_blk_eswap32
DSP_blk_eswap32
Endian-Swap a Block of 32-Bit Values
Function
void blk_eswap32(void * restrict x, void * restrict r, int nx)
Arguments
x [nx]
r [nx]
nx
Source data. Must be double-word aligned.
Destination array. Must be double-word aligned.
Number of 32-bit values to swap. Must be multiple of 4.
Description
The data in the x[] array is endian swapped, meaning that the byte-order of the
bytes within each word of the r[] array is reversed. This facilitates moving
big-endian data to a little-endian system or vice-versa.
When the r pointer is non-NULL, the endian-swap occurs out-of-place, similar
to a block move. When the r pointer is NULL, the endian-swap occurs in-place,
allowing the swap to occur without using any additional storage.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that the
assembly code is hand optimized and restrictions may apply.
void DSP_blk_eswap32(void *x, void *r, int nx)
{
int i;
char *_x, *_r;
if (r)
{
_x = (char *)x;
_r = (char *)r;
} else
{
_x = (char *)x;
_r = (char *)r;
}
for (i = 0; i < nx; i++)
{
char t0, t1, t2, t3;
t0 = _x[i*4 + 3];
t1 = _x[i*4 + 2];
4-80
DSP_blk_eswap32
t2 = _x[i*4 + 1];
t3 = _x[i*4 + 0];
_r[i*4 + 0] = t0;
_r[i*4 + 1] = t1;
_r[i*4 + 2] = t2;
_r[i*4 + 3] = t3;
}
}
Special Requirements
- Input and output arrays do not overlap, except where “r == NULL” so that
the operation occurs in-place.
- The input array and output array are expected to be double-word aligned,
and a multiple of 4 words must be processed.
Implementation Notes
Benchmarks
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Cycles
nx/4 + 20
Codesize 116 bytes
C64x+ DSPLIB Reference
4-81
DSP_blk_eswap64
DSP_blk_eswap64
Endian-Swap a Block of 64-Bit Values
Function
void blk_eswap64(void * restrict x, void * restrict r, int nx)
Arguments
x[nx]
r[nx]
nx
Source data. Must be double-word aligned.
Destination array. Must be double-word aligned.
Number of 64-bit values to swap. Must be multiple of 2.
Description
The data in the x[] array is endian swapped, meaning that the byte-order of the
bytes within each double-word of the r[] array is reversed. This facilitates
moving big-endian data to a little-endian system or vice-versa.
When the r pointer is non-NULL, the endian-swap occurs out-of-place, similar
to a block move. When the r pointer is NULL, the endian-swap occurs in-place,
allowing the swap to occur without using any additional storage.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that the
assembly code is hand optimized and restrictions may apply.
void DSP_blk_eswap64(void *x, void *r, int nx)
{
int i;
char *_x, *_r;
if (r)
{
_x = (char *)x;
_r = (char *)r;
} else
{
_x = (char *)x;
_r = (char *)r;
}
for (i = 0; i < nx; i++)
{
char t0, t1, t2, t3, t4, t5, t6, t7;
t0 = _x[i*8 + 7];
t1 = _x[i*8 + 6];
4-82
DSP_blk_eswap64
t2 = _x[i*8 + 5];
t3 = _x[i*8 + 4];
t4 = _x[i*8 + 3];
t5 = _x[i*8 + 2];
t6 = _x[i*8 + 1];
t7 = _x[i*8 + 0];
_r[i*8 + 0] = t0;
_r[i*8 + 1] = t1;
_r[i*8 + 2] = t2;
_r[i*8 + 3] = t3;
_r[i*8 + 4] = t4;
_r[i*8 + 5] = t5;
_r[i*8 + 6] = t6;
_r[i*8 + 7] = t7;
}
}
Special Requirements
- Input and output arrays do not overlap, except when “r == NULL” so that
the operation occurs in-place.
- The input array and output array are expected to be double-word aligned,
and a multiple of 2 double-words must be processed.
Implementation Notes
Benchmarks
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Cycles
nx/2 + 20
Codesize 116 bytes
C64x+ DSPLIB Reference
4-83
DSP_blk_move
DSP_blk_move
Block Move (Overlapping)
Function
void DSP_blk_move(short * x, short * r, int nx)
Arguments
x [nx]
r [nx]
nx
Block of data to be moved.
Destination of block of data.
Number of elements in block. Must be multiple of 8 and ≥32.
Description
Algorithm
This routine moves nx 16-bit elements from one memory location pointed to
by x to another pointed to by r. The source and destination blocks can be
overlapped.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_blk_move(short *x, short *r, int nx)
{
int i;
if( r < x )
{
for (I = 0; I < nx; i++)
r[i] = x[i];
} else
{
for (I = nx−1; I >= 0; i−−)
r[i] = x[i];
}
}
Special Requirements nx must be a multiple of 8 and ≥ 32.
Implementation Notes
- Twin input and output pointers are used.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is fully interruptible.
Benchmarks
Cycles
nx/4+18
Codesize 112 bytes
4-84
DSP_fltoq15
Float to Q15 Conversion
DSP_fltoq15
Function
void DSP_fltoq15 (float *x, short *r, short nx)
Arguments
x[nx]
r[nx]
nx
Pointer to floating-point input vector of size nx. x should contain
the numbers normalized between [−1,1).
Pointer to output data vector of size nx containing the Q.15
equivalent of vector x.
Length of input and output data vectors. Must be multiple of 2.
Description
Algorithm
Convert the IEEE floating point numbers stored in vector x[ ] into Q.15 format
numbers stored in vector r[ ]. Results are truncated toward zero. Values that
exceed the size limit will be saturated to 0x7fff if value is positive and 0x8000
if value is negative. All values too small to be correctly represented will be
truncated to 0.
This is the C equivalent of the assembly code without restrictions. Note that the
assembly code is hand optimized and restrictions may apply.
void fltoq15(float x[], short r[], short nx)
{
int i, a;
for(i = 0; i < nx; i++)
{
a = 32768 * x[i];
// saturate to 16−bit //
if (a>32767) a = 32767;
if (a<−32768) a = −32768;
r[i] = (short) a;
}
}
Special Requirements nx must be a multiple of 2.
C64x+ DSPLIB Reference
4-85
DSP_fltoq15
Implementation Notes
- Loop is unrolled twice.
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
Benchmarks
Cycles
3 * nx/2 + 14
Codesize 224 bytes
4-86
DSP_minerror
Minimum Energy Error Search
DSP_minerror
Function
int minerror (const short * restrict GSP0_TABLE, const short * restrict
errCoefs, int * restrict max_index)
Arguments
GSP0_TABLE[9*256] GSP0 terms array. Must be double-word aligned.
errCoefs[9]
max_index
return int
Array of error coefficients.
Pointer to GSP0_TABLE[max_index] found.
Maximum dot product result.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that the
assembly code is hand optimized and restrictions may apply.
int minerr
(
const short *restrict GSP0_TABLE,
const short *restrict errCoefs,
int
*restrict max_index
)
{
int val, maxVal = −50;
int i, j;
for (i = 0; i < GSP0_NUM; i++)
{
for (val = 0, j = 0; j < GSP0_TERMS; j++)
val += GSP0_TABLE[i*GSP0_TERMS+j] * errCoefs[j];
if (val > maxVal)
{
maxVal = val;
*max_index = i*GSP0_TERMS;
}
}
return (maxVal);
}
C64x+ DSPLIB Reference
4-87
DSP_minerror
Special Requirements Array GSP0_TABLE[] must be double-word aligned.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- The load double-word instruction is used to simultaneously load four
values in a single clock cycle.
- The inner loop is completely unrolled.
- The outer loop is 4 times unrolled.
Benchmarks
Cycles
256/4 * 9 + 17 = 593
Codesize 352 bytes
4-88
DSP_q15tofl
Q15 to Float Conversion
DSP_q15tofl
Function
void DSP_q15tofl (short *x, float *r, int nx)
Arguments
x[nx]
r[nx]
Pointer to Q.15 input vector of size nx.
Pointer to floating-point output data vector of size nx containing
the floating-point equivalent of vector x.
nx
Length of input and output data vectors. Must be multiple of 2.
Description
Algorithm
Converts the values stored in vector x[ ] in Q.15 format to IEEE floating point
numbers in output vector r[ ].
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_q15tofl(short *x, float *r, int nx)
{
int i;
for (i=0;i<nx;i++)
r[i] = (float) x[i] / 0x8000;
}
Special Requirements nx must be a multiple of 2.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Loop is unrolled twice
Benchmarks
Cycles
2 * nx + 14
Codesize 184 bytes
C64x+ DSPLIB Reference
4-89
DSP_bitrev_cplx
4.8 Obsolete Functions
4.8.1 FFT
Complex Bit-Reverse
DSP_bitrev_cplx
NOTE: This function is provided for backward compatibility with the C62x
DSPLIB. It has not been optimized for the C64x architecture. You are advised
to use one of the newly added FFT functions which have been optimized for the
C64x.
Function
void DSP_bitrev_cplx (int *x, short *index, int nx)
Arguments
x[nx]
Pointer to complex input vector x of size nx
index[ ]
Array of size ∼sqrt(nx) created by the routine digitrev_index
(provided in the directory ‘support\fft’).
nx
Number of elements in vector x. nx must be a power of 2.
Description
Algorithm
This function bit-reverses the position of elements in complex vector x. This
function is used in conjunction with FFT routines to provide the correct format
for the FFT input or output data. The bit-reversal of a bit-reversed order array
yields a linear-order array.
TI retains all rights, title and interest in this code and only authorizes the use
of this code on TI TMS320 DSPs manufactured by TI. This is the C equivalent
of the assembly code without restrictions. Note that the assembly code is hand
optimized and restrictions may apply.
void DSP_bitrev_cplx (int *x, short *index, int nx)
{
int
i;
short
short
int
i0, i1, i2, i3;
j0, j1, j2, j3;
xi0, xi1, xi2, xi3;
xj0, xj1, xj2, xj3;
t;
int
short
int
a, b, ia, ib, ibs;
mask;
int
4-90
DSP_bitrev_cplx
int
nbits, nbot, ntop, ndiff, n2, halfn;
*xs= (short *) x;
short
nbits = 0;
i = nx;
while (i > 1){
i = i >> 1;
nbits++;}
nbot = nbits >> 1;
ndiff = nbits & 1;
ntop = nbot + ndiff;
n2
= 1 << ntop;
mask = n2 − 1;
halfn = nx >> 1;
for(i0 = 0; i0 < halfn; i0 += 2) {
b = i0 & mask;
a = i0 >> nbot;
if (!b) ia
= index[a];
ib = index[b];
ibs= ib << nbot;
j0 = ibs + ia;
t = i0 < j0;
xi0= x[i0];
xj0= x[j0];
if (t){x[i0] = xj0;
x[j0] = xi0;}
i1 = i0 + 1;
j1 = j0 + halfn;
xi1= x[i1];
xj1= x[j1];
x[i1] = xj1;
x[j1] = xi1;
i3 = i1 + halfn;
j3 = j1 + 1;
xi3= x[i3];
xj3= x[j3];
C64x+ DSPLIB Reference
4-91
DSP_bitrev_cplx
if (t){x[i3] = xj3;
x[j3] = xi3;}
}
}
Special Requirements
- nx must be a power of 2.
