Add libwebrtc third-party pfft
https://bugs.webkit.org/show_bug.cgi?id=202733
Reviewed by Eric Carlson.
Initial check-in of pfft which is now used in libwebrtc.
* Source/third_party/pffft: Added.
git-svn-id: http://svn.webkit.org/repository/webkit/trunk@251248 268f45cc-cd09-0410-ab3c-d52691b4dbfc
diff --git a/Source/ThirdParty/libwebrtc/ChangeLog b/Source/ThirdParty/libwebrtc/ChangeLog
index 105bca9..a0a8e8a 100644
--- a/Source/ThirdParty/libwebrtc/ChangeLog
+++ b/Source/ThirdParty/libwebrtc/ChangeLog
@@ -1,3 +1,14 @@
+2019-10-17 Youenn Fablet <youenn@apple.com>
+
+ Add libwebrtc third-party pfft
+ https://bugs.webkit.org/show_bug.cgi?id=202733
+
+ Reviewed by Eric Carlson.
+
+ Initial check-in of pfft which is now used in libwebrtc.
+
+ * Source/third_party/pffft: Added.
+
2019-10-10 Youenn Fablet <youenn@apple.com>
Update libwebrtc third-party jsoncpp to M78
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/BUILD.gn b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/BUILD.gn
new file mode 100644
index 0000000..069eec5
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/BUILD.gn
@@ -0,0 +1,114 @@
+# Copyright 2019 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
+import("//build/config/arm.gni")
+import("//testing/libfuzzer/fuzzer_test.gni")
+import("//testing/test.gni")
+
+config("common_config") {
+ if (is_win) {
+ defines = [
+ # Required to use math constants from math.h.
+ "_USE_MATH_DEFINES",
+ ]
+ }
+
+ # PFFFT doesn't support SIMD on mipsel, so build a scalar version.
+ if ((current_cpu == "arm" && !arm_use_neon) || current_cpu == "mipsel") {
+ defines = [ "PFFFT_SIMD_DISABLE" ]
+ }
+}
+
+static_library("pffft") {
+ configs += [ ":common_config" ]
+ sources = [
+ "src/pffft.c",
+ "src/pffft.h",
+ ]
+}
+
+# Fuzzing.
+
+group("fuzzers") {
+ testonly = true
+ deps = [
+ ":pffft_complex_fuzzer",
+ ":pffft_real_fuzzer",
+ ]
+}
+
+fuzzer_testdata_dir = "$target_gen_dir/testdata"
+
+action("generate_pffft_fuzzer_corpus") {
+ script = "generate_seed_corpus.py"
+ sources = [
+ "generate_seed_corpus.py",
+ ]
+ args = [ rebase_path(fuzzer_testdata_dir, root_build_dir) ]
+ outputs = [
+ fuzzer_testdata_dir,
+ ]
+}
+
+fuzzer_test("pffft_complex_fuzzer") {
+ sources = [
+ "pffft_fuzzer.cc",
+ ]
+ cflags = [ "-DTRANSFORM_COMPLEX" ]
+ deps = [
+ ":pffft",
+ ]
+ seed_corpus = fuzzer_testdata_dir
+ seed_corpus_deps = [ ":generate_pffft_fuzzer_corpus" ]
+}
+
+fuzzer_test("pffft_real_fuzzer") {
+ sources = [
+ "pffft_fuzzer.cc",
+ ]
+ cflags = [ "-DTRANSFORM_REAL" ]
+ deps = [
+ ":pffft",
+ ]
+ seed_corpus = fuzzer_testdata_dir
+ seed_corpus_deps = [ ":generate_pffft_fuzzer_corpus" ]
+}
+
+# Unit tests and benchmark.
+
+# This target must be used only for testing and benchmark purposes.
+static_library("fftpack") {
+ testonly = true
+ configs += [ ":common_config" ]
+ sources = [
+ "src/fftpack.c",
+ "src/fftpack.h",
+ ]
+ visibility = [ ":*" ]
+}
+
+executable("pffft_benchmark") {
+ testonly = true
+ configs += [ ":common_config" ]
+ sources = [
+ "src/test_pffft.c",
+ ]
+ deps = [
+ ":fftpack",
+ ":pffft",
+ ]
+}
+
+test("pffft_unittest") {
+ testonly = true
+ sources = [
+ "pffft_unittest.cc",
+ ]
+ deps = [
+ ":fftpack",
+ ":pffft",
+ "//testing/gtest",
+ "//testing/gtest:gtest_main",
+ ]
+}
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/DEPS b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/DEPS
new file mode 100644
index 0000000..fca61fc
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/DEPS
@@ -0,0 +1,3 @@
+include_rules = [
+ "+testing/gtest/include/gtest",
+]
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/LICENSE b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/LICENSE
new file mode 100644
index 0000000..ea8623f
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/LICENSE
@@ -0,0 +1,45 @@
+Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
+
+Based on original fortran 77 code from FFTPACKv4 from NETLIB,
+authored by Dr Paul Swarztrauber of NCAR, in 1985.
+
+As confirmed by the NCAR fftpack software curators, the following
+FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
+released under the same terms.
+
+FFTPACK license:
+
+http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
+
+Copyright (c) 2004 the University Corporation for Atmospheric
+Research ("UCAR"). All rights reserved. Developed by NCAR's
+Computational and Information Systems Laboratory, UCAR,
+www.cisl.ucar.edu.
+
+Redistribution and use of the Software in source and binary forms,
+with or without modification, is permitted provided that the
+following conditions are met:
+
+- Neither the names of NCAR's Computational and Information Systems
+Laboratory, the University Corporation for Atmospheric Research,
+nor the names of its sponsors or contributors may be used to
+endorse or promote products derived from this Software without
+specific prior written permission.
+
+- Redistributions of source code must retain the above copyright
+notices, this list of conditions, and the disclaimer below.
+
+- Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions, and the disclaimer below in the
+documentation and/or other materials provided with the
+distribution.
+
+THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+SOFTWARE.
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/OWNERS b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/OWNERS
new file mode 100644
index 0000000..b956a23
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/OWNERS
@@ -0,0 +1,2 @@
+maxmorin@chromium.org
+olka@chromium.org
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.chromium b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.chromium
new file mode 100644
index 0000000..7c5b19c
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.chromium
@@ -0,0 +1,41 @@
+Name: PFFFT: a pretty fast FFT.
+Short Name: PFFFT
+URL: https://bitbucket.org/jpommier/pffft/
+Version: 0
+Date: 2014-08-09
+Revision: 483453d8f766
+License: BSD-like
+License File: LICENSE
+Security Critical: Yes
+License Android Compatible: Yes
+
+Description:
+PFFFT does 1D Fast Fourier Transforms, of single precision real and complex vectors. It tries do it fast, it tries to be correct, and it tries to be small. Computations do take advantage of SSE1 instructions on x86 cpus, Altivec on powerpc cpus, and NEON on ARM cpus.
+
+Note about the structure of //third_party/pffft:
+The imported third party code (with patches applied, see "Local Modifications") lives in //third_party/pffft/src/, whereas the fuzzer and unit test code lives in //third_party/pffft.
+
+Remarks on the C library and recommendations:
+- The C API is unsafe: input and output arrays are passed as pointers without size
+- When a scratch array is not provided (e.g., pffft_transform(/*work=*/nullptr)), VLA is used
+ * MSVC: stack or heap depending on size
+ * other compilers: always on the stack
+- According to the PFFFT documentation, when SIMD is enabled, input, output and scratch arrays must be allocated as aligned memory (16-byte boundary on intel and PowerPC);
+ as long as the SIMD extension API requirements are met, one may use different options (and not only pffft_aligned_malloc) such as std::vector
+- It is strongly recommended that a C++ wrapper is used to
+ (i) avoid pointer arguments (e.g., using absl::Span)
+ (ii) pre-allocate the scratch buffer for large FFT sizes
+ (iii) provide a function to check if an integer is a supported FFT size
+
+Local Modifications:
+
+Local modifications live in //third_party/pffft/patches/. To apply them run:
+$ for patch in third_party/pffft/patches/*; do patch -s -p1 < $patch; done
+
+In case of conflict, update those patches accordingly and save them back in //third_party/pffft/patches/.
+
+ * 01-rmv_printf.diff: remove printf and stop including stdio.h
+ * 02-decl_validate_simd.diff: declare validate_pffft_simd() in pffft.h
+ * 03-malloca.diff: replace _alloca (deprecated) with _malloca (MSVC case only) + cleanup
+ * 04-fix_ptr_cast.diff: avoid MSVC warnings by fixing pointer cast
+ * 05-fix-arch-detection.diff: better arch detection to avoid to define PFFFT_SIMD_DISABLE
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.md b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.md
new file mode 100644
index 0000000..e373a57
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.md
@@ -0,0 +1,69 @@
+# Notes on PFFFT
+We strongly recommend to **read this file** before using PFFFT and to **always wrap** the original C library within a C++ wrapper.
+
+[Example of PFFFT wrapper](https://cs.chromium.org/chromium/src/third_party/webrtc/modules/audio_processing/utility/pffft_wrapper.h).
+
+## Scratch buffer
+The caller can optionally provide a scratch buffer. When not provided, VLA is used to provide a thread-safe option.
+However, it is recommended to write a C++ wrapper which allocates its own scratch buffer.
+Note that the scratch buffer has the same memory alignment requirements of the input and output vectors.
+
+## Output layout
+PFFFT computes the forward transform with two possible output layouts:
+1. ordered
+2. unordered
+
+### Ordered layout
+Calling `pffft_transform_ordered` produces an array of **interleaved real and imaginary parts**.
+The last Fourier coefficient is purely real and stored in the imaginary part of the DC component (which is also purely real).
+
+### Unordered layout
+Calling `pffft_transform` produces an array with a more complex structure, but in a more efficient way than `pffft_transform_ordered`.
+Below, the output produced by Matlab and that produced by PFFFT are compared.
+The comparison is made for a 32 point transform of a 16 sample buffer.
+A 32 point transform has been chosen as this is the minimum supported by PFFFT.
+
+Important notes:
+- In Matlab the DC (Matlab index 1 [R1, I1]]) and Nyquist (Matlab index 17 [R17, I17]) values are not repeated as complex conjugates.
+- In PFFFT the Nyquist real and imaginary parts ([R17, I17]) are omitted entirely.
+- In PFFFT the final 8 values (4 real and 4 imaginary) are not in the same order as all of the others.
+- In PFFFT all imaginary parts are stored as negatives (like second half in Matlab).
+
+```
++-------+-----------+-------+-------+
+| Index | Matlab | Index | PFFFT |
++-------+-----------+-------+-------+
+| 1 | R1 + I1 | 0 | R1 |
+| 2 | R2+ I2 | 1 | R2 |
+| 3 | R3 + I3 | 2 | R3 |
+| 4 | R4 + I4 | 3 | R4 |
+| 5 | R5 + I5 | 4 | -I1 |
+| 6 | R6 + I6 | 5 | -I2 |
+| 7 | R7 + I7 | 6 | -I3 |
+| 8 | R8 + I8 | 7 | -I4 |
+| 9 | R9 + I9 | 8 | R5 |
+| 10 | R10 + I10 | 9 | R6 |
+| 11 | R11 + I11 | 10 | R7 |
+| 12 | R12 + I12 | 11 | R8 |
+| 13 | R13 + I13 | 12 | -I5 |
+| 14 | R14 + I14 | 13 | -I6 |
+| 15 | R15 + I15 | 14 | -I7 |
+| 16 | R16 + I16 | 15 | -I8 |
+| 17 | R17 + I17 | 16 | R9 |
+| 18 | R16 - I16 | 17 | R10 |
+| 19 | R15 - I15 | 18 | R11 |
+| 20 | R14 - I14 | 19 | R12 |
+| 21 | R13 - I13 | 20 | -I9 |
+| 22 | R12 - I12 | 21 | -I10 |
+| 23 | R11 - I11 | 22 | -I11 |
+| 24 | R10 - I10 | 23 | -I12 |
+| 25 | R9 - I9 | 24 | R13 |
+| 26 | R8 - I8 | 25 | R16 |
+| 27 | R7 - I7 | 26 | R15 |
+| 28 | R6 - I6 | 27 | R14 |
+| 29 | R5 - I5 | 28 | -I13 |
+| 30 | R4 - I4 | 29 | -I16 |
+| 31 | R3 - I3 | 30 | -I15 |
+| 32 | R2 - I2 | 31 | -I14 |
++-------+-----------+-------+-------+
+```
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.txt b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.txt
new file mode 100644
index 0000000..878f4a6
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/README.txt
@@ -0,0 +1,379 @@
+PFFFT: a pretty fast FFT.
+
+TL;DR
+--
+
+PFFFT does 1D Fast Fourier Transforms, of single precision real and
+complex vectors. It tries do it fast, it tries to be correct, and it
+tries to be small. Computations do take advantage of SSE1 instructions
+on x86 cpus, Altivec on powerpc cpus, and NEON on ARM cpus. The
+license is BSD-like.
+
+
+Why does it exist:
+--
+
+I was in search of a good performing FFT library , preferably very
+small and with a very liberal license.
+
+When one says "fft library", FFTW ("Fastest Fourier Transform in the
+West") is probably the first name that comes to mind -- I guess that
+99% of open-source projects that need a FFT do use FFTW, and are happy
+with it. However, it is quite a large library , which does everything
+fft related (2d transforms, 3d transforms, other transformations such
+as discrete cosine , or fast hartley). And it is licensed under the
+GNU GPL , which means that it cannot be used in non open-source
+products.
+
+An alternative to FFTW that is really small, is the venerable FFTPACK
+v4, which is available on NETLIB. A more recent version (v5) exists,
+but it is larger as it deals with multi-dimensional transforms. This
+is a library that is written in FORTRAN 77, a language that is now
+considered as a bit antiquated by many. FFTPACKv4 was written in 1985,
+by Dr Paul Swarztrauber of NCAR, more than 25 years ago ! And despite
+its age, benchmarks show it that it still a very good performing FFT
+library, see for example the 1d single precision benchmarks here:
+http://www.fftw.org/speed/opteron-2.2GHz-32bit/ . It is however not
+competitive with the fastest ones, such as FFTW, Intel MKL, AMD ACML,
+Apple vDSP. The reason for that is that those libraries do take
+advantage of the SSE SIMD instructions available on Intel CPUs,
+available since the days of the Pentium III. These instructions deal
+with small vectors of 4 floats at a time, instead of a single float
+for a traditionnal FPU, so when using these instructions one may expect
+a 4-fold performance improvement.
+
+The idea was to take this fortran fftpack v4 code, translate to C,
+modify it to deal with those SSE instructions, and check that the
+final performance is not completely ridiculous when compared to other
+SIMD FFT libraries. Translation to C was performed with f2c (
+http://www.netlib.org/f2c/ ). The resulting file was a bit edited in
+order to remove the thousands of gotos that were introduced by
+f2c. You will find the fftpack.h and fftpack.c sources in the
+repository, this a complete translation of
+http://www.netlib.org/fftpack/ , with the discrete cosine transform
+and the test program. There is no license information in the netlib
+repository, but it was confirmed to me by the fftpack v5 curators that
+the same terms do apply to fftpack v4:
+http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html . This is a
+"BSD-like" license, it is compatible with proprietary projects.
+
+Adapting fftpack to deal with the SIMD 4-element vectors instead of
+scalar single precision numbers was more complex than I originally
+thought, especially with the real transforms, and I ended up writing
+more code than I planned..
+
+
+The code:
+--
+
+Only two files, in good old C, pffft.c and pffft.h . The API is very
+very simple, just make sure that you read the comments in pffft.h.
+
+
+Comparison with other FFTs:
+--
+
+The idea was not to break speed records, but to get a decently fast
+fft that is at least 50% as fast as the fastest FFT -- especially on
+slowest computers . I'm more focused on getting the best performance
+on slow cpus (Atom, Intel Core 1, old Athlons, ARM Cortex-A9...), than
+on getting top performance on today fastest cpus.
+
+It can be used in a real-time context as the fft functions do not
+perform any memory allocation -- that is why they accept a 'work'
+array in their arguments.
+
+It is also a bit focused on performing 1D convolutions, that is why it
+provides "unordered" FFTs , and a fourier domain convolution
+operation.
+
+
+Benchmark results (cpu tested: core i7 2600, core 2 quad, core 1 duo, atom N270, cortex-A9)
+--
+
+The benchmark shows the performance of various fft implementations measured in
+MFlops, with the number of floating point operations being defined as 5Nlog2(N)
+for a length N complex fft, and 2.5*Nlog2(N) for a real fft.
+See http://www.fftw.org/speed/method.html for an explanation of these formulas.
+
+MacOS Lion, gcc 4.2, 64-bit, fftw 3.3 on a 3.4 GHz core i7 2600
+
+Built with:
+
+ gcc-4.2 -o test_pffft -arch x86_64 -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -DHAVE_VECLIB -framework veclib -DHAVE_FFTW -lfftw3f
+
+| input len |real FFTPack| real vDSP | real FFTW | real PFFFT | |cplx FFTPack| cplx vDSP | cplx FFTW | cplx PFFFT |
+|-----------+------------+------------+------------+------------| |------------+------------+------------+------------|
+| 64 | 2816 | 8596 | 7329 | 8187 | | 2887 | 14898 | 14668 | 11108 |
+| 96 | 3298 | n/a | 8378 | 7727 | | 3953 | n/a | 15680 | 10878 |
+| 128 | 3507 | 11575 | 9266 | 10108 | | 4233 | 17598 | 16427 | 12000 |
+| 160 | 3391 | n/a | 9838 | 10711 | | 4220 | n/a | 16653 | 11187 |
+| 192 | 3919 | n/a | 9868 | 10956 | | 4297 | n/a | 15770 | 12540 |
+| 256 | 4283 | 13179 | 10694 | 13128 | | 4545 | 19550 | 16350 | 13822 |
+| 384 | 3136 | n/a | 10810 | 12061 | | 3600 | n/a | 16103 | 13240 |
+| 480 | 3477 | n/a | 10632 | 12074 | | 3536 | n/a | 11630 | 12522 |
+| 512 | 3783 | 15141 | 11267 | 13838 | | 3649 | 20002 | 16560 | 13580 |
+| 640 | 3639 | n/a | 11164 | 13946 | | 3695 | n/a | 15416 | 13890 |
+| 768 | 3800 | n/a | 11245 | 13495 | | 3590 | n/a | 15802 | 14552 |
+| 800 | 3440 | n/a | 10499 | 13301 | | 3659 | n/a | 12056 | 13268 |
+| 1024 | 3924 | 15605 | 11450 | 15339 | | 3769 | 20963 | 13941 | 15467 |
+| 2048 | 4518 | 16195 | 11551 | 15532 | | 4258 | 20413 | 13723 | 15042 |
+| 2400 | 4294 | n/a | 10685 | 13078 | | 4093 | n/a | 12777 | 13119 |
+| 4096 | 4750 | 16596 | 11672 | 15817 | | 4157 | 19662 | 14316 | 14336 |
+| 8192 | 3820 | 16227 | 11084 | 12555 | | 3691 | 18132 | 12102 | 13813 |
+| 9216 | 3864 | n/a | 10254 | 12870 | | 3586 | n/a | 12119 | 13994 |
+| 16384 | 3822 | 15123 | 10454 | 12822 | | 3613 | 16874 | 12370 | 13881 |
+| 32768 | 4175 | 14512 | 10662 | 11095 | | 3881 | 14702 | 11619 | 11524 |
+| 262144 | 3317 | 11429 | 6269 | 9517 | | 2810 | 11729 | 7757 | 10179 |
+| 1048576 | 2913 | 10551 | 4730 | 5867 | | 2661 | 7881 | 3520 | 5350 |
+|-----------+------------+------------+------------+------------| |------------+------------+------------+------------|
+
+
+Debian 6, gcc 4.4.5, 64-bit, fftw 3.3.1 on a 3.4 GHz core i7 2600
+
+Built with:
+gcc -o test_pffft -DHAVE_FFTW -msse2 -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L$HOME/local/lib -I$HOME/local/include/ -lfftw3f -lm
+
+| N (input length) | real FFTPack | real FFTW | real PFFFT | | cplx FFTPack | cplx FFTW | cplx PFFFT |
+|------------------+--------------+--------------+--------------| |--------------+--------------+--------------|
+| 64 | 3840 | 7680 | 8777 | | 4389 | 20480 | 11171 |
+| 96 | 4214 | 9633 | 8429 | | 4816 | 22477 | 11238 |
+| 128 | 3584 | 10240 | 10240 | | 5120 | 23893 | 11947 |
+| 192 | 4854 | 11095 | 12945 | | 4854 | 22191 | 14121 |
+| 256 | 4096 | 11703 | 16384 | | 5120 | 23406 | 13653 |
+| 384 | 4395 | 14651 | 12558 | | 4884 | 19535 | 14651 |
+| 512 | 5760 | 13166 | 15360 | | 4608 | 23040 | 15360 |
+| 768 | 4907 | 14020 | 16357 | | 4461 | 19628 | 14020 |
+| 1024 | 5120 | 14629 | 14629 | | 5120 | 20480 | 15754 |
+| 2048 | 5632 | 14080 | 18773 | | 4693 | 12516 | 16091 |
+| 4096 | 5120 | 13653 | 17554 | | 4726 | 7680 | 14456 |
+| 8192 | 4160 | 7396 | 13312 | | 4437 | 14791 | 13312 |
+| 9216 | 4210 | 6124 | 13473 | | 4491 | 7282 | 14970 |
+| 16384 | 3976 | 11010 | 14313 | | 4210 | 11450 | 13631 |
+| 32768 | 4260 | 10224 | 10954 | | 4260 | 6816 | 11797 |
+| 262144 | 3736 | 6896 | 9961 | | 2359 | 8965 | 9437 |
+| 1048576 | 2796 | 4534 | 6453 | | 1864 | 3078 | 5592 |
+|------------------+--------------+--------------+--------------| |--------------+--------------+--------------|
+
+
+
+MacOS Snow Leopard, gcc 4.0, 32-bit, fftw 3.3 on a 1.83 GHz core 1 duo
+
+Built with:
+
+ gcc -o test_pffft -DHAVE_FFTW -DHAVE_VECLIB -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -framework veclib
+
+| input len |real FFTPack| real vDSP | real FFTW | real PFFFT | |cplx FFTPack| cplx vDSP | cplx FFTW | cplx PFFFT |
+|-----------+------------+------------+------------+------------| |------------+------------+------------+------------|
+| 64 | 745 | 2145 | 1706 | 2028 | | 961 | 3356 | 3313 | 2300 |
+| 96 | 877 | n/a | 1976 | 1978 | | 1059 | n/a | 3333 | 2233 |
+| 128 | 951 | 2808 | 2213 | 2279 | | 1202 | 3803 | 3739 | 2494 |
+| 192 | 1002 | n/a | 2456 | 2429 | | 1186 | n/a | 3701 | 2508 |
+| 256 | 1065 | 3205 | 2641 | 2793 | | 1302 | 4013 | 3912 | 2663 |
+| 384 | 845 | n/a | 2759 | 2499 | | 948 | n/a | 3729 | 2504 |
+| 512 | 900 | 3476 | 2956 | 2759 | | 974 | 4057 | 3954 | 2645 |
+| 768 | 910 | n/a | 2912 | 2737 | | 975 | n/a | 3837 | 2614 |
+| 1024 | 936 | 3583 | 3107 | 3009 | | 1006 | 4124 | 3821 | 2697 |
+| 2048 | 1057 | 3585 | 3091 | 2837 | | 1089 | 3889 | 3701 | 2513 |
+| 4096 | 1083 | 3524 | 3092 | 2733 | | 1039 | 3617 | 3462 | 2364 |
+| 8192 | 874 | 3252 | 2967 | 2363 | | 911 | 3106 | 2789 | 2302 |
+| 9216 | 898 | n/a | 2420 | 2290 | | 865 | n/a | 2676 | 2204 |
+| 16384 | 903 | 2892 | 2506 | 2421 | | 899 | 3026 | 2797 | 2289 |
+| 32768 | 965 | 2837 | 2550 | 2358 | | 920 | 2922 | 2763 | 2240 |
+| 262144 | 738 | 2422 | 1589 | 1708 | | 610 | 2038 | 1436 | 1091 |
+| 1048576 | 528 | 1207 | 845 | 880 | | 606 | 1020 | 669 | 1036 |
+|-----------+------------+------------+------------+------------| |------------+------------+------------+------------|
+
+
+
+Ubuntu 11.04, gcc 4.5, 32-bit, fftw 3.2 on a 2.66 core 2 quad
+
+Built with:
+gcc -o test_pffft -DHAVE_FFTW -msse -mfpmath=sse -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -lm
+
+| input len |real FFTPack| real FFTW | real PFFFT | |cplx FFTPack| cplx FFTW | cplx PFFFT |
+|-----------+------------+------------+------------| |------------+------------+------------|
+| 64 | 1920 | 3614 | 5120 | | 2194 | 7680 | 6467 |
+| 96 | 1873 | 3549 | 5187 | | 2107 | 8429 | 5863 |
+| 128 | 2240 | 3773 | 5514 | | 2560 | 7964 | 6827 |
+| 192 | 1765 | 4569 | 7767 | | 2284 | 9137 | 7061 |
+| 256 | 2048 | 5461 | 7447 | | 2731 | 9638 | 7802 |
+| 384 | 1998 | 5861 | 6762 | | 2313 | 9253 | 7644 |
+| 512 | 2095 | 6144 | 7680 | | 2194 | 10240 | 7089 |
+| 768 | 2230 | 5773 | 7549 | | 2045 | 10331 | 7010 |
+| 1024 | 2133 | 6400 | 8533 | | 2133 | 10779 | 7877 |
+| 2048 | 2011 | 7040 | 8665 | | 1942 | 10240 | 7768 |
+| 4096 | 2194 | 6827 | 8777 | | 1755 | 9452 | 6827 |
+| 8192 | 1849 | 6656 | 6656 | | 1752 | 7831 | 6827 |
+| 9216 | 1871 | 5858 | 6416 | | 1643 | 6909 | 6266 |
+| 16384 | 1883 | 6223 | 6506 | | 1664 | 7340 | 6982 |
+| 32768 | 1826 | 6390 | 6667 | | 1631 | 7481 | 6971 |
+| 262144 | 1546 | 4075 | 5977 | | 1299 | 3415 | 3551 |
+| 1048576 | 1104 | 2071 | 1730 | | 1104 | 1149 | 1834 |
+|-----------+------------+------------+------------| |------------+------------+------------|
+
+
+
+Ubuntu 11.04, gcc 4.5, 32-bit, fftw 3.3 on a 1.6 GHz Atom N270
+
+Built with:
+gcc -o test_pffft -DHAVE_FFTW -msse -mfpmath=sse -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -lm
+
+| N (input length) | real FFTPack | real FFTW | real PFFFT | | cplx FFTPack | cplx FFTW | cplx PFFFT |
+|------------------+--------------+--------------+--------------| |--------------+--------------+--------------|
+| 64 | 452 | 1041 | 1336 | | 549 | 2318 | 1781 |
+| 96 | 444 | 1297 | 1297 | | 503 | 2408 | 1686 |
+| 128 | 527 | 1525 | 1707 | | 543 | 2655 | 1886 |
+| 192 | 498 | 1653 | 1849 | | 539 | 2678 | 1942 |
+| 256 | 585 | 1862 | 2156 | | 594 | 2777 | 2244 |
+| 384 | 499 | 1870 | 1998 | | 511 | 2586 | 1890 |
+| 512 | 562 | 2095 | 2194 | | 542 | 2973 | 2194 |
+| 768 | 545 | 2045 | 2133 | | 545 | 2365 | 2133 |
+| 1024 | 595 | 2133 | 2438 | | 569 | 2695 | 2179 |
+| 2048 | 587 | 2125 | 2347 | | 521 | 2230 | 1707 |
+| 4096 | 495 | 1890 | 1834 | | 492 | 1876 | 1672 |
+| 8192 | 469 | 1548 | 1729 | | 438 | 1740 | 1664 |
+| 9216 | 468 | 1663 | 1663 | | 446 | 1585 | 1531 |
+| 16384 | 453 | 1608 | 1767 | | 398 | 1476 | 1664 |
+| 32768 | 456 | 1420 | 1503 | | 387 | 1388 | 1345 |
+| 262144 | 309 | 385 | 726 | | 262 | 415 | 840 |
+| 1048576 | 280 | 351 | 739 | | 261 | 313 | 797 |
+|------------------+--------------+--------------+--------------| |--------------+--------------+--------------|
+
+
+
+Windows 7, visual c++ 2010 on a 1.6 GHz Atom N270
+
+Built with:
+cl /Ox -D_USE_MATH_DEFINES /arch:SSE test_pffft.c pffft.c fftpack.c
+
+(visual c++ is definitively not very good with SSE intrinsics...)
+
+| N (input length) | real FFTPack | real PFFFT | | cplx FFTPack | cplx PFFFT |
+|------------------+--------------+--------------| |--------------+--------------|
+| 64 | 173 | 1009 | | 174 | 1159 |
+| 96 | 169 | 1029 | | 188 | 1201 |
+| 128 | 195 | 1242 | | 191 | 1275 |
+| 192 | 178 | 1312 | | 184 | 1276 |
+| 256 | 196 | 1591 | | 186 | 1281 |
+| 384 | 172 | 1409 | | 181 | 1281 |
+| 512 | 187 | 1640 | | 181 | 1313 |
+| 768 | 171 | 1614 | | 176 | 1258 |
+| 1024 | 186 | 1812 | | 178 | 1223 |
+| 2048 | 190 | 1707 | | 186 | 1099 |
+| 4096 | 182 | 1446 | | 177 | 975 |
+| 8192 | 175 | 1345 | | 169 | 1034 |
+| 9216 | 165 | 1271 | | 168 | 1023 |
+| 16384 | 166 | 1396 | | 165 | 949 |
+| 32768 | 172 | 1311 | | 161 | 881 |
+| 262144 | 136 | 632 | | 134 | 629 |
+| 1048576 | 134 | 698 | | 127 | 623 |
+|------------------+--------------+--------------| |--------------+--------------|
+
+
+
+Ubuntu 12.04, gcc-4.7.3, 32-bit, with fftw 3.3.3 (built with --enable-neon), on a 1.2GHz ARM Cortex A9 (Tegra 3)
+
+Built with:
+gcc-4.7 -O3 -DHAVE_FFTW -march=armv7-a -mtune=cortex-a9 -mfloat-abi=hard -mfpu=neon -ffast-math test_pffft.c pffft.c -o test_pffft_arm fftpack.c -lm -I/usr/local/include/ -L/usr/local/lib/ -lfftw3f
+
+| input len |real FFTPack| real FFTW | real PFFFT | |cplx FFTPack| cplx FFTW | cplx PFFFT |
+|-----------+------------+------------+------------| |------------+------------+------------|
+| 64 | 549 | 452 | 731 | | 512 | 602 | 640 |
+| 96 | 421 | 272 | 702 | | 496 | 571 | 602 |
+| 128 | 498 | 512 | 815 | | 597 | 618 | 652 |
+| 160 | 521 | 536 | 815 | | 586 | 669 | 625 |
+| 192 | 539 | 571 | 883 | | 485 | 597 | 626 |
+| 256 | 640 | 539 | 975 | | 569 | 611 | 671 |
+| 384 | 499 | 610 | 879 | | 499 | 602 | 637 |
+| 480 | 518 | 507 | 877 | | 496 | 661 | 616 |
+| 512 | 524 | 591 | 1002 | | 549 | 678 | 668 |
+| 640 | 542 | 612 | 955 | | 568 | 663 | 645 |
+| 768 | 557 | 613 | 981 | | 491 | 663 | 598 |
+| 800 | 514 | 353 | 882 | | 514 | 360 | 574 |
+| 1024 | 640 | 640 | 1067 | | 492 | 683 | 602 |
+| 2048 | 587 | 640 | 908 | | 486 | 640 | 552 |
+| 2400 | 479 | 368 | 777 | | 422 | 376 | 518 |
+| 4096 | 511 | 614 | 853 | | 426 | 640 | 534 |
+| 8192 | 415 | 584 | 708 | | 386 | 622 | 516 |
+| 9216 | 419 | 571 | 687 | | 364 | 586 | 506 |
+| 16384 | 426 | 577 | 716 | | 398 | 606 | 530 |
+| 32768 | 417 | 572 | 673 | | 399 | 572 | 468 |
+| 262144 | 219 | 380 | 293 | | 255 | 431 | 343 |
+| 1048576 | 202 | 274 | 237 | | 265 | 282 | 355 |
+|-----------+------------+------------+------------| |------------+------------+------------|
+
+Same platform as above, but this time pffft and fftpack are built with clang 3.2:
+
+clang -O3 -DHAVE_FFTW -march=armv7-a -mtune=cortex-a9 -mfloat-abi=hard -mfpu=neon -ffast-math test_pffft.c pffft.c -o test_pffft_arm fftpack.c -lm -I/usr/local/include/ -L/usr/local/lib/ -lfftw3f
+
+| input len |real FFTPack| real FFTW | real PFFFT | |cplx FFTPack| cplx FFTW | cplx PFFFT |
+|-----------+------------+------------+------------| |------------+------------+------------|
+| 64 | 427 | 452 | 853 | | 427 | 602 | 1024 |
+| 96 | 351 | 276 | 843 | | 337 | 571 | 963 |
+| 128 | 373 | 512 | 996 | | 390 | 618 | 1054 |
+| 160 | 426 | 536 | 987 | | 375 | 669 | 914 |
+| 192 | 404 | 571 | 1079 | | 388 | 588 | 1079 |
+| 256 | 465 | 539 | 1205 | | 445 | 602 | 1170 |
+| 384 | 366 | 610 | 1099 | | 343 | 594 | 1099 |
+| 480 | 356 | 507 | 1140 | | 335 | 651 | 931 |
+| 512 | 411 | 591 | 1213 | | 384 | 649 | 1124 |
+| 640 | 398 | 612 | 1193 | | 373 | 654 | 901 |
+| 768 | 409 | 613 | 1227 | | 383 | 663 | 1044 |
+| 800 | 411 | 348 | 1073 | | 353 | 358 | 809 |
+| 1024 | 427 | 640 | 1280 | | 413 | 692 | 1004 |
+| 2048 | 414 | 626 | 1126 | | 371 | 640 | 853 |
+| 2400 | 399 | 373 | 898 | | 319 | 368 | 653 |
+| 4096 | 404 | 602 | 1059 | | 357 | 633 | 778 |
+| 8192 | 332 | 584 | 792 | | 308 | 616 | 716 |
+| 9216 | 322 | 561 | 783 | | 299 | 586 | 687 |
+| 16384 | 344 | 568 | 778 | | 314 | 617 | 745 |
+| 32768 | 342 | 564 | 737 | | 314 | 552 | 629 |
+| 262144 | 201 | 383 | 313 | | 227 | 435 | 413 |
+| 1048576 | 187 | 262 | 251 | | 228 | 281 | 409 |
+|-----------+------------+------------+------------| |------------+------------+------------|
+
+So it looks like, on ARM, gcc 4.7 is the best at scalar floating point
+(the fftpack performance numbers are better with gcc), while clang is
+the best with neon intrinsics (see how pffft perf has improved with
+clang 3.2).
+
+
+NVIDIA Jetson TK1 board, gcc-4.8.2. The cpu is a 2.3GHz cortex A15 (Tegra K1).
+
+Built with:
+gcc -O3 -march=armv7-a -mtune=native -mfloat-abi=hard -mfpu=neon -ffast-math test_pffft.c pffft.c -o test_pffft_arm fftpack.c -lm
+
+| input len |real FFTPack| real PFFFT | |cplx FFTPack| cplx PFFFT |
+|-----------+------------+------------| |------------+------------|
+| 64 | 1735 | 3308 | | 1994 | 3744 |
+| 96 | 1596 | 3448 | | 1987 | 3572 |
+| 128 | 1807 | 4076 | | 2255 | 3960 |
+| 160 | 1769 | 4083 | | 2071 | 3845 |
+| 192 | 1990 | 4233 | | 2017 | 3939 |
+| 256 | 2191 | 4882 | | 2254 | 4346 |
+| 384 | 1878 | 4492 | | 2073 | 4012 |
+| 480 | 1748 | 4398 | | 1923 | 3951 |
+| 512 | 2030 | 5064 | | 2267 | 4195 |
+| 640 | 1918 | 4756 | | 2094 | 4184 |
+| 768 | 2099 | 4907 | | 2048 | 4297 |
+| 800 | 1822 | 4555 | | 1880 | 4063 |
+| 1024 | 2232 | 5355 | | 2187 | 4420 |
+| 2048 | 2176 | 4983 | | 2027 | 3602 |
+| 2400 | 1741 | 4256 | | 1710 | 3344 |
+| 4096 | 1816 | 3914 | | 1851 | 3349 |
+| 8192 | 1716 | 3481 | | 1700 | 3255 |
+| 9216 | 1735 | 3589 | | 1653 | 3094 |
+| 16384 | 1567 | 3483 | | 1637 | 3244 |
+| 32768 | 1624 | 3240 | | 1655 | 3156 |
+| 262144 | 1012 | 1898 | | 983 | 1503 |
+| 1048576 | 876 | 1154 | | 868 | 1341 |
+|-----------+------------+------------| |------------+------------|
+
+The performance on the tegra K1 is pretty impressive. I'm not
+including the FFTW numbers as they as slightly below the scalar
+fftpack numbers, so something must be wrong (however it seems to be
+correctly configured and is using neon simd instructions).
+
+When using clang 3.4 the pffft version is even a bit faster, reaching
+5.7 GFlops for real ffts of size 1024.
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/generate_seed_corpus.py b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/generate_seed_corpus.py
new file mode 100755
index 0000000..18c9d31
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/generate_seed_corpus.py
@@ -0,0 +1,74 @@
+#!/usr/bin/env python
+# Copyright 2019 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
+from __future__ import division
+from __future__ import print_function
+
+from array import array
+import os
+import random
+import shutil
+import sys
+
+MAX_INPUT_SIZE = 5000 # < 1 MB so we don't blow up fuzzer build sizes.
+MAX_FLOAT32 = 3.4028235e+38
+
+
+def IsValidSize(n):
+ if n == 0:
+ return False
+ # PFFFT only supports transforms for inputs of length N of the form
+ # N = (2^a)*(3^b)*(5^c) where a >= 5, b >=0, c >= 0.
+ FACTORS = [2, 3, 5]
+ factorization = [0, 0, 0]
+ for i, factor in enumerate(FACTORS):
+ while n % factor == 0:
+ n = n // factor
+ factorization[i] += 1
+ return factorization[0] >= 5 and n == 1
+
+
+def WriteFloat32ArrayToFile(file_path, size, generator):
+ """Generate an array of float32 values and writes to file."""
+ with open(file_path, 'wb') as f:
+ float_array = array('f', [generator() for _ in range(size)])
+ float_array.tofile(f)
+
+
+def main():
+ if len(sys.argv) < 2:
+ print('Usage: %s <path to output directory>' % sys.argv[0])
+ sys.exit(1)
+
+ output_path = sys.argv[1]
+ # Start with a clean output directory.