- The array index[] is generated by the routine bitrev_index provided in the
directory ‘support\fft’.
- If nx ≤ 4K, you can use the char (8-bit) data type for the “index” variable.
This requires changing the LDH when loading index values in the
assembly routine to LDB. This further reduces the size of the Index Table
by half.
Implementation Notes
Benchmarks
- Interruptibility: The code is interrupt-tolerant but not interruptible.
The performance of this function has not yet been characterized on the C64x+
4-92
DSP_radix2
Complex Forward FFT (radix 2)
DSP_radix2
NOTE: This function is provided for backward compatibility with the C62x
DSPLIB. It has not been optimized for the C64x architecture. You are advised
to use one of the newly added FFT functions which have been optimized for the
C64x.
Function
void DSP_radix2 (int nx, short * restrict x, const short * restrict w)
Arguments
nx
Number of complex elements in vector x. Must be a power of 2
such that 4 ≤ nx ≤ 65536.
x[2*nx]
w[nx]
Pointer to input and output sequences. Size 2*nx elements.
Pointer to vector of FFT coefficients of size nx elements.
Description
Algorithm
This routine is used to compute FFT of a complex sequence of size nx, a power
of 2, with “decimation-in-frequency decomposition” method. The output is in
bit-reversed order. Each complex value is with interleaved 16-bit real and
imaginary parts.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_radix2 (short x[ ],short nx,short w[ ])
{
short n1,n2,ie,ia,i,j,k,l;
short xt,yt,c,s;
n2 = nx;
ie = 1;
for (k=nx; k > 1; k = (k >> 1) ) {
n1 = n2;
n2 = n2>>1;
ia = 0;
for (j=0; j < n2; j++) {
c = w[2*ia];
s = w[2*ia+1];
ia = ia + ie;
for (i=j; i < nx; i += n1) {
l = i + n2;
C64x+ DSPLIB Reference
4-93
DSP_radix2
xt
= x[2*l] − x[2*i];
= x[2*i] + x[2*l];
= x[2*l+1] − x[2*i+1];
x[2*i]
yt
x[2*i+1] = x[2*i+1] + x[2*l+1];
x[2*l] = (c*xt + s*yt)>>15;
x[2*l+1] = (c*yt − s*xt)>>15;
}
}
ie = ie<<1;
}
}
Special Requirements
- 2 ≤ nx ≤ 32768 (nx is a power of 2)
- Input x and coefficients w should be in different data sections or memory
spaces to eliminate memory bank hits. If this is not possible, they should
be aligned on different word boundaries to minimize memory bank hits.
- x data is stored in the order real[0], image[0], real[1], ...
- The FFT coefficients (twiddle factors) are generated using the program
tw_radix2 provided in the directory ‘support\fft’.
Implementation Notes
- Bank Conflicts: See Benchmarks.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Loads input x and coefficient w as words.
- Both loops j and i0 shown in the C code are placed in the INNERLOOP of
the assembly code.
Benchmarks
The performance of this function has not yet been characterized on the C64x+.
4-94
DSP_r4fft
Complex Forward FFT (radix 4)
DSP_r4fft
NOTE: This function is provided for backward compatibility with the C62x
DSPLIB. It has not been optimized for the C64x architecture. You are advised
to use one of the newly added FFT functions which have been optimized for the
C64x.
Function
void DSP_r4fft (int nx, short * restrict x, const short * restrict w)
Arguments
nx
Number of complex elements in vector x. Must be a power of 4
such that 4 ≤ nx ≤ 65536.
x[2*nx]
w[nx]
Pointer to input and output sequences. Size 2*nx elements.
Pointer to vector of FFT coefficients of size nx elements.
Description
Algorithm
This routine is used to compute FFT of a complex sequence size nx, a power
of 4, with “decimation-in-frequency decomposition” method. The output is in
digit-reversed order. Each complex value is with interleaved 16-bit real and
imaginary parts.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
void DSP_r4fft (int nx, short x[ ], short w[ ])
{
int
n1, n2, ie, ia1, ia2, ia3, i0, i1, i2, i3,
j, k;
short t, r1, r2, s1, s2, co1, co2, co3, si1,
si2, si3;
n2 = nx;
ie = 1;
for (k = nx; k > 1; k >>= 2) {
n1 = n2;
n2 >>= 2;
ia1 = 0;
for (j = 0; j < n2; j++) {
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = w[ia1 * 2 + 1];
C64x+ DSPLIB Reference
4-95
DSP_r4fft
si1 = w[ia1 * 2];
co2 = w[ia2 * 2 + 1];
si2 = w[ia2 * 2];
co3 = w[ia3 * 2 + 1];
si3 = w[ia3 * 2];
ia1 = ia1 + ie;
for (i0 = j; i0 < nx; i0 += n1) {
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
r1 = x[2 * i0] + x[2 * i2];
r2 = x[2 * i0] − x[2 * i2];
t = x[2 * i1] + x[2 * i3];
x[2 * i0] = r1 + t;
r1 = r1 − t;
s1 = x[2 * i0 + 1] + x[2 * i2 + 1];
s2 = x[2 * i0 + 1] − x[2 * i2 + 1];
t = x[2 * i1 + 1] + x[2 * i3 + 1];
x[2 * i0 + 1] = s1 + t;
s1 = s1 − t;
x[2 * i2] = (r1 * co2 + s1 * si2) >>
15;
x[2 * i2 + 1] = (s1 * co2−r1 *
si2)>>15;
t = x[2 * i1 + 1] − x[2 * i3 + 1];
r1 = r2 + t;
r2 = r2 − t;
t = x[2 * i1] − x[2 * i3];
s1 = s2 − t;
s2 = s2 + t;
x[2 * i1] = (r1 * co1 + s1 * si1)
>>15;
x[2 * i1 + 1] = (s1 * co1−r1 *
si1)>>15;
x[2 * i3] = (r2 * co3 + s2 * si3)
4-96
DSP_r4fft
>>15;
x[2 * i3 + 1] = (s2 * co3−r2 *
si3)>>15;
}
}
ie <<= 2;
}
}
Special Requirements
- 4 ≤ nx ≤ 65536 (nx a power of 4)
- x is aligned on a 4*nx byte boundary for circular buffering
- Input x and coefficients w should be in different data sections or memory
spaces to eliminate memory bank hits. If this is not possible, w should be
aligned on an odd word boundary to minimize memory bank hits
- x data is stored in the order real[0], image[0], real[1], ...
- The FFT coefficients (twiddle factors) are generated using the program
tw_r4fft provided in the directory ‘support\fft’.
Implementation Notes
- Bank Conflicts: See Benchmarks.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Loads input x and coefficient w as words.
- Both loops j and i0 shown in the C code are placed in the INNERLOOP of
the assembly code.
Benchmarks
The performance of this function has not yet been characterized on the C64x+.
C64x+ DSPLIB Reference
4-97
DSP_fft
Complex Forward FFT With Digital Reversal
DSP_fft
Function
void DSP_fft (const short * restrict w, int nx, short * restrict x, short * restrict y)
Arguments
w[2*nx]
nx
Pointer to vector of Q.15 FFT coefficients of size 2 * nx
elements. Must be double-word aligned.
Number of complex elements in vector x. Must be a power of
4 and 4 ≤ nx ≤ 65536.
x[2*nx]
y[2*nx]
Pointer to input sequence of size 2 * nx elements. Must be
double-word aligned.
Pointer to output sequence of size 2 * nx elements. Must be
double-word aligned.
Description
This routine is used to compute an FFT of a complex sequence of size nx, a
power of 4, with “decimation-in-frequency decomposition” method. The output
is returned in a separate array y in normal order. This routine also performs
digit reversal as a special last step. Each complex value is stored as
interleaved 16-bit real and imaginary parts. The code uses a special ordering
of FFT factors and memory accesses to improve performance in the presence
of cache.
Algorithm
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The following macro is used to obtain a digit reversed index, of a given */
/* number i, into j where the number of bits in ”i” is ”m”. For the natural */
/* form of C code, this is done by first interchanging every set of ”2 bit” */
/* pairs, followed by exchanging nibbles, followed by exchanging bytes, and */
/* finally halfwords. To give an example, consider the following number:
/*
*/
*/
/* N = FEDCBA9876543210, where each digit represents a bit, the following */
/* steps illustrate the changes as the exchanges are performed: */
/* M = DCFE98BA54761032 is the number after every ”2 bits” are exchanged. */
/* O = 98BADCFE10325476 is the number after every nibble is exchanged.
/* P = 1032547698BADCFE is the number after every byte is exchanged.
*/
*/
/* Since only 16 digits were considered this represents the digit reversed */
/* index. Since the numbers are represented as 32 bits, there is one more */
/* step typically of exchanging the half words as well.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
4-98
DSP_fft
#include <stdio.h>
#include <stdlib.h>
#if 0
# define DIG_REV(i, m, j) ((j) = (_shfl(_rotl(_bitr(_deal(i)), 16)) >> (m)))
#else
# define DIG_REV(i, m, j)
\
\
\
\
\
\
\
\
do {
unsigned _ = (i);
_ = ((_ & 0x33333333) << 2) | ((_ & ~0x33333333) >> 2);
_ = ((_ & 0x0F0F0F0F) << 4) | ((_ & ~0x0F0F0F0F) >> 4);
_ = ((_ & 0x00FF00FF) << 8) | ((_ & ~0x00FF00FF) >> 8);
_ = ((_ & 0x0000FFFF) << 16) | ((_ & ~0x0000FFFF) >> 16);
(j) = _ >> (m);
} while (0)
#endif
void fft_cn
(
const short *restrict w,
int n,
short
short
*restrict x,
*restrict y
)
{
int stride, i, j, k, t, s, m;
short xh0, xh1, xh20, xh21;
short xl0, xl1, xl20, xl21;
short xt0, yt0, xt1, yt1;
short xt2, yt2, xt3, yt3;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Inform the compiler that the input array ”x”, twiddle factor array */
/* ”w” and output array ”y” are double word aligned. In addition, the */
/* number of points to be transformed is assumed to be greater than or */
/* equal to 16, and less than 32768.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
#ifndef NOASSUME
C64x+ DSPLIB Reference
4-99
DSP_fft
_nassert((int)x % 8 == 0);
_nassert((int)y % 8 == 0);
_nassert((int)w % 8 == 0);
_nassert(n >= 16);
_nassert(n < 32768);
#endif
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Perform initial stages of FFT in place w/out digit reversal.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
#ifndef NOASSUME
#pragma MUST_ITERATE(1,,1);
#endif
for (stride = n, t = 0; stride > 4; stride >>= 2)
{
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Perform each of the butterflies for this particular stride.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
s = stride >> 2;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* stride represents the seperation between the inputs of the radix */
/* 4 butterfly. The C code breaks the FFT, into two cases, one when */
/* the stride between the elements is greater than 4, other when
*/
/* the stride is less than 4. Since stride is greater than 16, it */
/* can be guaranteed that ”s” is greater than or equal to 4.