+ if os.path.exists(output_path):
+ shutil.rmtree(output_path)
+ os.makedirs(output_path)
+
+ # List of valid input sizes.
+ N = [n for n in range(MAX_INPUT_SIZE) if IsValidSize(n)]
+
+ # Set the seed to always generate the same random data.
+ random.seed(0)
+
+ # Generate different types of input arrays for each target length.
+ for n in N:
+ # Zeros.
+ WriteFloat32ArrayToFile(
+ os.path.join(output_path, 'zeros_%d' % n), n, lambda: 0)
+ # Max float 32.
+ WriteFloat32ArrayToFile(
+ os.path.join(output_path, 'max_%d' % n), n, lambda: MAX_FLOAT32)
+ # Random values in the s16 range.
+ rnd_s16 = lambda: 32768.0 * 2.0 * (random.random() - 0.5)
+ WriteFloat32ArrayToFile(
+ os.path.join(output_path, 'rnd_s16_%d' % n), n, rnd_s16)
+
+ sys.exit(0)
+
+
+if __name__ == '__main__':
+ main()
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/01-rmv_printf.diff b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/01-rmv_printf.diff
new file mode 100644
index 0000000..3a91494
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/01-rmv_printf.diff
@@ -0,0 +1,60 @@
+diff --git a/third_party/pffft/src/pffft.c b/third_party/pffft/src/pffft.c
+index 7934db448a09..2e0c2f651438 100644
+--- a/third_party/pffft/src/pffft.c
++++ b/third_party/pffft/src/pffft.c
+@@ -59,7 +59,7 @@
+
+ #include "pffft.h"
+ #include <stdlib.h>
+-#include <stdio.h>
++// #include <stdio.h>
+ #include <math.h>
+ #include <assert.h>
+
+@@ -222,31 +222,35 @@ void validate_pffft_simd() {
+ memcpy(a3.f, f+12, 4*sizeof(float));
+
+ t = a0; u = a1; t.v = VZERO();
+- printf("VZERO=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]); assertv4(t, 0, 0, 0, 0);
++ // printf("VZERO=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
++ assertv4(t, 0, 0, 0, 0);
+ t.v = VADD(a1.v, a2.v);
+- printf("VADD(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]); assertv4(t, 12, 14, 16, 18);
++ // printf("VADD(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
++ assertv4(t, 12, 14, 16, 18);
+ t.v = VMUL(a1.v, a2.v);
+- printf("VMUL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]); assertv4(t, 32, 45, 60, 77);
++ // printf("VMUL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
++ assertv4(t, 32, 45, 60, 77);
+ t.v = VMADD(a1.v, a2.v,a0.v);
+- printf("VMADD(4:7,8:11,0:3)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]); assertv4(t, 32, 46, 62, 80);
++ // printf("VMADD(4:7,8:11,0:3)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
++ assertv4(t, 32, 46, 62, 80);
+
+ INTERLEAVE2(a1.v,a2.v,t.v,u.v);
+- printf("INTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3], u.f[0], u.f[1], u.f[2], u.f[3]);
++ // printf("INTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3], u.f[0], u.f[1], u.f[2], u.f[3]);
+ assertv4(t, 4, 8, 5, 9); assertv4(u, 6, 10, 7, 11);
+ UNINTERLEAVE2(a1.v,a2.v,t.v,u.v);
+- printf("UNINTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3], u.f[0], u.f[1], u.f[2], u.f[3]);
++ // printf("UNINTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3], u.f[0], u.f[1], u.f[2], u.f[3]);
+ assertv4(t, 4, 6, 8, 10); assertv4(u, 5, 7, 9, 11);
+
+ t.v=LD_PS1(f[15]);
+- printf("LD_PS1(15)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
++ // printf("LD_PS1(15)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 15, 15, 15, 15);
+ t.v = VSWAPHL(a1.v, a2.v);
+- printf("VSWAPHL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
++ // printf("VSWAPHL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 8, 9, 6, 7);
+ VTRANSPOSE4(a0.v, a1.v, a2.v, a3.v);
+- printf("VTRANSPOSE4(0:3,4:7,8:11,12:15)=[%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g]\n",
+- a0.f[0], a0.f[1], a0.f[2], a0.f[3], a1.f[0], a1.f[1], a1.f[2], a1.f[3],
+- a2.f[0], a2.f[1], a2.f[2], a2.f[3], a3.f[0], a3.f[1], a3.f[2], a3.f[3]);
++ // printf("VTRANSPOSE4(0:3,4:7,8:11,12:15)=[%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g]\n",
++ // a0.f[0], a0.f[1], a0.f[2], a0.f[3], a1.f[0], a1.f[1], a1.f[2], a1.f[3],
++ // a2.f[0], a2.f[1], a2.f[2], a2.f[3], a3.f[0], a3.f[1], a3.f[2], a3.f[3]);
+ assertv4(a0, 0, 4, 8, 12); assertv4(a1, 1, 5, 9, 13); assertv4(a2, 2, 6, 10, 14); assertv4(a3, 3, 7, 11, 15);
+ }
+ #endif //!PFFFT_SIMD_DISABLE
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/02-decl_validate_simd.diff b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/02-decl_validate_simd.diff
new file mode 100644
index 0000000..4531511
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/02-decl_validate_simd.diff
@@ -0,0 +1,16 @@
+diff --git a/third_party/pffft/src/pffft.h b/third_party/pffft/src/pffft.h
+index 2bfa7b3ebcfb..bb6f78d4b795 100644
+--- a/third_party/pffft/src/pffft.h
++++ b/third_party/pffft/src/pffft.h
+@@ -83,6 +83,11 @@
+ extern "C" {
+ #endif
+
++#ifndef PFFFT_SIMD_DISABLE
++ // Detects compiler bugs with respect to simd instruction.
++ void validate_pffft_simd();
++#endif
++
+ /* opaque struct holding internal stuff (precomputed twiddle factors)
+ this struct can be shared by many threads as it contains only
+ read-only data.
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/03-malloca.diff b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/03-malloca.diff
new file mode 100644
index 0000000..ba7c4cf
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/03-malloca.diff
@@ -0,0 +1,82 @@
+diff --git a/third_party/pffft/src/pffft.c b/third_party/pffft/src/pffft.c
+index 776f564aa28c..643836626c0f 100644
+--- a/third_party/pffft/src/pffft.c
++++ b/third_party/pffft/src/pffft.c
+@@ -59,7 +59,6 @@
+
+ #include "pffft.h"
+ #include <stdlib.h>
+-// #include <stdio.h>
+ #include <math.h>
+ #include <assert.h>
+
+@@ -75,11 +74,14 @@
+ # define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))
+ # define RESTRICT __restrict
+ # define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ varname__[size__];
++# define VLA_ARRAY_ON_STACK_FREE(varname__)
+ #elif defined(COMPILER_MSVC)
++#include <malloc.h>
+ # define ALWAYS_INLINE(return_type) __forceinline return_type
+ # define NEVER_INLINE(return_type) __declspec(noinline) return_type
+ # define RESTRICT __restrict
+-# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (type__*)_alloca(size__ * sizeof(type__))
++# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (type__*)_malloca(size__ * sizeof(type__))
++# define VLA_ARRAY_ON_STACK_FREE(varname__) _freea(varname__)
+ #endif
+
+
+@@ -219,35 +221,24 @@ void validate_pffft_simd() {
+ memcpy(a3.f, f+12, 4*sizeof(float));
+
+ t = a0; u = a1; t.v = VZERO();
+- // printf("VZERO=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 0, 0, 0, 0);
+ t.v = VADD(a1.v, a2.v);
+- // printf("VADD(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 12, 14, 16, 18);
+ t.v = VMUL(a1.v, a2.v);
+- // printf("VMUL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 32, 45, 60, 77);
+ t.v = VMADD(a1.v, a2.v,a0.v);
+- // printf("VMADD(4:7,8:11,0:3)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 32, 46, 62, 80);
+
+ INTERLEAVE2(a1.v,a2.v,t.v,u.v);
+- // printf("INTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3], u.f[0], u.f[1], u.f[2], u.f[3]);
+ assertv4(t, 4, 8, 5, 9); assertv4(u, 6, 10, 7, 11);
+ UNINTERLEAVE2(a1.v,a2.v,t.v,u.v);
+- // printf("UNINTERLEAVE2(4:7,8:11)=[%2g %2g %2g %2g] [%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3], u.f[0], u.f[1], u.f[2], u.f[3]);
+ assertv4(t, 4, 6, 8, 10); assertv4(u, 5, 7, 9, 11);
+
+ t.v=LD_PS1(f[15]);
+- // printf("LD_PS1(15)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 15, 15, 15, 15);
+ t.v = VSWAPHL(a1.v, a2.v);
+- // printf("VSWAPHL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
+ assertv4(t, 8, 9, 6, 7);
+ VTRANSPOSE4(a0.v, a1.v, a2.v, a3.v);
+- // printf("VTRANSPOSE4(0:3,4:7,8:11,12:15)=[%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g] [%2g %2g %2g %2g]\n",
+- // a0.f[0], a0.f[1], a0.f[2], a0.f[3], a1.f[0], a1.f[1], a1.f[2], a1.f[3],
+- // a2.f[0], a2.f[1], a2.f[2], a2.f[3], a3.f[0], a3.f[1], a3.f[2], a3.f[3]);
+ assertv4(a0, 0, 4, 8, 12); assertv4(a1, 1, 5, 9, 13); assertv4(a2, 2, 6, 10, 14); assertv4(a3, 3, 7, 11, 15);
+ }
+ #endif //!PFFFT_SIMD_DISABLE
+@@ -1674,6 +1665,8 @@ void pffft_transform_internal(PFFFT_Setup *setup, const float *finput, float *fo
+ ib = !ib;
+ }
+ assert(buff[ib] == voutput);
++
++ VLA_ARRAY_ON_STACK_FREE(scratch_on_stack);
+ }
+
+ void pffft_zconvolve_accumulate(PFFFT_Setup *s, const float *a, const float *b, float *ab, float scaling) {
+@@ -1851,6 +1844,8 @@ void pffft_transform_internal_nosimd(PFFFT_Setup *setup, const float *input, flo
+ ib = !ib;
+ }
+ assert(buff[ib] == output);
++
++ VLA_ARRAY_ON_STACK_FREE(scratch_on_stack);
+ }
+
+ #define pffft_zconvolve_accumulate_nosimd pffft_zconvolve_accumulate
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/04-fix_ptr_cast.diff b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/04-fix_ptr_cast.diff
new file mode 100644
index 0000000..ae8ec0c
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/04-fix_ptr_cast.diff
@@ -0,0 +1,48 @@
+diff --git a/third_party/pffft/src/pffft.c b/third_party/pffft/src/pffft.c
+index 643836626c0f..3033e61b813e 100644
+--- a/third_party/pffft/src/pffft.c
++++ b/third_party/pffft/src/pffft.c
+@@ -58,6 +58,7 @@
+ */
+
+ #include "pffft.h"
++#include <stdint.h>
+ #include <stdlib.h>
+ #include <math.h>
+ #include <assert.h>
+@@ -125,7 +126,7 @@ inline v4sf ld_ps1(const float *p) { v4sf v=vec_lde(0,p); return vec_splat(vec_p
+ x3 = vec_mergel(y1, y3); \
+ }
+ # define VSWAPHL(a,b) vec_perm(a,b, (vector unsigned char)(16,17,18,19,20,21,22,23,8,9,10,11,12,13,14,15))
+-# define VALIGNED(ptr) ((((long)(ptr)) & 0xF) == 0)
++# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0xF) == 0)
+
+ /*
+ SSE1 support macros
+@@ -145,7 +146,7 @@ typedef __m128 v4sf;
+ # define UNINTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(2,0,2,0)); out2 = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(3,1,3,1)); out1 = tmp__; }
+ # define VTRANSPOSE4(x0,x1,x2,x3) _MM_TRANSPOSE4_PS(x0,x1,x2,x3)
+ # define VSWAPHL(a,b) _mm_shuffle_ps(b, a, _MM_SHUFFLE(3,2,1,0))
+-# define VALIGNED(ptr) ((((long)(ptr)) & 0xF) == 0)
++# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0xF) == 0)
+
+ /*
+ ARM NEON support macros
+@@ -172,7 +173,7 @@ typedef float32x4_t v4sf;
+ // marginally faster version
+ //# define VTRANSPOSE4(x0,x1,x2,x3) { asm("vtrn.32 %q0, %q1;\n vtrn.32 %q2,%q3\n vswp %f0,%e2\n vswp %f1,%e3" : "+w"(x0), "+w"(x1), "+w"(x2), "+w"(x3)::); }
+ # define VSWAPHL(a,b) vcombine_f32(vget_low_f32(b), vget_high_f32(a))
+-# define VALIGNED(ptr) ((((long)(ptr)) & 0x3) == 0)
++# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x3) == 0)
+ #else
+ # if !defined(PFFFT_SIMD_DISABLE)
+ # warning "building with simd disabled !\n";
+@@ -190,7 +191,7 @@ typedef float v4sf;
+ # define VMADD(a,b,c) ((a)*(b)+(c))
+ # define VSUB(a,b) ((a)-(b))
+ # define LD_PS1(p) (p)
+-# define VALIGNED(ptr) ((((long)(ptr)) & 0x3) == 0)
++# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x3) == 0)
+ #endif
+
+ // shortcuts for complex multiplcations
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/05-fix-arch-detection.diff b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/05-fix-arch-detection.diff
new file mode 100644
index 0000000..d6903ff
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/patches/05-fix-arch-detection.diff
@@ -0,0 +1,22 @@
+diff --git a/third_party/pffft/src/pffft.c b/third_party/pffft/src/pffft.c
+index 3033e61b813e..bdac4d784999 100644
+--- a/third_party/pffft/src/pffft.c
++++ b/third_party/pffft/src/pffft.c
+@@ -131,7 +131,7 @@ inline v4sf ld_ps1(const float *p) { v4sf v=vec_lde(0,p); return vec_splat(vec_p
+ /*
+ SSE1 support macros
+ */
+-#elif !defined(PFFFT_SIMD_DISABLE) && (defined(__x86_64__) || defined(_M_X64) || defined(i386) || defined(_M_IX86))
++#elif !defined(PFFFT_SIMD_DISABLE) && (defined(__x86_64__) || defined(_M_X64) || defined(i386) || defined(__i386__) || defined(_M_IX86))
+
+ #include <xmmintrin.h>
+ typedef __m128 v4sf;
+@@ -151,7 +151,7 @@ typedef __m128 v4sf;
+ /*
+ ARM NEON support macros
+ */
+-#elif !defined(PFFFT_SIMD_DISABLE) && defined(__arm__)
++#elif !defined(PFFFT_SIMD_DISABLE) && (defined(__arm__) || defined(__ARMEL__) || defined(__aarch64__) || defined(_M_ARM64))
+ # include <arm_neon.h>
+ typedef float32x4_t v4sf;
+ # define SIMD_SZ 4
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/pffft_fuzzer.cc b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/pffft_fuzzer.cc
new file mode 100644
index 0000000..904ad98
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/pffft_fuzzer.cc
@@ -0,0 +1,85 @@
+// Copyright 2019 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cstring>
+
+#include "third_party/pffft/src/pffft.h"
+
+namespace {
+
+#if defined(TRANSFORM_REAL)
+// Real FFT.
+constexpr pffft_transform_t kTransform = PFFFT_REAL;
+constexpr size_t kSizeOfOneSample = sizeof(float);
+#elif defined(TRANSFORM_COMPLEX)
+// Complex FFT.
+constexpr pffft_transform_t kTransform = PFFFT_COMPLEX;
+constexpr size_t kSizeOfOneSample = 2 * sizeof(float); // Real plus imaginary.
+#else
+#error FFT transform type not defined.
+#endif
+
+bool IsValidSize(size_t n) {
+ if (n == 0) {
+ return false;
+ }
+ // PFFFT only supports transforms for inputs of length N of the form
+ // N = (2^a)*(3^b)*(5^c) where a >= 5, b >=0, c >= 0.
+ constexpr std::array<int, 3> kFactors = {2, 3, 5};
+ std::array<int, kFactors.size()> factorization{};
+ for (size_t i = 0; i < kFactors.size(); ++i) {
+ const int factor = kFactors[i];
+ while (n % factor == 0) {
+ n /= factor;
+ factorization[i]++;
+ }
+ }
+ return factorization[0] >= 5 && n == 1;
+}
+
+float* AllocatePffftBuffer(size_t number_of_bytes) {
+ return static_cast<float*>(pffft_aligned_malloc(number_of_bytes));
+}
+
+} // namespace
+
+// Entry point for LibFuzzer.
+extern "C" int LLVMFuzzerTestOneInput(const uint8_t* data, size_t size) {
+ // Set the number of FFT points to use |data| as input vector.
+ // The latter is truncated if the number of bytes is not an integer
+ // multiple of the size of one sample (which is either a real or a complex
+ // floating point number).
+ const size_t fft_size = size / kSizeOfOneSample;
+ if (!IsValidSize(fft_size)) {
+ return 0;
+ }
+
+ const size_t number_of_bytes = fft_size * kSizeOfOneSample;
+ assert(number_of_bytes <= size);
+
+ // Allocate input and output buffers.
+ float* in = AllocatePffftBuffer(number_of_bytes);
+ float* out = AllocatePffftBuffer(number_of_bytes);
+
+ // Copy input data.
+ std::memcpy(in, reinterpret_cast<const float*>(data), number_of_bytes);
+
+ // Setup FFT.
+ PFFFT_Setup* pffft_setup = pffft_new_setup(fft_size, kTransform);
+
+ // Call different PFFFT functions to maximize the coverage.
+ pffft_transform(pffft_setup, in, out, nullptr, PFFFT_FORWARD);
+ pffft_zconvolve_accumulate(pffft_setup, out, out, out, 1.f);
+ pffft_transform_ordered(pffft_setup, in, out, nullptr, PFFFT_BACKWARD);
+
+ // Release memory.
+ pffft_aligned_free(in);
+ pffft_aligned_free(out);
+ pffft_destroy_setup(pffft_setup);
+
+ return 0;
+}
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/pffft_unittest.cc b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/pffft_unittest.cc
new file mode 100644
index 0000000..5597234
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/pffft_unittest.cc
@@ -0,0 +1,196 @@
+// Copyright 2019 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include <algorithm>
+#include <cmath>
+
+#include "testing/gtest/include/gtest/gtest-death-test.h"
+#include "testing/gtest/include/gtest/gtest.h"
+#include "third_party/pffft/src/fftpack.h"
+#include "third_party/pffft/src/pffft.h"
+
+namespace pffft {
+namespace test {
+namespace {
+
+static constexpr int kFftSizes[] = {
+ 16, 32, 64, 96, 128, 160, 192, 256, 288, 384, 5 * 96, 512,
+ 576, 5 * 128, 800, 864, 1024, 2048, 2592, 4000, 4096, 12000, 36864};
+
+double frand() {
+ return rand() / (double)RAND_MAX;
+}
+
+void PffftValidate(int fft_size, bool complex_fft) {
+ PFFFT_Setup* pffft_status =
+ pffft_new_setup(fft_size, complex_fft ? PFFFT_COMPLEX : PFFFT_REAL);
+ ASSERT_TRUE(pffft_status) << "FFT size (" << fft_size << ") not supported.";
+
+ int num_floats = fft_size * (complex_fft ? 2 : 1);
+ int num_bytes = num_floats * sizeof(float);
+ float* ref = static_cast<float*>(pffft_aligned_malloc(num_bytes));
+ float* in = static_cast<float*>(pffft_aligned_malloc(num_bytes));
+ float* out = static_cast<float*>(pffft_aligned_malloc(num_bytes));
+ float* tmp = static_cast<float*>(pffft_aligned_malloc(num_bytes));
+ float* tmp2 = static_cast<float*>(pffft_aligned_malloc(num_bytes));
+
+ for (int pass = 0; pass < 2; ++pass) {
+ SCOPED_TRACE(pass);
+ float ref_max = 0;
+ int k;
+
+ // Compute reference solution with FFTPACK.
+ if (pass == 0) {
+ float* fftpack_buff =
+ static_cast<float*>(malloc(2 * num_bytes + 15 * sizeof(float)));
+ for (k = 0; k < num_floats; ++k) {
+ ref[k] = in[k] = frand() * 2 - 1;
+ out[k] = 1e30;
+ }
+
+ if (!complex_fft) {
+ rffti(fft_size, fftpack_buff);
+ rfftf(fft_size, ref, fftpack_buff);
+ // Use our ordering for real FFTs instead of the one of fftpack.
+ {
+ float refN = ref[fft_size - 1];
+ for (k = fft_size - 2; k >= 1; --k)
+ ref[k + 1] = ref[k];
+ ref[1] = refN;
+ }
+ } else {
+ cffti(fft_size, fftpack_buff);
+ cfftf(fft_size, ref, fftpack_buff);
+ }
+
+ free(fftpack_buff);
+ }
+
+ for (k = 0; k < num_floats; ++k) {
+ ref_max = std::max(ref_max, fabs(ref[k]));
+ }
+
+ // Pass 0: non canonical ordering of transform coefficients.
+ if (pass == 0) {
+ // Test forward transform, with different input / output.
+ pffft_transform(pffft_status, in, tmp, nullptr, PFFFT_FORWARD);
+ memcpy(tmp2, tmp, num_bytes);
+ memcpy(tmp, in, num_bytes);
+ pffft_transform(pffft_status, tmp, tmp, nullptr, PFFFT_FORWARD);
+ for (k = 0; k < num_floats; ++k) {
+ SCOPED_TRACE(k);
+ EXPECT_EQ(tmp2[k], tmp[k]);
+ }
+
+ // Test reordering.
+ pffft_zreorder(pffft_status, tmp, out, PFFFT_FORWARD);
+ pffft_zreorder(pffft_status, out, tmp, PFFFT_BACKWARD);
+ for (k = 0; k < num_floats; ++k) {
+ SCOPED_TRACE(k);
+ EXPECT_EQ(tmp2[k], tmp[k]);
+ }
+ pffft_zreorder(pffft_status, tmp, out, PFFFT_FORWARD);
+ } else {
+ // Pass 1: canonical ordering of transform coefficients.
+ pffft_transform_ordered(pffft_status, in, tmp, nullptr, PFFFT_FORWARD);
+ memcpy(tmp2, tmp, num_bytes);
+ memcpy(tmp, in, num_bytes);
+ pffft_transform_ordered(pffft_status, tmp, tmp, nullptr, PFFFT_FORWARD);
+ for (k = 0; k < num_floats; ++k) {
+ SCOPED_TRACE(k);
+ EXPECT_EQ(tmp2[k], tmp[k]);
+ }
+ memcpy(out, tmp, num_bytes);
+ }
+
+ {
+ for (k = 0; k < num_floats; ++k) {
+ SCOPED_TRACE(k);
+ EXPECT_NEAR(ref[k], out[k], 1e-3 * ref_max) << "Forward FFT mismatch";
+ }
+
+ if (pass == 0) {
+ pffft_transform(pffft_status, tmp, out, nullptr, PFFFT_BACKWARD);
+ } else {
+ pffft_transform_ordered(pffft_status, tmp, out, nullptr,
+ PFFFT_BACKWARD);
+ }
+ memcpy(tmp2, out, num_bytes);
+ memcpy(out, tmp, num_bytes);
+ if (pass == 0) {
+ pffft_transform(pffft_status, out, out, nullptr, PFFFT_BACKWARD);
+ } else {
+ pffft_transform_ordered(pffft_status, out, out, nullptr,
+ PFFFT_BACKWARD);
+ }
+ for (k = 0; k < num_floats; ++k) {
+ assert(tmp2[k] == out[k]);
+ out[k] *= 1.f / fft_size;
+ }
+ for (k = 0; k < num_floats; ++k) {
+ SCOPED_TRACE(k);
+ EXPECT_NEAR(in[k], out[k], 1e-3 * ref_max) << "Reverse FFT mismatch";
+ }
+ }
+
+ // Quick test of the circular convolution in FFT domain.
+ {
+ float conv_err = 0, conv_max = 0;
+
+ pffft_zreorder(pffft_status, ref, tmp, PFFFT_FORWARD);
+ memset(out, 0, num_bytes);
+ pffft_zconvolve_accumulate(pffft_status, ref, ref, out, 1.0);
+ pffft_zreorder(pffft_status, out, tmp2, PFFFT_FORWARD);
+
+ for (k = 0; k < num_floats; k += 2) {
+ float ar = tmp[k], ai = tmp[k + 1];
+ if (complex_fft || k > 0) {
+ tmp[k] = ar * ar - ai * ai;
+ tmp[k + 1] = 2 * ar * ai;
+ } else {
+ tmp[0] = ar * ar;
+ tmp[1] = ai * ai;
+ }
+ }
+
+ for (k = 0; k < num_floats; ++k) {
+ float d = fabs(tmp[k] - tmp2[k]), e = fabs(tmp[k]);
+ if (d > conv_err)
+ conv_err = d;
+ if (e > conv_max)
+ conv_max = e;
+ }
+ EXPECT_LT(conv_err, 1e-5 * conv_max) << "zconvolve error";
+ }
+ }
+
+ pffft_destroy_setup(pffft_status);
+ pffft_aligned_free(ref);
+ pffft_aligned_free(in);
+ pffft_aligned_free(out);
+ pffft_aligned_free(tmp);
+ pffft_aligned_free(tmp2);
+}
+
+} // namespace
+
+TEST(PffftTest, ValidateReal) {
+ for (int fft_size : kFftSizes) {
+ SCOPED_TRACE(fft_size);
+ if (fft_size == 16) {
+ continue;
+ }
+ PffftValidate(fft_size, /*complex_fft=*/false);
+ }
+}
+
+TEST(PffftTest, ValidateComplex) {
+ for (int fft_size : kFftSizes) {
+ SCOPED_TRACE(fft_size);
+ PffftValidate(fft_size, /*complex_fft=*/true);
+ }
+}
+
+} // namespace test
+} // namespace pffft
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/fftpack.c b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/fftpack.c
new file mode 100644
index 0000000..b6375a8
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/fftpack.c
@@ -0,0 +1,3112 @@
+/*
+ compile with cc -DTESTING_FFTPACK fftpack.c in order to build the
+ test application.
+
+ This is an f2c translation of the full fftpack sources as found on
+ http://www.netlib.org/fftpack/ The translated code has been
+ slightlty edited to remove the ugliest artefacts of the translation
+ (a hundred of wild GOTOs were wiped during that operation).
+
+ The original fftpack file was written by Paul N. Swarztrauber
+ (Version 4, 1985), in fortran 77.
+
+ FFTPACK license:
+
+ http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
+
+ Copyright (c) 2004 the University Corporation for Atmospheric
+ Research ("UCAR"). All rights reserved. Developed by NCAR's
+ Computational and Information Systems Laboratory, UCAR,
+ www.cisl.ucar.edu.
+
+ Redistribution and use of the Software in source and binary forms,
+ with or without modification, is permitted provided that the
+ following conditions are met:
+
+ - Neither the names of NCAR's Computational and Information Systems
+ Laboratory, the University Corporation for Atmospheric Research,
+ nor the names of its sponsors or contributors may be used to
+ endorse or promote products derived from this Software without
+ specific prior written permission.
+
+ - Redistributions of source code must retain the above copyright
+ notices, this list of conditions, and the disclaimer below.
+
+ - Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions, and the disclaimer below in the
+ documentation and/or other materials provided with the
+ distribution.
+
+ THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+ HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+ SOFTWARE.
+
+ ChangeLog:
+ 2011/10/02: this is my first release of this file.
+*/
+
+#include "fftpack.h"
+#include <math.h>
+
+typedef fftpack_real real;
+typedef fftpack_int integer;
+
+typedef struct f77complex {
+ real r, i;
+} f77complex;
+
+#ifdef TESTING_FFTPACK
+static real c_abs(f77complex *c) { return sqrt(c->r*c->r + c->i*c->i); }
+static double dmax(double a, double b) { return a < b ? b : a; }
+#endif
+
+/* translated by f2c (version 20061008), and slightly edited */
+
+static void passfb(integer *nac, integer ido, integer ip, integer l1, integer idl1,
+ real *cc, real *c1, real *c2, real *ch, real *ch2, const real *wa, real fsign)
+{
+ /* System generated locals */
+ integer ch_offset, cc_offset,
+ c1_offset, c2_offset, ch2_offset;
+
+ /* Local variables */
+ integer i, j, k, l, jc, lc, ik, idj, idl, inc, idp;
+ real wai, war;
+ integer ipp2, idij, idlj, idot, ipph;
+
+
+#define c1_ref(a_1,a_2,a_3) c1[((a_3)*l1 + (a_2))*ido + a_1]
+#define c2_ref(a_1,a_2) c2[(a_2)*idl1 + a_1]
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*ip + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch2_ref(a_1,a_2) ch2[(a_2)*idl1 + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ c1_offset = 1 + ido * (1 + l1);
+ c1 -= c1_offset;
+ cc_offset = 1 + ido * (1 + ip);
+ cc -= cc_offset;
+ ch2_offset = 1 + idl1;
+ ch2 -= ch2_offset;
+ c2_offset = 1 + idl1;
+ c2 -= c2_offset;
+ --wa;
+
+ /* Function Body */
+ idot = ido / 2;
+ ipp2 = ip + 2;
+ ipph = (ip + 1) / 2;
+ idp = ip * ido;
+
+ if (ido >= l1) {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 1; i <= ido; ++i) {
+ ch_ref(i, k, j) = cc_ref(i, j, k) + cc_ref(i, jc, k);
+ ch_ref(i, k, jc) = cc_ref(i, j, k) - cc_ref(i, jc, k);
+ }
+ }
+ }
+ for (k = 1; k <= l1; ++k) {
+ for (i = 1; i <= ido; ++i) {
+ ch_ref(i, k, 1) = cc_ref(i, 1, k);
+ }
+ }
+ } else {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (i = 1; i <= ido; ++i) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(i, k, j) = cc_ref(i, j, k) + cc_ref(i, jc, k);
+ ch_ref(i, k, jc) = cc_ref(i, j, k) - cc_ref(i, jc, k);
+ }
+ }
+ }
+ for (i = 1; i <= ido; ++i) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(i, k, 1) = cc_ref(i, 1, k);
+ }
+ }
+ }
+ idl = 2 - ido;
+ inc = 0;
+ for (l = 2; l <= ipph; ++l) {
+ lc = ipp2 - l;
+ idl += ido;
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, l) = ch2_ref(ik, 1) + wa[idl - 1] * ch2_ref(ik, 2);
+ c2_ref(ik, lc) = fsign*wa[idl] * ch2_ref(ik, ip);
+ }
+ idlj = idl;
+ inc += ido;
+ for (j = 3; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ idlj += inc;
+ if (idlj > idp) {
+ idlj -= idp;
+ }
+ war = wa[idlj - 1];
+ wai = wa[idlj];
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, l) = c2_ref(ik, l) + war * ch2_ref(ik, j);
+ c2_ref(ik, lc) = c2_ref(ik, lc) + fsign*wai * ch2_ref(ik, jc);
+ }
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ for (ik = 1; ik <= idl1; ++ik) {
+ ch2_ref(ik, 1) = ch2_ref(ik, 1) + ch2_ref(ik, j);
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (ik = 2; ik <= idl1; ik += 2) {
+ ch2_ref(ik - 1, j) = c2_ref(ik - 1, j) - c2_ref(ik, jc);
+ ch2_ref(ik - 1, jc) = c2_ref(ik - 1, j) + c2_ref(ik, jc);
+ ch2_ref(ik, j) = c2_ref(ik, j) + c2_ref(ik - 1, jc);
+ ch2_ref(ik, jc) = c2_ref(ik, j) - c2_ref(ik - 1, jc);
+ }
+ }
+ *nac = 1;
+ if (ido == 2) {
+ return;
+ }
+ *nac = 0;
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, 1) = ch2_ref(ik, 1);
+ }
+ for (j = 2; j <= ip; ++j) {
+ for (k = 1; k <= l1; ++k) {
+ c1_ref(1, k, j) = ch_ref(1, k, j);
+ c1_ref(2, k, j) = ch_ref(2, k, j);
+ }
+ }
+ if (idot <= l1) {
+ idij = 0;
+ for (j = 2; j <= ip; ++j) {
+ idij += 2;
+ for (i = 4; i <= ido; i += 2) {
+ idij += 2;
+ for (k = 1; k <= l1; ++k) {
+ c1_ref(i - 1, k, j) = wa[idij - 1] * ch_ref(i - 1, k, j) - fsign*wa[idij] * ch_ref(i, k, j);
+ c1_ref(i, k, j) = wa[idij - 1] * ch_ref(i, k, j) + fsign*wa[idij] * ch_ref(i - 1, k, j);
+ }
+ }
+ }
+ return;
+ }
+ idj = 2 - ido;
+ for (j = 2; j <= ip; ++j) {
+ idj += ido;
+ for (k = 1; k <= l1; ++k) {
+ idij = idj;
+ for (i = 4; i <= ido; i += 2) {
+ idij += 2;
+ c1_ref(i - 1, k, j) = wa[idij - 1] * ch_ref(i - 1, k, j) - fsign*wa[idij] * ch_ref(i, k, j);
+ c1_ref(i, k, j) = wa[idij - 1] * ch_ref(i, k, j) + fsign*wa[idij] * ch_ref(i - 1, k, j);
+ }
+ }
+ }
+} /* passb */
+
+#undef ch2_ref
+#undef ch_ref
+#undef cc_ref
+#undef c2_ref
+#undef c1_ref
+
+
+static void passb2(integer ido, integer l1, const real *cc, real *ch, const real *wa1)
+{
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ti2, tr2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*2 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 3;
+ cc -= cc_offset;
+ --wa1;
+
+ /* Function Body */
+ if (ido <= 2) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + cc_ref(1, 2, k);
+ ch_ref(1, k, 2) = cc_ref(1, 1, k) - cc_ref(1, 2, k);
+ ch_ref(2, k, 1) = cc_ref(2, 1, k) + cc_ref(2, 2, k);
+ ch_ref(2, k, 2) = cc_ref(2, 1, k) - cc_ref(2, 2, k);
+ }
+ return;
+ }
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + cc_ref(i - 1, 2, k);
+ tr2 = cc_ref(i - 1, 1, k) - cc_ref(i - 1, 2, k);
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + cc_ref(i, 2, k);
+ ti2 = cc_ref(i, 1, k) - cc_ref(i, 2, k);
+ ch_ref(i, k, 2) = wa1[i - 1] * ti2 + wa1[i] * tr2;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * tr2 - wa1[i] * ti2;
+ }
+ }
+} /* passb2 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void passb3(integer ido, integer l1, const real *cc, real *ch, const real *wa1, const real *wa2)
+{
+ static const real taur = -.5f;
+ static const real taui = .866025403784439f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*3 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + (ido << 2);
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+
+ /* Function Body */
+ if (ido == 2) {
+ for (k = 1; k <= l1; ++k) {
+ tr2 = cc_ref(1, 2, k) + cc_ref(1, 3, k);
+ cr2 = cc_ref(1, 1, k) + taur * tr2;
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + tr2;
+ ti2 = cc_ref(2, 2, k) + cc_ref(2, 3, k);
+ ci2 = cc_ref(2, 1, k) + taur * ti2;
+ ch_ref(2, k, 1) = cc_ref(2, 1, k) + ti2;
+ cr3 = taui * (cc_ref(1, 2, k) - cc_ref(1, 3, k));
+ ci3 = taui * (cc_ref(2, 2, k) - cc_ref(2, 3, k));
+ ch_ref(1, k, 2) = cr2 - ci3;
+ ch_ref(1, k, 3) = cr2 + ci3;
+ ch_ref(2, k, 2) = ci2 + cr3;
+ ch_ref(2, k, 3) = ci2 - cr3;
+ }
+ } else {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ tr2 = cc_ref(i - 1, 2, k) + cc_ref(i - 1, 3, k);
+ cr2 = cc_ref(i - 1, 1, k) + taur * tr2;
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + tr2;
+ ti2 = cc_ref(i, 2, k) + cc_ref(i, 3, k);
+ ci2 = cc_ref(i, 1, k) + taur * ti2;
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + ti2;
+ cr3 = taui * (cc_ref(i - 1, 2, k) - cc_ref(i - 1, 3, k));
+ ci3 = taui * (cc_ref(i, 2, k) - cc_ref(i, 3, k));
+ dr2 = cr2 - ci3;
+ dr3 = cr2 + ci3;
+ di2 = ci2 + cr3;
+ di3 = ci2 - cr3;
+ ch_ref(i, k, 2) = wa1[i - 1] * di2 + wa1[i] * dr2;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * dr2 - wa1[i] * di2;
+ ch_ref(i, k, 3) = wa2[i - 1] * di3 + wa2[i] * dr3;
+ ch_ref(i - 1, k, 3) = wa2[i - 1] * dr3 - wa2[i] * di3;
+ }
+ }
+ }
+} /* passb3 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void passb4(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3)
+{
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*4 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 5;
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+
+ /* Function Body */
+ if (ido == 2) {
+ for (k = 1; k <= l1; ++k) {
+ ti1 = cc_ref(2, 1, k) - cc_ref(2, 3, k);
+ ti2 = cc_ref(2, 1, k) + cc_ref(2, 3, k);
+ tr4 = cc_ref(2, 4, k) - cc_ref(2, 2, k);
+ ti3 = cc_ref(2, 2, k) + cc_ref(2, 4, k);
+ tr1 = cc_ref(1, 1, k) - cc_ref(1, 3, k);
+ tr2 = cc_ref(1, 1, k) + cc_ref(1, 3, k);
+ ti4 = cc_ref(1, 2, k) - cc_ref(1, 4, k);
+ tr3 = cc_ref(1, 2, k) + cc_ref(1, 4, k);
+ ch_ref(1, k, 1) = tr2 + tr3;
+ ch_ref(1, k, 3) = tr2 - tr3;
+ ch_ref(2, k, 1) = ti2 + ti3;
+ ch_ref(2, k, 3) = ti2 - ti3;
+ ch_ref(1, k, 2) = tr1 + tr4;
+ ch_ref(1, k, 4) = tr1 - tr4;
+ ch_ref(2, k, 2) = ti1 + ti4;
+ ch_ref(2, k, 4) = ti1 - ti4;
+ }
+ } else {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ ti1 = cc_ref(i, 1, k) - cc_ref(i, 3, k);
+ ti2 = cc_ref(i, 1, k) + cc_ref(i, 3, k);
+ ti3 = cc_ref(i, 2, k) + cc_ref(i, 4, k);
+ tr4 = cc_ref(i, 4, k) - cc_ref(i, 2, k);
+ tr1 = cc_ref(i - 1, 1, k) - cc_ref(i - 1, 3, k);
+ tr2 = cc_ref(i - 1, 1, k) + cc_ref(i - 1, 3, k);
+ ti4 = cc_ref(i - 1, 2, k) - cc_ref(i - 1, 4, k);
+ tr3 = cc_ref(i - 1, 2, k) + cc_ref(i - 1, 4, k);
+ ch_ref(i - 1, k, 1) = tr2 + tr3;
+ cr3 = tr2 - tr3;
+ ch_ref(i, k, 1) = ti2 + ti3;
+ ci3 = ti2 - ti3;
+ cr2 = tr1 + tr4;
+ cr4 = tr1 - tr4;
+ ci2 = ti1 + ti4;
+ ci4 = ti1 - ti4;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * cr2 - wa1[i] * ci2;
+ ch_ref(i, k, 2) = wa1[i - 1] * ci2 + wa1[i] * cr2;
+ ch_ref(i - 1, k, 3) = wa2[i - 1] * cr3 - wa2[i] * ci3;
+ ch_ref(i, k, 3) = wa2[i - 1] * ci3 + wa2[i] * cr3;
+ ch_ref(i - 1, k, 4) = wa3[i - 1] * cr4 - wa3[i] * ci4;
+ ch_ref(i, k, 4) = wa3[i - 1] * ci4 + wa3[i] * cr4;
+ }
+ }
+ }
+} /* passb4 */
+
+#undef ch_ref
+#undef cc_ref
+
+/* passf5 and passb5 merged */
+static void passfb5(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3, const real *wa4, real fsign)
+{
+ const real tr11 = .309016994374947f;
+ const real ti11 = .951056516295154f*fsign;
+ const real tr12 = -.809016994374947f;
+ const real ti12 = .587785252292473f*fsign;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
+ ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*5 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 6;
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+ --wa4;
+
+ /* Function Body */
+ if (ido == 2) {
+ for (k = 1; k <= l1; ++k) {
+ ti5 = cc_ref(2, 2, k) - cc_ref(2, 5, k);
+ ti2 = cc_ref(2, 2, k) + cc_ref(2, 5, k);
+ ti4 = cc_ref(2, 3, k) - cc_ref(2, 4, k);
+ ti3 = cc_ref(2, 3, k) + cc_ref(2, 4, k);
+ tr5 = cc_ref(1, 2, k) - cc_ref(1, 5, k);
+ tr2 = cc_ref(1, 2, k) + cc_ref(1, 5, k);
+ tr4 = cc_ref(1, 3, k) - cc_ref(1, 4, k);
+ tr3 = cc_ref(1, 3, k) + cc_ref(1, 4, k);
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + tr2 + tr3;
+ ch_ref(2, k, 1) = cc_ref(2, 1, k) + ti2 + ti3;
+ cr2 = cc_ref(1, 1, k) + tr11 * tr2 + tr12 * tr3;
+ ci2 = cc_ref(2, 1, k) + tr11 * ti2 + tr12 * ti3;
+ cr3 = cc_ref(1, 1, k) + tr12 * tr2 + tr11 * tr3;
+ ci3 = cc_ref(2, 1, k) + tr12 * ti2 + tr11 * ti3;
+ cr5 = ti11 * tr5 + ti12 * tr4;
+ ci5 = ti11 * ti5 + ti12 * ti4;
+ cr4 = ti12 * tr5 - ti11 * tr4;
+ ci4 = ti12 * ti5 - ti11 * ti4;
+ ch_ref(1, k, 2) = cr2 - ci5;
+ ch_ref(1, k, 5) = cr2 + ci5;
+ ch_ref(2, k, 2) = ci2 + cr5;
+ ch_ref(2, k, 3) = ci3 + cr4;
+ ch_ref(1, k, 3) = cr3 - ci4;
+ ch_ref(1, k, 4) = cr3 + ci4;
+ ch_ref(2, k, 4) = ci3 - cr4;
+ ch_ref(2, k, 5) = ci2 - cr5;
+ }
+ } else {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ ti5 = cc_ref(i, 2, k) - cc_ref(i, 5, k);
+ ti2 = cc_ref(i, 2, k) + cc_ref(i, 5, k);
+ ti4 = cc_ref(i, 3, k) - cc_ref(i, 4, k);
+ ti3 = cc_ref(i, 3, k) + cc_ref(i, 4, k);
+ tr5 = cc_ref(i - 1, 2, k) - cc_ref(i - 1, 5, k);
+ tr2 = cc_ref(i - 1, 2, k) + cc_ref(i - 1, 5, k);
+ tr4 = cc_ref(i - 1, 3, k) - cc_ref(i - 1, 4, k);
+ tr3 = cc_ref(i - 1, 3, k) + cc_ref(i - 1, 4, k);
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + tr2 + tr3;
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + ti2 + ti3;
+ cr2 = cc_ref(i - 1, 1, k) + tr11 * tr2 + tr12 * tr3;
+ ci2 = cc_ref(i, 1, k) + tr11 * ti2 + tr12 * ti3;
+ cr3 = cc_ref(i - 1, 1, k) + tr12 * tr2 + tr11 * tr3;
+ ci3 = cc_ref(i, 1, k) + tr12 * ti2 + tr11 * ti3;
+ cr5 = ti11 * tr5 + ti12 * tr4;
+ ci5 = ti11 * ti5 + ti12 * ti4;
+ cr4 = ti12 * tr5 - ti11 * tr4;
+ ci4 = ti12 * ti5 - ti11 * ti4;
+ dr3 = cr3 - ci4;
+ dr4 = cr3 + ci4;
+ di3 = ci3 + cr4;
+ di4 = ci3 - cr4;
+ dr5 = cr2 + ci5;
+ dr2 = cr2 - ci5;
+ di5 = ci2 - cr5;
+ di2 = ci2 + cr5;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * dr2 - fsign*wa1[i] * di2;
+ ch_ref(i, k, 2) = wa1[i - 1] * di2 + fsign*wa1[i] * dr2;
+ ch_ref(i - 1, k, 3) = wa2[i - 1] * dr3 - fsign*wa2[i] * di3;
+ ch_ref(i, k, 3) = wa2[i - 1] * di3 + fsign*wa2[i] * dr3;
+ ch_ref(i - 1, k, 4) = wa3[i - 1] * dr4 - fsign*wa3[i] * di4;
+ ch_ref(i, k, 4) = wa3[i - 1] * di4 + fsign*wa3[i] * dr4;
+ ch_ref(i - 1, k, 5) = wa4[i - 1] * dr5 - fsign*wa4[i] * di5;
+ ch_ref(i, k, 5) = wa4[i - 1] * di5 + fsign*wa4[i] * dr5;
+ }
+ }
+ }
+} /* passb5 */
+
+#undef ch_ref
+#undef cc_ref
+
+static void passf2(integer ido, integer l1, const real *cc, real *ch, const real *wa1)
+{
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ti2, tr2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*2 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 3;
+ cc -= cc_offset;
+ --wa1;
+
+ /* Function Body */
+ if (ido == 2) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + cc_ref(1, 2, k);
+ ch_ref(1, k, 2) = cc_ref(1, 1, k) - cc_ref(1, 2, k);
+ ch_ref(2, k, 1) = cc_ref(2, 1, k) + cc_ref(2, 2, k);
+ ch_ref(2, k, 2) = cc_ref(2, 1, k) - cc_ref(2, 2, k);
+ }
+ } else {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + cc_ref(i - 1, 2,
+ k);
+ tr2 = cc_ref(i - 1, 1, k) - cc_ref(i - 1, 2, k);
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + cc_ref(i, 2, k);
+ ti2 = cc_ref(i, 1, k) - cc_ref(i, 2, k);
+ ch_ref(i, k, 2) = wa1[i - 1] * ti2 - wa1[i] * tr2;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * tr2 + wa1[i] * ti2;
+ }
+ }
+ }
+} /* passf2 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void passf3(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2)
+{
+ static const real taur = -.5f;
+ static const real taui = -.866025403784439f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*3 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + (ido << 2);
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+
+ /* Function Body */
+ if (ido == 2) {
+ for (k = 1; k <= l1; ++k) {
+ tr2 = cc_ref(1, 2, k) + cc_ref(1, 3, k);
+ cr2 = cc_ref(1, 1, k) + taur * tr2;
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + tr2;
+ ti2 = cc_ref(2, 2, k) + cc_ref(2, 3, k);
+ ci2 = cc_ref(2, 1, k) + taur * ti2;
+ ch_ref(2, k, 1) = cc_ref(2, 1, k) + ti2;
+ cr3 = taui * (cc_ref(1, 2, k) - cc_ref(1, 3, k));
+ ci3 = taui * (cc_ref(2, 2, k) - cc_ref(2, 3, k));
+ ch_ref(1, k, 2) = cr2 - ci3;
+ ch_ref(1, k, 3) = cr2 + ci3;
+ ch_ref(2, k, 2) = ci2 + cr3;
+ ch_ref(2, k, 3) = ci2 - cr3;
+ }
+ } else {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ tr2 = cc_ref(i - 1, 2, k) + cc_ref(i - 1, 3, k);
+ cr2 = cc_ref(i - 1, 1, k) + taur * tr2;
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + tr2;
+ ti2 = cc_ref(i, 2, k) + cc_ref(i, 3, k);
+ ci2 = cc_ref(i, 1, k) + taur * ti2;
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + ti2;
+ cr3 = taui * (cc_ref(i - 1, 2, k) - cc_ref(i - 1, 3, k));
+ ci3 = taui * (cc_ref(i, 2, k) - cc_ref(i, 3, k));
+ dr2 = cr2 - ci3;
+ dr3 = cr2 + ci3;
+ di2 = ci2 + cr3;
+ di3 = ci2 - cr3;
+ ch_ref(i, k, 2) = wa1[i - 1] * di2 - wa1[i] * dr2;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * dr2 + wa1[i] * di2;
+ ch_ref(i, k, 3) = wa2[i - 1] * di3 - wa2[i] * dr3;
+ ch_ref(i - 1, k, 3) = wa2[i - 1] * dr3 + wa2[i] * di3;
+ }
+ }
+ }
+} /* passf3 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void passf4(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3)
+{
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k;
+ real ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*4 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 5;
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+
+ /* Function Body */
+ if (ido == 2) {
+ for (k = 1; k <= l1; ++k) {
+ ti1 = cc_ref(2, 1, k) - cc_ref(2, 3, k);
+ ti2 = cc_ref(2, 1, k) + cc_ref(2, 3, k);
+ tr4 = cc_ref(2, 2, k) - cc_ref(2, 4, k);
+ ti3 = cc_ref(2, 2, k) + cc_ref(2, 4, k);
+ tr1 = cc_ref(1, 1, k) - cc_ref(1, 3, k);
+ tr2 = cc_ref(1, 1, k) + cc_ref(1, 3, k);
+ ti4 = cc_ref(1, 4, k) - cc_ref(1, 2, k);
+ tr3 = cc_ref(1, 2, k) + cc_ref(1, 4, k);
+ ch_ref(1, k, 1) = tr2 + tr3;
+ ch_ref(1, k, 3) = tr2 - tr3;
+ ch_ref(2, k, 1) = ti2 + ti3;
+ ch_ref(2, k, 3) = ti2 - ti3;
+ ch_ref(1, k, 2) = tr1 + tr4;
+ ch_ref(1, k, 4) = tr1 - tr4;
+ ch_ref(2, k, 2) = ti1 + ti4;
+ ch_ref(2, k, 4) = ti1 - ti4;
+ }
+ } else {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 2; i <= ido; i += 2) {
+ ti1 = cc_ref(i, 1, k) - cc_ref(i, 3, k);
+ ti2 = cc_ref(i, 1, k) + cc_ref(i, 3, k);
+ ti3 = cc_ref(i, 2, k) + cc_ref(i, 4, k);
+ tr4 = cc_ref(i, 2, k) - cc_ref(i, 4, k);
+ tr1 = cc_ref(i - 1, 1, k) - cc_ref(i - 1, 3, k);
+ tr2 = cc_ref(i - 1, 1, k) + cc_ref(i - 1, 3, k);
+ ti4 = cc_ref(i - 1, 4, k) - cc_ref(i - 1, 2, k);
+ tr3 = cc_ref(i - 1, 2, k) + cc_ref(i - 1, 4, k);
+ ch_ref(i - 1, k, 1) = tr2 + tr3;
+ cr3 = tr2 - tr3;
+ ch_ref(i, k, 1) = ti2 + ti3;
+ ci3 = ti2 - ti3;
+ cr2 = tr1 + tr4;
+ cr4 = tr1 - tr4;
+ ci2 = ti1 + ti4;
+ ci4 = ti1 - ti4;
+ ch_ref(i - 1, k, 2) = wa1[i - 1] * cr2 + wa1[i] * ci2;
+ ch_ref(i, k, 2) = wa1[i - 1] * ci2 - wa1[i] * cr2;
+ ch_ref(i - 1, k, 3) = wa2[i - 1] * cr3 + wa2[i] * ci3;
+ ch_ref(i, k, 3) = wa2[i - 1] * ci3 - wa2[i] * cr3;
+ ch_ref(i - 1, k, 4) = wa3[i - 1] * cr4 + wa3[i] * ci4;
+ ch_ref(i, k, 4) = wa3[i - 1] * ci4 - wa3[i] * cr4;
+ }
+ }
+ }
+} /* passf4 */
+
+#undef ch_ref
+#undef cc_ref
+
+static void radb2(integer ido, integer l1, const real *cc, real *ch, const real *wa1)
+{
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ti2, tr2;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*2 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 3;
+ cc -= cc_offset;
+ --wa1;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + cc_ref(ido, 2, k);
+ ch_ref(1, k, 2) = cc_ref(1, 1, k) - cc_ref(ido, 2, k);
+ }
+ if (ido < 2) return;
+ else if (ido != 2) {
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + cc_ref(ic - 1, 2,
+ k);
+ tr2 = cc_ref(i - 1, 1, k) - cc_ref(ic - 1, 2, k);
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) - cc_ref(ic, 2, k);
+ ti2 = cc_ref(i, 1, k) + cc_ref(ic, 2, k);
+ ch_ref(i - 1, k, 2) = wa1[i - 2] * tr2 - wa1[i - 1] * ti2;
+ ch_ref(i, k, 2) = wa1[i - 2] * ti2 + wa1[i - 1] * tr2;
+ }
+ }
+ if (ido % 2 == 1) return;
+ }
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(ido, k, 1) = cc_ref(ido, 1, k) + cc_ref(ido, 1, k);
+ ch_ref(ido, k, 2) = -(cc_ref(1, 2, k) + cc_ref(1, 2, k));
+ }
+} /* radb2 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radb3(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2)
+{
+ /* Initialized data */
+
+ static const real taur = -.5f;
+ static const real taui = .866025403784439f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*3 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + (ido << 2);
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ tr2 = cc_ref(ido, 2, k) + cc_ref(ido, 2, k);
+ cr2 = cc_ref(1, 1, k) + taur * tr2;
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + tr2;
+ ci3 = taui * (cc_ref(1, 3, k) + cc_ref(1, 3, k));
+ ch_ref(1, k, 2) = cr2 - ci3;
+ ch_ref(1, k, 3) = cr2 + ci3;
+ }
+ if (ido == 1) {
+ return;
+ }
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ tr2 = cc_ref(i - 1, 3, k) + cc_ref(ic - 1, 2, k);
+ cr2 = cc_ref(i - 1, 1, k) + taur * tr2;
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + tr2;
+ ti2 = cc_ref(i, 3, k) - cc_ref(ic, 2, k);
+ ci2 = cc_ref(i, 1, k) + taur * ti2;
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + ti2;
+ cr3 = taui * (cc_ref(i - 1, 3, k) - cc_ref(ic - 1, 2, k));
+ ci3 = taui * (cc_ref(i, 3, k) + cc_ref(ic, 2, k));
+ dr2 = cr2 - ci3;
+ dr3 = cr2 + ci3;
+ di2 = ci2 + cr3;
+ di3 = ci2 - cr3;
+ ch_ref(i - 1, k, 2) = wa1[i - 2] * dr2 - wa1[i - 1] * di2;
+ ch_ref(i, k, 2) = wa1[i - 2] * di2 + wa1[i - 1] * dr2;
+ ch_ref(i - 1, k, 3) = wa2[i - 2] * dr3 - wa2[i - 1] * di3;
+ ch_ref(i, k, 3) = wa2[i - 2] * di3 + wa2[i - 1] * dr3;
+ }
+ }
+} /* radb3 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radb4(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3)
+{
+ /* Initialized data */
+
+ static const real sqrt2 = 1.414213562373095f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*4 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 5;
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ tr1 = cc_ref(1, 1, k) - cc_ref(ido, 4, k);
+ tr2 = cc_ref(1, 1, k) + cc_ref(ido, 4, k);
+ tr3 = cc_ref(ido, 2, k) + cc_ref(ido, 2, k);
+ tr4 = cc_ref(1, 3, k) + cc_ref(1, 3, k);
+ ch_ref(1, k, 1) = tr2 + tr3;
+ ch_ref(1, k, 2) = tr1 - tr4;
+ ch_ref(1, k, 3) = tr2 - tr3;
+ ch_ref(1, k, 4) = tr1 + tr4;
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ ti1 = cc_ref(i, 1, k) + cc_ref(ic, 4, k);
+ ti2 = cc_ref(i, 1, k) - cc_ref(ic, 4, k);
+ ti3 = cc_ref(i, 3, k) - cc_ref(ic, 2, k);
+ tr4 = cc_ref(i, 3, k) + cc_ref(ic, 2, k);
+ tr1 = cc_ref(i - 1, 1, k) - cc_ref(ic - 1, 4, k);
+ tr2 = cc_ref(i - 1, 1, k) + cc_ref(ic - 1, 4, k);
+ ti4 = cc_ref(i - 1, 3, k) - cc_ref(ic - 1, 2, k);
+ tr3 = cc_ref(i - 1, 3, k) + cc_ref(ic - 1, 2, k);
+ ch_ref(i - 1, k, 1) = tr2 + tr3;
+ cr3 = tr2 - tr3;
+ ch_ref(i, k, 1) = ti2 + ti3;
+ ci3 = ti2 - ti3;
+ cr2 = tr1 - tr4;
+ cr4 = tr1 + tr4;
+ ci2 = ti1 + ti4;
+ ci4 = ti1 - ti4;
+ ch_ref(i - 1, k, 2) = wa1[i - 2] * cr2 - wa1[i - 1] * ci2;
+ ch_ref(i, k, 2) = wa1[i - 2] * ci2 + wa1[i - 1] * cr2;
+ ch_ref(i - 1, k, 3) = wa2[i - 2] * cr3 - wa2[i - 1] * ci3;
+ ch_ref(i, k, 3) = wa2[i - 2] * ci3 + wa2[i - 1] * cr3;
+ ch_ref(i - 1, k, 4) = wa3[i - 2] * cr4 - wa3[i - 1] * ci4;
+ ch_ref(i, k, 4) = wa3[i - 2] * ci4 + wa3[i - 1] * cr4;
+ }
+ }
+ if (ido % 2 == 1) return;
+ }
+ for (k = 1; k <= l1; ++k) {
+ ti1 = cc_ref(1, 2, k) + cc_ref(1, 4, k);
+ ti2 = cc_ref(1, 4, k) - cc_ref(1, 2, k);
+ tr1 = cc_ref(ido, 1, k) - cc_ref(ido, 3, k);
+ tr2 = cc_ref(ido, 1, k) + cc_ref(ido, 3, k);
+ ch_ref(ido, k, 1) = tr2 + tr2;
+ ch_ref(ido, k, 2) = sqrt2 * (tr1 - ti1);
+ ch_ref(ido, k, 3) = ti2 + ti2;
+ ch_ref(ido, k, 4) = -sqrt2 * (tr1 + ti1);
+ }
+} /* radb4 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radb5(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3, const real *wa4)
+{
+ /* Initialized data */
+
+ static const real tr11 = .309016994374947f;
+ static const real ti11 = .951056516295154f;
+ static const real tr12 = -.809016994374947f;
+ static const real ti12 = .587785252292473f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
+ ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*5 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 6;
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+ --wa4;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ ti5 = cc_ref(1, 3, k) + cc_ref(1, 3, k);
+ ti4 = cc_ref(1, 5, k) + cc_ref(1, 5, k);
+ tr2 = cc_ref(ido, 2, k) + cc_ref(ido, 2, k);
+ tr3 = cc_ref(ido, 4, k) + cc_ref(ido, 4, k);
+ ch_ref(1, k, 1) = cc_ref(1, 1, k) + tr2 + tr3;
+ cr2 = cc_ref(1, 1, k) + tr11 * tr2 + tr12 * tr3;
+ cr3 = cc_ref(1, 1, k) + tr12 * tr2 + tr11 * tr3;
+ ci5 = ti11 * ti5 + ti12 * ti4;
+ ci4 = ti12 * ti5 - ti11 * ti4;
+ ch_ref(1, k, 2) = cr2 - ci5;
+ ch_ref(1, k, 3) = cr3 - ci4;
+ ch_ref(1, k, 4) = cr3 + ci4;
+ ch_ref(1, k, 5) = cr2 + ci5;
+ }
+ if (ido == 1) {
+ return;
+ }
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ ti5 = cc_ref(i, 3, k) + cc_ref(ic, 2, k);
+ ti2 = cc_ref(i, 3, k) - cc_ref(ic, 2, k);
+ ti4 = cc_ref(i, 5, k) + cc_ref(ic, 4, k);
+ ti3 = cc_ref(i, 5, k) - cc_ref(ic, 4, k);
+ tr5 = cc_ref(i - 1, 3, k) - cc_ref(ic - 1, 2, k);
+ tr2 = cc_ref(i - 1, 3, k) + cc_ref(ic - 1, 2, k);
+ tr4 = cc_ref(i - 1, 5, k) - cc_ref(ic - 1, 4, k);
+ tr3 = cc_ref(i - 1, 5, k) + cc_ref(ic - 1, 4, k);
+ ch_ref(i - 1, k, 1) = cc_ref(i - 1, 1, k) + tr2 + tr3;
+ ch_ref(i, k, 1) = cc_ref(i, 1, k) + ti2 + ti3;
+ cr2 = cc_ref(i - 1, 1, k) + tr11 * tr2 + tr12 * tr3;
+ ci2 = cc_ref(i, 1, k) + tr11 * ti2 + tr12 * ti3;
+ cr3 = cc_ref(i - 1, 1, k) + tr12 * tr2 + tr11 * tr3;
+ ci3 = cc_ref(i, 1, k) + tr12 * ti2 + tr11 * ti3;
+ cr5 = ti11 * tr5 + ti12 * tr4;
+ ci5 = ti11 * ti5 + ti12 * ti4;
+ cr4 = ti12 * tr5 - ti11 * tr4;
+ ci4 = ti12 * ti5 - ti11 * ti4;
+ dr3 = cr3 - ci4;
+ dr4 = cr3 + ci4;
+ di3 = ci3 + cr4;
+ di4 = ci3 - cr4;
+ dr5 = cr2 + ci5;
+ dr2 = cr2 - ci5;
+ di5 = ci2 - cr5;
+ di2 = ci2 + cr5;
+ ch_ref(i - 1, k, 2) = wa1[i - 2] * dr2 - wa1[i - 1] * di2;
+ ch_ref(i, k, 2) = wa1[i - 2] * di2 + wa1[i - 1] * dr2;
+ ch_ref(i - 1, k, 3) = wa2[i - 2] * dr3 - wa2[i - 1] * di3;
+ ch_ref(i, k, 3) = wa2[i - 2] * di3 + wa2[i - 1] * dr3;
+ ch_ref(i - 1, k, 4) = wa3[i - 2] * dr4 - wa3[i - 1] * di4;
+ ch_ref(i, k, 4) = wa3[i - 2] * di4 + wa3[i - 1] * dr4;
+ ch_ref(i - 1, k, 5) = wa4[i - 2] * dr5 - wa4[i - 1] * di5;
+ ch_ref(i, k, 5) = wa4[i - 2] * di5 + wa4[i - 1] * dr5;
+ }
+ }
+} /* radb5 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radbg(integer ido, integer ip, integer l1, integer idl1,
+ const real *cc, real *c1, real *c2, real *ch, real *ch2, const real *wa)
+{
+ /* System generated locals */
+ integer ch_offset, cc_offset,
+ c1_offset, c2_offset, ch2_offset;
+
+ /* Local variables */
+ integer i, j, k, l, j2, ic, jc, lc, ik, is;
+ real dc2, ai1, ai2, ar1, ar2, ds2;
+ integer nbd;
+ real dcp, arg, dsp, ar1h, ar2h;
+ integer idp2, ipp2, idij, ipph;
+
+
+#define c1_ref(a_1,a_2,a_3) c1[((a_3)*l1 + (a_2))*ido + a_1]
+#define c2_ref(a_1,a_2) c2[(a_2)*idl1 + a_1]
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*ip + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch2_ref(a_1,a_2) ch2[(a_2)*idl1 + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ c1_offset = 1 + ido * (1 + l1);
+ c1 -= c1_offset;
+ cc_offset = 1 + ido * (1 + ip);
+ cc -= cc_offset;
+ ch2_offset = 1 + idl1;
+ ch2 -= ch2_offset;
+ c2_offset = 1 + idl1;
+ c2 -= c2_offset;
+ --wa;
+
+ /* Function Body */
+ arg = (2*M_PI) / (real) (ip);
+ dcp = cos(arg);
+ dsp = sin(arg);
+ idp2 = ido + 2;
+ nbd = (ido - 1) / 2;
+ ipp2 = ip + 2;
+ ipph = (ip + 1) / 2;
+ if (ido >= l1) {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 1; i <= ido; ++i) {
+ ch_ref(i, k, 1) = cc_ref(i, 1, k);
+ }
+ }
+ } else {
+ for (i = 1; i <= ido; ++i) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(i, k, 1) = cc_ref(i, 1, k);
+ }
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ j2 = j + j;
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, k, j) = cc_ref(ido, j2 - 2, k) + cc_ref(ido, j2 - 2, k);
+ ch_ref(1, k, jc) = cc_ref(1, j2 - 1, k) + cc_ref(1, j2 - 1, k);
+ }
+ }
+ if (ido != 1) {
+ if (nbd >= l1) {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ ch_ref(i - 1, k, j) = cc_ref(i - 1, (j << 1) - 1, k) + cc_ref(ic - 1, (j << 1) - 2, k);
+ ch_ref(i - 1, k, jc) = cc_ref(i - 1, (j << 1) - 1, k) - cc_ref(ic - 1, (j << 1) - 2, k);
+ ch_ref(i, k, j) = cc_ref(i, (j << 1) - 1, k) - cc_ref(ic, (j << 1) - 2, k);
+ ch_ref(i, k, jc) = cc_ref(i, (j << 1) - 1, k) + cc_ref(ic, (j << 1) - 2, k);
+ }
+ }
+ }
+ } else {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(i - 1, k, j) = cc_ref(i - 1, (j << 1) - 1, k) + cc_ref(ic - 1, (j << 1) - 2, k);
+ ch_ref(i - 1, k, jc) = cc_ref(i - 1, (j << 1) - 1, k) - cc_ref(ic - 1, (j << 1) - 2, k);
+ ch_ref(i, k, j) = cc_ref(i, (j << 1) - 1, k) - cc_ref(ic, (j << 1) - 2, k);
+ ch_ref(i, k, jc) = cc_ref(i, (j << 1) - 1, k) + cc_ref(ic, (j << 1) - 2, k);
+ }
+ }
+ }
+ }
+ }
+ ar1 = 1.f;
+ ai1 = 0.f;
+ for (l = 2; l <= ipph; ++l) {
+ lc = ipp2 - l;
+ ar1h = dcp * ar1 - dsp * ai1;
+ ai1 = dcp * ai1 + dsp * ar1;
+ ar1 = ar1h;
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, l) = ch2_ref(ik, 1) + ar1 * ch2_ref(ik, 2);
+ c2_ref(ik, lc) = ai1 * ch2_ref(ik, ip);
+ }
+ dc2 = ar1;
+ ds2 = ai1;
+ ar2 = ar1;
+ ai2 = ai1;
+ for (j = 3; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ ar2h = dc2 * ar2 - ds2 * ai2;
+ ai2 = dc2 * ai2 + ds2 * ar2;
+ ar2 = ar2h;
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, l) = c2_ref(ik, l) + ar2 * ch2_ref(ik, j);
+ c2_ref(ik, lc) = c2_ref(ik, lc) + ai2 * ch2_ref(ik, jc);
+ }
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ for (ik = 1; ik <= idl1; ++ik) {
+ ch2_ref(ik, 1) = ch2_ref(ik, 1) + ch2_ref(ik, j);
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, k, j) = c1_ref(1, k, j) - c1_ref(1, k, jc);
+ ch_ref(1, k, jc) = c1_ref(1, k, j) + c1_ref(1, k, jc);
+ }
+ }
+ if (ido != 1) {
+ if (nbd >= l1) {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ch_ref(i - 1, k, j) = c1_ref(i - 1, k, j) - c1_ref(i, k, jc);
+ ch_ref(i - 1, k, jc) = c1_ref(i - 1, k, j) + c1_ref(i, k, jc);
+ ch_ref(i, k, j) = c1_ref(i, k, j) + c1_ref(i - 1, k, jc);
+ ch_ref(i, k, jc) = c1_ref(i, k, j) - c1_ref(i - 1, k, jc);
+ }
+ }
+ }
+ } else {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (i = 3; i <= ido; i += 2) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(i - 1, k, j) = c1_ref(i - 1, k, j) - c1_ref(i, k, jc);
+ ch_ref(i - 1, k, jc) = c1_ref(i - 1, k, j) + c1_ref(i, k, jc);
+ ch_ref(i, k, j) = c1_ref(i, k, j) + c1_ref(i - 1, k, jc);
+ ch_ref(i, k, jc) = c1_ref(i, k, j) - c1_ref(i - 1, k, jc);
+ }
+ }
+ }
+ }
+ }
+ if (ido == 1) {
+ return;
+ }
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, 1) = ch2_ref(ik, 1);
+ }
+ for (j = 2; j <= ip; ++j) {
+ for (k = 1; k <= l1; ++k) {
+ c1_ref(1, k, j) = ch_ref(1, k, j);
+ }
+ }
+ if (nbd <= l1) {
+ is = -(ido);
+ for (j = 2; j <= ip; ++j) {
+ is += ido;
+ idij = is;
+ for (i = 3; i <= ido; i += 2) {
+ idij += 2;
+ for (k = 1; k <= l1; ++k) {
+ c1_ref(i - 1, k, j) = wa[idij - 1] * ch_ref(i - 1, k, j)
+ - wa[idij] * ch_ref(i, k, j);
+ c1_ref(i, k, j) = wa[idij - 1] * ch_ref(i, k, j) + wa[idij] * ch_ref(i - 1, k, j);
+ }
+ }
+ }
+ } else {
+ is = -(ido);
+ for (j = 2; j <= ip; ++j) {
+ is += ido;
+ for (k = 1; k <= l1; ++k) {
+ idij = is;
+ for (i = 3; i <= ido; i += 2) {
+ idij += 2;
+ c1_ref(i - 1, k, j) = wa[idij - 1] * ch_ref(i - 1, k, j)
+ - wa[idij] * ch_ref(i, k, j);
+ c1_ref(i, k, j) = wa[idij - 1] * ch_ref(i, k, j) + wa[idij] * ch_ref(i - 1, k, j);
+ }
+ }
+ }
+ }
+} /* radbg */
+
+#undef ch2_ref
+#undef ch_ref
+#undef cc_ref
+#undef c2_ref
+#undef c1_ref
+
+
+static void radf2(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1)
+{
+ /* System generated locals */
+ integer ch_offset, cc_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ti2, tr2;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*2 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * 3;
+ ch -= ch_offset;
+ cc_offset = 1 + ido * (1 + l1);
+ cc -= cc_offset;
+ --wa1;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, 1, k) = cc_ref(1, k, 1) + cc_ref(1, k, 2);
+ ch_ref(ido, 2, k) = cc_ref(1, k, 1) - cc_ref(1, k, 2);
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ tr2 = wa1[i - 2] * cc_ref(i - 1, k, 2) + wa1[i - 1] *
+ cc_ref(i, k, 2);
+ ti2 = wa1[i - 2] * cc_ref(i, k, 2) - wa1[i - 1] * cc_ref(
+ i - 1, k, 2);
+ ch_ref(i, 1, k) = cc_ref(i, k, 1) + ti2;
+ ch_ref(ic, 2, k) = ti2 - cc_ref(i, k, 1);
+ ch_ref(i - 1, 1, k) = cc_ref(i - 1, k, 1) + tr2;
+ ch_ref(ic - 1, 2, k) = cc_ref(i - 1, k, 1) - tr2;
+ }
+ }
+ if (ido % 2 == 1) {
+ return;
+ }
+ }
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, 2, k) = -cc_ref(ido, k, 2);
+ ch_ref(ido, 1, k) = cc_ref(ido, k, 1);
+ }
+} /* radf2 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radf3(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2)
+{
+ static const real taur = -.5f;
+ static const real taui = .866025403784439f;
+
+ /* System generated locals */