*/
/* In addition, it can also be shown that the loop that shares this */
/* stride will iterate at least once. The number of times this
/* loop iterates depends on how many butterflies in this stage
/* share a twiddle factor.
*/
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
#ifndef NOASSUME
_nassert(stride >= 16);
_nassert(s
>= 4);
#pragma MUST_ITERATE(1,,1);
#endif
for (i = 0; i < n; i += stride)
4-100
DSP_fft
{
#ifndef NOASSUME
_nassert(i % 4 == 0);
_nassert(s
>= 4);
#pragma MUST_ITERATE(2,,2);
#endif
for (j = 0; j < s; j += 2)
{
for (k = 0; k < 2; k++)
{
short
w1c, w1s, w2c, w2s, w3c, w3s;
short x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
short y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Read the four samples that are the input to this
/* particular butterfly.
*/
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
x0r = x[2*(i+j+k ) + 0]; x0i = x[2*(i+j+k ) + 1];
x1r = x[2*(i+j+k + s) + 0]; x1i = x[2*(i+j+k + s) + 1];
x2r = x[2*(i+j+k + 2*s) + 0]; x2i = x[2*(i+j+k + 2*s) + 1];
x3r = x[2*(i+j+k + 3*s) + 0]; x3i = x[2*(i+j+k + 3*s) + 1];
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Read the six twiddle factors that are needed for 3 */
/* of the four outputs. (The first output has no mpys.) */
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
w1s = w[t + 2*k + 6*j + 0];
w2s = w[t + 2*k + 6*j + 4];
w3s = w[t + 2*k + 6*j + 8];
w1c = w[t + 2*k + 6*j + 1];
w2c = w[t + 2*k + 6*j + 5];
w3c = w[t + 2*k + 6*j + 9];
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Calculate the four outputs, remembering that radix4 */
/* FFT accepts 4 inputs and produces 4 outputs. If we */
/* imagine the inputs as being complex, and look at the */
/* first stage as an example:
*/
*/
*/
/*
/* Four inputs are x(n) x(n+N/4) x(n+N/2) x(n+3N/4)
/* In general the four inputs can be generalized using */
C64x+ DSPLIB Reference
4-101
DSP_fft
/* the stride between the elements as follows:
*/
*/
*/
/* x(n), x(n + s), x(n + 2*s), x(n + 3*s).
/*
/* These four inputs are used to calculate four outputs */
/* as shown below:
/*
*/
*/
/* X(4k) = x(n) + x(n + N/4) + x(n + N/2) + x(n + 3N/4) */
/* X(4k+1)= x(n) −jx(n + N/4) − x(n + N/2) +jx(n + 3N/4) */
/* X(4k+2)= x(n) − x(n +N/4) + x(N + N/2) − x(n + 3N/4) */
/* X(4k+3)= x(n) +jx(n + N/4) − x(n + N/2) −jx(n + 3N/4) */
/*
*/
/* These four partial results can be re−written to show */
/* the underlying DIF structure similar to DSP_radix2 as */
/* follows:
/*
*/
*/
/* X(4k) = (x(n)+x(n + N/2)) + (x(n+N/4)+ x(n + 3N/4)) */
/* X(4k+1)= (x(n)−x(n + N/2)) −j(x(n+N/4) − x(n + 3N/4)) */
/* x(4k+2)= (x(n)+x(n + N/2)) − (x(n+N/4)+ x(n + 3N/4)) */
/* X(4k+3)= (x(n)−x(n + N/2)) +j(x(n+N/4) − x(n + 3N/4)) */
/*
*/
/* which leads to the real and imaginary values as foll: */
/*
*/
*/
*/
*/
*/
*/
*/
*/
*/
/* y0r = x0r + x2r + x1r + x3r
/* y0i = x0i + x2i + x1i + x3i
= xh0 + xh20
= xh1 + xh21
/* y1r = x0r − x2r + (x1i − x3i) = xl0 + xl21
/* y1i = x0i − x2i − (x1r − x3r) = xl1 − xl20
/* y2r = x0r + x2r − (x1r + x3r) = xh0 − xh20
/* y2i = x0i + x2i − (x1i + x3i
= xh1 − xh21
/* y3r = x0r − x2r − (x1i − x3i) = xl0 − xl21
/* y3i = x0i − x2i + (x1r − x3r) = xl1 + xl20
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
xh0 = x0r + x2r;
xh1 = x0i + x2i;
xh20 = x1r + x3r;
xh21 = x1i + x3i;
xl0 = x0r − x2r;
4-102
DSP_fft
xl1 = x0i − x2i;
xl20 = x1r − x3r;
xl21 = x1i − x3i;
xt0 = xh0 + xh20;
yt0 = xh1 + xh21;
xt1 = xl0 + xl21;
yt1 = xl1 − xl20;
xt2 = xh0 − xh20;
yt2 = xh1 − xh21;
xt3 = xl0 − xl21;
yt3 = xl1 + xl20;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Perform twiddle factor multiplies of three terms,top */
/* term does not have any multiplies. Note the twiddle */
/* factors for a normal FFT are C + j (−S). Since the
/* factors that are stored are C + j S, this is
/* corrected for in the multiplies.
/*
*/
*/
*/
*/
*/
/* Y1 = (xt1 + jyt1) (c + js) = (xc + ys) + (yc −xs)
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
y0r = xt0;
y0i = yt0;
y1r = (xt1 * w1c + yt1 * w1s) >> 15;
y1i = (yt1 * w1c − xt1 * w1s) >> 15;
y2r = (xt2 * w2c + yt2 * w2s) >> 15;
y2i = (yt2 * w2c − xt2 * w2s) >> 15;
y3r = (xt3 * w3c + yt3 * w3s) >> 15;
y3i = (yt3 * w3c − xt3 * w3s) >> 15;
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Store the final results back to the input array.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
x[2*(i+j+k
) + 0] = y0r; x[2*(i+j+k
) + 1] = y0i;
x[2*(i+j+k + s) + 0] = y1r; x[2*(i+j+k + s) + 1] = y1i;
x[2*(i+j+k + 2*s) + 0] = y2r; x[2*(i+j+k + 2*s) + 1] = y2i;
x[2*(i+j+k + 3*s) + 0] = y3r; x[2*(i+j+k + 3*s) + 1] = y3i;
}
}
}
C64x+ DSPLIB Reference
4-103
DSP_fft
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Offset to next subtable of twiddle factors. With each iteration */
/* of the above block, six twiddle factors get read, s times,
/* hence the offset into the twiddle factor array is advanced by */
/* this amount. */
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
t += 6 * s;
}
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Get the magnitude of ”n”, so we know how many digits to reverse. */
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
for (i = 31, m = 1; (n & (1 << i)) == 0; i−−, m++) ;
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Perform final stage with digit reversal.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
s = n >> 2;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* One of the nice features, of this last stage are that, no multiplies */
/* are required. In addition, the data always strides by a fixed amount */
/* namely 8 elements. Since the data is stored as interleaved pairs, of */
/* real and imaginary data, the first eight elements contain the data */
/* for the first four complex inputs. These are the inputs to the first */
/* radix4 butterfly.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
#ifndef NOASSUME
#pragma MUST_ITERATE(4,,4);
#endif
for (i = 0; i < n; i += 4)
{
short x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
short y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Read the four samples that are the input to this butterfly.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
4-104
DSP_fft
x0r = x[2*(i + 0) + 0];
x1r = x[2*(i + 1) + 0];
x2r = x[2*(i + 2) + 0];
x3r = x[2*(i + 3) + 0];
x0i = x[2*(i + 0) + 1];
x1i = x[2*(i + 1) + 1];
x2i = x[2*(i + 2) + 1];
x3i = x[2*(i + 3) + 1];
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Calculate the final FFT result from this butterfly. */
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
y0r = (x0r + x2r) + (x1r + x3r);
y0i = (x0i + x2i) + (x1i + x3i);
y1r = (x0r − x2r) + (x1i − x3i);
y1i = (x0i − x2i) − (x1r − x3r);
y2r = (x0r + x2r) − (x1r + x3r);
y2i = (x0i + x2i) − (x1i + x3i);
y3r = (x0r − x2r) − (x1i − x3i);
y3i = (x0i − x2i) + (x1r − x3r);
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Digit reverse our address to convert the digit−reversed input */
/* into a linearized output order. This actually results in a
/* digit−reversed store pattern since we’re loading linearly, but */
/* the end result is that the FFT bins are in linear order. */
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
DIG_REV(i, m, j); /* Note: Result is assigned to ’j’ by the macro. */
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
/* Store out the final FFT results.
*/
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− */
y[2*(j + 0) + 0] = y0r; y[2*(j + 0) + 1] = y0i;
y[2*(j + s) + 0] = y1r; y[2*(j + s) + 1] = y1i;
y[2*(j + 2*s) + 0] = y2r; y[2*(j + 2*s) + 1] = y2i;
y[2*(j + 3*s) + 0] = y3r; y[2*(j + 3*s) + 1] = y3i;
}
}
C64x+ DSPLIB Reference
4-105
DSP_fft
Special Requirements
- In-place computation is not allowed.
- nx must be a power of 4 and 4 ≤ nx ≤ 65536.
- Input x[ ] and output y[ ] are stored on double-word aligned boundaries.
- Input data x[ ] is stored in the order real0, img0, real1, img1, ...
- The FFT coefficients (twiddle factors) must be double-word aligned and
are generated using the program tw_fft16x16 provided in the directory
‘support\fft’.
Implementation Notes
- Bank Conflicts: No bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
- Loads input x[ ] and coefficient w[ ] as double words.
- Both loops j and i0 shown in the C code are placed in the inner loop of the
assembly code.
Benchmarks
Cycles
1.25 * nx * log (nx) – 0.5 * nx + 23 * log (nx) – 1
4
4
Codesize
984 bytes
4-106
DSP_fft16x16t
Complex Forward Mixed Radix 16- x 16-Bit FFT With Truncation
DSP_fft16x16t
Function
void DSP_fft16x16t(const short * restrict w, int nx, short * restrict x, short * re-
strict y)
Arguments
w[2*nx]
nx
Pointer to complex Q.15 FFT coefficients.
Length of FFT in complex samples. Must be power of 2 or 4
, and 16 ≤ nx ≤ 32768.
x[2*nx]
y[2*nx]
Pointer to complex 16-bit data input.
Pointer to complex 16-bit data output.
Description
Algorithm
This routine computes a complex forward mixed radix FFT with truncation and
digit reversal. Input data x[ ], output data y[ ], and coefficients w[ ] are 16-bit.
The output is returned in the separate array y[ ] in normal order. Each complex
value is stored with interleaved real and imaginary parts. The code uses a
special ordering of FFT coefficients (also called twiddle factors) and memory
accesses to improve performance in the presence of cache.
This is the C equivalent of the assembly code without restrictions. Note that
the assembly code is hand optimized and restrictions may apply.
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The following macro is used to obtain a digit reversed index, of a given */
/* number i, into j where the number of bits in ”i” is ”m”. For the natural */
/* form of C code, this is done by first interchanging every set of ”2 bit” */
/* pairs, followed by exchanging nibbles, followed by exchanging bytes, and */
/* finally halfwords. To give an example, consider the following number:
/*
*/
*/
/* N = FEDCBA9876543210, where each digit represents a bit, the following */
/* steps illustrate the changes as the exchanges are performed: */
/* M = DCFE98BA54761032 is the number after every ”2 bits” are exchanged. */
/* O = 98BADCFE10325476 is the number after every nibble is exchanged.
/* P = 1032547698BADCFE is the number after every byte is exchanged.
*/
*/
/* Since only 16 digits were considered this represents the digit reversed */
/* index. Since the numbers are represented as 32 bits, there is one more */
/* step typically of exchanging the half words as well.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
#if TMS320C6X
C64x+ DSPLIB Reference
4-107
DSP_fft16x16t
# define DIG_REV(i, m, j) ((j) = (_shfl(_rotl(_bitr(_deal(i)), 16)) >> (m)))
#else
# define DIG_REV(i, m, j)
\
\
\
\
\
\
\
\
do {
unsigned _ = (i);
_ = ((_ & 0x33333333) << 2) | ((_ & ~0x33333333) >> 2);
_ = ((_ & 0x0F0F0F0F) << 4) | ((_ & ~0x0F0F0F0F) >> 4);
_ = ((_ & 0x00FF00FF) << 8) | ((_ & ~0x00FF00FF) >> 8);
_ = ((_ & 0x0000FFFF) << 16) | ((_ & ~0x0000FFFF) >> 16);
(j) = _ >> (m);
} while (0)
#endif
void DSP_fft16x16t_cn(const short *restrict ptr_w, int npoints, short * ptr_x,
short * ptr_y)
{
int i, j, l1, l2, h2, predj, tw_offset, stride, fft_jmp;
short xt0_0, yt0_0, xt1_0, yt1_0, xt2_0, yt2_0;
short xt0_1, yt0_1, xt1_1, yt1_1, xt2_1, yt2_1;
short xh0_0, xh1_0, xh20_0, xh21_0, xl0_0, xl1_0, xl20_0, xl21_0;
short xh0_1, xh1_1, xh20_1, xh21_1, xl0_1, xl1_1, xl20_1, xl21_1;
short x_0, x_1, x_2, x_3, x_l1_0, x_l1_1, x_l1_2, x_l1_3, x_l2_0, x_l2_1;
short xh0_2, xh1_2, xl0_2, xl1_2, xh0_3, xh1_3, xl0_3, xl1_3;
short x_4, x_5, x_6, x_7, x_l2_2, x_l2_3, x_h2_0, x_h2_1, x_h2_2, x_h2_3;
short x_8, x_9, x_a, x_b, x_c, x_d, x_e, x_f;
short si10, si20, si30, co10, co20, co30;
short si11, si21, si31, co11, co21, co31;
short * x, * x2, * x0;
short * y0, * y1, * y2, *y3;
short n00, n10, n20, n30, n01, n11, n21, n31;
short n02, n12, n22, n32, n03, n13, n23, n33;
short y0r, y0i, y4r, y4i;
int n0, j0;
int radix, m;
int norm;
const short *w;
4-108
DSP_fft16x16t
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Determine the magnitude od the number of points to be transformed. */
/* Check whether we can use a radix4 decomposition or a mixed radix
/* transformation, by determining modulo 2.
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
for (i = 31, m = 1; (npoints & (1 << i)) == 0; i−−, m++) ;
radix
norm
= m & 1 ? 2 : 4;
= m − 2;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The stride is quartered with every iteration of the outer loop. It */
/* denotes the seperation between any two adjacent inputs to the butter */
/* −fly. This should start out at N/4, hence stride is initially set to */
/* N. For every stride, 6*stride twiddle factors are accessed. The
/* ”tw_offset” is the offset within the current twiddle factor sub−
*/
*/
/* table. This is set to zero, at the start of the code and is used to */
/* obtain the appropriate sub−table twiddle pointer by offsetting it
/* with the base pointer ”ptr_w”.
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
stride = npoints;
tw_offset = 0;
fft_jmp
= 6 * stride;
while (stride > radix)
{
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* At the start of every iteration of the outer loop, ”j” is set */
/* to zero, as ”w” is pointing to the correct location within the */
/* twiddle factor array. For every iteration of the inner loop
*/
*/
*/
*/
*/
*/
*/
/* 6 * stride twiddle factors are accessed. For eg,
/*
/* #Iteration of outer loop # twiddle factors
#times cycled
/* 1
6 N/4
1
4
/* 2
6 N/16
/* ...
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
= 0;
fft_jmp >>= 2;
j
C64x+ DSPLIB Reference
4-109
DSP_fft16x16t
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Set up offsets to access ”N/4”, ”N/2”, ”3N/4” complex point or */
/* ”N/2”, ”N”, ”3N/2” half word */
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
h2 = stride>>1;
l1 = stride;
l2 = stride + (stride >> 1);
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Reset ”x” to point to the start of the input data array.
/* ”tw_offset” starts off at 0, and increments by ”6 * stride”
/* The stride quarters with every iteration of the outer loop
*/
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x = ptr_x;
w = ptr_w + tw_offset;
tw_offset += fft_jmp;
stride >>= 2;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The following loop iterates through the different butterflies, */
/* within a given stage. Recall that there are logN to base 4
*/
/* stages. Certain butterflies share the twiddle factors. These */
/* are grouped together. On the very first stage there are no
/* butterflies that share the twiddle factor, all N/4 butter−
/* flies have different factors. On the next stage two sets of
/* N/8 butterflies share the same twiddle factor. Hence, after
/* half the butterflies are performed, j the index into the
*/
*/
*/
*/
*/
/* factor array resets to 0, and the twiddle factors are reused. */
/* When this happens, the data pointer ’x’ is incremented by the */
/* fft_jmp amount. In addition, the following code is unrolled to */
/* perform ”2” radix4 butterflies in parallel.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
for (i = 0; i < npoints; i += 8)
{
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Read the first 12 twiddle factors, six of which are used */
/* for one radix 4 butterfly and six of which are used for
/* next one.
*/
*/
4-110
DSP_fft16x16t
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
co10 = w[j+1];
co11 = w[j+3];
co20 = w[j+5];
co21 = w[j+7];
co30 = w[j+9];
si10 = w[j+0];
si11 = w[j+2];
si20 = w[j+4];
si21 = w[j+6];
si30 = w[j+8];
co31 = w[j+11]; si31 = w[j+10];
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Read in the first complex input for the butterflies.
/* 1st complex input to 1st butterfly: x[0] + jx[1]
/* 1st complex input to 2nd butterfly: x[2] + jx[3]
*/
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x_0 = x[0];
x_2 = x[2];
x_1 = x[1];
x_3 = x[3];
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Read in the complex inputs for the butterflies. Each of the*/
/* successive complex inputs of the butterfly are seperated */
/* by a fixed amount known as stride. The stride starts out */
/* at N/4, and quarters with every stage.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x_l1_0 = x[l1 ]; x_l1_1 = x[l1+1];
x_l1_2 = x[l1+2]; x_l1_3 = x[l1+3];
x_l2_0 = x[l2 ]; x_l2_1 = x[l2+1];
x_l2_2 = x[l2+2]; x_l2_3 = x[l2+3];
x_h2_0 = x[h2 ]; x_h2_1 = x[h2+1];
x_h2_2 = x[h2+2]; x_h2_3 = x[h2+3];
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Two butterflies are evaluated in parallel. The following */
/* results will be shown for one butterfly only, although
/* both are being evaluated in parallel.
/*
*/
*/
*/
*/
/* Perform DSP_radix2 style DIF butterflies.