+ integer ch_offset, cc_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ci2, di2, di3, cr2, dr2, dr3, ti2, ti3, tr2, tr3;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*3 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + (ido << 2);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * (1 + l1);
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ cr2 = cc_ref(1, k, 2) + cc_ref(1, k, 3);
+ ch_ref(1, 1, k) = cc_ref(1, k, 1) + cr2;
+ ch_ref(1, 3, k) = taui * (cc_ref(1, k, 3) - cc_ref(1, k, 2));
+ ch_ref(ido, 2, k) = cc_ref(1, k, 1) + taur * cr2;
+ }
+ if (ido == 1) {
+ return;
+ }
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ dr2 = wa1[i - 2] * cc_ref(i - 1, k, 2) + wa1[i - 1] *
+ cc_ref(i, k, 2);
+ di2 = wa1[i - 2] * cc_ref(i, k, 2) - wa1[i - 1] * cc_ref(
+ i - 1, k, 2);
+ dr3 = wa2[i - 2] * cc_ref(i - 1, k, 3) + wa2[i - 1] *
+ cc_ref(i, k, 3);
+ di3 = wa2[i - 2] * cc_ref(i, k, 3) - wa2[i - 1] * cc_ref(
+ i - 1, k, 3);
+ cr2 = dr2 + dr3;
+ ci2 = di2 + di3;
+ ch_ref(i - 1, 1, k) = cc_ref(i - 1, k, 1) + cr2;
+ ch_ref(i, 1, k) = cc_ref(i, k, 1) + ci2;
+ tr2 = cc_ref(i - 1, k, 1) + taur * cr2;
+ ti2 = cc_ref(i, k, 1) + taur * ci2;
+ tr3 = taui * (di2 - di3);
+ ti3 = taui * (dr3 - dr2);
+ ch_ref(i - 1, 3, k) = tr2 + tr3;
+ ch_ref(ic - 1, 2, k) = tr2 - tr3;
+ ch_ref(i, 3, k) = ti2 + ti3;
+ ch_ref(ic, 2, k) = ti3 - ti2;
+ }
+ }
+} /* radf3 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radf4(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3)
+{
+ /* Initialized data */
+
+ static const real hsqt2 = .7071067811865475f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*4 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * 5;
+ ch -= ch_offset;
+ cc_offset = 1 + ido * (1 + l1);
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ tr1 = cc_ref(1, k, 2) + cc_ref(1, k, 4);
+ tr2 = cc_ref(1, k, 1) + cc_ref(1, k, 3);
+ ch_ref(1, 1, k) = tr1 + tr2;
+ ch_ref(ido, 4, k) = tr2 - tr1;
+ ch_ref(ido, 2, k) = cc_ref(1, k, 1) - cc_ref(1, k, 3);
+ ch_ref(1, 3, k) = cc_ref(1, k, 4) - cc_ref(1, k, 2);
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ cr2 = wa1[i - 2] * cc_ref(i - 1, k, 2) + wa1[i - 1] *
+ cc_ref(i, k, 2);
+ ci2 = wa1[i - 2] * cc_ref(i, k, 2) - wa1[i - 1] * cc_ref(
+ i - 1, k, 2);
+ cr3 = wa2[i - 2] * cc_ref(i - 1, k, 3) + wa2[i - 1] *
+ cc_ref(i, k, 3);
+ ci3 = wa2[i - 2] * cc_ref(i, k, 3) - wa2[i - 1] * cc_ref(
+ i - 1, k, 3);
+ cr4 = wa3[i - 2] * cc_ref(i - 1, k, 4) + wa3[i - 1] *
+ cc_ref(i, k, 4);
+ ci4 = wa3[i - 2] * cc_ref(i, k, 4) - wa3[i - 1] * cc_ref(
+ i - 1, k, 4);
+ tr1 = cr2 + cr4;
+ tr4 = cr4 - cr2;
+ ti1 = ci2 + ci4;
+ ti4 = ci2 - ci4;
+ ti2 = cc_ref(i, k, 1) + ci3;
+ ti3 = cc_ref(i, k, 1) - ci3;
+ tr2 = cc_ref(i - 1, k, 1) + cr3;
+ tr3 = cc_ref(i - 1, k, 1) - cr3;
+ ch_ref(i - 1, 1, k) = tr1 + tr2;
+ ch_ref(ic - 1, 4, k) = tr2 - tr1;
+ ch_ref(i, 1, k) = ti1 + ti2;
+ ch_ref(ic, 4, k) = ti1 - ti2;
+ ch_ref(i - 1, 3, k) = ti4 + tr3;
+ ch_ref(ic - 1, 2, k) = tr3 - ti4;
+ ch_ref(i, 3, k) = tr4 + ti3;
+ ch_ref(ic, 2, k) = tr4 - ti3;
+ }
+ }
+ if (ido % 2 == 1) {
+ return;
+ }
+ }
+ for (k = 1; k <= l1; ++k) {
+ ti1 = -hsqt2 * (cc_ref(ido, k, 2) + cc_ref(ido, k, 4));
+ tr1 = hsqt2 * (cc_ref(ido, k, 2) - cc_ref(ido, k, 4));
+ ch_ref(ido, 1, k) = tr1 + cc_ref(ido, k, 1);
+ ch_ref(ido, 3, k) = cc_ref(ido, k, 1) - tr1;
+ ch_ref(1, 2, k) = ti1 - cc_ref(ido, k, 3);
+ ch_ref(1, 4, k) = ti1 + cc_ref(ido, k, 3);
+ }
+} /* radf4 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radf5(integer ido, integer l1, const real *cc, real *ch,
+ const real *wa1, const real *wa2, const real *wa3, const real *wa4)
+{
+ /* Initialized data */
+
+ static const real tr11 = .309016994374947f;
+ static const real ti11 = .951056516295154f;
+ static const real tr12 = -.809016994374947f;
+ static const real ti12 = .587785252292473f;
+
+ /* System generated locals */
+ integer cc_offset, ch_offset;
+
+ /* Local variables */
+ integer i, k, ic;
+ real ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3, dr4, dr5,
+ cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5;
+ integer idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*5 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * 6;
+ ch -= ch_offset;
+ cc_offset = 1 + ido * (1 + l1);
+ cc -= cc_offset;
+ --wa1;
+ --wa2;
+ --wa3;
+ --wa4;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ cr2 = cc_ref(1, k, 5) + cc_ref(1, k, 2);
+ ci5 = cc_ref(1, k, 5) - cc_ref(1, k, 2);
+ cr3 = cc_ref(1, k, 4) + cc_ref(1, k, 3);
+ ci4 = cc_ref(1, k, 4) - cc_ref(1, k, 3);
+ ch_ref(1, 1, k) = cc_ref(1, k, 1) + cr2 + cr3;
+ ch_ref(ido, 2, k) = cc_ref(1, k, 1) + tr11 * cr2 + tr12 * cr3;
+ ch_ref(1, 3, k) = ti11 * ci5 + ti12 * ci4;
+ ch_ref(ido, 4, k) = cc_ref(1, k, 1) + tr12 * cr2 + tr11 * cr3;
+ ch_ref(1, 5, k) = ti12 * ci5 - ti11 * ci4;
+ }
+ if (ido == 1) {
+ return;
+ }
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ dr2 = wa1[i - 2] * cc_ref(i - 1, k, 2) + wa1[i - 1] * cc_ref(i, k, 2);
+ di2 = wa1[i - 2] * cc_ref(i, k, 2) - wa1[i - 1] * cc_ref(i - 1, k, 2);
+ dr3 = wa2[i - 2] * cc_ref(i - 1, k, 3) + wa2[i - 1] * cc_ref(i, k, 3);
+ di3 = wa2[i - 2] * cc_ref(i, k, 3) - wa2[i - 1] * cc_ref(i - 1, k, 3);
+ dr4 = wa3[i - 2] * cc_ref(i - 1, k, 4) + wa3[i - 1] * cc_ref(i, k, 4);
+ di4 = wa3[i - 2] * cc_ref(i, k, 4) - wa3[i - 1] * cc_ref(i - 1, k, 4);
+ dr5 = wa4[i - 2] * cc_ref(i - 1, k, 5) + wa4[i - 1] * cc_ref(i, k, 5);
+ di5 = wa4[i - 2] * cc_ref(i, k, 5) - wa4[i - 1] * cc_ref(i - 1, k, 5);
+ cr2 = dr2 + dr5;
+ ci5 = dr5 - dr2;
+ cr5 = di2 - di5;
+ ci2 = di2 + di5;
+ cr3 = dr3 + dr4;
+ ci4 = dr4 - dr3;
+ cr4 = di3 - di4;
+ ci3 = di3 + di4;
+ ch_ref(i - 1, 1, k) = cc_ref(i - 1, k, 1) + cr2 + cr3;
+ ch_ref(i, 1, k) = cc_ref(i, k, 1) + ci2 + ci3;
+ tr2 = cc_ref(i - 1, k, 1) + tr11 * cr2 + tr12 * cr3;
+ ti2 = cc_ref(i, k, 1) + tr11 * ci2 + tr12 * ci3;
+ tr3 = cc_ref(i - 1, k, 1) + tr12 * cr2 + tr11 * cr3;
+ ti3 = cc_ref(i, k, 1) + tr12 * ci2 + tr11 * ci3;
+ tr5 = ti11 * cr5 + ti12 * cr4;
+ ti5 = ti11 * ci5 + ti12 * ci4;
+ tr4 = ti12 * cr5 - ti11 * cr4;
+ ti4 = ti12 * ci5 - ti11 * ci4;
+ ch_ref(i - 1, 3, k) = tr2 + tr5;
+ ch_ref(ic - 1, 2, k) = tr2 - tr5;
+ ch_ref(i, 3, k) = ti2 + ti5;
+ ch_ref(ic, 2, k) = ti5 - ti2;
+ ch_ref(i - 1, 5, k) = tr3 + tr4;
+ ch_ref(ic - 1, 4, k) = tr3 - tr4;
+ ch_ref(i, 5, k) = ti3 + ti4;
+ ch_ref(ic, 4, k) = ti4 - ti3;
+ }
+ }
+} /* radf5 */
+
+#undef ch_ref
+#undef cc_ref
+
+
+static void radfg(integer ido, integer ip, integer l1, integer idl1,
+ real *cc, real *c1, real *c2, real *ch, real *ch2, const real *wa)
+{
+ /* System generated locals */
+ integer ch_offset, cc_offset,
+ c1_offset, c2_offset, ch2_offset;
+
+ /* Local variables */
+ integer i, j, k, l, j2, ic, jc, lc, ik, is;
+ real dc2, ai1, ai2, ar1, ar2, ds2;
+ integer nbd;
+ real dcp, arg, dsp, ar1h, ar2h;
+ integer idp2, ipp2, idij, ipph;
+
+
+#define c1_ref(a_1,a_2,a_3) c1[((a_3)*l1 + (a_2))*ido + a_1]
+#define c2_ref(a_1,a_2) c2[(a_2)*idl1 + a_1]
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*ip + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch2_ref(a_1,a_2) ch2[(a_2)*idl1 + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ c1_offset = 1 + ido * (1 + l1);
+ c1 -= c1_offset;
+ cc_offset = 1 + ido * (1 + ip);
+ cc -= cc_offset;
+ ch2_offset = 1 + idl1;
+ ch2 -= ch2_offset;
+ c2_offset = 1 + idl1;
+ c2 -= c2_offset;
+ --wa;
+
+ /* Function Body */
+ arg = (2*M_PI) / (real) (ip);
+ dcp = cos(arg);
+ dsp = sin(arg);
+ ipph = (ip + 1) / 2;
+ ipp2 = ip + 2;
+ idp2 = ido + 2;
+ nbd = (ido - 1) / 2;
+ if (ido == 1) {
+ for (ik = 1; ik <= idl1; ++ik) {
+ c2_ref(ik, 1) = ch2_ref(ik, 1);
+ }
+ } else {
+ for (ik = 1; ik <= idl1; ++ik) {
+ ch2_ref(ik, 1) = c2_ref(ik, 1);
+ }
+ for (j = 2; j <= ip; ++j) {
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(1, k, j) = c1_ref(1, k, j);
+ }
+ }
+ if (nbd <= l1) {
+ is = -(ido);
+ for (j = 2; j <= ip; ++j) {
+ is += ido;
+ idij = is;
+ for (i = 3; i <= ido; i += 2) {
+ idij += 2;
+ for (k = 1; k <= l1; ++k) {
+ ch_ref(i - 1, k, j) = wa[idij - 1] * c1_ref(i - 1, k, j)
+ + wa[idij] * c1_ref(i, k, j);
+ ch_ref(i, k, j) = wa[idij - 1] * c1_ref(i, k, j) - wa[
+ idij] * c1_ref(i - 1, k, j);
+ }
+ }
+ }
+ } else {
+ is = -(ido);
+ for (j = 2; j <= ip; ++j) {
+ is += ido;
+ for (k = 1; k <= l1; ++k) {
+ idij = is;
+ for (i = 3; i <= ido; i += 2) {
+ idij += 2;
+ ch_ref(i - 1, k, j) = wa[idij - 1] * c1_ref(i - 1, k, j)
+ + wa[idij] * c1_ref(i, k, j);
+ ch_ref(i, k, j) = wa[idij - 1] * c1_ref(i, k, j) - wa[
+ idij] * c1_ref(i - 1, k, j);
+ }
+ }
+ }
+ }
+ if (nbd >= l1) {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ c1_ref(i - 1, k, j) = ch_ref(i - 1, k, j) + ch_ref(i -
+ 1, k, jc);
+ c1_ref(i - 1, k, jc) = ch_ref(i, k, j) - ch_ref(i, k,
+ jc);
+ c1_ref(i, k, j) = ch_ref(i, k, j) + ch_ref(i, k, jc);
+ c1_ref(i, k, jc) = ch_ref(i - 1, k, jc) - ch_ref(i - 1,
+ k, j);
+ }
+ }
+ }
+ } else {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (i = 3; i <= ido; i += 2) {
+ for (k = 1; k <= l1; ++k) {
+ c1_ref(i - 1, k, j) = ch_ref(i - 1, k, j) + ch_ref(i -
+ 1, k, jc);
+ c1_ref(i - 1, k, jc) = ch_ref(i, k, j) - ch_ref(i, k,
+ jc);
+ c1_ref(i, k, j) = ch_ref(i, k, j) + ch_ref(i, k, jc);
+ c1_ref(i, k, jc) = ch_ref(i - 1, k, jc) - ch_ref(i - 1,
+ k, j);
+ }
+ }
+ }
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ for (k = 1; k <= l1; ++k) {
+ c1_ref(1, k, j) = ch_ref(1, k, j) + ch_ref(1, k, jc);
+ c1_ref(1, k, jc) = ch_ref(1, k, jc) - ch_ref(1, k, j);
+ }
+ }
+
+ ar1 = 1.f;
+ ai1 = 0.f;
+ for (l = 2; l <= ipph; ++l) {
+ lc = ipp2 - l;
+ ar1h = dcp * ar1 - dsp * ai1;
+ ai1 = dcp * ai1 + dsp * ar1;
+ ar1 = ar1h;
+ for (ik = 1; ik <= idl1; ++ik) {
+ ch2_ref(ik, l) = c2_ref(ik, 1) + ar1 * c2_ref(ik, 2);
+ ch2_ref(ik, lc) = ai1 * c2_ref(ik, ip);
+ }
+ dc2 = ar1;
+ ds2 = ai1;
+ ar2 = ar1;
+ ai2 = ai1;
+ for (j = 3; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ ar2h = dc2 * ar2 - ds2 * ai2;
+ ai2 = dc2 * ai2 + ds2 * ar2;
+ ar2 = ar2h;
+ for (ik = 1; ik <= idl1; ++ik) {
+ ch2_ref(ik, l) = ch2_ref(ik, l) + ar2 * c2_ref(ik, j);
+ ch2_ref(ik, lc) = ch2_ref(ik, lc) + ai2 * c2_ref(ik, jc);
+ }
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ for (ik = 1; ik <= idl1; ++ik) {
+ ch2_ref(ik, 1) = ch2_ref(ik, 1) + c2_ref(ik, j);
+ }
+ }
+
+ if (ido >= l1) {
+ for (k = 1; k <= l1; ++k) {
+ for (i = 1; i <= ido; ++i) {
+ cc_ref(i, 1, k) = ch_ref(i, k, 1);
+ }
+ }
+ } else {
+ for (i = 1; i <= ido; ++i) {
+ for (k = 1; k <= l1; ++k) {
+ cc_ref(i, 1, k) = ch_ref(i, k, 1);
+ }
+ }
+ }
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ j2 = j + j;
+ for (k = 1; k <= l1; ++k) {
+ cc_ref(ido, j2 - 2, k) = ch_ref(1, k, j);
+ cc_ref(1, j2 - 1, k) = ch_ref(1, k, jc);
+ }
+ }
+ if (ido == 1) {
+ return;
+ }
+ if (nbd >= l1) {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ j2 = j + j;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ cc_ref(i - 1, j2 - 1, k) = ch_ref(i - 1, k, j) + ch_ref(
+ i - 1, k, jc);
+ cc_ref(ic - 1, j2 - 2, k) = ch_ref(i - 1, k, j) - ch_ref(
+ i - 1, k, jc);
+ cc_ref(i, j2 - 1, k) = ch_ref(i, k, j) + ch_ref(i, k,
+ jc);
+ cc_ref(ic, j2 - 2, k) = ch_ref(i, k, jc) - ch_ref(i, k, j)
+ ;
+ }
+ }
+ }
+ } else {
+ for (j = 2; j <= ipph; ++j) {
+ jc = ipp2 - j;
+ j2 = j + j;
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ for (k = 1; k <= l1; ++k) {
+ cc_ref(i - 1, j2 - 1, k) = ch_ref(i - 1, k, j) + ch_ref(
+ i - 1, k, jc);
+ cc_ref(ic - 1, j2 - 2, k) = ch_ref(i - 1, k, j) - ch_ref(
+ i - 1, k, jc);
+ cc_ref(i, j2 - 1, k) = ch_ref(i, k, j) + ch_ref(i, k,
+ jc);
+ cc_ref(ic, j2 - 2, k) = ch_ref(i, k, jc) - ch_ref(i, k, j)
+ ;
+ }
+ }
+ }
+ }
+} /* radfg */
+
+#undef ch2_ref
+#undef ch_ref
+#undef cc_ref
+#undef c2_ref
+#undef c1_ref
+
+
+static void cfftb1(integer n, real *c, real *ch, const real *wa, integer *ifac)
+{
+ integer i, k1, l1, l2, na, nf, ip, iw, ix2, ix3, ix4, nac, ido,
+ idl1, idot;
+
+ /* Function Body */
+ nf = ifac[1];
+ na = 0;
+ l1 = 1;
+ iw = 0;
+ for (k1 = 1; k1 <= nf; ++k1) {
+ ip = ifac[k1 + 1];
+ l2 = ip * l1;
+ ido = n / l2;
+ idot = ido + ido;
+ idl1 = idot * l1;
+ switch (ip) {
+ case 4:
+ ix2 = iw + idot;
+ ix3 = ix2 + idot;
+ passb4(idot, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2], &wa[ix3]);
+ na = 1 - na;
+ break;
+ case 2:
+ passb2(idot, l1, na?ch:c, na?c:ch, &wa[iw]);
+ na = 1 - na;
+ break;
+ case 3:
+ ix2 = iw + idot;
+ passb3(idot, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2]);
+ na = 1 - na;
+ break;
+ case 5:
+ ix2 = iw + idot;
+ ix3 = ix2 + idot;
+ ix4 = ix3 + idot;
+ passfb5(idot, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], +1);
+ na = 1 - na;
+ break;
+ default:
+ if (na == 0) {
+ passfb(&nac, idot, ip, l1, idl1, c, c, c, ch, ch, &wa[iw], +1);
+ } else {
+ passfb(&nac, idot, ip, l1, idl1, ch, ch, ch, c, c, &wa[iw], +1);
+ }
+ if (nac != 0) {
+ na = 1 - na;
+ }
+ break;
+ }
+ l1 = l2;
+ iw += (ip - 1) * idot;
+ }
+ if (na == 0) {
+ return;
+ }
+ for (i = 0; i < 2*n; ++i) {
+ c[i] = ch[i];
+ }
+} /* cfftb1 */
+
+void cfftb(integer n, real *c, real *wsave)
+{
+ integer iw1, iw2;
+
+ /* Parameter adjustments */
+ --wsave;
+ --c;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ iw1 = 2*n + 1;
+ iw2 = iw1 + 2*n;
+ cfftb1(n, &c[1], &wsave[1], &wsave[iw1], (int*)&wsave[iw2]);
+} /* cfftb */
+
+static void cfftf1(integer n, real *c, real *ch, const real *wa, integer *ifac)
+{
+ /* Local variables */
+ integer i, k1, l1, l2, na, nf, ip, iw, ix2, ix3, ix4, nac, ido,
+ idl1, idot;
+
+ /* Function Body */
+ nf = ifac[1];
+ na = 0;
+ l1 = 1;
+ iw = 0;
+ for (k1 = 1; k1 <= nf; ++k1) {
+ ip = ifac[k1 + 1];
+ l2 = ip * l1;
+ ido = n / l2;
+ idot = ido + ido;
+ idl1 = idot * l1;
+ switch (ip) {
+ case 4:
+ ix2 = iw + idot;
+ ix3 = ix2 + idot;
+ passf4(idot, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2], &wa[ix3]);
+ na = 1 - na;
+ break;
+ case 2:
+ passf2(idot, l1, na?ch:c, na?c:ch, &wa[iw]);
+ na = 1 - na;
+ break;
+ case 3:
+ ix2 = iw + idot;
+ passf3(idot, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2]);
+ na = 1 - na;
+ break;
+ case 5:
+ ix2 = iw + idot;
+ ix3 = ix2 + idot;
+ ix4 = ix3 + idot;
+ passfb5(idot, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], -1);
+ na = 1 - na;
+ break;
+ default:
+ if (na == 0) {
+ passfb(&nac, idot, ip, l1, idl1, c, c, c, ch, ch, &wa[iw], -1);
+ } else {
+ passfb(&nac, idot, ip, l1, idl1, ch, ch, ch, c, c, &wa[iw], -1);
+ }
+ if (nac != 0) {
+ na = 1 - na;
+ }
+ break;
+ }
+ l1 = l2;
+ iw += (ip - 1)*idot;
+ }
+ if (na == 0) {
+ return;
+ }
+ for (i = 0; i < 2*n; ++i) {
+ c[i] = ch[i];
+ }
+} /* cfftf1 */
+
+void cfftf(integer n, real *c, real *wsave)
+{
+ integer iw1, iw2;
+
+ /* Parameter adjustments */
+ --wsave;
+ --c;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ iw1 = 2*n + 1;
+ iw2 = iw1 + 2*n;
+ cfftf1(n, &c[1], &wsave[1], &wsave[iw1], (int*)&wsave[iw2]);
+} /* cfftf */
+
+static int decompose(integer n, integer *ifac, integer ntryh[4]) {
+ integer ntry=0, nl = n, nf = 0, nq, nr, i, j = 0;
+ do {
+ if (j < 4) {
+ ntry = ntryh[j];
+ } else {
+ ntry += 2;
+ }
+ ++j;
+ L104:
+ nq = nl / ntry;
+ nr = nl - ntry * nq;
+ if (nr != 0) continue;
+ ++nf;
+ ifac[nf + 2] = ntry;
+ nl = nq;
+ if (ntry == 2 && nf != 1) {
+ for (i = 2; i <= nf; ++i) {
+ integer ib = nf - i + 2;
+ ifac[ib + 2] = ifac[ib + 1];
+ }
+ ifac[3] = 2;
+ }
+ if (nl != 1) {
+ goto L104;
+ }
+ } while (nl != 1);
+ ifac[1] = n;
+ ifac[2] = nf;
+ return nf;
+}
+
+static void cffti1(integer n, real *wa, integer *ifac)
+{
+ static integer ntryh[4] = { 3,4,2,5 };
+
+ /* Local variables */
+ integer i, j, i1, k1, l1, l2;
+ real fi;
+ integer ld, ii, nf, ip;
+ real arg;
+ integer ido, ipm;
+ real argh;
+ integer idot;
+ real argld;
+
+ /* Parameter adjustments */
+ --ifac;
+ --wa;
+
+ nf = decompose(n, ifac, ntryh);
+
+ argh = (2*M_PI) / (real) (n);
+ i = 2;
+ l1 = 1;
+ for (k1 = 1; k1 <= nf; ++k1) {
+ ip = ifac[k1 + 2];
+ ld = 0;
+ l2 = l1 * ip;
+ ido = n / l2;
+ idot = ido + ido + 2;
+ ipm = ip - 1;
+ for (j = 1; j <= ipm; ++j) {
+ i1 = i;
+ wa[i - 1] = 1.f;
+ wa[i] = 0.f;
+ ld += l1;
+ fi = 0.f;
+ argld = (real) ld * argh;
+ for (ii = 4; ii <= idot; ii += 2) {
+ i += 2;
+ fi += 1.f;
+ arg = fi * argld;
+ wa[i - 1] = cos(arg);
+ wa[i] = sin(arg);
+ }
+ if (ip > 5) {
+ wa[i1 - 1] = wa[i - 1];
+ wa[i1] = wa[i];
+ };
+ }
+ l1 = l2;
+ }
+} /* cffti1 */
+
+void cffti(integer n, real *wsave)
+{
+ integer iw1, iw2;
+ /* Parameter adjustments */
+ --wsave;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ iw1 = 2*n + 1;
+ iw2 = iw1 + 2*n;
+ cffti1(n, &wsave[iw1], (int*)&wsave[iw2]);
+ return;
+} /* cffti */
+
+static void rfftb1(integer n, real *c, real *ch, const real *wa, integer *ifac)
+{
+ /* Local variables */
+ integer i, k1, l1, l2, na, nf, ip, iw, ix2, ix3, ix4, ido, idl1;
+
+ /* Function Body */
+ nf = ifac[1];
+ na = 0;
+ l1 = 1;
+ iw = 0;
+ for (k1 = 1; k1 <= nf; ++k1) {
+ ip = ifac[k1 + 1];
+ l2 = ip * l1;
+ ido = n / l2;
+ idl1 = ido * l1;
+ switch (ip) {
+ case 4:
+ ix2 = iw + ido;
+ ix3 = ix2 + ido;
+ radb4(ido, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2], &wa[ix3]);
+ na = 1 - na;
+ break;
+ case 2:
+ radb2(ido, l1, na?ch:c, na?c:ch, &wa[iw]);
+ na = 1 - na;
+ break;
+ case 3:
+ ix2 = iw + ido;
+ radb3(ido, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2]);
+ na = 1 - na;
+ break;
+ case 5:
+ ix2 = iw + ido;
+ ix3 = ix2 + ido;
+ ix4 = ix3 + ido;
+ radb5(ido, l1, na?ch:c, na?c:ch, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
+ na = 1 - na;
+ break;
+ default:
+ if (na == 0) {
+ radbg(ido, ip, l1, idl1, c, c, c, ch, ch, &wa[iw]);
+ } else {
+ radbg(ido, ip, l1, idl1, ch, ch, ch, c, c, &wa[iw]);
+ }
+ if (ido == 1) {
+ na = 1 - na;
+ }
+ break;
+ }
+ l1 = l2;
+ iw += (ip - 1) * ido;
+ }
+ if (na == 0) {
+ return;
+ }
+ for (i = 0; i < n; ++i) {
+ c[i] = ch[i];
+ }
+} /* rfftb1 */
+
+static void rfftf1(integer n, real *c, real *ch, const real *wa, integer *ifac)
+{
+ /* Local variables */
+ integer i, k1, l1, l2, na, kh, nf, ip, iw, ix2, ix3, ix4, ido, idl1;
+
+ /* Function Body */
+ nf = ifac[1];
+ na = 1;
+ l2 = n;
+ iw = n-1;
+ for (k1 = 1; k1 <= nf; ++k1) {
+ kh = nf - k1;
+ ip = ifac[kh + 2];
+ l1 = l2 / ip;
+ ido = n / l2;
+ idl1 = ido * l1;
+ iw -= (ip - 1) * ido;
+ na = 1 - na;
+ switch (ip) {
+ case 4:
+ ix2 = iw + ido;
+ ix3 = ix2 + ido;
+ radf4(ido, l1, na ? ch : c, na ? c : ch, &wa[iw], &wa[ix2], &wa[ix3]);
+ break;
+ case 2:
+ radf2(ido, l1, na ? ch : c, na ? c : ch, &wa[iw]);
+ break;
+ case 3:
+ ix2 = iw + ido;
+ radf3(ido, l1, na ? ch : c, na ? c : ch, &wa[iw], &wa[ix2]);
+ break;
+ case 5:
+ ix2 = iw + ido;
+ ix3 = ix2 + ido;
+ ix4 = ix3 + ido;
+ radf5(ido, l1, na ? ch : c, na ? c : ch, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
+ break;
+ default:
+ if (ido == 1) {
+ na = 1 - na;
+ }
+ if (na == 0) {
+ radfg(ido, ip, l1, idl1, c, c, c, ch, ch, &wa[iw]);
+ na = 1;
+ } else {
+ radfg(ido, ip, l1, idl1, ch, ch, ch, c, c, &wa[iw]);
+ na = 0;
+ }
+ break;
+ }
+ l2 = l1;
+ }
+ if (na == 1) {
+ return;
+ }
+ for (i = 0; i < n; ++i) {
+ c[i] = ch[i];
+ }
+}
+
+void rfftb(integer n, real *r, real *wsave)
+{
+
+ /* Parameter adjustments */
+ --wsave;
+ --r;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ rfftb1(n, &r[1], &wsave[1], &wsave[n + 1], (int*)&wsave[(n << 1) + 1]);
+} /* rfftb */
+
+static void rffti1(integer n, real *wa, integer *ifac)
+{
+ static integer ntryh[4] = { 4,2,3,5 };
+
+ /* Local variables */
+ integer i, j, k1, l1, l2;
+ real fi;
+ integer ld, ii, nf, ip, is;
+ real arg;
+ integer ido, ipm;
+ integer nfm1;
+ real argh;
+ real argld;
+
+ /* Parameter adjustments */
+ --ifac;
+ --wa;
+
+ nf = decompose(n, ifac, ntryh);
+
+ argh = (2*M_PI) / (real) (n);
+ is = 0;
+ nfm1 = nf - 1;
+ l1 = 1;
+ if (nfm1 == 0) {
+ return;
+ }
+ for (k1 = 1; k1 <= nfm1; ++k1) {
+ ip = ifac[k1 + 2];
+ ld = 0;
+ l2 = l1 * ip;
+ ido = n / l2;
+ ipm = ip - 1;
+ for (j = 1; j <= ipm; ++j) {
+ ld += l1;
+ i = is;
+ argld = (real) ld * argh;
+ fi = 0.f;
+ for (ii = 3; ii <= ido; ii += 2) {
+ i += 2;
+ fi += 1.f;
+ arg = fi * argld;
+ wa[i - 1] = cos(arg);
+ wa[i] = sin(arg);
+ }
+ is += ido;
+ }
+ l1 = l2;
+ }
+} /* rffti1 */
+
+void rfftf(integer n, real *r, real *wsave)
+{
+
+ /* Parameter adjustments */
+ --wsave;
+ --r;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ rfftf1(n, &r[1], &wsave[1], &wsave[n + 1], (int*)&wsave[(n << 1) + 1]);
+} /* rfftf */
+
+void rffti(integer n, real *wsave)
+{
+ /* Parameter adjustments */
+ --wsave;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ rffti1(n, &wsave[n + 1], (int*)&wsave[(n << 1) + 1]);
+ return;
+} /* rffti */
+
+static void cosqb1(integer n, real *x, real *w, real *xh)
+{
+ /* Local variables */
+ integer i, k, kc, np2, ns2;
+ real xim1;
+ integer modn;
+
+ /* Parameter adjustments */
+ --xh;
+ --w;
+ --x;
+
+ /* Function Body */
+ ns2 = (n + 1) / 2;
+ np2 = n + 2;
+ for (i = 3; i <= n; i += 2) {
+ xim1 = x[i - 1] + x[i];
+ x[i] -= x[i - 1];
+ x[i - 1] = xim1;
+ }
+ x[1] += x[1];
+ modn = n % 2;
+ if (modn == 0) {
+ x[n] += x[n];
+ }
+ rfftb(n, &x[1], &xh[1]);
+ for (k = 2; k <= ns2; ++k) {
+ kc = np2 - k;
+ xh[k] = w[k - 1] * x[kc] + w[kc - 1] * x[k];
+ xh[kc] = w[k - 1] * x[k] - w[kc - 1] * x[kc];
+ }
+ if (modn == 0) {
+ x[ns2 + 1] = w[ns2] * (x[ns2 + 1] + x[ns2 + 1]);
+ }
+ for (k = 2; k <= ns2; ++k) {
+ kc = np2 - k;
+ x[k] = xh[k] + xh[kc];
+ x[kc] = xh[k] - xh[kc];
+ }
+ x[1] += x[1];
+} /* cosqb1 */
+
+void cosqb(integer n, real *x, real *wsave)
+{
+ static const real tsqrt2 = 2.82842712474619f;
+
+ /* Local variables */
+ real x1;
+
+ /* Parameter adjustments */
+ --wsave;
+ --x;
+
+ if (n < 2) {
+ x[1] *= 4.f;
+ } else if (n == 2) {
+ x1 = (x[1] + x[2]) * 4.f;
+ x[2] = tsqrt2 * (x[1] - x[2]);
+ x[1] = x1;
+ } else {
+ cosqb1(n, &x[1], &wsave[1], &wsave[n + 1]);
+ }
+} /* cosqb */
+
+static void cosqf1(integer n, real *x, real *w, real *xh)
+{
+ /* Local variables */
+ integer i, k, kc, np2, ns2;
+ real xim1;
+ integer modn;
+
+ /* Parameter adjustments */
+ --xh;
+ --w;
+ --x;
+
+ /* Function Body */
+ ns2 = (n + 1) / 2;
+ np2 = n + 2;
+ for (k = 2; k <= ns2; ++k) {
+ kc = np2 - k;
+ xh[k] = x[k] + x[kc];
+ xh[kc] = x[k] - x[kc];
+ }
+ modn = n % 2;
+ if (modn == 0) {
+ xh[ns2 + 1] = x[ns2 + 1] + x[ns2 + 1];
+ }
+ for (k = 2; k <= ns2; ++k) {
+ kc = np2 - k;
+ x[k] = w[k - 1] * xh[kc] + w[kc - 1] * xh[k];
+ x[kc] = w[k - 1] * xh[k] - w[kc - 1] * xh[kc];
+ }
+ if (modn == 0) {
+ x[ns2 + 1] = w[ns2] * xh[ns2 + 1];
+ }
+ rfftf(n, &x[1], &xh[1]);
+ for (i = 3; i <= n; i += 2) {
+ xim1 = x[i - 1] - x[i];
+ x[i] = x[i - 1] + x[i];
+ x[i - 1] = xim1;
+ }
+} /* cosqf1 */
+
+void cosqf(integer n, real *x, real *wsave)
+{
+ static const real sqrt2 = 1.4142135623731f;
+
+ /* Local variables */
+ real tsqx;
+
+ /* Parameter adjustments */
+ --wsave;
+ --x;
+
+ if (n == 2) {
+ tsqx = sqrt2 * x[2];
+ x[2] = x[1] - tsqx;
+ x[1] += tsqx;
+ } else if (n > 2) {
+ cosqf1(n, &x[1], &wsave[1], &wsave[n + 1]);
+ }
+} /* cosqf */
+
+void cosqi(integer n, real *wsave)
+{
+ /* Local variables */
+ integer k;
+ real fk, dt;
+
+ /* Parameter adjustments */
+ --wsave;
+
+ dt = M_PI/2 / (real) (n);
+ fk = 0.f;
+ for (k = 1; k <= n; ++k) {
+ fk += 1.f;
+ wsave[k] = cos(fk * dt);
+ }
+ rffti(n, &wsave[n + 1]);
+} /* cosqi */
+
+void cost(integer n, real *x, real *wsave)
+{
+ /* Local variables */
+ integer i, k;
+ real c1, t1, t2;
+ integer kc;
+ real xi;
+ integer nm1, np1;
+ real x1h;
+ integer ns2;
+ real tx2, x1p3, xim2;
+ integer modn;
+
+ /* Parameter adjustments */
+ --wsave;
+ --x;
+
+ /* Function Body */
+ nm1 = n - 1;
+ np1 = n + 1;
+ ns2 = n / 2;
+ if (n < 2) {
+ } else if (n == 2) {
+ x1h = x[1] + x[2];
+ x[2] = x[1] - x[2];
+ x[1] = x1h;
+ } else if (n == 3) {
+ x1p3 = x[1] + x[3];
+ tx2 = x[2] + x[2];
+ x[2] = x[1] - x[3];
+ x[1] = x1p3 + tx2;
+ x[3] = x1p3 - tx2;
+ } else {
+ c1 = x[1] - x[n];
+ x[1] += x[n];
+ for (k = 2; k <= ns2; ++k) {
+ kc = np1 - k;
+ t1 = x[k] + x[kc];
+ t2 = x[k] - x[kc];
+ c1 += wsave[kc] * t2;
+ t2 = wsave[k] * t2;
+ x[k] = t1 - t2;
+ x[kc] = t1 + t2;
+ }
+ modn = n % 2;
+ if (modn != 0) {
+ x[ns2 + 1] += x[ns2 + 1];
+ }
+ rfftf(nm1, &x[1], &wsave[n + 1]);
+ xim2 = x[2];
+ x[2] = c1;
+ for (i = 4; i <= n; i += 2) {
+ xi = x[i];
+ x[i] = x[i - 2] - x[i - 1];
+ x[i - 1] = xim2;
+ xim2 = xi;
+ }
+ if (modn != 0) {
+ x[n] = xim2;
+ }
+ }
+} /* cost */
+
+void costi(integer n, real *wsave)
+{
+ /* Initialized data */
+
+ /* Local variables */
+ integer k, kc;
+ real fk, dt;
+ integer nm1, np1, ns2;
+
+ /* Parameter adjustments */
+ --wsave;
+
+ /* Function Body */
+ if (n <= 3) {
+ return;
+ }
+ nm1 = n - 1;
+ np1 = n + 1;
+ ns2 = n / 2;
+ dt = M_PI / (real) nm1;
+ fk = 0.f;
+ for (k = 2; k <= ns2; ++k) {
+ kc = np1 - k;
+ fk += 1.f;
+ wsave[k] = sin(fk * dt) * 2.f;
+ wsave[kc] = cos(fk * dt) * 2.f;
+ }
+ rffti(nm1, &wsave[n + 1]);
+} /* costi */
+
+void sinqb(integer n, real *x, real *wsave)
+{
+ /* Local variables */
+ integer k, kc, ns2;
+ real xhold;
+
+ /* Parameter adjustments */
+ --wsave;
+ --x;
+
+ /* Function Body */
+ if (n <= 1) {
+ x[1] *= 4.f;
+ return;
+ }
+ ns2 = n / 2;
+ for (k = 2; k <= n; k += 2) {
+ x[k] = -x[k];
+ }
+ cosqb(n, &x[1], &wsave[1]);
+ for (k = 1; k <= ns2; ++k) {
+ kc = n - k;
+ xhold = x[k];
+ x[k] = x[kc + 1];
+ x[kc + 1] = xhold;
+ }
+} /* sinqb */
+
+void sinqf(integer n, real *x, real *wsave)
+{
+ /* Local variables */
+ integer k, kc, ns2;
+ real xhold;
+
+ /* Parameter adjustments */
+ --wsave;
+ --x;
+
+ /* Function Body */
+ if (n == 1) {
+ return;
+ }
+ ns2 = n / 2;
+ for (k = 1; k <= ns2; ++k) {
+ kc = n - k;
+ xhold = x[k];
+ x[k] = x[kc + 1];
+ x[kc + 1] = xhold;
+ }
+ cosqf(n, &x[1], &wsave[1]);
+ for (k = 2; k <= n; k += 2) {
+ x[k] = -x[k];
+ }
+} /* sinqf */
+
+void sinqi(integer n, real *wsave)
+{
+
+ /* Parameter adjustments */
+ --wsave;
+
+ /* Function Body */
+ cosqi(n, &wsave[1]);
+} /* sinqi */
+
+static void sint1(integer n, real *war, real *was, real *xh, real *
+ x, integer *ifac)
+{
+ /* Initialized data */
+
+ static const real sqrt3 = 1.73205080756888f;
+
+ /* Local variables */
+ integer i, k;
+ real t1, t2;
+ integer kc, np1, ns2, modn;
+ real xhold;
+
+ /* Parameter adjustments */
+ --ifac;
+ --x;
+ --xh;
+ --was;
+ --war;
+
+ /* Function Body */
+ for (i = 1; i <= n; ++i) {
+ xh[i] = war[i];
+ war[i] = x[i];
+ }
+
+ if (n < 2) {
+ xh[1] += xh[1];
+ } else if (n == 2) {
+ xhold = sqrt3 * (xh[1] + xh[2]);
+ xh[2] = sqrt3 * (xh[1] - xh[2]);
+ xh[1] = xhold;
+ } else {
+ np1 = n + 1;
+ ns2 = n / 2;
+ x[1] = 0.f;
+ for (k = 1; k <= ns2; ++k) {
+ kc = np1 - k;
+ t1 = xh[k] - xh[kc];
+ t2 = was[k] * (xh[k] + xh[kc]);
+ x[k + 1] = t1 + t2;
+ x[kc + 1] = t2 - t1;
+ }
+ modn = n % 2;
+ if (modn != 0) {
+ x[ns2 + 2] = xh[ns2 + 1] * 4.f;
+ }
+ rfftf1(np1, &x[1], &xh[1], &war[1], &ifac[1]);
+ xh[1] = x[1] * .5f;
+ for (i = 3; i <= n; i += 2) {
+ xh[i - 1] = -x[i];
+ xh[i] = xh[i - 2] + x[i - 1];
+ }
+ if (modn == 0) {
+ xh[n] = -x[n + 1];
+ }
+ }
+ for (i = 1; i <= n; ++i) {
+ x[i] = war[i];
+ war[i] = xh[i];
+ }
+} /* sint1 */
+
+void sinti(integer n, real *wsave)
+{
+ /* Local variables */
+ integer k;
+ real dt;
+ integer np1, ns2;
+
+ /* Parameter adjustments */
+ --wsave;
+
+ /* Function Body */
+ if (n <= 1) {
+ return;
+ }
+ ns2 = n / 2;
+ np1 = n + 1;
+ dt = M_PI / (real) np1;
+ for (k = 1; k <= ns2; ++k) {
+ wsave[k] = sin(k * dt) * 2.f;
+ }
+ rffti(np1, &wsave[ns2 + 1]);
+} /* sinti */
+
+void sint(integer n, real *x, real *wsave)
+{
+ integer np1, iw1, iw2, iw3;
+
+ /* Parameter adjustments */
+ --wsave;
+ --x;
+
+ /* Function Body */
+ np1 = n + 1;
+ iw1 = n / 2 + 1;
+ iw2 = iw1 + np1;
+ iw3 = iw2 + np1;
+ sint1(n, &x[1], &wsave[1], &wsave[iw1], &wsave[iw2], (int*)&wsave[iw3]);
+} /* sint */
+
+#ifdef TESTING_FFTPACK
+#include <stdio.h>
+
+int main(void)
+{
+ static integer nd[] = { 120,91,54,49,32,28,24,8,4,3,2 };
+
+ /* System generated locals */
+ real r1, r2, r3;
+ f77complex q1, q2, q3;
+
+ /* Local variables */
+ integer i, j, k, n;
+ real w[2000], x[200], y[200], cf, fn, dt;
+ f77complex cx[200], cy[200];
+ real xh[200];
+ integer nz, nm1, np1, ns2;
+ real arg, tfn;
+ real sum, arg1, arg2;
+ real sum1, sum2, dcfb;
+ integer modn;
+ real rftb, rftf;
+ real sqrt2;
+ real rftfb;
+ real costt, sintt, dcfftb, dcfftf, cosqfb, costfb;
+ real sinqfb;
+ real sintfb;
+ real cosqbt, cosqft, sinqbt, sinqft;
+
+
+
+ /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
+
+ /* VERSION 4 APRIL 1985 */
+
+ /* A TEST DRIVER FOR */
+ /* A PACKAGE OF FORTRAN SUBPROGRAMS FOR THE FAST FOURIER */
+ /* TRANSFORM OF PERIODIC AND OTHER SYMMETRIC SEQUENCES */
+
+ /* BY */
+
+ /* PAUL N SWARZTRAUBER */
+
+ /* NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER,COLORADO 80307 */
+
+ /* WHICH IS SPONSORED BY THE NATIONAL SCIENCE FOUNDATION */
+
+ /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
+
+
+ /* THIS PROGRAM TESTS THE PACKAGE OF FAST FOURIER */
+ /* TRANSFORMS FOR BOTH COMPLEX AND REAL PERIODIC SEQUENCES AND */
+ /* CERTIAN OTHER SYMMETRIC SEQUENCES THAT ARE LISTED BELOW. */
+
+ /* 1. RFFTI INITIALIZE RFFTF AND RFFTB */
+ /* 2. RFFTF FORWARD TRANSFORM OF A REAL PERIODIC SEQUENCE */
+ /* 3. RFFTB BACKWARD TRANSFORM OF A REAL COEFFICIENT ARRAY */
+
+ /* 4. EZFFTI INITIALIZE EZFFTF AND EZFFTB */
+ /* 5. EZFFTF A SIMPLIFIED REAL PERIODIC FORWARD TRANSFORM */
+ /* 6. EZFFTB A SIMPLIFIED REAL PERIODIC BACKWARD TRANSFORM */
+
+ /* 7. SINTI INITIALIZE SINT */
+ /* 8. SINT SINE TRANSFORM OF A REAL ODD SEQUENCE */
+
+ /* 9. COSTI INITIALIZE COST */
+ /* 10. COST COSINE TRANSFORM OF A REAL EVEN SEQUENCE */
+
+ /* 11. SINQI INITIALIZE SINQF AND SINQB */
+ /* 12. SINQF FORWARD SINE TRANSFORM WITH ODD WAVE NUMBERS */
+ /* 13. SINQB UNNORMALIZED INVERSE OF SINQF */
+
+ /* 14. COSQI INITIALIZE COSQF AND COSQB */
+ /* 15. COSQF FORWARD COSINE TRANSFORM WITH ODD WAVE NUMBERS */
+ /* 16. COSQB UNNORMALIZED INVERSE OF COSQF */
+
+ /* 17. CFFTI INITIALIZE CFFTF AND CFFTB */
+ /* 18. CFFTF FORWARD TRANSFORM OF A COMPLEX PERIODIC SEQUENCE */
+ /* 19. CFFTB UNNORMALIZED INVERSE OF CFFTF */
+
+
+ sqrt2 = sqrt(2.f);
+ int all_ok = 1;
+ for (nz = 1; nz <= (int)(sizeof nd/sizeof nd[0]); ++nz) {
+ n = nd[nz - 1];
+ modn = n % 2;
+ fn = (real) n;
+ tfn = fn + fn;
+ np1 = n + 1;
+ nm1 = n - 1;
+ for (j = 1; j <= np1; ++j) {
+ x[j - 1] = sin((real) j * sqrt2);
+ y[j - 1] = x[j - 1];
+ xh[j - 1] = x[j - 1];
+ }
+
+ /* TEST SUBROUTINES RFFTI,RFFTF AND RFFTB */
+
+ rffti(n, w);
+ dt = (2*M_PI) / fn;
+ ns2 = (n + 1) / 2;
+ if (ns2 < 2) {
+ goto L104;
+ }
+ for (k = 2; k <= ns2; ++k) {
+ sum1 = 0.f;
+ sum2 = 0.f;
+ arg = (real) (k - 1) * dt;
+ for (i = 1; i <= n; ++i) {
+ arg1 = (real) (i - 1) * arg;
+ sum1 += x[i - 1] * cos(arg1);
+ sum2 += x[i - 1] * sin(arg1);
+ }
+ y[(k << 1) - 3] = sum1;
+ y[(k << 1) - 2] = -sum2;
+ }
+ L104:
+ sum1 = 0.f;
+ sum2 = 0.f;
+ for (i = 1; i <= nm1; i += 2) {
+ sum1 += x[i - 1];
+ sum2 += x[i];
+ }
+ if (modn == 1) {
+ sum1 += x[n - 1];
+ }
+ y[0] = sum1 + sum2;
+ if (modn == 0) {
+ y[n - 1] = sum1 - sum2;
+ }
+ rfftf(n, x, w);
+ rftf = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = rftf, r3 = (r1 = x[i - 1] - y[i - 1], fabs(r1));
+ rftf = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ }
+ rftf /= fn;
+ for (i = 1; i <= n; ++i) {
+ sum = x[0] * .5f;
+ arg = (real) (i - 1) * dt;
+ if (ns2 < 2) {
+ goto L108;
+ }
+ for (k = 2; k <= ns2; ++k) {
+ arg1 = (real) (k - 1) * arg;