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
xh0_0 = x_0
xh0_1 = x_2
xl0_0 = x_0
+ x_l1_0;
+ x_l1_2;
− x_l1_0;
xh1_0 = x_1
xh1_1 = x_3
xl1_0 = x_1
+ x_l1_1;
+ x_l1_3;
− x_l1_1;
C64x+ DSPLIB Reference
4-111
DSP_fft16x16t
xl0_1 = x_2
− x_l1_2;
xl1_1 = x_3
− x_l1_3;
xh20_0 = x_h2_0 + x_l2_0;
xh20_1 = x_h2_2 + x_l2_2;
xl20_0 = x_h2_0 − x_l2_0;
xl20_1 = x_h2_2 − x_l2_2;
xh21_0 = x_h2_1 + x_l2_1;
xh21_1 = x_h2_3 + x_l2_3;
xl21_0 = x_h2_1 − x_l2_1;
xl21_1 = x_h2_3 − x_l2_3;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Derive output pointers using the input pointer ”x” */
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x0 = x;
x2 = x0;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* When the twiddle factors are not to be reused, j is
*/
/* incremented by 12, to reflect the fact that 12 half words */
/* are consumed in every iteration. The input data pointer */
/* increments by 4. Note that within a stage, the stride
/* does not change and hence the offsets for the other three */
/* legs, 0, h2, l1, l2. */
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
j += 12;
x += 4;
predj = (j − fft_jmp);
if (!predj) x += fft_jmp;
if (!predj) j = 0;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* These four partial results can be re−written to show
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
/* the underlying DIF structure similar to DSP_radix2 as
/* follows:
/*
/* X(4k) = (x(n)+x(n + N/2)) + (x(n+N/4)+ x(n + 3N/4))
/* X(4k+1)= (x(n)−x(n + N/2)) −j(x(n+N/4) − x(n + 3N/4))
/* x(4k+2)= (x(n)+x(n + N/2)) − (x(n+N/4)+ x(n + 3N/4))
/* X(4k+3)= (x(n)−x(n + N/2)) +j(x(n+N/4) − x(n + 3N/4))
/*
/* which leads to the real and imaginary values as foll:
/*
/* y0r = x0r + x2r + x1r + x3r
= xh0 + xh20
4-112
DSP_fft16x16t
/* y0i = x0i + x2i + x1i + x3i
= xh1 + xh21
*/
*/
*/
*/
*/
*/
*/
/* y1r = x0r − x2r + (x1i − x3i) = xl0 + xl21
/* y1i = x0i − x2i − (x1r − x3r) = xl1 − xl20
/* y2r = x0r + x2r − (x1r + x3r) = xh0 − xh20
/* y2i = x0i + x2i − (x1i + x3i
= xh1 − xh21
/* y3r = x0r − x2r − (x1i − x3i) = xl0 − xl21
/* y3i = x0i − x2i + (x1r − x3r) = xl1 + xl20
/* −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
y0r = xh0_0 + xh20_0; y0i = xh1_0 + xh21_0;
y4r = xh0_1 + xh20_1; y4i = xh1_1 + xh21_1;
xt0_0 = xh0_0 − xh20_0; yt0_0 = xh1_0 − xh21_0;
xt0_1 = xh0_1 − xh20_1; yt0_1 = xh1_1 − xh21_1;
xt1_0 = xl0_0 + xl21_0; yt2_0 = xl1_0 + xl20_0;
xt2_0 = xl0_0 − xl21_0; yt1_0 = xl1_0 − xl20_0;
xt1_1 = xl0_1 + xl21_1; yt2_1 = xl1_1 + xl20_1;
xt2_1 = xl0_1 − xl21_1; yt1_1 = xl1_1 − xl20_1;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Store out first output, of the four outputs of a radix4 */
/* butterfly. Since two such radix4 butterflies are per− */
/* formed in parallel, there are 2 such 1st outputs.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x2[0] = y0r;
x2[2] = y4r;
x2[1] = y0i;
x2[3] = y4i;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Perform twiddle factor multiplies of three terms,top
/* term does not have any multiplies. Note the twiddle
/* factors for a normal FFT are C + j (−S). Since the
/* factors that are stored are C + j S, this is
/* corrected for in the multiplies.
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
/*
/* Y1 = (xt1 + jyt1) (c + js) = (xc + ys) + (yc −xs)
/* Perform the multiplies using 16 by 32 multiply macro
/* defined. This treats the twiddle factor as 16 bits
/* and incoming data as 32 bits.
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x2[h2 ] = (si10 * yt1_0 + co10 * xt1_0) >> 15;
C64x+ DSPLIB Reference
4-113
DSP_fft16x16t
x2[h2+1] = (co10 * yt1_0 − si10 * xt1_0) >> 15;
x2[h2+2] = (si11 * yt1_1 + co11 * xt1_1) >> 15;
x2[h2+3] = (co11 * yt1_1 − si11 * xt1_1) >> 15;
x2[l1 ] = (si20 * yt0_0 + co20 * xt0_0) >> 15;
x2[l1+1] = (co20 * yt0_0 − si20 * xt0_0) >> 15;
x2[l1+2] = (si21 * yt0_1 + co21 * xt0_1) >> 15;
x2[l1+3] = (co21 * yt0_1 − si21 * xt0_1) >> 15;
x2[l2 ] = (si30 * yt2_0 + co30 * xt2_0) >> 15;
x2[l2+1] = (co30 * yt2_0 − si30 * xt2_0) >> 15;
x2[l2+2] = (si31 * yt2_1 + co31 * xt2_1) >> 15;
x2[l2+3] = (co31 * yt2_1 − si31 * xt2_1) >> 15;
}
}
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The following code performs either a standard radix4 pass or a */
/* DSP_radix2 pass. Two pointers are used to access the input data.*/
/* The input data is read ”N/4” complex samples apart or ”N/2”
/* words apart using pointers ”x0” and ”x2”. This produces out−
/* puts that are 0, N/4, N/2, 3N/4 for a radix4 FFT, and 0, N/8
/* N/2, 3N/8 for radix 2.
*/
*/
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
y0 = ptr_y;
y2 = ptr_y + (int) npoints;
x0 = ptr_x;
x2 = ptr_x + (int) (npoints >> 1);
if (radix == 2)
{
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The pointers are set at the following locations which are half */
/* the offsets of a radix4 FFT.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
y1 = y0 + (int) (npoints >> 2);
y3 = y2 + (int) (npoints >> 2);
l1 = norm + 1;
j0 = 8;
n0 = npoints>>1;
4-114
DSP_fft16x16t
}
else
{
y1 = y0 + (int) (npoints >> 1);
y3 = y2 + (int) (npoints >> 1);
l1 = norm + 2;
j0 = 4;
n0 = npoints >> 2;
}
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* The following code reads data indentically for either a radix 4
/* or a radix 2 style decomposition. It writes out at different
/* locations though. It checks if either half the points, or a
/* quarter of the complex points have been exhausted to jump to
/* pervent double reversal.
*/
*/
*/
*/
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
j = 0;
for (i = 0; i < npoints; i += 8)
{
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Digit reverse the index starting from 0. The increment to ”j” */
/* is either by 4, or 8.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
DIG_REV(j, l1, h2);
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Read in the input data, from the first eight locations. These */
/* are transformed either as a radix4 or as a radix 2.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x_0 = x0[0];
x_1 = x0[1];
x_3 = x0[3];
x_5 = x0[5];
x_7 = x0[7];
x_2 = x0[2];
x_4 = x0[4];
x_6 = x0[6];
x0 += 8;
xh0_0 = x_0 + x_4;
xl0_0 = x_0 − x_4;
xh0_1 = x_2 + x_6;
xh1_0 = x_1 + x_5;
xl1_0 = x_1 − x_5;
xh1_1 = x_3 + x_7;
C64x+ DSPLIB Reference
4-115
DSP_fft16x16t
xl0_1 = x_2 − x_6;
xl1_1 = x_3 − x_7;
n00 = xh0_0 + xh0_1; n01 = xh1_0 + xh1_1;
n10 = xl0_0 + xl1_1; n11 = xl1_0 − xl0_1;
n20 = xh0_0 − xh0_1; n21 = xh1_0 − xh1_1;
n30 = xl0_0 − xl1_1; n31 = xl1_0 + xl0_1;
if (radix == 2)
{
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Perform DSP_radix2 style decomposition.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
n00 = x_0 + x_2;
n20 = x_0 − x_2;
n10 = x_4 + x_6;
n30 = x_4 − x_6;
n01 = x_1 + x_3;
n21 = x_1 − x_3;
n11 = x_5 + x_7;
n31 = x_5 − x_7;
}
y0[2*h2] = n00;
y1[2*h2] = n10;
y2[2*h2] = n20;
y3[2*h2] = n30;
y0[2*h2 + 1] = n01;
y1[2*h2 + 1] = n11;
y2[2*h2 + 1] = n21;
y3[2*h2 + 1] = n31;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Read in the next eight inputs, and perform radix4 or DSP_radix2*/
/* decomposition.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
x_8 = x2[0];
x_9 = x2[1];
x_b = x2[3];
x_d = x2[5];
x_f = x2[7];
x_a = x2[2];
x_c = x2[4];
x_e = x2[6];
x2 += 8;
xh0_2 = x_8 + x_c;
xl0_2 = x_8 − x_c;
xh0_3 = x_a + x_e;
xl0_3 = x_a − x_e;
n02 = xh0_2 + xh0_3;
n12 = xl0_2 + xl1_3;
n22 = xh0_2 − xh0_3;
n32 = xl0_2 − xl1_3;
xh1_2 = x_9 + x_d;
xl1_2 = x_9 − x_d;
xh1_3 = x_b + x_f;
xl1_3 = x_b − x_f;
n03 = xh1_2 + xh1_3;
n13 = xl1_2 − xl0_3;
n23 = xh1_2 − xh1_3;
n33 = xl1_2 + xl0_3;
4-116
DSP_fft16x16t
if (radix == 2)
{
n02 = x_8 + x_a;
n22 = x_8 − x_a;
n12 = x_c + x_e;
n32 = x_c − x_e;
}
n03 = x_9 + x_b;
n23 = x_9 − x_b;
n13 = x_d + x_f;
n33 = x_d − x_f;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Points that are read from succesive locations map to y, y[N/4] */
/* y[N/2], y[3N/4] in a radix4 scheme, y, y[N/8], y[N/2],y[5N/8] */
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
y0[2*h2+2] = n02;
y1[2*h2+2] = n12;
y2[2*h2+2] = n22;
y3[2*h2+2] = n32;
y0[2*h2+3] = n03;
y1[2*h2+3] = n13;
y2[2*h2+3] = n23;
y3[2*h2+3] = n33;
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
/* Increment ”j” by ”j0”. If j equals n0, then increment both ”x0” */
/* and ”x2” so that double inversion is avoided.
*/
/*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/
j += j0;
if (j == n0)
{
j += n0;
x0 += (int) npoints>>1;
x2 += (int) npoints>>1;
}
}
}
C64x+ DSPLIB Reference
4-117
DSP_fft16x16t
Special Requirements
- In-place computation is not allowed.
- The size of the FFT, nx, must be power of 2 or 4, and 16 ≤ nx ≤ 32768.
- The arrays for the complex input data x[ ], complex output data y[ ], and
twiddle factors w[ ] must be double-word aligned.
- The input and output data are complex, with the real/imaginary
components stored in adjacent locations in the array. The real
components are stored at even array indices, and the imaginary
components are stored at odd array indices. All data are in short precision
or Q.15 format.
- The FFT coefficients (twiddle factors) are generated using the program
tw_fft16x16 provided in the directory ‘support\fft’. The scale factor must be
32767.5. No scaling is done with the function; thus, the input data must be
log2(nx)
scaled by 2
to completely prevent overflow.
Implementation Notes
- Bank Conflicts: nx/8 bank conflicts occur.
- Interruptibility: The code is interrupt-tolerant but not interruptible.
The routine uses log (nx) − 1 stages of radix-4 transform and performs either
4
a radix-2 or radix-4 transform on the last stage depending on nx. If nx is a
power of 4, then this last stage is also a radix-4 transform, otherwise it is a
radix-2 transform. The conventional Cooley Tukey FFT is written using three
loops. The outermost loop “k” cycles through the stages. There are log N to
the base 4 stages in all. The loop “j” cycles through the groups of butterflies
with different twiddle factors, and loop “i” reuses the twiddle factors for the
different butterflies within a stage. Note the following:
Butterflies With Common
Twiddle Factors
Stage
Groups
Groups*Butterflies
1
N/4
1
4
N/4
2
..
N/16
N/4
..
..
1
..
logN
N/4
N/4
4-118
DSP_fft16x16t
The following statements can be made based on above observations:
1) Inner loop “i0” iterates a variable number of times. In particular, the number
of iterations quadruples every time from 1..N/4. Hence, software pipelining
a loop that iterates a variable number of times is not profitable.
2) Outer loop “j” iterates a variable number of times as well. However, the
number of iterations is quartered every time from N/4 ..1. Hence, the
behavior in (a) and (b) are exactly opposite to each other.
3) If the two loops “i” and “j” are coalesced together, then they will iterate for
a fixed number of times, namely N/4. This allows us to combine the “i” and
“j” loops into one loop. Optimized implementations will make use of this
fact.
In addition, the Cooley Tukey FFT accesses three twiddle factors per iteration
of the inner loop, as the butterflies that re-use twiddle factors are lumped
together. This leads to accessing the twiddle factor array at three points each
separated by “ie”. Note that “ie” is initially 1, and is quadrupled with every
iteration. Therefore, these three twiddle factors are not even contiguous in the
array.
To vectorize the FFT, it is desirable to access twiddle factor array using double
word wide loads and fetch the twiddle factors needed. To do this, a modified
twiddle factor array is created, in which the factors WN/4, WN/2, W3N/4 are
arranged to be contiguous. This eliminates the separation between twiddle
factors within a butterfly. However, this implies that we maintain a redundant
version of the twiddle factor array as the loop is traversed from one stage to
another. Hence, the size of the twiddle factor array increases as compared to
the normal Cooley Tukey FFT. The modified twiddle factor array is of size “2
* N”, where the conventional Cooley Tukey FFT is of size “3N/4”, where N is
the number of complex points to be transformed. The routine that generates
the modified twiddle factor array was presented earlier. With the above
transformation of the FFT, both the input data and the twiddle factor array can
be accessed using double-word wide loads to enable packed data processing.
The final stage is optimized to remove the multiplication as w0 = 1. This stage
also performs digit reversal on the data, so the final output is in natural order.
In addition, if the number of points to be transformed is a power of 2, the final
stage applies a DSP_radix2 pass instead of a radix 4. In any case, the outputs
are returned in normal order.
The code shown here performs the bulk of the computation in place. However,
because digit-reversal cannot be performed in-place, the final result is written
to a separate array, y[].
C64x+ DSPLIB Reference
4-119
DSP_fft16x16t
There is one slight break in the flow of packed processing. The real part of the
complex number is in the lower half, and the imaginary part is in the upper half.
The flow breaks for “xl0” and “xl1” because in this case the real part needs to
be combined with the imaginary part because of the multiplication by “j”. This
requires a packed quantity like “xl21xl20” to be rotated as “xl20xl21” so that
it can be combined using ADD2s and SUB2s. Hence, the natural version of C
code shown below is transformed using packed data processing as shown:
xl0 = x[2 * i0
xl1 = x[2 * i0 + 1] − x[2 * i2 + 1];
xl20 = x[2 * i1 ] − x[2 * i3 ];
] − x[2 * i2
];
xl21 = x[2 * i1 + 1] − x[2 * i3 + 1];
xt1 = xl0 + xl21;
yt2 = xl1 + xl20;
xt2 = xl0 − xl21;
yt1 = xl1 − xl20;
xl1_xl0 = _sub2(x21_x20, x21_x20)
xl21_xl20 = _sub2(x32_x22, x23_x22)
xl20_xl21 = _rotl(xl21_xl20, 16)
yt2_xt1 = _add2(xl1_xl0, xl20_xl21)
yt1_xt2 = _sub2(xl1_xl0, xl20_xl21)
Also notice that xt1, yt1 end up on separate words, these need to be packed
together to take advantage of the packed twiddle factors that have been
loaded. To achiev this, they are re-aligned as follows:
yt1_xt1 = _packhl2(yt1_xt2, yt2_xt1)
yt2_xt2 = _packhl2(yt2_xt1, yt1_xt2)
The packed words “yt1_xt1” allow the loaded “sc” twiddle factor to be used for
the complex multiplies. The real part of the complex multiply is implemented
using DOTP2. The imaginary part of the complex multiply is implemented
using DOTPN2 after the twiddle factors are swizzled within the half word.
(X + jY) ( C + j S) = (XC + YS) + j (YC − XS).
The actual twiddle factors for the FFT are cosine, − sine. The twiddle factors
stored in the table are cosine and sine, hence the sign of the ”sine” term is
comprehended during multiplication as shown above.
Benchmarks
Cycles
(10 * nx/8 + 19) * ceil[log (nx) − 1] + (nx/8 + 2) * 7 + 28 + BC
4
where BC = N/8, the number of bank conflicts.
Codesize 1004 bytes
4-120
Appendix A
Performance/Fractional Q Formats
This appendix describes performance considerations related to the C64x+
DSPLIB and provides information about the Q format used by DSPLIB
functions.
Topic
Page
A.1 Performance Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2
A.2 Fractional Q Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
A-1
Performance Considerations
A.1 Performance Considerations
The ceil( ) is used in some benchmark formulas to accurately describe the
number of cycles. It returns a number rounded up, away from zero, to the
nearest integer. For example, ceil(1.1) returns 2.
Although DSPLIB can be used as a first estimation of processor performance
for a specific function, you should be aware that the generic nature of DSPLIB
might add extra cycles not required for customer specific usage.
Benchmark cycles presented assume best case conditions, typically
assuming all code and data are placed in L1 memory. Any extra cycles due to
placement of code or data in L2/external memory or cache-associated effects
(cache-hits or misses) are not considered when computing the cycle counts.
You should also be aware that execution speed in a system is dependent on
where the different sections of program and data are located in memory. You
should account for such differences when trying to explain why a routine is
taking more time than the reported DSPLIB benchmarks.
For more information on additional stall cycles due to memory hierarchy, see
the Signal Processing Examples Using TMS320C64x Digital Signal
Processing Library(SPRA884). The TMS320C6000 DSP Cache User’s Guide
(SPRU656A) presents how to optimize algorithms and function calls for better
cache performance.
A-2
Fractional Q Formats
A.2 Fractional Q Formats
Unless specifically noted, DSPLIB functions use Q15 format, or to be more
exact, Q0.15. In a Qm.n format, there are m bits used to represent the two’s
complement integer portion of the number, and n bits used to represent the
two’s complement fractional portion. m+n+1 bits are needed to store a general
Qm.n number. The extra bit is needed to store the sign of the number in the
most-significant bit position. The representable integer range is specified by
m
m
−n
(−2 ,2 ) and the finest fractional resolution is 2 .
For example, the most commonly used format is Q.15. Q.15 means that a
16-bit word is used to express a signed number between positive and negative
one. The most-significant binary digit is interpreted as the sign bit in any Q
format number. Thus, in Q.15 format, the decimal point is placed immediately
to the right of the sign bit. The fractional portion to the right of the sign bit is
stored in regular two’s complement format.
A.2.1 Q3.12 Format
Q.3.12 format places the sign bit after the fourth binary digit from the right, and
the next 12 bits contain the two’s complement fractional component. The
approximate allowable range of numbers in Q.3.12 representation is (−8,8)
−12
−4
and the finest fractional resolution is 2
= 2.441 × 10 .
Table A−1. Q3.12 Bit Fields
Bit
15
S
14
I3
13
I2
12
I1
11
Q11
10
9
…
…
0
Value
Q10
Q9
Q0
A.2.2 Q.15 Format
Q.15 format places the sign bit at the leftmost binary digit, and the next 15
leftmost bits contain the two’s complement fractional component. The
approximate allowable range of numbers in Q.15 representation is (−1,1) and
−15
−5
the finest fractional resolution is 2
= 3.05 × 10 .
Table A−2. Q.15 Bit Fields
Bit
Value
15
S
14
13
12
Q12
11
10
9
…
…
0
Q14
Q13
Q11
Q10
Q9
Q0
Performance/Fractional Q Formats
A-3
Fractional Q Formats
A.2.3 Q.31 Format
Q.31 format spans two 16-bit memory words. The 16-bit word stored in the
lower memory location contains the 16 least significant bits, and the higher
memory location contains the most significant 15 bits and the sign bit. The
approximate allowable range of numbers in Q.31 representation is (−1,1) and
−31
−10
the finest fractional resolution is 2
= 4.66 × 10
.
Table A−3. Q.31 Low Memory Location Bit Fields
Bit
15
14
13
12
…
3
2
1
0
Value
Q15
Q14
Q13
Q12
…
Q3
Q2
Q1
Q0
Table A−4. Q.31 High Memory Location Bit Fields
Bit
15
S
14
13
12
…
…
3
2
1
0
Value
Q30
Q29
Q28
Q19
Q18
Q17
Q16
A-4
Appendix B
Software Updates and Customer Support
This appendix provides information about software updates and customer
support.
Topic
Page
B.1 DSPLIB Software Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2
B.2 DSPLIB Customer Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2
B-1
DSPLIB Software Updates / DSPLIB Customer Support
B.1 DSPLIB Software Updates
C64x DSPLIB software updates may be periodically released incorporating
product enhancements and fixes as they become available. You should read
the README.TXT available in the root directory of every release.
B.2 DSPLIB Customer Support
If you have questions or want to report problems or suggestions regarding the
B-2
Appendix C
Glossary
A
address: The location of program code or data stored; an individually
accessible memory location.
A-law companding: See compress and expand (compand).
API: See application programming interface.
application programming interface (API): Used for proprietary
application programs to interact with communications software or to
conform to protocols from another vendor’s product.
assembler: A software program that creates a machine language program
from a source file that contains assembly language instructions,
directives, and macros. The assembler substitutes absolute operation
codes for symbolic operation codes and absolute or relocatable
addresses for symbolic addresses.
assert: To make a digital logic device pin active. If the pin is active low, then
a low voltage on the pin asserts it. If the pin is active high, then a high
voltage asserts it.