+ sum = sum + x[(k << 1) - 3] * cos(arg1) - x[(k << 1) - 2] *
+ sin(arg1);
+ }
+ L108:
+ if (modn == 0) {
+ sum += (real)pow(-1, i-1) * .5f * x[n - 1];
+ }
+ y[i - 1] = sum + sum;
+ }
+ rfftb(n, x, w);
+ rftb = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = rftb, r3 = (r1 = x[i - 1] - y[i - 1], fabs(r1));
+ rftb = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ y[i - 1] = xh[i - 1];
+ }
+ rfftb(n, y, w);
+ rfftf(n, y, w);
+ cf = 1.f / fn;
+ rftfb = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = rftfb, r3 = (r1 = cf * y[i - 1] - x[i - 1], fabs(
+ r1));
+ rftfb = dmax(r2,r3);
+ }
+
+ /* TEST SUBROUTINES SINTI AND SINT */
+
+ dt = M_PI / fn;
+ for (i = 1; i <= nm1; ++i) {
+ x[i - 1] = xh[i - 1];
+ }
+ for (i = 1; i <= nm1; ++i) {
+ y[i - 1] = 0.f;
+ arg1 = (real) i * dt;
+ for (k = 1; k <= nm1; ++k) {
+ y[i - 1] += x[k - 1] * sin((real) k * arg1);
+ }
+ y[i - 1] += y[i - 1];
+ }
+ sinti(nm1, w);
+ sint(nm1, x, w);
+ cf = .5f / fn;
+ sintt = 0.f;
+ for (i = 1; i <= nm1; ++i) {
+ /* Computing MAX */
+ r2 = sintt, r3 = (r1 = x[i - 1] - y[i - 1], fabs(r1));
+ sintt = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ y[i - 1] = x[i - 1];
+ }
+ sintt = cf * sintt;
+ sint(nm1, x, w);
+ sint(nm1, x, w);
+ sintfb = 0.f;
+ for (i = 1; i <= nm1; ++i) {
+ /* Computing MAX */
+ r2 = sintfb, r3 = (r1 = cf * x[i - 1] - y[i - 1], fabs(
+ r1));
+ sintfb = dmax(r2,r3);
+ }
+
+ /* TEST SUBROUTINES COSTI AND COST */
+
+ for (i = 1; i <= np1; ++i) {
+ x[i - 1] = xh[i - 1];
+ }
+ for (i = 1; i <= np1; ++i) {
+ y[i - 1] = (x[0] + (real) pow(-1, i+1) * x[n]) * .5f;
+ arg = (real) (i - 1) * dt;
+ for (k = 2; k <= n; ++k) {
+ y[i - 1] += x[k - 1] * cos((real) (k - 1) * arg);
+ }
+ y[i - 1] += y[i - 1];
+ }
+ costi(np1, w);
+ cost(np1, x, w);
+ costt = 0.f;
+ for (i = 1; i <= np1; ++i) {
+ /* Computing MAX */
+ r2 = costt, r3 = (r1 = x[i - 1] - y[i - 1], fabs(r1));
+ costt = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ y[i - 1] = xh[i - 1];
+ }
+ costt = cf * costt;
+ cost(np1, x, w);
+ cost(np1, x, w);
+ costfb = 0.f;
+ for (i = 1; i <= np1; ++i) {
+ /* Computing MAX */
+ r2 = costfb, r3 = (r1 = cf * x[i - 1] - y[i - 1], fabs(
+ r1));
+ costfb = dmax(r2,r3);
+ }
+
+ /* TEST SUBROUTINES SINQI,SINQF AND SINQB */
+
+ cf = .25f / fn;
+ for (i = 1; i <= n; ++i) {
+ y[i - 1] = xh[i - 1];
+ }
+ dt = M_PI / (fn + fn);
+ for (i = 1; i <= n; ++i) {
+ x[i - 1] = 0.f;
+ arg = dt * (real) i;
+ for (k = 1; k <= n; ++k) {
+ x[i - 1] += y[k - 1] * sin((real) (k + k - 1) * arg);
+ }
+ x[i - 1] *= 4.f;
+ }
+ sinqi(n, w);
+ sinqb(n, y, w);
+ sinqbt = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = sinqbt, r3 = (r1 = y[i - 1] - x[i - 1], fabs(r1))
+ ;
+ sinqbt = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ }
+ sinqbt = cf * sinqbt;
+ for (i = 1; i <= n; ++i) {
+ arg = (real) (i + i - 1) * dt;
+ y[i - 1] = (real) pow(-1, i+1) * .5f * x[n - 1];
+ for (k = 1; k <= nm1; ++k) {
+ y[i - 1] += x[k - 1] * sin((real) k * arg);
+ }
+ y[i - 1] += y[i - 1];
+ }
+ sinqf(n, x, w);
+ sinqft = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = sinqft, r3 = (r1 = x[i - 1] - y[i - 1], fabs(r1))
+ ;
+ sinqft = dmax(r2,r3);
+ y[i - 1] = xh[i - 1];
+ x[i - 1] = xh[i - 1];
+ }
+ sinqf(n, y, w);
+ sinqb(n, y, w);
+ sinqfb = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = sinqfb, r3 = (r1 = cf * y[i - 1] - x[i - 1], fabs(
+ r1));
+ sinqfb = dmax(r2,r3);
+ }
+
+ /* TEST SUBROUTINES COSQI,COSQF AND COSQB */
+
+ for (i = 1; i <= n; ++i) {
+ y[i - 1] = xh[i - 1];
+ }
+ for (i = 1; i <= n; ++i) {
+ x[i - 1] = 0.f;
+ arg = (real) (i - 1) * dt;
+ for (k = 1; k <= n; ++k) {
+ x[i - 1] += y[k - 1] * cos((real) (k + k - 1) * arg);
+ }
+ x[i - 1] *= 4.f;
+ }
+ cosqi(n, w);
+ cosqb(n, y, w);
+ cosqbt = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = cosqbt, r3 = (r1 = x[i - 1] - y[i - 1], fabs(r1))
+ ;
+ cosqbt = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ }
+ cosqbt = cf * cosqbt;
+ for (i = 1; i <= n; ++i) {
+ y[i - 1] = x[0] * .5f;
+ arg = (real) (i + i - 1) * dt;
+ for (k = 2; k <= n; ++k) {
+ y[i - 1] += x[k - 1] * cos((real) (k - 1) * arg);
+ }
+ y[i - 1] += y[i - 1];
+ }
+ cosqf(n, x, w);
+ cosqft = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = cosqft, r3 = (r1 = y[i - 1] - x[i - 1], fabs(r1))
+ ;
+ cosqft = dmax(r2,r3);
+ x[i - 1] = xh[i - 1];
+ y[i - 1] = xh[i - 1];
+ }
+ cosqft = cf * cosqft;
+ cosqb(n, x, w);
+ cosqf(n, x, w);
+ cosqfb = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ r2 = cosqfb, r3 = (r1 = cf * x[i - 1] - y[i - 1], fabs(r1));
+ cosqfb = dmax(r2,r3);
+ }
+
+ /* TEST CFFTI,CFFTF,CFFTB */
+
+ for (i = 1; i <= n; ++i) {
+ r1 = cos(sqrt2 * (real) i);
+ r2 = sin(sqrt2 * (real) (i * i));
+ q1.r = r1, q1.i = r2;
+ cx[i-1].r = q1.r, cx[i-1].i = q1.i;
+ }
+ dt = (2*M_PI) / fn;
+ for (i = 1; i <= n; ++i) {
+ arg1 = -((real) (i - 1)) * dt;
+ cy[i-1].r = 0.f, cy[i-1].i = 0.f;
+ for (k = 1; k <= n; ++k) {
+ arg2 = (real) (k - 1) * arg1;
+ r1 = cos(arg2);
+ r2 = sin(arg2);
+ q3.r = r1, q3.i = r2;
+ q2.r = q3.r * cx[k-1].r - q3.i * cx[k-1].i, q2.i =
+ q3.r * cx[k-1].i + q3.i * cx[k-1].r;
+ q1.r = cy[i-1].r + q2.r, q1.i = cy[i-1].i + q2.i;
+ cy[i-1].r = q1.r, cy[i-1].i = q1.i;
+ }
+ }
+ cffti(n, w);
+ cfftf(n, (real*)cx, w);
+ dcfftf = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ q1.r = cx[i-1].r - cy[i-1].r, q1.i = cx[i-1].i - cy[i-1]
+ .i;
+ r1 = dcfftf, r2 = c_abs(&q1);
+ dcfftf = dmax(r1,r2);
+ q1.r = cx[i-1].r / fn, q1.i = cx[i-1].i / fn;
+ cx[i-1].r = q1.r, cx[i-1].i = q1.i;
+ }
+ dcfftf /= fn;
+ for (i = 1; i <= n; ++i) {
+ arg1 = (real) (i - 1) * dt;
+ cy[i-1].r = 0.f, cy[i-1].i = 0.f;
+ for (k = 1; k <= n; ++k) {
+ arg2 = (real) (k - 1) * arg1;
+ r1 = cos(arg2);
+ r2 = sin(arg2);
+ q3.r = r1, q3.i = r2;
+ q2.r = q3.r * cx[k-1].r - q3.i * cx[k-1].i, q2.i =
+ q3.r * cx[k-1].i + q3.i * cx[k-1].r;
+ q1.r = cy[i-1].r + q2.r, q1.i = cy[i-1].i + q2.i;
+ cy[i-1].r = q1.r, cy[i-1].i = q1.i;
+ }
+ }
+ cfftb(n, (real*)cx, w);
+ dcfftb = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ q1.r = cx[i-1].r - cy[i-1].r, q1.i = cx[i-1].i - cy[i-1].i;
+ r1 = dcfftb, r2 = c_abs(&q1);
+ dcfftb = dmax(r1,r2);
+ cx[i-1].r = cy[i-1].r, cx[i-1].i = cy[i-1].i;
+ }
+ cf = 1.f / fn;
+ cfftf(n, (real*)cx, w);
+ cfftb(n, (real*)cx, w);
+ dcfb = 0.f;
+ for (i = 1; i <= n; ++i) {
+ /* Computing MAX */
+ q2.r = cf * cx[i-1].r, q2.i = cf * cx[i-1].i;
+ q1.r = q2.r - cy[i-1].r, q1.i = q2.i - cy[i-1].i;
+ r1 = dcfb, r2 = c_abs(&q1);
+ dcfb = dmax(r1,r2);
+ }
+ printf("%d\tRFFTF %10.3g\tRFFTB %10.ge\tRFFTFB %10.3g", n, rftf, rftb, rftfb);
+ printf( "\tSINT %10.3g\tSINTFB %10.ge\tCOST %10.3g\n", sintt, sintfb, costt);
+ printf( "\tCOSTFB %10.3g\tSINQF %10.ge\tSINQB %10.3g", costfb, sinqft, sinqbt);
+ printf( "\tSINQFB %10.3g\tCOSQF %10.ge\tCOSQB %10.3g\n", sinqfb, cosqft, cosqbt);
+ printf( "\tCOSQFB %10.3g\t", cosqfb);
+ printf( "\tCFFTF %10.ge\tCFFTB %10.3g\n", dcfftf, dcfftb);
+ printf( "\tCFFTFB %10.3g\n", dcfb);
+
+#define CHECK(x) if (x > 1e-3) { printf(#x " failed: %g\n", x); all_ok = 0; }
+ CHECK(rftf); CHECK(rftb); CHECK(rftfb); CHECK(sintt); CHECK(sintfb); CHECK(costt);
+ CHECK(costfb); CHECK(sinqft); CHECK(sinqbt); CHECK(sinqfb); CHECK(cosqft); CHECK(cosqbt);
+ CHECK(cosqfb); CHECK(dcfftf); CHECK(dcfftb);
+ }
+
+ if (all_ok) printf("Everything looks fine.\n");
+ else printf("ERRORS WERE DETECTED.\n");
+ /*
+ expected:
+ 120 RFFTF 2.786e-06 RFFTB 6.847e-04 RFFTFB 2.795e-07 SINT 1.312e-06 SINTFB 1.237e-06 COST 1.319e-06
+ COSTFB 4.355e-06 SINQF 3.281e-04 SINQB 1.876e-06 SINQFB 2.198e-07 COSQF 6.199e-07 COSQB 2.193e-06
+ COSQFB 2.300e-07 DEZF 5.573e-06 DEZB 1.363e-05 DEZFB 1.371e-06 CFFTF 5.590e-06 CFFTB 4.751e-05
+ CFFTFB 4.215e-07
+ 54 RFFTF 4.708e-07 RFFTB 3.052e-05 RFFTFB 3.439e-07 SINT 3.532e-07 SINTFB 4.145e-07 COST 3.002e-07
+ COSTFB 6.343e-07 SINQF 4.959e-05 SINQB 4.415e-07 SINQFB 2.882e-07 COSQF 2.826e-07 COSQB 2.472e-07
+ COSQFB 3.439e-07 DEZF 9.388e-07 DEZB 5.066e-06 DEZFB 5.960e-07 CFFTF 1.426e-06 CFFTB 9.482e-06
+ CFFTFB 2.980e-07
+ 49 RFFTF 4.476e-07 RFFTB 5.341e-05 RFFTFB 2.574e-07 SINT 9.196e-07 SINTFB 9.401e-07 COST 8.174e-07
+ COSTFB 1.331e-06 SINQF 4.005e-05 SINQB 9.342e-07 SINQFB 3.057e-07 COSQF 2.530e-07 COSQB 6.228e-07
+ COSQFB 4.826e-07 DEZF 9.071e-07 DEZB 4.590e-06 DEZFB 5.960e-07 CFFTF 2.095e-06 CFFTB 1.414e-05
+ CFFTFB 7.398e-07
+ 32 RFFTF 4.619e-07 RFFTB 2.861e-05 RFFTFB 1.192e-07 SINT 3.874e-07 SINTFB 4.172e-07 COST 4.172e-07
+ COSTFB 1.699e-06 SINQF 2.551e-05 SINQB 6.407e-07 SINQFB 2.980e-07 COSQF 1.639e-07 COSQB 1.714e-07
+ COSQFB 2.384e-07 DEZF 1.013e-06 DEZB 2.339e-06 DEZFB 7.749e-07 CFFTF 1.127e-06 CFFTB 6.744e-06
+ CFFTFB 2.666e-07
+ 4 RFFTF 1.490e-08 RFFTB 1.490e-07 RFFTFB 5.960e-08 SINT 7.451e-09 SINTFB 0.000e+00 COST 2.980e-08
+ COSTFB 1.192e-07 SINQF 4.768e-07 SINQB 2.980e-08 SINQFB 5.960e-08 COSQF 2.608e-08 COSQB 5.960e-08
+ COSQFB 1.192e-07 DEZF 2.980e-08 DEZB 5.960e-08 DEZFB 0.000e+00 CFFTF 6.664e-08 CFFTB 5.960e-08
+ CFFTFB 6.144e-08
+ 3 RFFTF 3.974e-08 RFFTB 1.192e-07 RFFTFB 3.303e-08 SINT 1.987e-08 SINTFB 1.069e-08 COST 4.967e-08
+ COSTFB 5.721e-08 SINQF 8.941e-08 SINQB 2.980e-08 SINQFB 1.259e-07 COSQF 7.451e-09 COSQB 4.967e-08
+ COSQFB 7.029e-08 DEZF 1.192e-07 DEZB 5.960e-08 DEZFB 5.960e-08 CFFTF 7.947e-08 CFFTB 8.429e-08
+ CFFTFB 9.064e-08
+ 2 RFFTF 0.000e+00 RFFTB 0.000e+00 RFFTFB 0.000e+00 SINT 0.000e+00 SINTFB 0.000e+00 COST 0.000e+00
+ COSTFB 0.000e+00 SINQF 1.192e-07 SINQB 2.980e-08 SINQFB 5.960e-08 COSQF 7.451e-09 COSQB 1.490e-08
+ COSQFB 0.000e+00 DEZF 0.000e+00 DEZB 0.000e+00 DEZFB 0.000e+00 CFFTF 0.000e+00 CFFTB 5.960e-08
+ CFFTFB 5.960e-08
+ Everything looks fine.
+
+ */
+
+ return all_ok ? 0 : 1;
+}
+#endif //TESTING_FFTPACK
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/fftpack.h b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/fftpack.h
new file mode 100644
index 0000000..381bcc6
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/fftpack.h
@@ -0,0 +1,799 @@
+/*
+ Interface for the f2c translation of fftpack as found on http://www.netlib.org/fftpack/
+
+ FFTPACK license:
+
+ http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
+
+ Copyright (c) 2004 the University Corporation for Atmospheric
+ Research ("UCAR"). All rights reserved. Developed by NCAR's
+ Computational and Information Systems Laboratory, UCAR,
+ www.cisl.ucar.edu.
+
+ Redistribution and use of the Software in source and binary forms,
+ with or without modification, is permitted provided that the
+ following conditions are met:
+
+ - Neither the names of NCAR's Computational and Information Systems
+ Laboratory, the University Corporation for Atmospheric Research,
+ nor the names of its sponsors or contributors may be used to
+ endorse or promote products derived from this Software without
+ specific prior written permission.
+
+ - Redistributions of source code must retain the above copyright
+ notices, this list of conditions, and the disclaimer below.
+
+ - Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions, and the disclaimer below in the
+ documentation and/or other materials provided with the
+ distribution.
+
+ THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+ HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+ SOFTWARE.
+
+ ChangeLog:
+ 2011/10/02: this is my first release of this file.
+*/
+
+#ifndef FFTPACK_H
+#define FFTPACK_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+// just define FFTPACK_DOUBLE_PRECISION if you want to build it as a double precision fft
+
+#ifndef FFTPACK_DOUBLE_PRECISION
+ typedef float fftpack_real;
+ typedef int fftpack_int;
+#else
+ typedef double fftpack_real;
+ typedef int fftpack_int;
+#endif
+
+ void cffti(fftpack_int n, fftpack_real *wsave);
+
+ void cfftf(fftpack_int n, fftpack_real *c, fftpack_real *wsave);
+
+ void cfftb(fftpack_int n, fftpack_real *c, fftpack_real *wsave);
+
+ void rffti(fftpack_int n, fftpack_real *wsave);
+ void rfftf(fftpack_int n, fftpack_real *r, fftpack_real *wsave);
+ void rfftb(fftpack_int n, fftpack_real *r, fftpack_real *wsave);
+
+ void cosqi(fftpack_int n, fftpack_real *wsave);
+ void cosqf(fftpack_int n, fftpack_real *x, fftpack_real *wsave);
+ void cosqb(fftpack_int n, fftpack_real *x, fftpack_real *wsave);
+
+ void costi(fftpack_int n, fftpack_real *wsave);
+ void cost(fftpack_int n, fftpack_real *x, fftpack_real *wsave);
+
+ void sinqi(fftpack_int n, fftpack_real *wsave);
+ void sinqb(fftpack_int n, fftpack_real *x, fftpack_real *wsave);
+ void sinqf(fftpack_int n, fftpack_real *x, fftpack_real *wsave);
+
+ void sinti(fftpack_int n, fftpack_real *wsave);
+ void sint(fftpack_int n, fftpack_real *x, fftpack_real *wsave);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* FFTPACK_H */
+
+/*
+
+ FFTPACK
+
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+
+ version 4 april 1985
+
+ a package of fortran subprograms for the fast fourier
+ transform of periodic and other symmetric sequences
+
+ by
+
+ paul n swarztrauber
+
+ national center for atmospheric research boulder,colorado 80307
+
+ which is sponsored by the national science foundation
+
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+
+
+this package consists of programs which perform fast fourier
+transforms for both complex and real periodic sequences and
+certain other symmetric sequences that are listed below.
+
+1. rffti initialize rfftf and rfftb
+2. rfftf forward transform of a real periodic sequence
+3. rfftb backward transform of a real coefficient array
+
+4. ezffti initialize ezfftf and ezfftb
+5. ezfftf a simplified real periodic forward transform
+6. ezfftb a simplified real periodic backward transform
+
+7. sinti initialize sint
+8. sint sine transform of a real odd sequence
+
+9. costi initialize cost
+10. cost cosine transform of a real even sequence
+
+11. sinqi initialize sinqf and sinqb
+12. sinqf forward sine transform with odd wave numbers
+13. sinqb unnormalized inverse of sinqf
+
+14. cosqi initialize cosqf and cosqb
+15. cosqf forward cosine transform with odd wave numbers
+16. cosqb unnormalized inverse of cosqf
+
+17. cffti initialize cfftf and cfftb
+18. cfftf forward transform of a complex periodic sequence
+19. cfftb unnormalized inverse of cfftf
+
+
+******************************************************************
+
+subroutine rffti(n,wsave)
+
+ ****************************************************************
+
+subroutine rffti initializes the array wsave which is used in
+both rfftf and rfftb. the prime factorization of n together with
+a tabulation of the trigonometric functions are computed and
+stored in wsave.
+
+input parameter
+
+n the length of the sequence to be transformed.
+
+output parameter
+
+wsave a work array which must be dimensioned at least 2*n+15.
+ the same work array can be used for both rfftf and rfftb
+ as long as n remains unchanged. different wsave arrays
+ are required for different values of n. the contents of
+ wsave must not be changed between calls of rfftf or rfftb.
+
+******************************************************************
+
+subroutine rfftf(n,r,wsave)
+
+******************************************************************
+
+subroutine rfftf computes the fourier coefficients of a real
+perodic sequence (fourier analysis). the transform is defined
+below at output parameter r.
+
+input parameters
+
+n the length of the array r to be transformed. the method
+ is most efficient when n is a product of small primes.
+ n may change so long as different work arrays are provided
+
+r a real array of length n which contains the sequence
+ to be transformed
+
+wsave a work array which must be dimensioned at least 2*n+15.
+ in the program that calls rfftf. the wsave array must be
+ initialized by calling subroutine rffti(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+ the same wsave array can be used by rfftf and rfftb.
+
+
+output parameters
+
+r r(1) = the sum from i=1 to i=n of r(i)
+
+ if n is even set l =n/2 , if n is odd set l = (n+1)/2
+
+ then for k = 2,...,l
+
+ r(2*k-2) = the sum from i = 1 to i = n of
+
+ r(i)*cos((k-1)*(i-1)*2*pi/n)
+
+ r(2*k-1) = the sum from i = 1 to i = n of
+
+ -r(i)*sin((k-1)*(i-1)*2*pi/n)
+
+ if n is even
+
+ r(n) = the sum from i = 1 to i = n of
+
+ (-1)**(i-1)*r(i)
+
+ ***** note
+ this transform is unnormalized since a call of rfftf
+ followed by a call of rfftb will multiply the input
+ sequence by n.
+
+wsave contains results which must not be destroyed between
+ calls of rfftf or rfftb.
+
+
+******************************************************************
+
+subroutine rfftb(n,r,wsave)
+
+******************************************************************
+
+subroutine rfftb computes the real perodic sequence from its
+fourier coefficients (fourier synthesis). the transform is defined
+below at output parameter r.
+
+input parameters
+
+n the length of the array r to be transformed. the method
+ is most efficient when n is a product of small primes.
+ n may change so long as different work arrays are provided
+
+r a real array of length n which contains the sequence
+ to be transformed
+
+wsave a work array which must be dimensioned at least 2*n+15.
+ in the program that calls rfftb. the wsave array must be
+ initialized by calling subroutine rffti(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+ the same wsave array can be used by rfftf and rfftb.
+
+
+output parameters
+
+r for n even and for i = 1,...,n
+
+ r(i) = r(1)+(-1)**(i-1)*r(n)
+
+ plus the sum from k=2 to k=n/2 of
+
+ 2.*r(2*k-2)*cos((k-1)*(i-1)*2*pi/n)
+
+ -2.*r(2*k-1)*sin((k-1)*(i-1)*2*pi/n)
+
+ for n odd and for i = 1,...,n
+
+ r(i) = r(1) plus the sum from k=2 to k=(n+1)/2 of
+
+ 2.*r(2*k-2)*cos((k-1)*(i-1)*2*pi/n)
+
+ -2.*r(2*k-1)*sin((k-1)*(i-1)*2*pi/n)
+
+ ***** note
+ this transform is unnormalized since a call of rfftf
+ followed by a call of rfftb will multiply the input
+ sequence by n.
+
+wsave contains results which must not be destroyed between
+ calls of rfftb or rfftf.
+
+******************************************************************
+
+subroutine sinti(n,wsave)
+
+******************************************************************
+
+subroutine sinti initializes the array wsave which is used in
+subroutine sint. the prime factorization of n together with
+a tabulation of the trigonometric functions are computed and
+stored in wsave.
+
+input parameter
+
+n the length of the sequence to be transformed. the method
+ is most efficient when n+1 is a product of small primes.
+
+output parameter
+
+wsave a work array with at least int(2.5*n+15) locations.
+ different wsave arrays are required for different values
+ of n. the contents of wsave must not be changed between
+ calls of sint.
+
+******************************************************************
+
+subroutine sint(n,x,wsave)
+
+******************************************************************
+
+subroutine sint computes the discrete fourier sine transform
+of an odd sequence x(i). the transform is defined below at
+output parameter x.
+
+sint is the unnormalized inverse of itself since a call of sint
+followed by another call of sint will multiply the input sequence
+x by 2*(n+1).
+
+the array wsave which is used by subroutine sint must be
+initialized by calling subroutine sinti(n,wsave).
+
+input parameters
+
+n the length of the sequence to be transformed. the method
+ is most efficient when n+1 is the product of small primes.
+
+x an array which contains the sequence to be transformed
+
+
+wsave a work array with dimension at least int(2.5*n+15)
+ in the program that calls sint. the wsave array must be
+ initialized by calling subroutine sinti(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+
+output parameters
+
+x for i=1,...,n
+
+ x(i)= the sum from k=1 to k=n
+
+ 2*x(k)*sin(k*i*pi/(n+1))
+
+ a call of sint followed by another call of
+ sint will multiply the sequence x by 2*(n+1).
+ hence sint is the unnormalized inverse
+ of itself.
+
+wsave contains initialization calculations which must not be
+ destroyed between calls of sint.
+
+******************************************************************
+
+subroutine costi(n,wsave)
+
+******************************************************************
+
+subroutine costi initializes the array wsave which is used in
+subroutine cost. the prime factorization of n together with
+a tabulation of the trigonometric functions are computed and
+stored in wsave.
+
+input parameter
+
+n the length of the sequence to be transformed. the method
+ is most efficient when n-1 is a product of small primes.
+
+output parameter
+
+wsave a work array which must be dimensioned at least 3*n+15.
+ different wsave arrays are required for different values
+ of n. the contents of wsave must not be changed between
+ calls of cost.
+
+******************************************************************
+
+subroutine cost(n,x,wsave)
+
+******************************************************************
+
+subroutine cost computes the discrete fourier cosine transform
+of an even sequence x(i). the transform is defined below at output
+parameter x.
+
+cost is the unnormalized inverse of itself since a call of cost
+followed by another call of cost will multiply the input sequence
+x by 2*(n-1). the transform is defined below at output parameter x
+
+the array wsave which is used by subroutine cost must be
+initialized by calling subroutine costi(n,wsave).
+
+input parameters
+
+n the length of the sequence x. n must be greater than 1.
+ the method is most efficient when n-1 is a product of
+ small primes.
+
+x an array which contains the sequence to be transformed
+
+wsave a work array which must be dimensioned at least 3*n+15
+ in the program that calls cost. the wsave array must be
+ initialized by calling subroutine costi(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+
+output parameters
+
+x for i=1,...,n
+
+ x(i) = x(1)+(-1)**(i-1)*x(n)
+
+ + the sum from k=2 to k=n-1
+
+ 2*x(k)*cos((k-1)*(i-1)*pi/(n-1))
+
+ a call of cost followed by another call of
+ cost will multiply the sequence x by 2*(n-1)
+ hence cost is the unnormalized inverse
+ of itself.
+
+wsave contains initialization calculations which must not be
+ destroyed between calls of cost.
+
+******************************************************************
+
+subroutine sinqi(n,wsave)
+
+******************************************************************
+
+subroutine sinqi initializes the array wsave which is used in
+both sinqf and sinqb. the prime factorization of n together with
+a tabulation of the trigonometric functions are computed and
+stored in wsave.
+
+input parameter
+
+n the length of the sequence to be transformed. the method
+ is most efficient when n is a product of small primes.
+
+output parameter
+
+wsave a work array which must be dimensioned at least 3*n+15.
+ the same work array can be used for both sinqf and sinqb
+ as long as n remains unchanged. different wsave arrays
+ are required for different values of n. the contents of
+ wsave must not be changed between calls of sinqf or sinqb.
+
+******************************************************************
+
+subroutine sinqf(n,x,wsave)
+
+******************************************************************
+
+subroutine sinqf computes the fast fourier transform of quarter
+wave data. that is , sinqf computes the coefficients in a sine
+series representation with only odd wave numbers. the transform
+is defined below at output parameter x.
+
+sinqb is the unnormalized inverse of sinqf since a call of sinqf
+followed by a call of sinqb will multiply the input sequence x
+by 4*n.
+
+the array wsave which is used by subroutine sinqf must be
+initialized by calling subroutine sinqi(n,wsave).
+
+
+input parameters
+
+n the length of the array x to be transformed. the method
+ is most efficient when n is a product of small primes.
+
+x an array which contains the sequence to be transformed
+
+wsave a work array which must be dimensioned at least 3*n+15.
+ in the program that calls sinqf. the wsave array must be
+ initialized by calling subroutine sinqi(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+
+output parameters
+
+x for i=1,...,n
+
+ x(i) = (-1)**(i-1)*x(n)
+
+ + the sum from k=1 to k=n-1 of
+
+ 2*x(k)*sin((2*i-1)*k*pi/(2*n))
+
+ a call of sinqf followed by a call of
+ sinqb will multiply the sequence x by 4*n.
+ therefore sinqb is the unnormalized inverse
+ of sinqf.
+
+wsave contains initialization calculations which must not
+ be destroyed between calls of sinqf or sinqb.
+
+******************************************************************
+
+subroutine sinqb(n,x,wsave)
+
+******************************************************************
+
+subroutine sinqb computes the fast fourier transform of quarter
+wave data. that is , sinqb computes a sequence from its
+representation in terms of a sine series with odd wave numbers.
+the transform is defined below at output parameter x.
+
+sinqf is the unnormalized inverse of sinqb since a call of sinqb
+followed by a call of sinqf will multiply the input sequence x
+by 4*n.
+
+the array wsave which is used by subroutine sinqb must be
+initialized by calling subroutine sinqi(n,wsave).
+
+
+input parameters
+
+n the length of the array x to be transformed. the method
+ is most efficient when n is a product of small primes.
+
+x an array which contains the sequence to be transformed
+
+wsave a work array which must be dimensioned at least 3*n+15.
+ in the program that calls sinqb. the wsave array must be
+ initialized by calling subroutine sinqi(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+
+output parameters
+
+x for i=1,...,n
+
+ x(i)= the sum from k=1 to k=n of
+
+ 4*x(k)*sin((2k-1)*i*pi/(2*n))
+
+ a call of sinqb followed by a call of
+ sinqf will multiply the sequence x by 4*n.
+ therefore sinqf is the unnormalized inverse
+ of sinqb.
+
+wsave contains initialization calculations which must not
+ be destroyed between calls of sinqb or sinqf.
+
+******************************************************************
+
+subroutine cosqi(n,wsave)
+
+******************************************************************
+
+subroutine cosqi initializes the array wsave which is used in
+both cosqf and cosqb. the prime factorization of n together with
+a tabulation of the trigonometric functions are computed and
+stored in wsave.
+
+input parameter
+
+n the length of the array to be transformed. the method
+ is most efficient when n is a product of small primes.
+
+output parameter
+
+wsave a work array which must be dimensioned at least 3*n+15.
+ the same work array can be used for both cosqf and cosqb
+ as long as n remains unchanged. different wsave arrays
+ are required for different values of n. the contents of
+ wsave must not be changed between calls of cosqf or cosqb.
+
+******************************************************************
+
+subroutine cosqf(n,x,wsave)
+
+******************************************************************
+
+subroutine cosqf computes the fast fourier transform of quarter
+wave data. that is , cosqf computes the coefficients in a cosine
+series representation with only odd wave numbers. the transform
+is defined below at output parameter x
+
+cosqf is the unnormalized inverse of cosqb since a call of cosqf
+followed by a call of cosqb will multiply the input sequence x
+by 4*n.
+
+the array wsave which is used by subroutine cosqf must be
+initialized by calling subroutine cosqi(n,wsave).
+
+
+input parameters
+
+n the length of the array x to be transformed. the method
+ is most efficient when n is a product of small primes.
+
+x an array which contains the sequence to be transformed
+
+wsave a work array which must be dimensioned at least 3*n+15
+ in the program that calls cosqf. the wsave array must be
+ initialized by calling subroutine cosqi(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+
+output parameters
+
+x for i=1,...,n
+
+ x(i) = x(1) plus the sum from k=2 to k=n of
+
+ 2*x(k)*cos((2*i-1)*(k-1)*pi/(2*n))
+
+ a call of cosqf followed by a call of
+ cosqb will multiply the sequence x by 4*n.
+ therefore cosqb is the unnormalized inverse
+ of cosqf.
+
+wsave contains initialization calculations which must not
+ be destroyed between calls of cosqf or cosqb.
+
+******************************************************************
+
+subroutine cosqb(n,x,wsave)
+
+******************************************************************
+
+subroutine cosqb computes the fast fourier transform of quarter
+wave data. that is , cosqb computes a sequence from its
+representation in terms of a cosine series with odd wave numbers.
+the transform is defined below at output parameter x.
+
+cosqb is the unnormalized inverse of cosqf since a call of cosqb
+followed by a call of cosqf will multiply the input sequence x
+by 4*n.
+
+the array wsave which is used by subroutine cosqb must be
+initialized by calling subroutine cosqi(n,wsave).
+
+
+input parameters
+
+n the length of the array x to be transformed. the method
+ is most efficient when n is a product of small primes.
+
+x an array which contains the sequence to be transformed
+
+wsave a work array that must be dimensioned at least 3*n+15
+ in the program that calls cosqb. the wsave array must be
+ initialized by calling subroutine cosqi(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+
+output parameters
+
+x for i=1,...,n
+
+ x(i)= the sum from k=1 to k=n of
+
+ 4*x(k)*cos((2*k-1)*(i-1)*pi/(2*n))
+
+ a call of cosqb followed by a call of
+ cosqf will multiply the sequence x by 4*n.
+ therefore cosqf is the unnormalized inverse
+ of cosqb.
+
+wsave contains initialization calculations which must not
+ be destroyed between calls of cosqb or cosqf.
+
+******************************************************************
+
+subroutine cffti(n,wsave)
+
+******************************************************************
+
+subroutine cffti initializes the array wsave which is used in
+both cfftf and cfftb. the prime factorization of n together with
+a tabulation of the trigonometric functions are computed and
+stored in wsave.
+
+input parameter
+
+n the length of the sequence to be transformed
+
+output parameter
+
+wsave a work array which must be dimensioned at least 4*n+15
+ the same work array can be used for both cfftf and cfftb
+ as long as n remains unchanged. different wsave arrays
+ are required for different values of n. the contents of
+ wsave must not be changed between calls of cfftf or cfftb.
+
+******************************************************************
+
+subroutine cfftf(n,c,wsave)
+
+******************************************************************
+
+subroutine cfftf computes the forward complex discrete fourier
+transform (the fourier analysis). equivalently , cfftf computes
+the fourier coefficients of a complex periodic sequence.
+the transform is defined below at output parameter c.
+
+the transform is not normalized. to obtain a normalized transform
+the output must be divided by n. otherwise a call of cfftf
+followed by a call of cfftb will multiply the sequence by n.
+
+the array wsave which is used by subroutine cfftf must be
+initialized by calling subroutine cffti(n,wsave).