B
bit: A binary digit, either a 0 or 1.
big endian: An addressing protocol in which bytes are numbered from left
to right within a word. More significant bytes in a word have lower
numbered addresses. Endian ordering is specific to hardware and is
determined at reset. See also little endian.
block: The three least significant bits of the program address. These
correspond to the address within a fetch packet of the first instruction
being addressed.
C-1
Glossary
board support library (BSL): The BSL is a set of application programming
interfaces (APIs) consisting of target side DSP code used to configure
and control board level peripherals.
boot: The process of loading a program into program memory.
boot mode: The method of loading a program into program memory. The
C6x DSP supports booting from external ROM or the host port interface
(HPI).
BSL: See board support library.
byte: A sequence of eight adjacent bits operated upon as a unit.
C
cache: A fast storage buffer in the central processing unit of a computer.
cache controller: System component that coordinates program accesses
between CPU program fetch mechanism, cache, and external memory.
CCS: Code Composer Studio.
central processing unit (CPU): The portion of the processor involved in
arithmetic, shifting, and Boolean logic operations, as well as the
generation of data- and program-memory addresses. The CPU includes
the central arithmetic logic unit (CALU), the multiplier, and the auxiliary
register arithmetic unit (ARAU).
chip support library (CSL): The CSL is a set of application programming
interfaces (APIs) consisting of target side DSP code used to configure
and control all on-chip peripherals.
clock cycle: A periodic or sequence of events based on the input from the
external clock.
clock modes: Options used by the clock generator to change the internal
CPU clock frequency to a fraction or multiple of the frequency of the input
clock signal.
code: A set of instructions written to perform a task; a computer program or
part of a program.
coder-decoder or compression/decompression (codec): A device that
codes in one direction of transmission and decodes in another direction
of transmission.
compiler: A computer program that translates programs in a high-level
language into their assembly-language equivalents.
C-2
Glossary
compress and expand (compand): A quantization scheme for audio
signals in which the input signal is compressed and then, after
processing, is reconstructed at the output by expansion. There are two
distinct companding schemes: A-law (used in Europe) and μ-law (used
in the United States).
control register: A register that contains bit fields that define the way a
device operates.
control register file: A set of control registers.
CSL: See chip support library.
D
device ID: Configuration register that identifies each peripheral component
interconnect (PCI).
digital signal processor (DSP): A semiconductor that turns analog
signals—such as sound or light—into digital signals, which are discrete
or discontinuous electrical impulses, so that they can be manipulated.
direct memory access (DMA): A mechanism whereby a device other than
the host processor contends for and receives mastery of the memory bus
so that data transfers can take place independent of the host.
DMA : See direct memory access.
DMA source: The module where the DMA data originates. DMA data is read
from the DMA source.
DMA transfer: The process of transferring data from one part of memory to
another. Each DMA transfer consists of a read bus cycle (source to DMA
holding register) and a write bus cycle (DMA holding register to
destination).
DSP_autocor: Autocorrelation.
DSP_bexp: Block exponent implementation.
DSP_bitrev_cplx: Complex bit reverse.
DSP_blk_eswap16: Endian-swap a block of 16-bit values.
DSP_blk_eswap32: Endian-swap a block of 32-bit values.
DSP_blk_eswap64: Endian-swap a block of 64-bit values.
Glossary
C-3
Glossary
DSP_blk_move: Block move.
DSP_dotp_sqr: Vector dot product and square.
DSP_dotprod: Vector dot product.
DSP_fft: Complex forward FFT with digital reversal.
DSP_fft16x16r: Complex forward mixed radix 16- x 16-bit FFT with
rounding.
DSP_fft16x16t: Complex forward mixed radix 16- x 16-bit FFT with
truncation.
DSP_fft16x32: Complex forward mixed radix 16- x 32-bit FFT with rounding.
DSP_fft32x32: Complex forward mixed radix 32- x 32-bit FFT with rounding.
DSP_fft32x32s: Complex forward mixed radix 32- x 32-bit FFT with scaling.
DSP_fir_cplx: Complex FIR filter (radix 2).
DSP_fir_gen: FIR filter (general purpose).
DSP_firlms2: LMS FIR (radix 2).
DSP_fir_r4: FIR filter (radix 4).
DSP_fir_r8: FIR filter (radix 8).
DSP_fir_sym: Symmetric FIR filter (radix 8).
DSP_fltoq15: Float to Q15 conversion.
DSP_ifft16x32: Complex inverse mixed radix 16- x 32-bit FFT with
rounding.
DSP_ifft32x32: Complex inverse mixed radix 32- x 32-bit FFT with
rounding.
DSP_iir: IIR with 5 coefficients per biquad.
DSP_mat_mul: Matrix multiplication.
DSP_mat_trans: Matrix transpose.
DSP_maxidx: Index of the maximum element of a vector.
DSP_maxval: Maximum value of a vector.
DSP_minerror: Minimum energy error search.
C-4
Glossary
DSP_minval: Minimum value of a vector.
DSP_mul32: 32-bit vector multiply.
DSP_neg32: 32-bit vector negate.
DSP_q15tofl: Q15 to float conversion.
DSP_radix2: Complex forward FFT (radix 2).
DSP_recip16: 16-bit reciprocal.
DSP_r4fft: Complex forward FFT (radix 4).
DSP_vecsumsq: Sum of squares.
DSP_w_vec: Weighted vector sum.
E
F
evaluation module (EVM): Board and software tools that allow the user to
evaluate a specific device.
external interrupt: A hardware interrupt triggered by a specific value on a
pin.
external memory interface (EMIF): Microprocessor hardware that is used
to read to and write from off-chip memory.
fast Fourier transform (FFT): An efficient method of computing the discrete
Fourier transform algorithm, which transforms functions between the
time domain and the frequency domain.
fetch packet: A contiguous 8-word series of instructions fetched by the CPU
and aligned on an 8-word boundary.
FFT: See fast fourier transform.
flag: A binary status indicator whose state indicates whether a particular
condition has occurred or is in effect.
frame: An 8-word space in the cache RAMs. Each fetch packet in the cache
resides in only one frame. A cache update loads a frame with the
requested fetch packet. The cache contains 512 frames.
G
global interrupt enable bit (GIE): A bit in the control status register (CSR)
that is used to enable or disable maskable interrupts.
Glossary
C-5
Glossary
H
HAL: Hardware abstraction layer of the CSL. The HAL underlies the service
layer and provides it a set of macros and constants for manipulating the
peripheral registers at the lowest level. It is a low-level symbolic interface
into the hardware providing symbols that describe peripheral
registers/bitfields, and macros for manipulating them.
host: A device to which other devices (peripherals) are connected and that
generally controls those devices.
host port interface (HPI): A parallel interface that the CPU uses to
communicate with a host processor.
HPI: See host port interface; see also HPI module.
I
index: A relative offset in the program address that specifies which frame is
used out of the 512 frames in the cache into which the current access is
mapped.
indirect addressing: An addressing mode in which an address points to
another pointer rather than to the actual data; this mode is prohibited in
RISC architecture.
instruction fetch packet: A group of up to eight instructions held in memory
for execution by the CPU.
internal interrupt: A hardware interrupt caused by an on-chip peripheral.
interrupt: A signal sent by hardware or software to a processor requesting
attention. An interrupt tells the processor to suspend its current
operation, save the current task status, and perform a particular set of
instructions. Interrupts communicate with the operating system and
prioritize tasks to be performed.
interrupt service fetch packet (ISFP): A fetch packet used to service
interrupts. If eight instructions are insufficient, you must branch out of this
block for additional interrupt service. If the delay slots of the branch do
not reside within the ISFP, execution continues from execute packets in
the next fetch packet (the next ISFP).
interrupt service routine (ISR): A module of code that is executed in
response to a hardware or software interrupt.
C-6
Glossary
interrupt service table (IST) A table containing a corresponding entry for
each of the 16 physical interrupts. Each entry is a single-fetch packet and
has a label associated with it.
Internal peripherals: Devices connected to and controlled by a host device.
The C6x internal peripherals include the direct memory access (DMA)
controller, multichannel buffered serial ports (McBSPs), host port
interface (HPI), external memory-interface (EMIF), and runtime support
timers.
IST: See interrupt service table.
L
least significant bit (LSB): The lowest-order bit in a word.
linker: A software tool that combines object files to form an object module,
which can be loaded into memory and executed.
little endian: An addressing protocol in which bytes are numbered from right
to left within a word. More significant bytes in a word have
higher-numbered addresses. Endian ordering is specific to hardware
and is determined at reset. See also big endian.
M
maskable interrupt: A hardware interrupt that can be enabled or disabled
through software.
memory map: A graphical representation of a computer system’s memory,
showing the locations of program space, data space, reserved space,
and other memory-resident elements.
memory-mapped register: An on-chip register mapped to an address in
memory. Some memory-mapped registers are mapped to data memory,
and some are mapped to input/output memory.
most significant bit (MSB): The highest order bit in a word.
m-law companding: See compress and expand (compand).
multichannel buffered serial port (McBSP): An on-chip full-duplex circuit
that provides direct serial communication through several channels to
external serial devices.
multiplexer: A device for selecting one of several available signals.
Glossary
C-7
Glossary
N
nonmaskable interrupt (NMI): An interrupt that can be neither masked nor
disabled.
O
P
object file: A file that has been assembled or linked and contains machine
language object code.
off chip: A state of being external to a device.
on chip: A state of being internal to a device.
peripheral: A device connected to and usually controlled by a host device.
program cache: A fast memory cache for storing program instructions
allowing for quick execution.
program memory: Memory accessed through the C6x’s program fetch
interface.
PWR: Power; see PWR module.
PWR module: PWR is an API module that is used to configure the
power-down control registers, if applicable, and to invoke various
power-down modes.
R
random-access memory (RAM): A type of memory device in which the
individual locations can be accessed in any order.
register: A small area of high speed memory located within a processor or
electronic device that is used for temporarily storing data or instructions.
Each register is given a name, contains a few bytes of information, and
is referenced by programs.
reduced-instruction-set computer (RISC): A computer whose instruction
set and related decode mechanism are much simpler than those of
microprogrammed complex instruction set computers. The result is a
higher instruction throughput and a faster real-time interrupt service
response from a smaller, cost-effective chip.
C-8
Glossary
reset: A means of bringing the CPU to a known state by setting the registers
and control bits to predetermined values and signaling execution to start
at a specified address.
RTOS Real-time operating system.
S
service layer: The top layer of the 2-layer chip support library architecture
providing high-level APIs into the CSL and BSL. The service layer is
where the actual APIs are defined and is the interface layer.
synchronous-burst static random-access memory (SBSRAM): RAM
whose contents do not have to be refreshed periodically. Transfer of data
is at a fixed rate relative to the clock speed of the device, but the speed
is increased.
synchronous dynamic random-access memory (SDRAM): RAM whose
contents are refreshed periodically so the data is not lost. Transfer of
data is at a fixed rate relative to the clock speed of the device.
syntax: The grammatical and structural rules of a language. All higher-level
programming languages possess a formal syntax.
system software: The blanketing term used to denote collectively the chip
support libraries and board support libraries.
T
tag: The 18 most significant bits of the program address. This value
corresponds to the physical address of the fetch packet that is in that
frame.
timer: A programmable peripheral used to generate pulses or to time
events.
TIMER module: TIMER is an API module used for configuring the timer
registers.
W
word: A multiple of eight bits that is operated upon as a unit. For the C6x,
a word is 32 bits in length.
Glossary
C-9
C-10
Index
compiler, defined C-2
A
compress and expand (compand), defined C-3
control register, defined C-3
adaptive filtering functions 3-4
DSPLIB reference 4-2
control register file, defined C-3
address, defined C-1
correlation functions 3-4
DSPLIB reference 4-4
A-law companding, defined C-1
API, defined C-1
CSL, defined C-3
customer support B-2
application programming interface, defined C-1
argument conventions 3-2
arguments, DSPLIB 2-3
assembler, defined C-1
D
data types, DSPLIB, table 2-3
assert, defined C-1
device ID, defined C-3
digital signal processor (DSP), defined C-3
B
direct memory access (DMA)
defined C-3
big endian, defined C-1
source, defined C-3
transfer, defined C-3
bit, defined C-1
block, defined C-1
DMA, defined C-3
board support library, defined C-2
boot, defined C-2
DSP_autocor
defined C-3
boot mode, defined C-2
BSL, defined C-2
DSPLIB reference 4-4, 4-6
DSP_bexp
defined C-3
byte, defined C-2
DSPLIB reference 4-76
DSP_bitrev_cplx
defined C-3
C
DSPLIB reference 4-90
cache, defined C-2
DSP_blk_eswap16, defined C-3
DSP_blk_eswap32, defined C-3
DSP_blk_eswap64, defined C-3
cache controller, defined C-2
CCS, defined C-2
central processing unit (CPU), defined C-2
chip support library, defined C-2
clock cycle, defined C-2
clock modes, defined C-2
code, defined C-2
DSP_blk_move
defined C-4
DSPLIB reference 4-78, 4-80, 4-82, 4-84
DSP_dotp_sqr
defined C-4
coder-decoder, defined C-2
DSPLIB reference 4-58
Index-1
Index
DSP_dotprod
DSP_ifft32x32
defined C-4
defined C-4
DSPLIB reference 4-60
DSPLIB reference 4-36
DSP_iir
DSP_fft
defined C-4
DSPLIB reference 4-54
defined C-4
DSPLIB reference 4-98
DSP_iirlat, DSPLIB reference 4-56
DSP_lat_fwd, DSPLIB reference 4-56
DSP_fft16x16r
defined C-4
DSPLIB reference 4-14
DSP_mat_trans
defined C-4
DSPLIB reference 4-75
DSP_fft16x16t
defined C-4
DSP_maxidx
DSPLIB reference 4-8, 4-11, 4-107
defined C-4
DSPLIB reference 4-63
DSP_fft16x32
defined C-4
DSPLIB reference 4-24
DSP_maxval
defined C-4
DSPLIB reference 4-62
DSP_fft32x32
defined C-4
DSPLIB reference 4-26
DSP_minerror
defined C-4
DSPLIB reference 4-87
DSP_fft32x32s
defined C-4
DSPLIB reference 4-28
DSP_minval
defined C-5
DSP_fir_cplx
DSPLIB reference 4-65
defined C-4
DSPLIB reference 4-38, 4-40
DSP_mmul
defined C-4
DSPLIB reference 4-73
DSP_fir_gen
defined C-4
DSP_mul32
DSPLIB reference 4-42 4-44
defined C-5
DSPLIB reference 4-66
DSP_firlms2
DSP_neg32
defined C-4
defined C-5
DSPLIB reference 4-2
DSPLIB reference 4-68
DSP_fir_r4
DSP_q15tofl
defined C-4
DSPLIB reference 4-46
defined C-5
DSPLIB reference 4-89
DSP_fir_r8
DSP_r4fft
defined C-4
DSPLIB reference 4-48, 4-50
defined C-5
DSPLIB reference 4-95
DSP_fir_sym
DSP_radix2
defined C-4
DSPLIB reference 4-52
defined C-5
DSPLIB reference 4-93
DSP_fltoq15
DSP_recip16
defined C-4
DSPLIB reference 4-85
defined C-5
DSPLIB reference 4-69
DSP_ifft16x32
DSP_vecsumsq
defined C-4
defined C-5
DSPLIB reference 4-30, 4-32, 4-34
DSPLIB reference 4-71
Index-2
DSP_w_vec
DSP_blk_move 4-78, 4-80, 4-82, 4-84
DSP_dotp_sqr 4-58
DSP_dotprod 4-60
DSP_fft 4-98
defined C-5
DSPLIB reference 4-72
DSPLIB
DSP_fft16x16r 4-14
DSP_fft16x16t 4-8, 4-11, 4-107
DSP_fft16x32 4-24
DSP_fft32x32 4-26
DSP_fft32x32s 4-28
DSP_fir_cplx 4-38, 4-40
DSP_fir_gen 4-42, 4-44
DSP_firlms2 4-2
argument conventions, table 3-2
arguments 2-3
arguments and data types 2-3
calling a function from Assembly 2-4
calling a function from C 2-4
customer support B-2
data types, table 2-3
features and benefits 1-4
fractional Q formats A-3
functional categories 1-2
functions 3-3
DSP_fir_r4 4-46
DSP_fir_r8 4-48, 4-50
DSP_fir_sym 4-52
DSP_fltoq15 4-85
DSP_ifft16x32 4-30, 4-32, 4-34
DSP_ifft32x32 4-36
DSP_iir 4-54
DSP_iirlat 4-56
DSP_lat_fwd 4-56
DSP_mat_trans 4-75
DSP_maxidx 4-63
DSP_maxval 4-62
DSP_minerror 4-87
DSP_minval 4-65
DSP_mmul 4-73
DSP_mul32 4-66
DSP_neg32 4-68
DSP_q15tofl 4-89
DSP_r4fft 4-95
DSP_radix2 4-93
adaptive filtering 3-4
correlation 3-4
FFT (fast Fourier transform) 3-4
filtering and convolution 3-5
math 3-6
matrix 3-6
miscellaneous 3-7
how DSPLIB deals with overflow and
scaling 2-4, 2-5
how to install 2-2
how to rebuild DSPLIB 2-5
introduction 1-2
lib directory 2-2
performance considerations A-2
Q.3.12 bit fields A-3
Q.3.12 format A-3
Q.3.15 bit fields A-3
Q.3.15 format A-3
DSP_recip16 4-69
DSP_vecsumsq 4-71
DSP_w_vec 4-72
Q.31 format A-4
Q.31 high-memory location bit fields A-4
Q.31 low-memory location bit fields A-4
reference 4-1
software updates B-2
testing, how DSPLIB is tested 2-4
using DSPLIB 2-3
FFT functions 4-8
filtering and convolution functions 4-38
math functions 4-58
matrix functions 4-73
miscellaneous functions 4-76
DSPLIB reference
E
adaptive filtering functions 4-2
correlation functions 4-4
DSP_autocor 4-4, 4-6
DSP_bexp 4-76
evaluation module, defined C-5
external interrupt, defined C-5
DSP_bitrev_cplx 4-90
external memory interface (EMIF), defined C-5
Index-3
Index
F
L
least significant bit (LSB), defined C-7
fetch packet, defined C-5
lib directory 2-2
FFT (fast Fourier transform)
defined C-5
linker, defined C-7
functions 3-4
little endian, defined C-7
FFT (fast Fourier transform) functions,
DSPLIB reference 4-8
M
filtering and convolution functions 3-5
DSPLIB reference 4-38
maskable interrupt, defined C-7
flag, defined C-5
math functions 3-6
fractional Q formats A-3
frame, defined C-5
DSPLIB reference 4-58
matrix functions 3-6
function
DSPLIB reference 4-73
calling a DSPLIB function from Assembly 2-4
calling a DSPLIB function from C 2-4
memory map, defined C-7
memory-mapped register, defined C-7
functions, DSPLIB 3-3
miscellaneous functions 3-7
DSPLIB reference 4-76
most significant bit (MSB), defined C-7
m-law companding, defined C-7
G
multichannel buffered serial port (McBSP),
defined C-7
GIE bit, defined C-5
multiplexer, defined C-7
H
N
HAL, defined C-6
host, defined C-6
nonmaskable interrupt (NMI), defined C-8
host port interface (HPI), defined C-6
HPI, defined C-6
O
object file, defined C-8
I
off chip, defined C-8
index, defined C-6
on chip, defined C-8
indirect addressing, defined C-6
installing DSPLIB 2-2
overflow and scaling 2-4, 2-5
instruction fetch packet, defined C-6
internal interrupt, defined C-6
internal peripherals, defined C-7
interrupt, defined C-6
P
performance considerations A-2
peripheral, defined C-8
interrupt service fetch packet (ISFP), defined C-6
interrupt service routine (ISR), defined C-6
interrupt service table (IST), defined C-7
IST, defined C-7
program cache, defined C-8
program memory, defined C-8
PWR, defined C-8
PWR module, defined C-8
Index-4
Q
S
service layer, defined C-9
Q.3.12 bit fields A-3
software updates B-2
Q.3.12 format A-3
STDINC module, defined C-9
synchronous-burst static random-access memory
(SBSRAM), defined C-9
Q.3.15 bit fields A-3
Q.3.15 format A-3
synchronous dynamic random-access memory
(SDRAM), defined C-9
Q.31 format A-4
syntax, defined C-9
Q.31 high-memory location bit fields A-4
Q.31 low-memory location bit fields A-4
system software, defined C-9
T
tag, defined C-9
R
testing, how DSPLIB is tested 2-4
timer, defined C-9
random-access memory (RAM), defined C-8
rebuilding DSPLIB 2-5
TIMER module, defined C-9
reduced-instruction-set computer (RISC),
defined C-8
U
using DSPLIB 2-3
register, defined C-8
reset, defined C-9
W
routines, DSPLIB functional categories 1-2
RTOS, defined C-9
word, defined C-9
Index-5
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