+
+input parameters
+
+
+n the length of the complex sequence c. the method is
+ more efficient when n is the product of small primes. n
+
+c a complex array of length n which contains the sequence
+
+wsave a real work array which must be dimensioned at least 4n+15
+ in the program that calls cfftf. the wsave array must be
+ initialized by calling subroutine cffti(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+ the same wsave array can be used by cfftf and cfftb.
+
+output parameters
+
+c for j=1,...,n
+
+ c(j)=the sum from k=1,...,n of
+
+ c(k)*exp(-i*(j-1)*(k-1)*2*pi/n)
+
+ where i=sqrt(-1)
+
+wsave contains initialization calculations which must not be
+ destroyed between calls of subroutine cfftf or cfftb
+
+******************************************************************
+
+subroutine cfftb(n,c,wsave)
+
+******************************************************************
+
+subroutine cfftb computes the backward complex discrete fourier
+transform (the fourier synthesis). equivalently , cfftb computes
+a complex periodic sequence from its fourier coefficients.
+the transform is defined below at output parameter c.
+
+a call of cfftf followed by a call of cfftb will multiply the
+sequence by n.
+
+the array wsave which is used by subroutine cfftb must be
+initialized by calling subroutine cffti(n,wsave).
+
+input parameters
+
+
+n the length of the complex sequence c. the method is
+ more efficient when n is the product of small primes.
+
+c a complex array of length n which contains the sequence
+
+wsave a real work array which must be dimensioned at least 4n+15
+ in the program that calls cfftb. the wsave array must be
+ initialized by calling subroutine cffti(n,wsave) and a
+ different wsave array must be used for each different
+ value of n. this initialization does not have to be
+ repeated so long as n remains unchanged thus subsequent
+ transforms can be obtained faster than the first.
+ the same wsave array can be used by cfftf and cfftb.
+
+output parameters
+
+c for j=1,...,n
+
+ c(j)=the sum from k=1,...,n of
+
+ c(k)*exp(i*(j-1)*(k-1)*2*pi/n)
+
+ where i=sqrt(-1)
+
+wsave contains initialization calculations which must not be
+ destroyed between calls of subroutine cfftf or cfftb
+
+*/
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/pffft.c b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/pffft.c
new file mode 100644
index 0000000..bdac4d7
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/pffft.c
@@ -0,0 +1,1881 @@
+/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
+
+ Based on original fortran 77 code from FFTPACKv4 from NETLIB
+ (http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
+ of NCAR, in 1985.
+
+ As confirmed by the NCAR fftpack software curators, the following
+ FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
+ released under the same terms.
+
+ FFTPACK license:
+
+ http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
+
+ Copyright (c) 2004 the University Corporation for Atmospheric
+ Research ("UCAR"). All rights reserved. Developed by NCAR's
+ Computational and Information Systems Laboratory, UCAR,
+ www.cisl.ucar.edu.
+
+ Redistribution and use of the Software in source and binary forms,
+ with or without modification, is permitted provided that the
+ following conditions are met:
+
+ - Neither the names of NCAR's Computational and Information Systems
+ Laboratory, the University Corporation for Atmospheric Research,
+ nor the names of its sponsors or contributors may be used to
+ endorse or promote products derived from this Software without
+ specific prior written permission.
+
+ - Redistributions of source code must retain the above copyright
+ notices, this list of conditions, and the disclaimer below.
+
+ - Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions, and the disclaimer below in the
+ documentation and/or other materials provided with the
+ distribution.
+
+ THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+ HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+ SOFTWARE.
+
+
+ PFFFT : a Pretty Fast FFT.
+
+ This file is largerly based on the original FFTPACK implementation, modified in
+ order to take advantage of SIMD instructions of modern CPUs.
+*/
+
+/*
+ ChangeLog:
+ - 2011/10/02, version 1: This is the very first release of this file.
+*/
+
+#include "pffft.h"
+#include <stdint.h>
+#include <stdlib.h>
+#include <math.h>
+#include <assert.h>
+
+/* detect compiler flavour */
+#if defined(_MSC_VER)
+# define COMPILER_MSVC
+#elif defined(__GNUC__)
+# define COMPILER_GCC
+#endif
+
+#if defined(COMPILER_GCC)
+# define ALWAYS_INLINE(return_type) inline return_type __attribute__ ((always_inline))
+# define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))
+# define RESTRICT __restrict
+# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ varname__[size__];
+# define VLA_ARRAY_ON_STACK_FREE(varname__)
+#elif defined(COMPILER_MSVC)
+#include <malloc.h>
+# define ALWAYS_INLINE(return_type) __forceinline return_type
+# define NEVER_INLINE(return_type) __declspec(noinline) return_type
+# define RESTRICT __restrict
+# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (type__*)_malloca(size__ * sizeof(type__))
+# define VLA_ARRAY_ON_STACK_FREE(varname__) _freea(varname__)
+#endif
+
+
+/*
+ vector support macros: the rest of the code is independant of
+ SSE/Altivec/NEON -- adding support for other platforms with 4-element
+ vectors should be limited to these macros
+*/
+
+
+// define PFFFT_SIMD_DISABLE if you want to use scalar code instead of simd code
+//#define PFFFT_SIMD_DISABLE
+
+/*
+ Altivec support macros
+*/
+#if !defined(PFFFT_SIMD_DISABLE) && (defined(__ppc__) || defined(__ppc64__))
+typedef vector float v4sf;
+# define SIMD_SZ 4
+# define VZERO() ((vector float) vec_splat_u8(0))
+# define VMUL(a,b) vec_madd(a,b, VZERO())
+# define VADD(a,b) vec_add(a,b)
+# define VMADD(a,b,c) vec_madd(a,b,c)
+# define VSUB(a,b) vec_sub(a,b)
+inline v4sf ld_ps1(const float *p) { v4sf v=vec_lde(0,p); return vec_splat(vec_perm(v, v, vec_lvsl(0, p)), 0); }
+# define LD_PS1(p) ld_ps1(&p)
+# define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = vec_mergeh(in1, in2); out2 = vec_mergel(in1, in2); out1 = tmp__; }
+# define UNINTERLEAVE2(in1, in2, out1, out2) { \
+ vector unsigned char vperm1 = (vector unsigned char)(0,1,2,3,8,9,10,11,16,17,18,19,24,25,26,27); \
+ vector unsigned char vperm2 = (vector unsigned char)(4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31); \
+ v4sf tmp__ = vec_perm(in1, in2, vperm1); out2 = vec_perm(in1, in2, vperm2); out1 = tmp__; \
+ }
+# define VTRANSPOSE4(x0,x1,x2,x3) { \
+ v4sf y0 = vec_mergeh(x0, x2); \
+ v4sf y1 = vec_mergel(x0, x2); \
+ v4sf y2 = vec_mergeh(x1, x3); \
+ v4sf y3 = vec_mergel(x1, x3); \
+ x0 = vec_mergeh(y0, y2); \
+ x1 = vec_mergel(y0, y2); \
+ x2 = vec_mergeh(y1, y3); \
+ x3 = vec_mergel(y1, y3); \
+ }
+# define VSWAPHL(a,b) vec_perm(a,b, (vector unsigned char)(16,17,18,19,20,21,22,23,8,9,10,11,12,13,14,15))
+# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0xF) == 0)
+
+/*
+ SSE1 support macros
+*/
+#elif !defined(PFFFT_SIMD_DISABLE) && (defined(__x86_64__) || defined(_M_X64) || defined(i386) || defined(__i386__) || defined(_M_IX86))
+
+#include <xmmintrin.h>
+typedef __m128 v4sf;
+# define SIMD_SZ 4 // 4 floats by simd vector -- this is pretty much hardcoded in the preprocess/finalize functions anyway so you will have to work if you want to enable AVX with its 256-bit vectors.
+# define VZERO() _mm_setzero_ps()
+# define VMUL(a,b) _mm_mul_ps(a,b)
+# define VADD(a,b) _mm_add_ps(a,b)
+# define VMADD(a,b,c) _mm_add_ps(_mm_mul_ps(a,b), c)
+# define VSUB(a,b) _mm_sub_ps(a,b)
+# define LD_PS1(p) _mm_set1_ps(p)
+# define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_unpacklo_ps(in1, in2); out2 = _mm_unpackhi_ps(in1, in2); out1 = tmp__; }
+# define UNINTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(2,0,2,0)); out2 = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(3,1,3,1)); out1 = tmp__; }
+# define VTRANSPOSE4(x0,x1,x2,x3) _MM_TRANSPOSE4_PS(x0,x1,x2,x3)
+# define VSWAPHL(a,b) _mm_shuffle_ps(b, a, _MM_SHUFFLE(3,2,1,0))
+# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0xF) == 0)
+
+/*
+ ARM NEON support macros
+*/
+#elif !defined(PFFFT_SIMD_DISABLE) && (defined(__arm__) || defined(__ARMEL__) || defined(__aarch64__) || defined(_M_ARM64))
+# include <arm_neon.h>
+typedef float32x4_t v4sf;
+# define SIMD_SZ 4
+# define VZERO() vdupq_n_f32(0)
+# define VMUL(a,b) vmulq_f32(a,b)
+# define VADD(a,b) vaddq_f32(a,b)
+# define VMADD(a,b,c) vmlaq_f32(c,a,b)
+# define VSUB(a,b) vsubq_f32(a,b)
+# define LD_PS1(p) vld1q_dup_f32(&(p))
+# define INTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vzipq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }
+# define UNINTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vuzpq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }
+# define VTRANSPOSE4(x0,x1,x2,x3) { \
+ float32x4x2_t t0_ = vzipq_f32(x0, x2); \
+ float32x4x2_t t1_ = vzipq_f32(x1, x3); \
+ float32x4x2_t u0_ = vzipq_f32(t0_.val[0], t1_.val[0]); \
+ float32x4x2_t u1_ = vzipq_f32(t0_.val[1], t1_.val[1]); \
+ x0 = u0_.val[0]; x1 = u0_.val[1]; x2 = u1_.val[0]; x3 = u1_.val[1]; \
+ }
+// marginally faster version
+//# define VTRANSPOSE4(x0,x1,x2,x3) { asm("vtrn.32 %q0, %q1;\n vtrn.32 %q2,%q3\n vswp %f0,%e2\n vswp %f1,%e3" : "+w"(x0), "+w"(x1), "+w"(x2), "+w"(x3)::); }
+# define VSWAPHL(a,b) vcombine_f32(vget_low_f32(b), vget_high_f32(a))
+# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x3) == 0)
+#else
+# if !defined(PFFFT_SIMD_DISABLE)
+# warning "building with simd disabled !\n";
+# define PFFFT_SIMD_DISABLE // fallback to scalar code
+# endif
+#endif
+
+// fallback mode for situations where SSE/Altivec are not available, use scalar mode instead
+#ifdef PFFFT_SIMD_DISABLE
+typedef float v4sf;
+# define SIMD_SZ 1
+# define VZERO() 0.f
+# define VMUL(a,b) ((a)*(b))
+# define VADD(a,b) ((a)+(b))
+# define VMADD(a,b,c) ((a)*(b)+(c))
+# define VSUB(a,b) ((a)-(b))
+# define LD_PS1(p) (p)
+# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x3) == 0)
+#endif
+
+// shortcuts for complex multiplcations
+#define VCPLXMUL(ar,ai,br,bi) { v4sf tmp; tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VSUB(ar,VMUL(ai,bi)); ai=VMUL(ai,br); ai=VADD(ai,tmp); }
+#define VCPLXMULCONJ(ar,ai,br,bi) { v4sf tmp; tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VADD(ar,VMUL(ai,bi)); ai=VMUL(ai,br); ai=VSUB(ai,tmp); }
+#ifndef SVMUL
+// multiply a scalar with a vector
+#define SVMUL(f,v) VMUL(LD_PS1(f),v)
+#endif
+
+#if !defined(PFFFT_SIMD_DISABLE)
+typedef union v4sf_union {
+ v4sf v;
+ float f[4];
+} v4sf_union;
+
+#include <string.h>
+
+#define assertv4(v,f0,f1,f2,f3) assert(v.f[0] == (f0) && v.f[1] == (f1) && v.f[2] == (f2) && v.f[3] == (f3))
+
+/* detect bugs with the vector support macros */
+void validate_pffft_simd() {
+ float f[16] = { 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 };
+ v4sf_union a0, a1, a2, a3, t, u;
+ memcpy(a0.f, f, 4*sizeof(float));
+ memcpy(a1.f, f+4, 4*sizeof(float));
+ memcpy(a2.f, f+8, 4*sizeof(float));
+ memcpy(a3.f, f+12, 4*sizeof(float));
+
+ t = a0; u = a1; t.v = VZERO();
+ assertv4(t, 0, 0, 0, 0);
+ t.v = VADD(a1.v, a2.v);
+ assertv4(t, 12, 14, 16, 18);
+ t.v = VMUL(a1.v, a2.v);
+ assertv4(t, 32, 45, 60, 77);
+ t.v = VMADD(a1.v, a2.v,a0.v);
+ assertv4(t, 32, 46, 62, 80);
+
+ INTERLEAVE2(a1.v,a2.v,t.v,u.v);
+ assertv4(t, 4, 8, 5, 9); assertv4(u, 6, 10, 7, 11);
+ UNINTERLEAVE2(a1.v,a2.v,t.v,u.v);
+ assertv4(t, 4, 6, 8, 10); assertv4(u, 5, 7, 9, 11);
+
+ t.v=LD_PS1(f[15]);
+ assertv4(t, 15, 15, 15, 15);
+ t.v = VSWAPHL(a1.v, a2.v);
+ assertv4(t, 8, 9, 6, 7);
+ VTRANSPOSE4(a0.v, a1.v, a2.v, a3.v);
+ assertv4(a0, 0, 4, 8, 12); assertv4(a1, 1, 5, 9, 13); assertv4(a2, 2, 6, 10, 14); assertv4(a3, 3, 7, 11, 15);
+}
+#endif //!PFFFT_SIMD_DISABLE
+
+/* SSE and co like 16-bytes aligned pointers */
+#define MALLOC_V4SF_ALIGNMENT 64 // with a 64-byte alignment, we are even aligned on L2 cache lines...
+void *pffft_aligned_malloc(size_t nb_bytes) {
+ void *p, *p0 = malloc(nb_bytes + MALLOC_V4SF_ALIGNMENT);
+ if (!p0) return (void *) 0;
+ p = (void *) (((size_t) p0 + MALLOC_V4SF_ALIGNMENT) & (~((size_t) (MALLOC_V4SF_ALIGNMENT-1))));
+ *((void **) p - 1) = p0;
+ return p;
+}
+
+void pffft_aligned_free(void *p) {
+ if (p) free(*((void **) p - 1));
+}
+
+int pffft_simd_size() { return SIMD_SZ; }
+
+/*
+ passf2 and passb2 has been merged here, fsign = -1 for passf2, +1 for passb2
+*/
+static NEVER_INLINE(void) passf2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1, float fsign) {
+ int k, i;
+ int l1ido = l1*ido;
+ if (ido <= 2) {
+ for (k=0; k < l1ido; k += ido, ch += ido, cc+= 2*ido) {
+ ch[0] = VADD(cc[0], cc[ido+0]);
+ ch[l1ido] = VSUB(cc[0], cc[ido+0]);
+ ch[1] = VADD(cc[1], cc[ido+1]);
+ ch[l1ido + 1] = VSUB(cc[1], cc[ido+1]);
+ }
+ } else {
+ for (k=0; k < l1ido; k += ido, ch += ido, cc += 2*ido) {
+ for (i=0; i<ido-1; i+=2) {
+ v4sf tr2 = VSUB(cc[i+0], cc[i+ido+0]);
+ v4sf ti2 = VSUB(cc[i+1], cc[i+ido+1]);
+ v4sf wr = LD_PS1(wa1[i]), wi = VMUL(LD_PS1(fsign), LD_PS1(wa1[i+1]));
+ ch[i] = VADD(cc[i+0], cc[i+ido+0]);
+ ch[i+1] = VADD(cc[i+1], cc[i+ido+1]);
+ VCPLXMUL(tr2, ti2, wr, wi);
+ ch[i+l1ido] = tr2;
+ ch[i+l1ido+1] = ti2;
+ }
+ }
+ }
+}
+
+/*
+ passf3 and passb3 has been merged here, fsign = -1 for passf3, +1 for passb3
+*/
+static NEVER_INLINE(void) passf3_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
+ const float *wa1, const float *wa2, float fsign) {
+ static const float taur = -0.5f;
+ float taui = 0.866025403784439f*fsign;
+ int i, k;
+ v4sf tr2, ti2, cr2, ci2, cr3, ci3, dr2, di2, dr3, di3;
+ int l1ido = l1*ido;
+ float wr1, wi1, wr2, wi2;
+ assert(ido > 2);
+ for (k=0; k< l1ido; k += ido, cc+= 3*ido, ch +=ido) {
+ for (i=0; i<ido-1; i+=2) {
+ tr2 = VADD(cc[i+ido], cc[i+2*ido]);
+ cr2 = VADD(cc[i], SVMUL(taur,tr2));
+ ch[i] = VADD(cc[i], tr2);
+ ti2 = VADD(cc[i+ido+1], cc[i+2*ido+1]);
+ ci2 = VADD(cc[i +1], SVMUL(taur,ti2));
+ ch[i+1] = VADD(cc[i+1], ti2);
+ cr3 = SVMUL(taui, VSUB(cc[i+ido], cc[i+2*ido]));
+ ci3 = SVMUL(taui, VSUB(cc[i+ido+1], cc[i+2*ido+1]));
+ dr2 = VSUB(cr2, ci3);
+ dr3 = VADD(cr2, ci3);
+ di2 = VADD(ci2, cr3);
+ di3 = VSUB(ci2, cr3);
+ wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1];
+ VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
+ ch[i+l1ido] = dr2;
+ ch[i+l1ido + 1] = di2;
+ VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
+ ch[i+2*l1ido] = dr3;
+ ch[i+2*l1ido+1] = di3;
+ }
+ }
+} /* passf3 */
+
+static NEVER_INLINE(void) passf4_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
+ const float *wa1, const float *wa2, const float *wa3, float fsign) {
+ /* isign == -1 for forward transform and +1 for backward transform */
+
+ int i, k;
+ v4sf ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
+ int l1ido = l1*ido;
+ if (ido == 2) {
+ for (k=0; k < l1ido; k += ido, ch += ido, cc += 4*ido) {
+ tr1 = VSUB(cc[0], cc[2*ido + 0]);
+ tr2 = VADD(cc[0], cc[2*ido + 0]);
+ ti1 = VSUB(cc[1], cc[2*ido + 1]);
+ ti2 = VADD(cc[1], cc[2*ido + 1]);
+ ti4 = VMUL(VSUB(cc[1*ido + 0], cc[3*ido + 0]), LD_PS1(fsign));
+ tr4 = VMUL(VSUB(cc[3*ido + 1], cc[1*ido + 1]), LD_PS1(fsign));
+ tr3 = VADD(cc[ido + 0], cc[3*ido + 0]);
+ ti3 = VADD(cc[ido + 1], cc[3*ido + 1]);
+
+ ch[0*l1ido + 0] = VADD(tr2, tr3);
+ ch[0*l1ido + 1] = VADD(ti2, ti3);
+ ch[1*l1ido + 0] = VADD(tr1, tr4);
+ ch[1*l1ido + 1] = VADD(ti1, ti4);
+ ch[2*l1ido + 0] = VSUB(tr2, tr3);
+ ch[2*l1ido + 1] = VSUB(ti2, ti3);
+ ch[3*l1ido + 0] = VSUB(tr1, tr4);
+ ch[3*l1ido + 1] = VSUB(ti1, ti4);
+ }
+ } else {
+ for (k=0; k < l1ido; k += ido, ch+=ido, cc += 4*ido) {
+ for (i=0; i<ido-1; i+=2) {
+ float wr1, wi1, wr2, wi2, wr3, wi3;
+ tr1 = VSUB(cc[i + 0], cc[i + 2*ido + 0]);
+ tr2 = VADD(cc[i + 0], cc[i + 2*ido + 0]);
+ ti1 = VSUB(cc[i + 1], cc[i + 2*ido + 1]);
+ ti2 = VADD(cc[i + 1], cc[i + 2*ido + 1]);
+ tr4 = VMUL(VSUB(cc[i + 3*ido + 1], cc[i + 1*ido + 1]), LD_PS1(fsign));
+ ti4 = VMUL(VSUB(cc[i + 1*ido + 0], cc[i + 3*ido + 0]), LD_PS1(fsign));
+ tr3 = VADD(cc[i + ido + 0], cc[i + 3*ido + 0]);
+ ti3 = VADD(cc[i + ido + 1], cc[i + 3*ido + 1]);
+
+ ch[i] = VADD(tr2, tr3);
+ cr3 = VSUB(tr2, tr3);
+ ch[i + 1] = VADD(ti2, ti3);
+ ci3 = VSUB(ti2, ti3);
+
+ cr2 = VADD(tr1, tr4);
+ cr4 = VSUB(tr1, tr4);
+ ci2 = VADD(ti1, ti4);
+ ci4 = VSUB(ti1, ti4);
+ wr1=wa1[i], wi1=fsign*wa1[i+1];
+ VCPLXMUL(cr2, ci2, LD_PS1(wr1), LD_PS1(wi1));
+ wr2=wa2[i], wi2=fsign*wa2[i+1];
+ ch[i + l1ido] = cr2;
+ ch[i + l1ido + 1] = ci2;
+
+ VCPLXMUL(cr3, ci3, LD_PS1(wr2), LD_PS1(wi2));
+ wr3=wa3[i], wi3=fsign*wa3[i+1];
+ ch[i + 2*l1ido] = cr3;
+ ch[i + 2*l1ido + 1] = ci3;
+
+ VCPLXMUL(cr4, ci4, LD_PS1(wr3), LD_PS1(wi3));
+ ch[i + 3*l1ido] = cr4;
+ ch[i + 3*l1ido + 1] = ci4;
+ }
+ }
+ }
+} /* passf4 */
+
+/*
+ passf5 and passb5 has been merged here, fsign = -1 for passf5, +1 for passb5
+*/
+static NEVER_INLINE(void) passf5_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
+ const float *wa1, const float *wa2,
+ const float *wa3, const float *wa4, float fsign) {
+ static const float tr11 = .309016994374947f;
+ const float ti11 = .951056516295154f*fsign;
+ static const float tr12 = -.809016994374947f;
+ const float ti12 = .587785252292473f*fsign;
+
+ /* Local variables */
+ int i, k;
+ v4sf ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
+ ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
+
+ float wr1, wi1, wr2, wi2, wr3, wi3, wr4, wi4;
+
+#define cc_ref(a_1,a_2) cc[(a_2-1)*ido + a_1 + 1]
+#define ch_ref(a_1,a_3) ch[(a_3-1)*l1*ido + a_1 + 1]
+
+ assert(ido > 2);
+ for (k = 0; k < l1; ++k, cc += 5*ido, ch += ido) {
+ for (i = 0; i < ido-1; i += 2) {
+ ti5 = VSUB(cc_ref(i , 2), cc_ref(i , 5));
+ ti2 = VADD(cc_ref(i , 2), cc_ref(i , 5));
+ ti4 = VSUB(cc_ref(i , 3), cc_ref(i , 4));
+ ti3 = VADD(cc_ref(i , 3), cc_ref(i , 4));
+ tr5 = VSUB(cc_ref(i-1, 2), cc_ref(i-1, 5));
+ tr2 = VADD(cc_ref(i-1, 2), cc_ref(i-1, 5));
+ tr4 = VSUB(cc_ref(i-1, 3), cc_ref(i-1, 4));
+ tr3 = VADD(cc_ref(i-1, 3), cc_ref(i-1, 4));
+ ch_ref(i-1, 1) = VADD(cc_ref(i-1, 1), VADD(tr2, tr3));
+ ch_ref(i , 1) = VADD(cc_ref(i , 1), VADD(ti2, ti3));
+ cr2 = VADD(cc_ref(i-1, 1), VADD(SVMUL(tr11, tr2),SVMUL(tr12, tr3)));
+ ci2 = VADD(cc_ref(i , 1), VADD(SVMUL(tr11, ti2),SVMUL(tr12, ti3)));
+ cr3 = VADD(cc_ref(i-1, 1), VADD(SVMUL(tr12, tr2),SVMUL(tr11, tr3)));
+ ci3 = VADD(cc_ref(i , 1), VADD(SVMUL(tr12, ti2),SVMUL(tr11, ti3)));
+ cr5 = VADD(SVMUL(ti11, tr5), SVMUL(ti12, tr4));
+ ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));
+ cr4 = VSUB(SVMUL(ti12, tr5), SVMUL(ti11, tr4));
+ ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));
+ dr3 = VSUB(cr3, ci4);
+ dr4 = VADD(cr3, ci4);
+ di3 = VADD(ci3, cr4);
+ di4 = VSUB(ci3, cr4);
+ dr5 = VADD(cr2, ci5);
+ dr2 = VSUB(cr2, ci5);
+ di5 = VSUB(ci2, cr5);
+ di2 = VADD(ci2, cr5);
+ wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1];
+ wr3=wa3[i], wi3=fsign*wa3[i+1], wr4=wa4[i], wi4=fsign*wa4[i+1];
+ VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
+ ch_ref(i - 1, 2) = dr2;
+ ch_ref(i, 2) = di2;
+ VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
+ ch_ref(i - 1, 3) = dr3;
+ ch_ref(i, 3) = di3;
+ VCPLXMUL(dr4, di4, LD_PS1(wr3), LD_PS1(wi3));
+ ch_ref(i - 1, 4) = dr4;
+ ch_ref(i, 4) = di4;
+ VCPLXMUL(dr5, di5, LD_PS1(wr4), LD_PS1(wi4));
+ ch_ref(i - 1, 5) = dr5;
+ ch_ref(i, 5) = di5;
+ }
+ }
+#undef ch_ref
+#undef cc_ref
+}
+
+static NEVER_INLINE(void) radf2_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch, const float *wa1) {
+ static const float minus_one = -1.f;
+ int i, k, l1ido = l1*ido;
+ for (k=0; k < l1ido; k += ido) {
+ v4sf a = cc[k], b = cc[k + l1ido];
+ ch[2*k] = VADD(a, b);
+ ch[2*(k+ido)-1] = VSUB(a, b);
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ for (k=0; k < l1ido; k += ido) {
+ for (i=2; i<ido; i+=2) {
+ v4sf tr2 = cc[i - 1 + k + l1ido], ti2 = cc[i + k + l1ido];
+ v4sf br = cc[i - 1 + k], bi = cc[i + k];
+ VCPLXMULCONJ(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));
+ ch[i + 2*k] = VADD(bi, ti2);
+ ch[2*(k+ido) - i] = VSUB(ti2, bi);
+ ch[i - 1 + 2*k] = VADD(br, tr2);
+ ch[2*(k+ido) - i -1] = VSUB(br, tr2);
+ }
+ }
+ if (ido % 2 == 1) return;
+ }
+ for (k=0; k < l1ido; k += ido) {
+ ch[2*k + ido] = SVMUL(minus_one, cc[ido-1 + k + l1ido]);
+ ch[2*k + ido-1] = cc[k + ido-1];
+ }
+} /* radf2 */
+
+
+static NEVER_INLINE(void) radb2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1) {
+ static const float minus_two=-2;
+ int i, k, l1ido = l1*ido;
+ v4sf a,b,c,d, tr2, ti2;
+ for (k=0; k < l1ido; k += ido) {
+ a = cc[2*k]; b = cc[2*(k+ido) - 1];
+ ch[k] = VADD(a, b);
+ ch[k + l1ido] =VSUB(a, b);
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ for (k = 0; k < l1ido; k += ido) {
+ for (i = 2; i < ido; i += 2) {
+ a = cc[i-1 + 2*k]; b = cc[2*(k + ido) - i - 1];
+ c = cc[i+0 + 2*k]; d = cc[2*(k + ido) - i + 0];
+ ch[i-1 + k] = VADD(a, b);
+ tr2 = VSUB(a, b);
+ ch[i+0 + k] = VSUB(c, d);
+ ti2 = VADD(c, d);
+ VCPLXMUL(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));
+ ch[i-1 + k + l1ido] = tr2;
+ ch[i+0 + k + l1ido] = ti2;
+ }
+ }
+ if (ido % 2 == 1) return;
+ }
+ for (k = 0; k < l1ido; k += ido) {
+ a = cc[2*k + ido-1]; b = cc[2*k + ido];
+ ch[k + ido-1] = VADD(a,a);
+ ch[k + ido-1 + l1ido] = SVMUL(minus_two, b);
+ }
+} /* radb2 */
+
+static void radf3_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,
+ const float *wa1, const float *wa2) {
+ static const float taur = -0.5f;
+ static const float taui = 0.866025403784439f;
+ int i, k, ic;
+ v4sf ci2, di2, di3, cr2, dr2, dr3, ti2, ti3, tr2, tr3, wr1, wi1, wr2, wi2;
+ for (k=0; k<l1; k++) {
+ cr2 = VADD(cc[(k + l1)*ido], cc[(k + 2*l1)*ido]);
+ ch[3*k*ido] = VADD(cc[k*ido], cr2);
+ ch[(3*k+2)*ido] = SVMUL(taui, VSUB(cc[(k + l1*2)*ido], cc[(k + l1)*ido]));
+ ch[ido-1 + (3*k + 1)*ido] = VADD(cc[k*ido], SVMUL(taur, cr2));
+ }
+ if (ido == 1) return;
+ for (k=0; k<l1; k++) {
+ for (i=2; i<ido; i+=2) {
+ ic = ido - i;
+ wr1 = LD_PS1(wa1[i - 2]); wi1 = LD_PS1(wa1[i - 1]);
+ dr2 = cc[i - 1 + (k + l1)*ido]; di2 = cc[i + (k + l1)*ido];
+ VCPLXMULCONJ(dr2, di2, wr1, wi1);
+
+ wr2 = LD_PS1(wa2[i - 2]); wi2 = LD_PS1(wa2[i - 1]);
+ dr3 = cc[i - 1 + (k + l1*2)*ido]; di3 = cc[i + (k + l1*2)*ido];
+ VCPLXMULCONJ(dr3, di3, wr2, wi2);
+
+ cr2 = VADD(dr2, dr3);
+ ci2 = VADD(di2, di3);
+ ch[i - 1 + 3*k*ido] = VADD(cc[i - 1 + k*ido], cr2);
+ ch[i + 3*k*ido] = VADD(cc[i + k*ido], ci2);
+ tr2 = VADD(cc[i - 1 + k*ido], SVMUL(taur, cr2));
+ ti2 = VADD(cc[i + k*ido], SVMUL(taur, ci2));
+ tr3 = SVMUL(taui, VSUB(di2, di3));
+ ti3 = SVMUL(taui, VSUB(dr3, dr2));
+ ch[i - 1 + (3*k + 2)*ido] = VADD(tr2, tr3);
+ ch[ic - 1 + (3*k + 1)*ido] = VSUB(tr2, tr3);
+ ch[i + (3*k + 2)*ido] = VADD(ti2, ti3);
+ ch[ic + (3*k + 1)*ido] = VSUB(ti3, ti2);
+ }
+ }
+} /* radf3 */
+
+
+static void radb3_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
+ const float *wa1, const float *wa2)
+{
+ static const float taur = -0.5f;
+ static const float taui = 0.866025403784439f;
+ static const float taui_2 = 0.866025403784439f*2;
+ int i, k, ic;
+ v4sf ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
+ for (k=0; k<l1; k++) {
+ tr2 = cc[ido-1 + (3*k + 1)*ido]; tr2 = VADD(tr2,tr2);
+ cr2 = VMADD(LD_PS1(taur), tr2, cc[3*k*ido]);
+ ch[k*ido] = VADD(cc[3*k*ido], tr2);
+ ci3 = SVMUL(taui_2, cc[(3*k + 2)*ido]);
+ ch[(k + l1)*ido] = VSUB(cr2, ci3);
+ ch[(k + 2*l1)*ido] = VADD(cr2, ci3);
+ }
+ if (ido == 1) return;
+ for (k=0; k<l1; k++) {
+ for (i=2; i<ido; i+=2) {
+ ic = ido - i;
+ tr2 = VADD(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]);
+ cr2 = VMADD(LD_PS1(taur), tr2, cc[i - 1 + 3*k*ido]);
+ ch[i - 1 + k*ido] = VADD(cc[i - 1 + 3*k*ido], tr2);
+ ti2 = VSUB(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]);
+ ci2 = VMADD(LD_PS1(taur), ti2, cc[i + 3*k*ido]);
+ ch[i + k*ido] = VADD(cc[i + 3*k*ido], ti2);
+ cr3 = SVMUL(taui, VSUB(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]));
+ ci3 = SVMUL(taui, VADD(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]));
+ dr2 = VSUB(cr2, ci3);
+ dr3 = VADD(cr2, ci3);
+ di2 = VADD(ci2, cr3);
+ di3 = VSUB(ci2, cr3);
+ VCPLXMUL(dr2, di2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));
+ ch[i - 1 + (k + l1)*ido] = dr2;
+ ch[i + (k + l1)*ido] = di2;
+ VCPLXMUL(dr3, di3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));
+ ch[i - 1 + (k + 2*l1)*ido] = dr3;
+ ch[i + (k + 2*l1)*ido] = di3;
+ }
+ }
+} /* radb3 */
+
+static NEVER_INLINE(void) radf4_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf * RESTRICT ch,
+ const float * RESTRICT wa1, const float * RESTRICT wa2, const float * RESTRICT wa3)
+{
+ static const float minus_hsqt2 = (float)-0.7071067811865475;
+ int i, k, l1ido = l1*ido;
+ {
+ const v4sf *RESTRICT cc_ = cc, * RESTRICT cc_end = cc + l1ido;
+ v4sf * RESTRICT ch_ = ch;
+ while (cc < cc_end) {
+ // this loop represents between 25% and 40% of total radf4_ps cost !
+ v4sf a0 = cc[0], a1 = cc[l1ido];
+ v4sf a2 = cc[2*l1ido], a3 = cc[3*l1ido];
+ v4sf tr1 = VADD(a1, a3);
+ v4sf tr2 = VADD(a0, a2);
+ ch[2*ido-1] = VSUB(a0, a2);
+ ch[2*ido ] = VSUB(a3, a1);
+ ch[0 ] = VADD(tr1, tr2);
+ ch[4*ido-1] = VSUB(tr2, tr1);
+ cc += ido; ch += 4*ido;
+ }
+ cc = cc_; ch = ch_;
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ for (k = 0; k < l1ido; k += ido) {
+ const v4sf * RESTRICT pc = (v4sf*)(cc + 1 + k);
+ for (i=2; i<ido; i += 2, pc += 2) {
+ int ic = ido - i;
+ v4sf wr, wi, cr2, ci2, cr3, ci3, cr4, ci4;
+ v4sf tr1, ti1, tr2, ti2, tr3, ti3, tr4, ti4;
+
+ cr2 = pc[1*l1ido+0];
+ ci2 = pc[1*l1ido+1];
+ wr=LD_PS1(wa1[i - 2]);
+ wi=LD_PS1(wa1[i - 1]);
+ VCPLXMULCONJ(cr2,ci2,wr,wi);
+
+ cr3 = pc[2*l1ido+0];
+ ci3 = pc[2*l1ido+1];
+ wr = LD_PS1(wa2[i-2]);
+ wi = LD_PS1(wa2[i-1]);
+ VCPLXMULCONJ(cr3, ci3, wr, wi);
+
+ cr4 = pc[3*l1ido];
+ ci4 = pc[3*l1ido+1];
+ wr = LD_PS1(wa3[i-2]);
+ wi = LD_PS1(wa3[i-1]);
+ VCPLXMULCONJ(cr4, ci4, wr, wi);
+
+ /* at this point, on SSE, five of "cr2 cr3 cr4 ci2 ci3 ci4" should be loaded in registers */
+
+ tr1 = VADD(cr2,cr4);
+ tr4 = VSUB(cr4,cr2);
+ tr2 = VADD(pc[0],cr3);
+ tr3 = VSUB(pc[0],cr3);
+ ch[i - 1 + 4*k] = VADD(tr1,tr2);
+ ch[ic - 1 + 4*k + 3*ido] = VSUB(tr2,tr1); // at this point tr1 and tr2 can be disposed
+ ti1 = VADD(ci2,ci4);
+ ti4 = VSUB(ci2,ci4);
+ ch[i - 1 + 4*k + 2*ido] = VADD(ti4,tr3);
+ ch[ic - 1 + 4*k + 1*ido] = VSUB(tr3,ti4); // dispose tr3, ti4
+ ti2 = VADD(pc[1],ci3);
+ ti3 = VSUB(pc[1],ci3);
+ ch[i + 4*k] = VADD(ti1, ti2);
+ ch[ic + 4*k + 3*ido] = VSUB(ti1, ti2);
+ ch[i + 4*k + 2*ido] = VADD(tr4, ti3);
+ ch[ic + 4*k + 1*ido] = VSUB(tr4, ti3);
+ }
+ }
+ if (ido % 2 == 1) return;
+ }
+ for (k=0; k<l1ido; k += ido) {
+ v4sf a = cc[ido-1 + k + l1ido], b = cc[ido-1 + k + 3*l1ido];
+ v4sf c = cc[ido-1 + k], d = cc[ido-1 + k + 2*l1ido];
+ v4sf ti1 = SVMUL(minus_hsqt2, VADD(a, b));
+ v4sf tr1 = SVMUL(minus_hsqt2, VSUB(b, a));
+ ch[ido-1 + 4*k] = VADD(tr1, c);
+ ch[ido-1 + 4*k + 2*ido] = VSUB(c, tr1);
+ ch[4*k + 1*ido] = VSUB(ti1, d);
+ ch[4*k + 3*ido] = VADD(ti1, d);
+ }
+} /* radf4 */
+
+
+static NEVER_INLINE(void) radb4_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,
+ const float * RESTRICT wa1, const float * RESTRICT wa2, const float *RESTRICT wa3)
+{
+ static const float minus_sqrt2 = (float)-1.414213562373095;
+ static const float two = 2.f;
+ int i, k, l1ido = l1*ido;
+ v4sf ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
+ {
+ const v4sf *RESTRICT cc_ = cc, * RESTRICT ch_end = ch + l1ido;
+ v4sf *ch_ = ch;
+ while (ch < ch_end) {
+ v4sf a = cc[0], b = cc[4*ido-1];
+ v4sf c = cc[2*ido], d = cc[2*ido-1];
+ tr3 = SVMUL(two,d);
+ tr2 = VADD(a,b);
+ tr1 = VSUB(a,b);
+ tr4 = SVMUL(two,c);
+ ch[0*l1ido] = VADD(tr2, tr3);
+ ch[2*l1ido] = VSUB(tr2, tr3);
+ ch[1*l1ido] = VSUB(tr1, tr4);
+ ch[3*l1ido] = VADD(tr1, tr4);
+
+ cc += 4*ido; ch += ido;
+ }
+ cc = cc_; ch = ch_;
+ }
+ if (ido < 2) return;
+ if (ido != 2) {
+ for (k = 0; k < l1ido; k += ido) {
+ const v4sf * RESTRICT pc = (v4sf*)(cc - 1 + 4*k);
+ v4sf * RESTRICT ph = (v4sf*)(ch + k + 1);
+ for (i = 2; i < ido; i += 2) {
+
+ tr1 = VSUB(pc[i], pc[4*ido - i]);
+ tr2 = VADD(pc[i], pc[4*ido - i]);
+ ti4 = VSUB(pc[2*ido + i], pc[2*ido - i]);
+ tr3 = VADD(pc[2*ido + i], pc[2*ido - i]);
+ ph[0] = VADD(tr2, tr3);
+ cr3 = VSUB(tr2, tr3);
+
+ ti3 = VSUB(pc[2*ido + i + 1], pc[2*ido - i + 1]);
+ tr4 = VADD(pc[2*ido + i + 1], pc[2*ido - i + 1]);
+ cr2 = VSUB(tr1, tr4);
+ cr4 = VADD(tr1, tr4);
+
+ ti1 = VADD(pc[i + 1], pc[4*ido - i + 1]);
+ ti2 = VSUB(pc[i + 1], pc[4*ido - i + 1]);
+
+ ph[1] = VADD(ti2, ti3); ph += l1ido;
+ ci3 = VSUB(ti2, ti3);
+ ci2 = VADD(ti1, ti4);
+ ci4 = VSUB(ti1, ti4);
+ VCPLXMUL(cr2, ci2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));
+ ph[0] = cr2;
+ ph[1] = ci2; ph += l1ido;
+ VCPLXMUL(cr3, ci3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));
+ ph[0] = cr3;
+ ph[1] = ci3; ph += l1ido;
+ VCPLXMUL(cr4, ci4, LD_PS1(wa3[i-2]), LD_PS1(wa3[i-1]));
+ ph[0] = cr4;
+ ph[1] = ci4; ph = ph - 3*l1ido + 2;
+ }
+ }
+ if (ido % 2 == 1) return;
+ }
+ for (k=0; k < l1ido; k+=ido) {
+ int i0 = 4*k + ido;
+ v4sf c = cc[i0-1], d = cc[i0 + 2*ido-1];
+ v4sf a = cc[i0+0], b = cc[i0 + 2*ido+0];
+ tr1 = VSUB(c,d);
+ tr2 = VADD(c,d);
+ ti1 = VADD(b,a);
+ ti2 = VSUB(b,a);
+ ch[ido-1 + k + 0*l1ido] = VADD(tr2,tr2);
+ ch[ido-1 + k + 1*l1ido] = SVMUL(minus_sqrt2, VSUB(ti1, tr1));
+ ch[ido-1 + k + 2*l1ido] = VADD(ti2, ti2);
+ ch[ido-1 + k + 3*l1ido] = SVMUL(minus_sqrt2, VADD(ti1, tr1));
+ }
+} /* radb4 */
+
+static void radf5_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,
+ const float *wa1, const float *wa2, const float *wa3, const float *wa4)
+{
+ static const float tr11 = .309016994374947f;
+ static const float ti11 = .951056516295154f;
+ static const float tr12 = -.809016994374947f;
+ static const float ti12 = .587785252292473f;
+
+ /* System generated locals */
+ int cc_offset, ch_offset;
+
+ /* Local variables */
+ int i, k, ic;
+ v4sf ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3, dr4, dr5,
+ cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5;
+ int idp2;
+
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*5 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * 6;
+ ch -= ch_offset;
+ cc_offset = 1 + ido * (1 + l1);
+ cc -= cc_offset;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ cr2 = VADD(cc_ref(1, k, 5), cc_ref(1, k, 2));
+ ci5 = VSUB(cc_ref(1, k, 5), cc_ref(1, k, 2));
+ cr3 = VADD(cc_ref(1, k, 4), cc_ref(1, k, 3));
+ ci4 = VSUB(cc_ref(1, k, 4), cc_ref(1, k, 3));
+ ch_ref(1, 1, k) = VADD(cc_ref(1, k, 1), VADD(cr2, cr3));
+ ch_ref(ido, 2, k) = VADD(cc_ref(1, k, 1), VADD(SVMUL(tr11, cr2), SVMUL(tr12, cr3)));
+ ch_ref(1, 3, k) = VADD(SVMUL(ti11, ci5), SVMUL(ti12, ci4));
+ ch_ref(ido, 4, k) = VADD(cc_ref(1, k, 1), VADD(SVMUL(tr12, cr2), SVMUL(tr11, cr3)));
+ ch_ref(1, 5, k) = VSUB(SVMUL(ti12, ci5), SVMUL(ti11, ci4));
+ //printf("pffft: radf5, k=%d ch_ref=%f, ci4=%f\n", k, ch_ref(1, 5, k), ci4);
+ }
+ if (ido == 1) {
+ return;
+ }
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ dr2 = LD_PS1(wa1[i-3]); di2 = LD_PS1(wa1[i-2]);
+ dr3 = LD_PS1(wa2[i-3]); di3 = LD_PS1(wa2[i-2]);
+ dr4 = LD_PS1(wa3[i-3]); di4 = LD_PS1(wa3[i-2]);
+ dr5 = LD_PS1(wa4[i-3]); di5 = LD_PS1(wa4[i-2]);
+ VCPLXMULCONJ(dr2, di2, cc_ref(i-1, k, 2), cc_ref(i, k, 2));
+ VCPLXMULCONJ(dr3, di3, cc_ref(i-1, k, 3), cc_ref(i, k, 3));
+ VCPLXMULCONJ(dr4, di4, cc_ref(i-1, k, 4), cc_ref(i, k, 4));
+ VCPLXMULCONJ(dr5, di5, cc_ref(i-1, k, 5), cc_ref(i, k, 5));
+ cr2 = VADD(dr2, dr5);
+ ci5 = VSUB(dr5, dr2);
+ cr5 = VSUB(di2, di5);
+ ci2 = VADD(di2, di5);
+ cr3 = VADD(dr3, dr4);
+ ci4 = VSUB(dr4, dr3);
+ cr4 = VSUB(di3, di4);
+ ci3 = VADD(di3, di4);
+ ch_ref(i - 1, 1, k) = VADD(cc_ref(i - 1, k, 1), VADD(cr2, cr3));
+ ch_ref(i, 1, k) = VSUB(cc_ref(i, k, 1), VADD(ci2, ci3));//
+ tr2 = VADD(cc_ref(i - 1, k, 1), VADD(SVMUL(tr11, cr2), SVMUL(tr12, cr3)));
+ ti2 = VSUB(cc_ref(i, k, 1), VADD(SVMUL(tr11, ci2), SVMUL(tr12, ci3)));//
+ tr3 = VADD(cc_ref(i - 1, k, 1), VADD(SVMUL(tr12, cr2), SVMUL(tr11, cr3)));
+ ti3 = VSUB(cc_ref(i, k, 1), VADD(SVMUL(tr12, ci2), SVMUL(tr11, ci3)));//
+ tr5 = VADD(SVMUL(ti11, cr5), SVMUL(ti12, cr4));
+ ti5 = VADD(SVMUL(ti11, ci5), SVMUL(ti12, ci4));
+ tr4 = VSUB(SVMUL(ti12, cr5), SVMUL(ti11, cr4));
+ ti4 = VSUB(SVMUL(ti12, ci5), SVMUL(ti11, ci4));
+ ch_ref(i - 1, 3, k) = VSUB(tr2, tr5);
+ ch_ref(ic - 1, 2, k) = VADD(tr2, tr5);
+ ch_ref(i, 3, k) = VADD(ti2, ti5);
+ ch_ref(ic, 2, k) = VSUB(ti5, ti2);
+ ch_ref(i - 1, 5, k) = VSUB(tr3, tr4);
+ ch_ref(ic - 1, 4, k) = VADD(tr3, tr4);
+ ch_ref(i, 5, k) = VADD(ti3, ti4);
+ ch_ref(ic, 4, k) = VSUB(ti4, ti3);
+ }
+ }
+#undef cc_ref
+#undef ch_ref
+} /* radf5 */
+
+static void radb5_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,
+ const float *wa1, const float *wa2, const float *wa3, const float *wa4)
+{
+ static const float tr11 = .309016994374947f;
+ static const float ti11 = .951056516295154f;
+ static const float tr12 = -.809016994374947f;
+ static const float ti12 = .587785252292473f;
+
+ int cc_offset, ch_offset;
+
+ /* Local variables */
+ int i, k, ic;
+ v4sf ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
+ ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
+ int idp2;
+
+#define cc_ref(a_1,a_2,a_3) cc[((a_3)*5 + (a_2))*ido + a_1]
+#define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]
+
+ /* Parameter adjustments */
+ ch_offset = 1 + ido * (1 + l1);
+ ch -= ch_offset;
+ cc_offset = 1 + ido * 6;
+ cc -= cc_offset;
+
+ /* Function Body */
+ for (k = 1; k <= l1; ++k) {
+ ti5 = VADD(cc_ref(1, 3, k), cc_ref(1, 3, k));
+ ti4 = VADD(cc_ref(1, 5, k), cc_ref(1, 5, k));
+ tr2 = VADD(cc_ref(ido, 2, k), cc_ref(ido, 2, k));
+ tr3 = VADD(cc_ref(ido, 4, k), cc_ref(ido, 4, k));
+ ch_ref(1, k, 1) = VADD(cc_ref(1, 1, k), VADD(tr2, tr3));
+ cr2 = VADD(cc_ref(1, 1, k), VADD(SVMUL(tr11, tr2), SVMUL(tr12, tr3)));
+ cr3 = VADD(cc_ref(1, 1, k), VADD(SVMUL(tr12, tr2), SVMUL(tr11, tr3)));
+ ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));
+ ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));
+ ch_ref(1, k, 2) = VSUB(cr2, ci5);
+ ch_ref(1, k, 3) = VSUB(cr3, ci4);
+ ch_ref(1, k, 4) = VADD(cr3, ci4);
+ ch_ref(1, k, 5) = VADD(cr2, ci5);
+ }
+ if (ido == 1) {
+ return;
+ }
+ idp2 = ido + 2;
+ for (k = 1; k <= l1; ++k) {
+ for (i = 3; i <= ido; i += 2) {
+ ic = idp2 - i;
+ ti5 = VADD(cc_ref(i , 3, k), cc_ref(ic , 2, k));
+ ti2 = VSUB(cc_ref(i , 3, k), cc_ref(ic , 2, k));
+ ti4 = VADD(cc_ref(i , 5, k), cc_ref(ic , 4, k));
+ ti3 = VSUB(cc_ref(i , 5, k), cc_ref(ic , 4, k));
+ tr5 = VSUB(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k));
+ tr2 = VADD(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k));
+ tr4 = VSUB(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k));
+ tr3 = VADD(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k));
+ ch_ref(i - 1, k, 1) = VADD(cc_ref(i-1, 1, k), VADD(tr2, tr3));
+ ch_ref(i, k, 1) = VADD(cc_ref(i, 1, k), VADD(ti2, ti3));
+ cr2 = VADD(cc_ref(i-1, 1, k), VADD(SVMUL(tr11, tr2), SVMUL(tr12, tr3)));
+ ci2 = VADD(cc_ref(i , 1, k), VADD(SVMUL(tr11, ti2), SVMUL(tr12, ti3)));
+ cr3 = VADD(cc_ref(i-1, 1, k), VADD(SVMUL(tr12, tr2), SVMUL(tr11, tr3)));
+ ci3 = VADD(cc_ref(i , 1, k), VADD(SVMUL(tr12, ti2), SVMUL(tr11, ti3)));
+ cr5 = VADD(SVMUL(ti11, tr5), SVMUL(ti12, tr4));
+ ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));
+ cr4 = VSUB(SVMUL(ti12, tr5), SVMUL(ti11, tr4));
+ ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));
+ dr3 = VSUB(cr3, ci4);
+ dr4 = VADD(cr3, ci4);
+ di3 = VADD(ci3, cr4);
+ di4 = VSUB(ci3, cr4);
+ dr5 = VADD(cr2, ci5);
+ dr2 = VSUB(cr2, ci5);
+ di5 = VSUB(ci2, cr5);
+ di2 = VADD(ci2, cr5);
+ VCPLXMUL(dr2, di2, LD_PS1(wa1[i-3]), LD_PS1(wa1[i-2]));
+ VCPLXMUL(dr3, di3, LD_PS1(wa2[i-3]), LD_PS1(wa2[i-2]));
+ VCPLXMUL(dr4, di4, LD_PS1(wa3[i-3]), LD_PS1(wa3[i-2]));
+ VCPLXMUL(dr5, di5, LD_PS1(wa4[i-3]), LD_PS1(wa4[i-2]));
+
+ ch_ref(i-1, k, 2) = dr2; ch_ref(i, k, 2) = di2;
+ ch_ref(i-1, k, 3) = dr3; ch_ref(i, k, 3) = di3;
+ ch_ref(i-1, k, 4) = dr4; ch_ref(i, k, 4) = di4;
+ ch_ref(i-1, k, 5) = dr5; ch_ref(i, k, 5) = di5;
+ }
+ }
+#undef cc_ref
+#undef ch_ref
+} /* radb5 */
+
+static NEVER_INLINE(v4sf *) rfftf1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2,
+ const float *wa, const int *ifac) {
+ v4sf *in = (v4sf*)input_readonly;
+ v4sf *out = (in == work2 ? work1 : work2);
+ int nf = ifac[1], k1;
+ int l2 = n;
+ int iw = n-1;
+ assert(in != out && work1 != work2);
+ for (k1 = 1; k1 <= nf; ++k1) {
+ int kh = nf - k1;
+ int ip = ifac[kh + 2];
+ int l1 = l2 / ip;
+ int ido = n / l2;
+ iw -= (ip - 1)*ido;
+ switch (ip) {
+ case 5: {
+ int ix2 = iw + ido;
+ int ix3 = ix2 + ido;
+ int ix4 = ix3 + ido;
+ radf5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
+ } break;
+ case 4: {
+ int ix2 = iw + ido;
+ int ix3 = ix2 + ido;
+ radf4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);
+ } break;
+ case 3: {
+ int ix2 = iw + ido;
+ radf3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);
+ } break;
+ case 2:
+ radf2_ps(ido, l1, in, out, &wa[iw]);
+ break;
+ default:
+ assert(0);
+ break;
+ }
+ l2 = l1;
+ if (out == work2) {
+ out = work1; in = work2;
+ } else {
+ out = work2; in = work1;
+ }
+ }
+ return in; /* this is in fact the output .. */
+} /* rfftf1 */
+
+static NEVER_INLINE(v4sf *) rfftb1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2,
+ const float *wa, const int *ifac) {
+ v4sf *in = (v4sf*)input_readonly;
+ v4sf *out = (in == work2 ? work1 : work2);
+ int nf = ifac[1], k1;
+ int l1 = 1;
+ int iw = 0;
+ assert(in != out);
+ for (k1=1; k1<=nf; k1++) {
+ int ip = ifac[k1 + 1];
+ int l2 = ip*l1;
+ int ido = n / l2;
+ switch (ip) {
+ case 5: {
+ int ix2 = iw + ido;
+ int ix3 = ix2 + ido;
+ int ix4 = ix3 + ido;
+ radb5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
+ } break;
+ case 4: {
+ int ix2 = iw + ido;
+ int ix3 = ix2 + ido;
+ radb4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);
+ } break;
+ case 3: {
+ int ix2 = iw + ido;
+ radb3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);
+ } break;
+ case 2:
+ radb2_ps(ido, l1, in, out, &wa[iw]);
+ break;
+ default:
+ assert(0);
+ break;
+ }
+ l1 = l2;
+ iw += (ip - 1)*ido;
+
+ if (out == work2) {
+ out = work1; in = work2;
+ } else {
+ out = work2; in = work1;
+ }
+ }
+ return in; /* this is in fact the output .. */
+}
+
+static int decompose(int n, int *ifac, const int *ntryh) {
+ int nl = n, nf = 0, i, j = 0;
+ for (j=0; ntryh[j]; ++j) {
+ int ntry = ntryh[j];
+ while (nl != 1) {
+ int nq = nl / ntry;
+ int nr = nl - ntry * nq;
+ if (nr == 0) {
+ ifac[2+nf++] = ntry;
+ nl = nq;
+ if (ntry == 2 && nf != 1) {
+ for (i = 2; i <= nf; ++i) {
+ int ib = nf - i + 2;
+ ifac[ib + 1] = ifac[ib];
+ }
+ ifac[2] = 2;
+ }
+ } else break;
+ }
+ }
+ ifac[0] = n;
+ ifac[1] = nf;
+ return nf;
+}
+
+
+
+static void rffti1_ps(int n, float *wa, int *ifac)
+{
+ static const int ntryh[] = { 4,2,3,5,0 };
+ int k1, j, ii;
+
+ int nf = decompose(n,ifac,ntryh);
+ float argh = (2*M_PI) / n;
+ int is = 0;
+ int nfm1 = nf - 1;
+ int l1 = 1;
+ for (k1 = 1; k1 <= nfm1; k1++) {
+ int ip = ifac[k1 + 1];
+ int ld = 0;
+ int l2 = l1*ip;
+ int ido = n / l2;
+ int ipm = ip - 1;
+ for (j = 1; j <= ipm; ++j) {
+ float argld;
+ int i = is, fi=0;
+ ld += l1;
+ argld = ld*argh;
+ for (ii = 3; ii <= ido; ii += 2) {
+ i += 2;
+ fi += 1;
+ wa[i - 2] = cos(fi*argld);
+ wa[i - 1] = sin(fi*argld);
+ }
+ is += ido;
+ }
+ l1 = l2;
+ }
+} /* rffti1 */
+
+void cffti1_ps(int n, float *wa, int *ifac)
+{
+ static const int ntryh[] = { 5,3,4,2,0 };
+ int k1, j, ii;
+
+ int nf = decompose(n,ifac,ntryh);
+ float argh = (2*M_PI)/(float)n;
+ int i = 1;
+ int l1 = 1;
+ for (k1=1; k1<=nf; k1++) {
+ int ip = ifac[k1+1];
+ int ld = 0;
+ int l2 = l1*ip;
+ int ido = n / l2;
+ int idot = ido + ido + 2;
+ int ipm = ip - 1;
+ for (j=1; j<=ipm; j++) {
+ float argld;
+ int i1 = i, fi = 0;
+ wa[i-1] = 1;
+ wa[i] = 0;
+ ld += l1;
+ argld = ld*argh;
+ for (ii = 4; ii <= idot; ii += 2) {
+ i += 2;
+ fi += 1;
+ wa[i-1] = cos(fi*argld);
+ wa[i] = sin(fi*argld);
+ }
+ if (ip > 5) {
+ wa[i1-1] = wa[i-1];
+ wa[i1] = wa[i];
+ }
+ }
+ l1 = l2;
+ }
+} /* cffti1 */
+
+
+v4sf *cfftf1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2, const float *wa, const int *ifac, int isign) {
+ v4sf *in = (v4sf*)input_readonly;
+ v4sf *out = (in == work2 ? work1 : work2);
+ int nf = ifac[1], k1;
+ int l1 = 1;
+ int iw = 0;
+ assert(in != out && work1 != work2);
+ for (k1=2; k1<=nf+1; k1++) {
+ int ip = ifac[k1];
+ int l2 = ip*l1;
+ int ido = n / l2;
+ int idot = ido + ido;
+ switch (ip) {
+ case 5: {
+ int ix2 = iw + idot;
+ int ix3 = ix2 + idot;
+ int ix4 = ix3 + idot;
+ passf5_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
+ } break;
+ case 4: {
+ int ix2 = iw + idot;
+ int ix3 = ix2 + idot;
+ passf4_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], isign);
+ } break;
+ case 2: {
+ passf2_ps(idot, l1, in, out, &wa[iw], isign);
+ } break;
+ case 3: {
+ int ix2 = iw + idot;
+ passf3_ps(idot, l1, in, out, &wa[iw], &wa[ix2], isign);
+ } break;
+ default:
+ assert(0);
+ }
+ l1 = l2;
+ iw += (ip - 1)*idot;
+ if (out == work2) {
+ out = work1; in = work2;
+ } else {
+ out = work2; in = work1;
+ }
+ }
+
+ return in; /* this is in fact the output .. */
+}
+
+
+struct PFFFT_Setup {
+ int N;
+ int Ncvec; // nb of complex simd vectors (N/4 if PFFFT_COMPLEX, N/8 if PFFFT_REAL)
+ int ifac[15];
+ pffft_transform_t transform;
+ v4sf *data; // allocated room for twiddle coefs
+ float *e; // points into 'data' , N/4*3 elements
+ float *twiddle; // points into 'data', N/4 elements
+};
+
+PFFFT_Setup *pffft_new_setup(int N, pffft_transform_t transform) {
+ PFFFT_Setup *s = (PFFFT_Setup*)malloc(sizeof(PFFFT_Setup));
+ int k, m;
+ /* unfortunately, the fft size must be a multiple of 16 for complex FFTs
+ and 32 for real FFTs -- a lot of stuff would need to be rewritten to
+ handle other cases (or maybe just switch to a scalar fft, I don't know..) */
+ if (transform == PFFFT_REAL) { assert((N%(2*SIMD_SZ*SIMD_SZ))==0 && N>0); }
+ if (transform == PFFFT_COMPLEX) { assert((N%(SIMD_SZ*SIMD_SZ))==0 && N>0); }
+ //assert((N % 32) == 0);
+ s->N = N;
+ s->transform = transform;
+ /* nb of complex simd vectors */
+ s->Ncvec = (transform == PFFFT_REAL ? N/2 : N)/SIMD_SZ;
+ s->data = (v4sf*)pffft_aligned_malloc(2*s->Ncvec * sizeof(v4sf));
+ s->e = (float*)s->data;
+ s->twiddle = (float*)(s->data + (2*s->Ncvec*(SIMD_SZ-1))/SIMD_SZ);
+
+ if (transform == PFFFT_REAL) {
+ for (k=0; k < s->Ncvec; ++k) {
+ int i = k/SIMD_SZ;
+ int j = k%SIMD_SZ;
+ for (m=0; m < SIMD_SZ-1; ++m) {
+ float A = -2*M_PI*(m+1)*k / N;
+ s->e[(2*(i*3 + m) + 0) * SIMD_SZ + j] = cos(A);
+ s->e[(2*(i*3 + m) + 1) * SIMD_SZ + j] = sin(A);
+ }
+ }
+ rffti1_ps(N/SIMD_SZ, s->twiddle, s->ifac);
+ } else {
+ for (k=0; k < s->Ncvec; ++k) {
+ int i = k/SIMD_SZ;
+ int j = k%SIMD_SZ;
+ for (m=0; m < SIMD_SZ-1; ++m) {
+ float A = -2*M_PI*(m+1)*k / N;
+ s->e[(2*(i*3 + m) + 0)*SIMD_SZ + j] = cos(A);
+ s->e[(2*(i*3 + m) + 1)*SIMD_SZ + j] = sin(A);
+ }
+ }
+ cffti1_ps(N/SIMD_SZ, s->twiddle, s->ifac);
+ }
+
+ /* check that N is decomposable with allowed prime factors */
+ for (k=0, m=1; k < s->ifac[1]; ++k) { m *= s->ifac[2+k]; }
+ if (m != N/SIMD_SZ) {
+ pffft_destroy_setup(s); s = 0;
+ }
+
+ return s;
+}
+
+
+void pffft_destroy_setup(PFFFT_Setup *s) {
+ pffft_aligned_free(s->data);
+ free(s);
+}
+
+#if !defined(PFFFT_SIMD_DISABLE)
+
+/* [0 0 1 2 3 4 5 6 7 8] -> [0 8 7 6 5 4 3 2 1] */
+static void reversed_copy(int N, const v4sf *in, int in_stride, v4sf *out) {
+ v4sf g0, g1;
+ int k;
+ INTERLEAVE2(in[0], in[1], g0, g1); in += in_stride;
+
+ *--out = VSWAPHL(g0, g1); // [g0l, g0h], [g1l g1h] -> [g1l, g0h]
+ for (k=1; k < N; ++k) {
+ v4sf h0, h1;
+ INTERLEAVE2(in[0], in[1], h0, h1); in += in_stride;
+ *--out = VSWAPHL(g1, h0);
+ *--out = VSWAPHL(h0, h1);
+ g1 = h1;
+ }
+ *--out = VSWAPHL(g1, g0);
+}
+
+static void unreversed_copy(int N, const v4sf *in, v4sf *out, int out_stride) {
+ v4sf g0, g1, h0, h1;
+ int k;
+ g0 = g1 = in[0]; ++in;
+ for (k=1; k < N; ++k) {
+ h0 = *in++; h1 = *in++;
+ g1 = VSWAPHL(g1, h0);
+ h0 = VSWAPHL(h0, h1);
+ UNINTERLEAVE2(h0, g1, out[0], out[1]); out += out_stride;
+ g1 = h1;
+ }
+ h0 = *in++; h1 = g0;
+ g1 = VSWAPHL(g1, h0);
+ h0 = VSWAPHL(h0, h1);
+ UNINTERLEAVE2(h0, g1, out[0], out[1]);
+}
+
+void pffft_zreorder(PFFFT_Setup *setup, const float *in, float *out, pffft_direction_t direction) {
+ int k, N = setup->N, Ncvec = setup->Ncvec;
+ const v4sf *vin = (const v4sf*)in;
+ v4sf *vout = (v4sf*)out;
+ assert(in != out);
+ if (setup->transform == PFFFT_REAL) {
+ int k, dk = N/32;
+ if (direction == PFFFT_FORWARD) {
+ for (k=0; k < dk; ++k) {
+ INTERLEAVE2(vin[k*8 + 0], vin[k*8 + 1], vout[2*(0*dk + k) + 0], vout[2*(0*dk + k) + 1]);
+ INTERLEAVE2(vin[k*8 + 4], vin[k*8 + 5], vout[2*(2*dk + k) + 0], vout[2*(2*dk + k) + 1]);
+ }
+ reversed_copy(dk, vin+2, 8, (v4sf*)(out + N/2));
+ reversed_copy(dk, vin+6, 8, (v4sf*)(out + N));
+ } else {
+ for (k=0; k < dk; ++k) {
+ UNINTERLEAVE2(vin[2*(0*dk + k) + 0], vin[2*(0*dk + k) + 1], vout[k*8 + 0], vout[k*8 + 1]);
+ UNINTERLEAVE2(vin[2*(2*dk + k) + 0], vin[2*(2*dk + k) + 1], vout[k*8 + 4], vout[k*8 + 5]);
+ }
+ unreversed_copy(dk, (v4sf*)(in + N/4), (v4sf*)(out + N - 6*SIMD_SZ), -8);
+ unreversed_copy(dk, (v4sf*)(in + 3*N/4), (v4sf*)(out + N - 2*SIMD_SZ), -8);
+ }
+ } else {
+ if (direction == PFFFT_FORWARD) {
+ for (k=0; k < Ncvec; ++k) {
+ int kk = (k/4) + (k%4)*(Ncvec/4);
+ INTERLEAVE2(vin[k*2], vin[k*2+1], vout[kk*2], vout[kk*2+1]);
+ }
+ } else {
+ for (k=0; k < Ncvec; ++k) {
+ int kk = (k/4) + (k%4)*(Ncvec/4);
+ UNINTERLEAVE2(vin[kk*2], vin[kk*2+1], vout[k*2], vout[k*2+1]);
+ }
+ }
+ }
+}
+
+void pffft_cplx_finalize(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {
+ int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks
+ v4sf r0, i0, r1, i1, r2, i2, r3, i3;
+ v4sf sr0, dr0, sr1, dr1, si0, di0, si1, di1;
+ assert(in != out);
+ for (k=0; k < dk; ++k) {
+ r0 = in[8*k+0]; i0 = in[8*k+1];
+ r1 = in[8*k+2]; i1 = in[8*k+3];
+ r2 = in[8*k+4]; i2 = in[8*k+5];
+ r3 = in[8*k+6]; i3 = in[8*k+7];
+ VTRANSPOSE4(r0,r1,r2,r3);
+ VTRANSPOSE4(i0,i1,i2,i3);
+ VCPLXMUL(r1,i1,e[k*6+0],e[k*6+1]);
+ VCPLXMUL(r2,i2,e[k*6+2],e[k*6+3]);
+ VCPLXMUL(r3,i3,e[k*6+4],e[k*6+5]);
+
+ sr0 = VADD(r0,r2); dr0 = VSUB(r0, r2);
+ sr1 = VADD(r1,r3); dr1 = VSUB(r1, r3);
+ si0 = VADD(i0,i2); di0 = VSUB(i0, i2);
+ si1 = VADD(i1,i3); di1 = VSUB(i1, i3);
+
+ /*
+ transformation for each column is:
+
+ [1 1 1 1 0 0 0 0] [r0]
+ [1 0 -1 0 0 -1 0 1] [r1]
+ [1 -1 1 -1 0 0 0 0] [r2]
+ [1 0 -1 0 0 1 0 -1] [r3]
+ [0 0 0 0 1 1 1 1] * [i0]
+ [0 1 0 -1 1 0 -1 0] [i1]
+ [0 0 0 0 1 -1 1 -1] [i2]
+ [0 -1 0 1 1 0 -1 0] [i3]
+ */
+
+ r0 = VADD(sr0, sr1); i0 = VADD(si0, si1);
+ r1 = VADD(dr0, di1); i1 = VSUB(di0, dr1);
+ r2 = VSUB(sr0, sr1); i2 = VSUB(si0, si1);
+ r3 = VSUB(dr0, di1); i3 = VADD(di0, dr1);
+
+ *out++ = r0; *out++ = i0; *out++ = r1; *out++ = i1;
+ *out++ = r2; *out++ = i2; *out++ = r3; *out++ = i3;
+ }
+}
+
+void pffft_cplx_preprocess(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {
+ int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks
+ v4sf r0, i0, r1, i1, r2, i2, r3, i3;
+ v4sf sr0, dr0, sr1, dr1, si0, di0, si1, di1;
+ assert(in != out);
+ for (k=0; k < dk; ++k) {
+ r0 = in[8*k+0]; i0 = in[8*k+1];
+ r1 = in[8*k+2]; i1 = in[8*k+3];
+ r2 = in[8*k+4]; i2 = in[8*k+5];
+ r3 = in[8*k+6]; i3 = in[8*k+7];
+
+ sr0 = VADD(r0,r2); dr0 = VSUB(r0, r2);
+ sr1 = VADD(r1,r3); dr1 = VSUB(r1, r3);
+ si0 = VADD(i0,i2); di0 = VSUB(i0, i2);
+ si1 = VADD(i1,i3); di1 = VSUB(i1, i3);
+
+ r0 = VADD(sr0, sr1); i0 = VADD(si0, si1);
+ r1 = VSUB(dr0, di1); i1 = VADD(di0, dr1);
+ r2 = VSUB(sr0, sr1); i2 = VSUB(si0, si1);
+ r3 = VADD(dr0, di1); i3 = VSUB(di0, dr1);
+
+ VCPLXMULCONJ(r1,i1,e[k*6+0],e[k*6+1]);
+ VCPLXMULCONJ(r2,i2,e[k*6+2],e[k*6+3]);
+ VCPLXMULCONJ(r3,i3,e[k*6+4],e[k*6+5]);
+
+ VTRANSPOSE4(r0,r1,r2,r3);
+ VTRANSPOSE4(i0,i1,i2,i3);
+
+ *out++ = r0; *out++ = i0; *out++ = r1; *out++ = i1;
+ *out++ = r2; *out++ = i2; *out++ = r3; *out++ = i3;
+ }
+}
+
+
+static ALWAYS_INLINE(void) pffft_real_finalize_4x4(const v4sf *in0, const v4sf *in1, const v4sf *in,
+ const v4sf *e, v4sf *out) {
+ v4sf r0, i0, r1, i1, r2, i2, r3, i3;
+ v4sf sr0, dr0, sr1, dr1, si0, di0, si1, di1;
+ r0 = *in0; i0 = *in1;
+ r1 = *in++; i1 = *in++; r2 = *in++; i2 = *in++; r3 = *in++; i3 = *in++;
+ VTRANSPOSE4(r0,r1,r2,r3);
+ VTRANSPOSE4(i0,i1,i2,i3);
+
+ /*
+ transformation for each column is:
+
+ [1 1 1 1 0 0 0 0] [r0]
+ [1 0 -1 0 0 -1 0 1] [r1]
+ [1 0 -1 0 0 1 0 -1] [r2]
+ [1 -1 1 -1 0 0 0 0] [r3]
+ [0 0 0 0 1 1 1 1] * [i0]
+ [0 -1 0 1 -1 0 1 0] [i1]
+ [0 -1 0 1 1 0 -1 0] [i2]
+ [0 0 0 0 -1 1 -1 1] [i3]
+ */
+
+ //cerr << "matrix initial, before e , REAL:\n 1: " << r0 << "\n 1: " << r1 << "\n 1: " << r2 << "\n 1: " << r3 << "\n";
+ //cerr << "matrix initial, before e, IMAG :\n 1: " << i0 << "\n 1: " << i1 << "\n 1: " << i2 << "\n 1: " << i3 << "\n";
+
+ VCPLXMUL(r1,i1,e[0],e[1]);
+ VCPLXMUL(r2,i2,e[2],e[3]);
+ VCPLXMUL(r3,i3,e[4],e[5]);
+
+ //cerr << "matrix initial, real part:\n 1: " << r0 << "\n 1: " << r1 << "\n 1: " << r2 << "\n 1: " << r3 << "\n";
+ //cerr << "matrix initial, imag part:\n 1: " << i0 << "\n 1: " << i1 << "\n 1: " << i2 << "\n 1: " << i3 << "\n";
+
+ sr0 = VADD(r0,r2); dr0 = VSUB(r0,r2);
+ sr1 = VADD(r1,r3); dr1 = VSUB(r3,r1);
+ si0 = VADD(i0,i2); di0 = VSUB(i0,i2);
+ si1 = VADD(i1,i3); di1 = VSUB(i3,i1);
+
+ r0 = VADD(sr0, sr1);
+ r3 = VSUB(sr0, sr1);
+ i0 = VADD(si0, si1);
+ i3 = VSUB(si1, si0);
+ r1 = VADD(dr0, di1);
+ r2 = VSUB(dr0, di1);
+ i1 = VSUB(dr1, di0);
+ i2 = VADD(dr1, di0);
+
+ *out++ = r0;
+ *out++ = i0;
+ *out++ = r1;
+ *out++ = i1;
+ *out++ = r2;
+ *out++ = i2;
+ *out++ = r3;
+ *out++ = i3;
+
+}
+
+static NEVER_INLINE(void) pffft_real_finalize(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {
+ int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks
+ /* fftpack order is f0r f1r f1i f2r f2i ... f(n-1)r f(n-1)i f(n)r */
+
+ v4sf_union cr, ci, *uout = (v4sf_union*)out;
+ v4sf save = in[7], zero=VZERO();
+ float xr0, xi0, xr1, xi1, xr2, xi2, xr3, xi3;
+ static const float s = M_SQRT2/2;
+
+ cr.v = in[0]; ci.v = in[Ncvec*2-1];
+ assert(in != out);
+ pffft_real_finalize_4x4(&zero, &zero, in+1, e, out);
+
+ /*
+ [cr0 cr1 cr2 cr3 ci0 ci1 ci2 ci3]
+
+ [Xr(1)] ] [1 1 1 1 0 0 0 0]
+ [Xr(N/4) ] [0 0 0 0 1 s 0 -s]
+ [Xr(N/2) ] [1 0 -1 0 0 0 0 0]
+ [Xr(3N/4)] [0 0 0 0 1 -s 0 s]
+ [Xi(1) ] [1 -1 1 -1 0 0 0 0]
+ [Xi(N/4) ] [0 0 0 0 0 -s -1 -s]
+ [Xi(N/2) ] [0 -1 0 1 0 0 0 0]
+ [Xi(3N/4)] [0 0 0 0 0 -s 1 -s]
+ */
+
+ xr0=(cr.f[0]+cr.f[2]) + (cr.f[1]+cr.f[3]); uout[0].f[0] = xr0;
+ xi0=(cr.f[0]+cr.f[2]) - (cr.f[1]+cr.f[3]); uout[1].f[0] = xi0;
+ xr2=(cr.f[0]-cr.f[2]); uout[4].f[0] = xr2;
+ xi2=(cr.f[3]-cr.f[1]); uout[5].f[0] = xi2;
+ xr1= ci.f[0] + s*(ci.f[1]-ci.f[3]); uout[2].f[0] = xr1;
+ xi1=-ci.f[2] - s*(ci.f[1]+ci.f[3]); uout[3].f[0] = xi1;
+ xr3= ci.f[0] - s*(ci.f[1]-ci.f[3]); uout[6].f[0] = xr3;
+ xi3= ci.f[2] - s*(ci.f[1]+ci.f[3]); uout[7].f[0] = xi3;
+
+ for (k=1; k < dk; ++k) {
+ v4sf save_next = in[8*k+7];
+ pffft_real_finalize_4x4(&save, &in[8*k+0], in + 8*k+1,
+ e + k*6, out + k*8);
+ save = save_next;
+ }
+
+}
+
+static ALWAYS_INLINE(void) pffft_real_preprocess_4x4(const v4sf *in,
+ const v4sf *e, v4sf *out, int first) {
+ v4sf r0=in[0], i0=in[1], r1=in[2], i1=in[3], r2=in[4], i2=in[5], r3=in[6], i3=in[7];
+ /*
+ transformation for each column is:
+
+ [1 1 1 1 0 0 0 0] [r0]
+ [1 0 0 -1 0 -1 -1 0] [r1]
+ [1 -1 -1 1 0 0 0 0] [r2]
+ [1 0 0 -1 0 1 1 0] [r3]
+ [0 0 0 0 1 -1 1 -1] * [i0]
+ [0 -1 1 0 1 0 0 1] [i1]
+ [0 0 0 0 1 1 -1 -1] [i2]
+ [0 1 -1 0 1 0 0 1] [i3]
+ */
+
+ v4sf sr0 = VADD(r0,r3), dr0 = VSUB(r0,r3);
+ v4sf sr1 = VADD(r1,r2), dr1 = VSUB(r1,r2);
+ v4sf si0 = VADD(i0,i3), di0 = VSUB(i0,i3);
+ v4sf si1 = VADD(i1,i2), di1 = VSUB(i1,i2);
+
+ r0 = VADD(sr0, sr1);
+ r2 = VSUB(sr0, sr1);
+ r1 = VSUB(dr0, si1);
+ r3 = VADD(dr0, si1);
+ i0 = VSUB(di0, di1);
+ i2 = VADD(di0, di1);
+ i1 = VSUB(si0, dr1);
+ i3 = VADD(si0, dr1);
+
+ VCPLXMULCONJ(r1,i1,e[0],e[1]);
+ VCPLXMULCONJ(r2,i2,e[2],e[3]);
+ VCPLXMULCONJ(r3,i3,e[4],e[5]);
+
+ VTRANSPOSE4(r0,r1,r2,r3);
+ VTRANSPOSE4(i0,i1,i2,i3);
+
+ if (!first) {
+ *out++ = r0;
+ *out++ = i0;
+ }
+ *out++ = r1;
+ *out++ = i1;
+ *out++ = r2;
+ *out++ = i2;
+ *out++ = r3;
+ *out++ = i3;
+}
+
+static NEVER_INLINE(void) pffft_real_preprocess(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {
+ int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks
+ /* fftpack order is f0r f1r f1i f2r f2i ... f(n-1)r f(n-1)i f(n)r */
+
+ v4sf_union Xr, Xi, *uout = (v4sf_union*)out;
+ float cr0, ci0, cr1, ci1, cr2, ci2, cr3, ci3;
+ static const float s = M_SQRT2;
+ assert(in != out);
+ for (k=0; k < 4; ++k) {
+ Xr.f[k] = ((float*)in)[8*k];
+ Xi.f[k] = ((float*)in)[8*k+4];
+ }
+
+ pffft_real_preprocess_4x4(in, e, out+1, 1); // will write only 6 values
+
+ /*
+ [Xr0 Xr1 Xr2 Xr3 Xi0 Xi1 Xi2 Xi3]
+
+ [cr0] [1 0 2 0 1 0 0 0]
+ [cr1] [1 0 0 0 -1 0 -2 0]
+ [cr2] [1 0 -2 0 1 0 0 0]
+ [cr3] [1 0 0 0 -1 0 2 0]
+ [ci0] [0 2 0 2 0 0 0 0]
+ [ci1] [0 s 0 -s 0 -s 0 -s]
+ [ci2] [0 0 0 0 0 -2 0 2]
+ [ci3] [0 -s 0 s 0 -s 0 -s]
+ */
+ for (k=1; k < dk; ++k) {
+ pffft_real_preprocess_4x4(in+8*k, e + k*6, out-1+k*8, 0);
+ }
+
+ cr0=(Xr.f[0]+Xi.f[0]) + 2*Xr.f[2]; uout[0].f[0] = cr0;
+ cr1=(Xr.f[0]-Xi.f[0]) - 2*Xi.f[2]; uout[0].f[1] = cr1;
+ cr2=(Xr.f[0]+Xi.f[0]) - 2*Xr.f[2]; uout[0].f[2] = cr2;
+ cr3=(Xr.f[0]-Xi.f[0]) + 2*Xi.f[2]; uout[0].f[3] = cr3;
+ ci0= 2*(Xr.f[1]+Xr.f[3]); uout[2*Ncvec-1].f[0] = ci0;
+ ci1= s*(Xr.f[1]-Xr.f[3]) - s*(Xi.f[1]+Xi.f[3]); uout[2*Ncvec-1].f[1] = ci1;
+ ci2= 2*(Xi.f[3]-Xi.f[1]); uout[2*Ncvec-1].f[2] = ci2;
+ ci3=-s*(Xr.f[1]-Xr.f[3]) - s*(Xi.f[1]+Xi.f[3]); uout[2*Ncvec-1].f[3] = ci3;
+}
+
+
+void pffft_transform_internal(PFFFT_Setup *setup, const float *finput, float *foutput, v4sf *scratch,
+ pffft_direction_t direction, int ordered) {
+ int k, Ncvec = setup->Ncvec;
+ int nf_odd = (setup->ifac[1] & 1);
+
+ // temporary buffer is allocated on the stack if the scratch pointer is NULL
+ int stack_allocate = (scratch == 0 ? Ncvec*2 : 1);
+ VLA_ARRAY_ON_STACK(v4sf, scratch_on_stack, stack_allocate);
+
+ const v4sf *vinput = (const v4sf*)finput;
+ v4sf *voutput = (v4sf*)foutput;
+ v4sf *buff[2] = { voutput, scratch ? scratch : scratch_on_stack };
+ int ib = (nf_odd ^ ordered ? 1 : 0);
+
+ assert(VALIGNED(finput) && VALIGNED(foutput));
+
+ //assert(finput != foutput);
+ if (direction == PFFFT_FORWARD) {
+ ib = !ib;
+ if (setup->transform == PFFFT_REAL) {
+ ib = (rfftf1_ps(Ncvec*2, vinput, buff[ib], buff[!ib],
+ setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);
+ pffft_real_finalize(Ncvec, buff[ib], buff[!ib], (v4sf*)setup->e);
+ } else {
+ v4sf *tmp = buff[ib];
+ for (k=0; k < Ncvec; ++k) {
+ UNINTERLEAVE2(vinput[k*2], vinput[k*2+1], tmp[k*2], tmp[k*2+1]);
+ }
+ ib = (cfftf1_ps(Ncvec, buff[ib], buff[!ib], buff[ib],
+ setup->twiddle, &setup->ifac[0], -1) == buff[0] ? 0 : 1);
+ pffft_cplx_finalize(Ncvec, buff[ib], buff[!ib], (v4sf*)setup->e);
+ }
+ if (ordered) {
+ pffft_zreorder(setup, (float*)buff[!ib], (float*)buff[ib], PFFFT_FORWARD);
+ } else ib = !ib;
+ } else {
+ if (vinput == buff[ib]) {
+ ib = !ib; // may happen when finput == foutput
+ }
+ if (ordered) {
+ pffft_zreorder(setup, (float*)vinput, (float*)buff[ib], PFFFT_BACKWARD);
+ vinput = buff[ib]; ib = !ib;
+ }
+ if (setup->transform == PFFFT_REAL) {
+ pffft_real_preprocess(Ncvec, vinput, buff[ib], (v4sf*)setup->e);
+ ib = (rfftb1_ps(Ncvec*2, buff[ib], buff[0], buff[1],
+ setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);
+ } else {
+ pffft_cplx_preprocess(Ncvec, vinput, buff[ib], (v4sf*)setup->e);
+ ib = (cfftf1_ps(Ncvec, buff[ib], buff[0], buff[1],
+ setup->twiddle, &setup->ifac[0], +1) == buff[0] ? 0 : 1);
+ for (k=0; k < Ncvec; ++k) {
+ INTERLEAVE2(buff[ib][k*2], buff[ib][k*2+1], buff[ib][k*2], buff[ib][k*2+1]);
+ }
+ }
+ }
+
+ if (buff[ib] != voutput) {
+ /* extra copy required -- this situation should only happen when finput == foutput */
+ assert(finput==foutput);
+ for (k=0; k < Ncvec; ++k) {
+ v4sf a = buff[ib][2*k], b = buff[ib][2*k+1];
+ voutput[2*k] = a; voutput[2*k+1] = b;
+ }
+ ib = !ib;
+ }
+ assert(buff[ib] == voutput);
+
+ VLA_ARRAY_ON_STACK_FREE(scratch_on_stack);
+}
+
+void pffft_zconvolve_accumulate(PFFFT_Setup *s, const float *a, const float *b, float *ab, float scaling) {
+ int Ncvec = s->Ncvec;
+ const v4sf * RESTRICT va = (const v4sf*)a;
+ const v4sf * RESTRICT vb = (const v4sf*)b;
+ v4sf * RESTRICT vab = (v4sf*)ab;
+
+#ifdef __arm__
+ __builtin_prefetch(va);
+ __builtin_prefetch(vb);
+ __builtin_prefetch(vab);
+ __builtin_prefetch(va+2);
+ __builtin_prefetch(vb+2);
+ __builtin_prefetch(vab+2);
+ __builtin_prefetch(va+4);
+ __builtin_prefetch(vb+4);
+ __builtin_prefetch(vab+4);
+ __builtin_prefetch(va+6);
+ __builtin_prefetch(vb+6);
+ __builtin_prefetch(vab+6);
+# ifndef __clang__
+# define ZCONVOLVE_USING_INLINE_NEON_ASM
+# endif
+#endif
+
+ float ar, ai, br, bi, abr, abi;
+#ifndef ZCONVOLVE_USING_INLINE_ASM
+ v4sf vscal = LD_PS1(scaling);
+ int i;
+#endif
+
+ assert(VALIGNED(a) && VALIGNED(b) && VALIGNED(ab));
+ ar = ((v4sf_union*)va)[0].f[0];
+ ai = ((v4sf_union*)va)[1].f[0];
+ br = ((v4sf_union*)vb)[0].f[0];
+ bi = ((v4sf_union*)vb)[1].f[0];
+ abr = ((v4sf_union*)vab)[0].f[0];
+ abi = ((v4sf_union*)vab)[1].f[0];
+
+#ifdef ZCONVOLVE_USING_INLINE_ASM // inline asm version, unfortunately miscompiled by clang 3.2, at least on ubuntu.. so this will be restricted to gcc
+ const float *a_ = a, *b_ = b; float *ab_ = ab;
+ int N = Ncvec;
+ asm volatile("mov r8, %2 \n"
+ "vdup.f32 q15, %4 \n"
+ "1: \n"
+ "pld [%0,#64] \n"
+ "pld [%1,#64] \n"
+ "pld [%2,#64] \n"
+ "pld [%0,#96] \n"
+ "pld [%1,#96] \n"
+ "pld [%2,#96] \n"
+ "vld1.f32 {q0,q1}, [%0,:128]! \n"
+ "vld1.f32 {q4,q5}, [%1,:128]! \n"
+ "vld1.f32 {q2,q3}, [%0,:128]! \n"
+ "vld1.f32 {q6,q7}, [%1,:128]! \n"
+ "vld1.f32 {q8,q9}, [r8,:128]! \n"
+
+ "vmul.f32 q10, q0, q4 \n"
+ "vmul.f32 q11, q0, q5 \n"
+ "vmul.f32 q12, q2, q6 \n"
+ "vmul.f32 q13, q2, q7 \n"
+ "vmls.f32 q10, q1, q5 \n"
+ "vmla.f32 q11, q1, q4 \n"
+ "vld1.f32 {q0,q1}, [r8,:128]! \n"
+ "vmls.f32 q12, q3, q7 \n"
+ "vmla.f32 q13, q3, q6 \n"
+ "vmla.f32 q8, q10, q15 \n"
+ "vmla.f32 q9, q11, q15 \n"
+ "vmla.f32 q0, q12, q15 \n"
+ "vmla.f32 q1, q13, q15 \n"
+ "vst1.f32 {q8,q9},[%2,:128]! \n"
+ "vst1.f32 {q0,q1},[%2,:128]! \n"
+ "subs %3, #2 \n"
+ "bne 1b \n"
+ : "+r"(a_), "+r"(b_), "+r"(ab_), "+r"(N) : "r"(scaling) : "r8", "q0","q1","q2","q3","q4","q5","q6","q7","q8","q9", "q10","q11","q12","q13","q15","memory");
+#else // default routine, works fine for non-arm cpus with current compilers
+ for (i=0; i < Ncvec; i += 2) {
+ v4sf ar, ai, br, bi;
+ ar = va[2*i+0]; ai = va[2*i+1];
+ br = vb[2*i+0]; bi = vb[2*i+1];
+ VCPLXMUL(ar, ai, br, bi);
+ vab[2*i+0] = VMADD(ar, vscal, vab[2*i+0]);
+ vab[2*i+1] = VMADD(ai, vscal, vab[2*i+1]);
+ ar = va[2*i+2]; ai = va[2*i+3];
+ br = vb[2*i+2]; bi = vb[2*i+3];
+ VCPLXMUL(ar, ai, br, bi);
+ vab[2*i+2] = VMADD(ar, vscal, vab[2*i+2]);
+ vab[2*i+3] = VMADD(ai, vscal, vab[2*i+3]);
+ }
+#endif
+ if (s->transform == PFFFT_REAL) {
+ ((v4sf_union*)vab)[0].f[0] = abr + ar*br*scaling;
+ ((v4sf_union*)vab)[1].f[0] = abi + ai*bi*scaling;
+ }
+}
+
+
+#else // defined(PFFFT_SIMD_DISABLE)
+
+// standard routine using scalar floats, without SIMD stuff.
+
+#define pffft_zreorder_nosimd pffft_zreorder
+void pffft_zreorder_nosimd(PFFFT_Setup *setup, const float *in, float *out, pffft_direction_t direction) {
+ int k, N = setup->N;
+ if (setup->transform == PFFFT_COMPLEX) {
+ for (k=0; k < 2*N; ++k) out[k] = in[k];
+ return;
+ }
+ else if (direction == PFFFT_FORWARD) {
+ float x_N = in[N-1];
+ for (k=N-1; k > 1; --k) out[k] = in[k-1];
+ out[0] = in[0];
+ out[1] = x_N;
+ } else {
+ float x_N = in[1];
+ for (k=1; k < N-1; ++k) out[k] = in[k+1];
+ out[0] = in[0];
+ out[N-1] = x_N;
+ }
+}
+
+#define pffft_transform_internal_nosimd pffft_transform_internal
+void pffft_transform_internal_nosimd(PFFFT_Setup *setup, const float *input, float *output, float *scratch,
+ pffft_direction_t direction, int ordered) {
+ int Ncvec = setup->Ncvec;
+ int nf_odd = (setup->ifac[1] & 1);
+
+ // temporary buffer is allocated on the stack if the scratch pointer is NULL
+ int stack_allocate = (scratch == 0 ? Ncvec*2 : 1);
+ VLA_ARRAY_ON_STACK(v4sf, scratch_on_stack, stack_allocate);
+ float *buff[2];
+ int ib;
+ if (scratch == 0) scratch = scratch_on_stack;
+ buff[0] = output; buff[1] = scratch;
+
+ if (setup->transform == PFFFT_COMPLEX) ordered = 0; // it is always ordered.
+ ib = (nf_odd ^ ordered ? 1 : 0);
+
+ if (direction == PFFFT_FORWARD) {
+ if (setup->transform == PFFFT_REAL) {
+ ib = (rfftf1_ps(Ncvec*2, input, buff[ib], buff[!ib],
+ setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);
+ } else {
+ ib = (cfftf1_ps(Ncvec, input, buff[ib], buff[!ib],
+ setup->twiddle, &setup->ifac[0], -1) == buff[0] ? 0 : 1);
+ }
+ if (ordered) {
+ pffft_zreorder(setup, buff[ib], buff[!ib], PFFFT_FORWARD); ib = !ib;
+ }
+ } else {
+ if (input == buff[ib]) {
+ ib = !ib; // may happen when finput == foutput
+ }
+ if (ordered) {
+ pffft_zreorder(setup, input, buff[!ib], PFFFT_BACKWARD);
+ input = buff[!ib];
+ }
+ if (setup->transform == PFFFT_REAL) {
+ ib = (rfftb1_ps(Ncvec*2, input, buff[ib], buff[!ib],
+ setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);
+ } else {
+ ib = (cfftf1_ps(Ncvec, input, buff[ib], buff[!ib],
+ setup->twiddle, &setup->ifac[0], +1) == buff[0] ? 0 : 1);
+ }
+ }
+ if (buff[ib] != output) {
+ int k;
+ // extra copy required -- this situation should happens only when finput == foutput
+ assert(input==output);
+ for (k=0; k < Ncvec; ++k) {
+ float a = buff[ib][2*k], b = buff[ib][2*k+1];
+ output[2*k] = a; output[2*k+1] = b;
+ }
+ ib = !ib;
+ }
+ assert(buff[ib] == output);
+
+ VLA_ARRAY_ON_STACK_FREE(scratch_on_stack);
+}
+
+#define pffft_zconvolve_accumulate_nosimd pffft_zconvolve_accumulate
+void pffft_zconvolve_accumulate_nosimd(PFFFT_Setup *s, const float *a, const float *b,
+ float *ab, float scaling) {
+ int i, Ncvec = s->Ncvec;
+
+ if (s->transform == PFFFT_REAL) {
+ // take care of the fftpack ordering
+ ab[0] += a[0]*b[0]*scaling;
+ ab[2*Ncvec-1] += a[2*Ncvec-1]*b[2*Ncvec-1]*scaling;
+ ++ab; ++a; ++b; --Ncvec;
+ }
+ for (i=0; i < Ncvec; ++i) {
+ float ar, ai, br, bi;
+ ar = a[2*i+0]; ai = a[2*i+1];
+ br = b[2*i+0]; bi = b[2*i+1];
+ VCPLXMUL(ar, ai, br, bi);
+ ab[2*i+0] += ar*scaling;
+ ab[2*i+1] += ai*scaling;
+ }
+}
+
+#endif // defined(PFFFT_SIMD_DISABLE)
+
+void pffft_transform(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction) {
+ pffft_transform_internal(setup, input, output, (v4sf*)work, direction, 0);
+}
+
+void pffft_transform_ordered(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction) {
+ pffft_transform_internal(setup, input, output, (v4sf*)work, direction, 1);
+}
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/pffft.h b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/pffft.h
new file mode 100644
index 0000000..7aef4db
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/pffft.h
@@ -0,0 +1,198 @@
+/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
+
+ Based on original fortran 77 code from FFTPACKv4 from NETLIB,
+ authored by Dr Paul Swarztrauber of NCAR, in 1985.
+
+ As confirmed by the NCAR fftpack software curators, the following
+ FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
+ released under the same terms.
+
+ FFTPACK license:
+
+ http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
+
+ Copyright (c) 2004 the University Corporation for Atmospheric
+ Research ("UCAR"). All rights reserved. Developed by NCAR's
+ Computational and Information Systems Laboratory, UCAR,
+ www.cisl.ucar.edu.
+
+ Redistribution and use of the Software in source and binary forms,
+ with or without modification, is permitted provided that the
+ following conditions are met:
+
+ - Neither the names of NCAR's Computational and Information Systems
+ Laboratory, the University Corporation for Atmospheric Research,
+ nor the names of its sponsors or contributors may be used to
+ endorse or promote products derived from this Software without
+ specific prior written permission.
+
+ - Redistributions of source code must retain the above copyright
+ notices, this list of conditions, and the disclaimer below.
+
+ - Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions, and the disclaimer below in the
+ documentation and/or other materials provided with the
+ distribution.
+
+ THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
+ HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
+ SOFTWARE.
+*/
+
+/*
+ PFFFT : a Pretty Fast FFT.
+
+ This is basically an adaptation of the single precision fftpack
+ (v4) as found on netlib taking advantage of SIMD instruction found
+ on cpus such as intel x86 (SSE1), powerpc (Altivec), and arm (NEON).
+
+ For architectures where no SIMD instruction is available, the code
+ falls back to a scalar version.
+
+ Restrictions:
+
+ - 1D transforms only, with 32-bit single precision.
+
+ - supports only transforms for inputs of length N of the form
+ N=(2^a)*(3^b)*(5^c), a >= 5, b >=0, c >= 0 (32, 48, 64, 96, 128,
+ 144, 160, etc are all acceptable lengths). Performance is best for
+ 128<=N<=8192.
+
+ - all (float*) pointers in the functions below are expected to
+ have an "simd-compatible" alignment, that is 16 bytes on x86 and
+ powerpc CPUs.
+
+ You can allocate such buffers with the functions
+ pffft_aligned_malloc / pffft_aligned_free (or with stuff like
+ posix_memalign..)
+
+*/
+
+#ifndef PFFFT_H
+#define PFFFT_H
+
+#include <stddef.h> // for size_t
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef PFFFT_SIMD_DISABLE
+// Detects compiler bugs with respect to simd instruction.
+void validate_pffft_simd(void);
+#endif
+
+/* opaque struct holding internal stuff (precomputed twiddle factors)
+ this struct can be shared by many threads as it contains only
+ read-only data.
+*/
+typedef struct PFFFT_Setup PFFFT_Setup;
+
+/* direction of the transform */
+typedef enum { PFFFT_FORWARD, PFFFT_BACKWARD } pffft_direction_t;
+
+/* type of transform */
+typedef enum { PFFFT_REAL, PFFFT_COMPLEX } pffft_transform_t;
+
+/*
+ prepare for performing transforms of size N -- the returned
+ PFFFT_Setup structure is read-only so it can safely be shared by
+ multiple concurrent threads.
+*/
+PFFFT_Setup* pffft_new_setup(int N, pffft_transform_t transform);
+void pffft_destroy_setup(PFFFT_Setup*);
+/*
+ Perform a Fourier transform , The z-domain data is stored in the
+ most efficient order for transforming it back, or using it for
+ convolution. If you need to have its content sorted in the
+ "usual" way, that is as an array of interleaved complex numbers,
+ either use pffft_transform_ordered , or call pffft_zreorder after
+ the forward fft, and before the backward fft.
+
+ Transforms are not scaled: PFFFT_BACKWARD(PFFFT_FORWARD(x)) = N*x.
+ Typically you will want to scale the backward transform by 1/N.
+
+ The 'work' pointer should point to an area of N (2*N for complex
+ fft) floats, properly aligned. If 'work' is NULL, then stack will
+ be used instead (this is probably the best strategy for small
+ FFTs, say for N < 16384).
+
+ input and output may alias.
+*/
+void pffft_transform(PFFFT_Setup* setup,
+ const float* input,
+ float* output,
+ float* work,
+ pffft_direction_t direction);
+
+/*
+ Similar to pffft_transform, but makes sure that the output is
+ ordered as expected (interleaved complex numbers). This is
+ similar to calling pffft_transform and then pffft_zreorder.
+
+ input and output may alias.
+*/
+void pffft_transform_ordered(PFFFT_Setup* setup,
+ const float* input,
+ float* output,
+ float* work,
+ pffft_direction_t direction);
+
+/*
+ call pffft_zreorder(.., PFFFT_FORWARD) after pffft_transform(...,
+ PFFFT_FORWARD) if you want to have the frequency components in
+ the correct "canonical" order, as interleaved complex numbers.
+
+ (for real transforms, both 0-frequency and half frequency
+ components, which are real, are assembled in the first entry as
+ F(0)+i*F(n/2+1). Note that the original fftpack did place
+ F(n/2+1) at the end of the arrays).
+
+ input and output should not alias.
+*/
+void pffft_zreorder(PFFFT_Setup* setup,
+ const float* input,
+ float* output,
+ pffft_direction_t direction);
+
+/*
+ Perform a multiplication of the frequency components of dft_a and
+ dft_b and accumulate them into dft_ab. The arrays should have
+ been obtained with pffft_transform(.., PFFFT_FORWARD) and should
+ *not* have been reordered with pffft_zreorder (otherwise just
+ perform the operation yourself as the dft coefs are stored as
+ interleaved complex numbers).
+
+ the operation performed is: dft_ab += (dft_a * fdt_b)*scaling
+
+ The dft_a, dft_b and dft_ab pointers may alias.
+*/
+void pffft_zconvolve_accumulate(PFFFT_Setup* setup,
+ const float* dft_a,
+ const float* dft_b,
+ float* dft_ab,
+ float scaling);
+
+/*
+ the float buffers must have the correct alignment (16-byte boundary
+ on intel and powerpc). This function may be used to obtain such
+ correctly aligned buffers.
+*/
+void* pffft_aligned_malloc(size_t nb_bytes);
+void pffft_aligned_free(void*);
+
+/* return 4 or 1 wether support SSE/Altivec instructions was enable when
+ * building pffft.c */
+int pffft_simd_size(void);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // PFFFT_H
diff --git a/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/test_pffft.c b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/test_pffft.c
new file mode 100644
index 0000000..ab78b4d
--- /dev/null
+++ b/Source/ThirdParty/libwebrtc/Source/third_party/pffft/src/test_pffft.c
@@ -0,0 +1,415 @@
+/*
+ Copyright (c) 2013 Julien Pommier.
+
+ Small test & bench for PFFFT, comparing its performance with the scalar FFTPACK, FFTW, and Apple vDSP
+
+ How to build:
+
+ on linux, with fftw3:
+ gcc -o test_pffft -DHAVE_FFTW -msse -mfpmath=sse -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -lm
+
+ on macos, without fftw3:
+ gcc-4.2 -o test_pffft -DHAVE_VECLIB -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -framework veclib
+
+ on macos, with fftw3:
+ gcc-4.2 -o test_pffft -DHAVE_FFTW -DHAVE_VECLIB -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -framework veclib
+
+ on windows, with visual c++:
+ cl /Ox -D_USE_MATH_DEFINES /arch:SSE test_pffft.c pffft.c fftpack.c
+
+ build without SIMD instructions:
+ gcc -o test_pffft -DPFFFT_SIMD_DISABLE -O3 -Wall -W pffft.c test_pffft.c fftpack.c -lm
+
+ */
+
+#include "pffft.h"
+#include "fftpack.h"
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#include <assert.h>
+#include <string.h>
+
+#ifdef HAVE_SYS_TIMES
+# include <sys/times.h>
+# include <unistd.h>
+#endif
+
+#ifdef HAVE_VECLIB
+# include <vecLib/vDSP.h>
+#endif
+
+#ifdef HAVE_FFTW
+# include <fftw3.h>
+#endif
+
+#define MAX(x,y) ((x)>(y)?(x):(y))
+
+double frand() {
+ return rand()/(double)RAND_MAX;
+}
+
+#if defined(HAVE_SYS_TIMES)
+ inline double uclock_sec(void) {
+ static double ttclk = 0.;
+ if (ttclk == 0.) ttclk = sysconf(_SC_CLK_TCK);
+ struct tms t; return ((double)times(&t)) / ttclk;
+ }
+# else
+ double uclock_sec(void)
+{ return (double)clock()/(double)CLOCKS_PER_SEC; }
+#endif
+
+
+/* compare results with the regular fftpack */
+void pffft_validate_N(int N, int cplx) {
+ int Nfloat = N*(cplx?2:1);
+ int Nbytes = Nfloat * sizeof(float);
+ float *ref, *in, *out, *tmp, *tmp2;
+ PFFFT_Setup *s = pffft_new_setup(N, cplx ? PFFFT_COMPLEX : PFFFT_REAL);
+ int pass;
+
+ if (!s) { printf("Skipping N=%d, not supported\n", N); return; }
+ ref = pffft_aligned_malloc(Nbytes);
+ in = pffft_aligned_malloc(Nbytes);
+ out = pffft_aligned_malloc(Nbytes);
+ tmp = pffft_aligned_malloc(Nbytes);
+ tmp2 = pffft_aligned_malloc(Nbytes);
+
+ for (pass=0; pass < 2; ++pass) {
+ float ref_max = 0;
+ int k;
+ //printf("N=%d pass=%d cplx=%d\n", N, pass, cplx);
+ // compute reference solution with FFTPACK
+ if (pass == 0) {
+ float *wrk = malloc(2*Nbytes+15*sizeof(float));
+ for (k=0; k < Nfloat; ++k) {
+ ref[k] = in[k] = frand()*2-1;
+ out[k] = 1e30;
+ }
+ if (!cplx) {
+ rffti(N, wrk);
+ rfftf(N, ref, wrk);
+ // use our ordering for real ffts instead of the one of fftpack
+ {
+ float refN=ref[N-1];
+ for (k=N-2; k >= 1; --k) ref[k+1] = ref[k];
+ ref[1] = refN;
+ }
+ } else {
+ cffti(N, wrk);
+ cfftf(N, ref, wrk);
+ }
+ free(wrk);
+ }
+
+ for (k = 0; k < Nfloat; ++k) ref_max = MAX(ref_max, fabs(ref[k]));
+
+
+ // pass 0 : non canonical ordering of transform coefficients
+ if (pass == 0) {
+ // test forward transform, with different input / output
+ pffft_transform(s, in, tmp, 0, PFFFT_FORWARD);
+ memcpy(tmp2, tmp, Nbytes);
+ memcpy(tmp, in, Nbytes);
+ pffft_transform(s, tmp, tmp, 0, PFFFT_FORWARD);
+ for (k = 0; k < Nfloat; ++k) {
+ assert(tmp2[k] == tmp[k]);
+ }
+
+ // test reordering
+ pffft_zreorder(s, tmp, out, PFFFT_FORWARD);
+ pffft_zreorder(s, out, tmp, PFFFT_BACKWARD);
+ for (k = 0; k < Nfloat; ++k) {
+ assert(tmp2[k] == tmp[k]);
+ }
+ pffft_zreorder(s, tmp, out, PFFFT_FORWARD);
+ } else {
+ // pass 1 : canonical ordering of transform coeffs.
+ pffft_transform_ordered(s, in, tmp, 0, PFFFT_FORWARD);
+ memcpy(tmp2, tmp, Nbytes);
+ memcpy(tmp, in, Nbytes);
+ pffft_transform_ordered(s, tmp, tmp, 0, PFFFT_FORWARD);
+ for (k = 0; k < Nfloat; ++k) {
+ assert(tmp2[k] == tmp[k]);
+ }
+ memcpy(out, tmp, Nbytes);
+ }
+
+ {
+ for (k=0; k < Nfloat; ++k) {
+ if (!(fabs(ref[k] - out[k]) < 1e-3*ref_max)) {
+ printf("%s forward PFFFT mismatch found for N=%d\n", (cplx?"CPLX":"REAL"), N);
+ exit(1);
+ }
+ }
+
+ if (pass == 0) pffft_transform(s, tmp, out, 0, PFFFT_BACKWARD);
+ else pffft_transform_ordered(s, tmp, out, 0, PFFFT_BACKWARD);
+ memcpy(tmp2, out, Nbytes);
+ memcpy(out, tmp, Nbytes);
+ if (pass == 0) pffft_transform(s, out, out, 0, PFFFT_BACKWARD);
+ else pffft_transform_ordered(s, out, out, 0, PFFFT_BACKWARD);
+ for (k = 0; k < Nfloat; ++k) {
+ assert(tmp2[k] == out[k]);
+ out[k] *= 1.f/N;
+ }
+ for (k = 0; k < Nfloat; ++k) {
+ if (fabs(in[k] - out[k]) > 1e-3 * ref_max) {
+ printf("pass=%d, %s IFFFT does not match for N=%d\n", pass, (cplx?"CPLX":"REAL"), N); break;
+ exit(1);
+ }
+ }
+ }
+
+ // quick test of the circular convolution in fft domain
+ {
+ float conv_err = 0, conv_max = 0;
+
+ pffft_zreorder(s, ref, tmp, PFFFT_FORWARD);
+ memset(out, 0, Nbytes);
+ pffft_zconvolve_accumulate(s, ref, ref, out, 1.0);
+ pffft_zreorder(s, out, tmp2, PFFFT_FORWARD);
+
+ for (k=0; k < Nfloat; k += 2) {
+ float ar = tmp[k], ai=tmp[k+1];
+ if (cplx || k > 0) {
+ tmp[k] = ar*ar - ai*ai;
+ tmp[k+1] = 2*ar*ai;
+ } else {
+ tmp[0] = ar*ar;
+ tmp[1] = ai*ai;
+ }
+ }
+
+ for (k=0; k < Nfloat; ++k) {
+ float d = fabs(tmp[k] - tmp2[k]), e = fabs(tmp[k]);
+ if (d > conv_err) conv_err = d;
+ if (e > conv_max) conv_max = e;
+ }
+ if (conv_err > 1e-5*conv_max) {
+ printf("zconvolve error ? %g %g\n", conv_err, conv_max); exit(1);
+ }
+ }
+
+ }
+
+ printf("%s PFFFT is OK for N=%d\n", (cplx?"CPLX":"REAL"), N); fflush(stdout);
+
+ pffft_destroy_setup(s);
+ pffft_aligned_free(ref);
+ pffft_aligned_free(in);
+ pffft_aligned_free(out);
+ pffft_aligned_free(tmp);
+ pffft_aligned_free(tmp2);
+}
+
+void pffft_validate(int cplx) {
+ static int Ntest[] = { 16, 32, 64, 96, 128, 160, 192, 256, 288, 384, 5*96, 512, 576, 5*128, 800, 864, 1024, 2048, 2592, 4000, 4096, 12000, 36864, 0};
+ int k;
+ for (k = 0; Ntest[k]; ++k) {
+ int N = Ntest[k];
+ if (N == 16 && !cplx) continue;
+ pffft_validate_N(N, cplx);
+ }
+}
+
+int array_output_format = 0;
+
+void show_output(const char *name, int N, int cplx, float flops, float t0, float t1, int max_iter) {
+ float mflops = flops/1e6/(t1 - t0 + 1e-16);
+ if (array_output_format) {
+ if (flops != -1) {
+ printf("|%9.0f ", mflops);
+ } else printf("| n/a ");
+ } else {
+ if (flops != -1) {
+ printf("N=%5d, %s %16s : %6.0f MFlops [t=%6.0f ns, %d runs]\n", N, (cplx?"CPLX":"REAL"), name, mflops, (t1-t0)/2/max_iter * 1e9, max_iter);
+ }
+ }
+ fflush(stdout);
+}
+
+void benchmark_ffts(int N, int cplx) {
+ int Nfloat = (cplx ? N*2 : N);
+ int Nbytes = Nfloat * sizeof(float);
+ float *X = pffft_aligned_malloc(Nbytes), *Y = pffft_aligned_malloc(Nbytes), *Z = pffft_aligned_malloc(Nbytes);
+
+ double t0, t1, flops;
+
+ int k;
+ int max_iter = 5120000/N*4;
+#ifdef __arm__
+ max_iter /= 4;
+#endif
+ int iter;
+
+ for (k = 0; k < Nfloat; ++k) {
+ X[k] = 0; //sqrtf(k+1);
+ }
+
+ // FFTPack benchmark
+ {
+ float *wrk = malloc(2*Nbytes + 15*sizeof(float));
+ int max_iter_ = max_iter/pffft_simd_size(); if (max_iter_ == 0) max_iter_ = 1;
+ if (cplx) cffti(N, wrk);
+ else rffti(N, wrk);
+ t0 = uclock_sec();
+
+ for (iter = 0; iter < max_iter_; ++iter) {
+ if (cplx) {
+ cfftf(N, X, wrk);
+ cfftb(N, X, wrk);
+ } else {
+ rfftf(N, X, wrk);
+ rfftb(N, X, wrk);
+ }
+ }
+ t1 = uclock_sec();
+ free(wrk);
+
+ flops = (max_iter_*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
+ show_output("FFTPack", N, cplx, flops, t0, t1, max_iter_);
+ }
+
+#ifdef HAVE_VECLIB
+ int log2N = (int)(log(N)/log(2) + 0.5f);
+ if (N == (1<<log2N)) {
+ FFTSetup setup;
+
+ setup = vDSP_create_fftsetup(log2N, FFT_RADIX2);
+ DSPSplitComplex zsamples;
+ zsamples.realp = &X[0];
+ zsamples.imagp = &X[Nfloat/2];
+ t0 = uclock_sec();
+ for (iter = 0; iter < max_iter; ++iter) {
+ if (cplx) {
+ vDSP_fft_zip(setup, &zsamples, 1, log2N, kFFTDirection_Forward);
+ vDSP_fft_zip(setup, &zsamples, 1, log2N, kFFTDirection_Inverse);
+ } else {
+ vDSP_fft_zrip(setup, &zsamples, 1, log2N, kFFTDirection_Forward);
+ vDSP_fft_zrip(setup, &zsamples, 1, log2N, kFFTDirection_Inverse);
+ }
+ }
+ t1 = uclock_sec();
+ vDSP_destroy_fftsetup(setup);
+
+ flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
+ show_output("vDSP", N, cplx, flops, t0, t1, max_iter);
+ } else {
+ show_output("vDSP", N, cplx, -1, -1, -1, -1);
+ }
+#endif
+
+#ifdef HAVE_FFTW
+ {
+ fftwf_plan planf, planb;
+ fftw_complex *in = (fftw_complex*) fftwf_malloc(sizeof(fftw_complex) * N);
+ fftw_complex *out = (fftw_complex*) fftwf_malloc(sizeof(fftw_complex) * N);
+ memset(in, 0, sizeof(fftw_complex) * N);
+ int flags = (N < 40000 ? FFTW_MEASURE : FFTW_ESTIMATE); // measure takes a lot of time on largest ffts
+ //int flags = FFTW_ESTIMATE;
+ if (cplx) {
+ planf = fftwf_plan_dft_1d(N, (fftwf_complex*)in, (fftwf_complex*)out, FFTW_FORWARD, flags);
+ planb = fftwf_plan_dft_1d(N, (fftwf_complex*)in, (fftwf_complex*)out, FFTW_BACKWARD, flags);
+ } else {
+ planf = fftwf_plan_dft_r2c_1d(N, (float*)in, (fftwf_complex*)out, flags);
+ planb = fftwf_plan_dft_c2r_1d(N, (fftwf_complex*)in, (float*)out, flags);
+ }
+
+ t0 = uclock_sec();
+ for (iter = 0; iter < max_iter; ++iter) {
+ fftwf_execute(planf);
+ fftwf_execute(planb);
+ }
+ t1 = uclock_sec();
+
+ fftwf_destroy_plan(planf);
+ fftwf_destroy_plan(planb);
+ fftwf_free(in); fftwf_free(out);
+
+ flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
+ show_output((flags == FFTW_MEASURE ? "FFTW (meas.)" : " FFTW (estim)"), N, cplx, flops, t0, t1, max_iter);
+ }
+#endif
+
+ // PFFFT benchmark
+ {
+ PFFFT_Setup *s = pffft_new_setup(N, cplx ? PFFFT_COMPLEX : PFFFT_REAL);
+ if (s) {
+ t0 = uclock_sec();
+ for (iter = 0; iter < max_iter; ++iter) {
+ pffft_transform(s, X, Z, Y, PFFFT_FORWARD);
+ pffft_transform(s, X, Z, Y, PFFFT_BACKWARD);
+ }
+ t1 = uclock_sec();
+ pffft_destroy_setup(s);
+
+ flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
+ show_output("PFFFT", N, cplx, flops, t0, t1, max_iter);
+ }
+ }
+
+ if (!array_output_format) {
+ printf("--\n");
+ }
+
+ pffft_aligned_free(X);
+ pffft_aligned_free(Y);
+ pffft_aligned_free(Z);
+}
+
+int main(int argc, char **argv) {
+ int Nvalues[] = { 64, 96, 128, 160, 192, 256, 384, 5*96, 512, 5*128, 3*256, 800, 1024, 2048, 2400, 4096, 8192, 9*1024, 16384, 32768, 256*1024, 1024*1024, -1 };
+ int i;
+
+ if (argc > 1 && strcmp(argv[1], "--array-format") == 0) {
+ array_output_format = 1;
+ }
+
+#ifndef PFFFT_SIMD_DISABLE
+ validate_pffft_simd();
+#endif
+ pffft_validate(1);
+ pffft_validate(0);
+ if (!array_output_format) {
+ for (i=0; Nvalues[i] > 0; ++i) {
+ benchmark_ffts(Nvalues[i], 0 /* real fft */);
+ }
+ for (i=0; Nvalues[i] > 0; ++i) {
+ benchmark_ffts(Nvalues[i], 1 /* cplx fft */);
+ }
+ } else {
+ printf("| input len ");
+ printf("|real FFTPack");
+#ifdef HAVE_VECLIB
+ printf("| real vDSP ");
+#endif
+#ifdef HAVE_FFTW
+ printf("| real FFTW ");
+#endif
+ printf("| real PFFFT | ");
+
+ printf("|cplx FFTPack");
+#ifdef HAVE_VECLIB
+ printf("| cplx vDSP ");
+#endif
+#ifdef HAVE_FFTW
+ printf("| cplx FFTW ");
+#endif
+ printf("| cplx PFFFT |\n");
+ for (i=0; Nvalues[i] > 0; ++i) {
+ printf("|%9d ", Nvalues[i]);
+ benchmark_ffts(Nvalues[i], 0);
+ printf("| ");
+ benchmark_ffts(Nvalues[i], 1);
+ printf("|\n");
+ }
+ printf(" (numbers are given in MFlops)\n");
+ }
+
+
+ return 0;
+}
