1730 lines
58 KiB
C
1730 lines
58 KiB
C
/* Copyright (c) 2011 Julien Pommier ( pommier@modartt.com )
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Based on original fortran 77 code from FFTPACKv4 from NETLIB
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(http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
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of NCAR, in 1985.
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As confirmed by the NCAR fftpack software curators, the following
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FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
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released under the same terms.
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FFTPACK license:
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http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
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Copyright (c) 2004 the University Corporation for Atmospheric
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Research ("UCAR"). All rights reserved. Developed by NCAR's
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Computational and Information Systems Laboratory, UCAR,
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www.cisl.ucar.edu.
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Redistribution and use of the Software in source and binary forms,
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with or without modification, is permitted provided that the
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following conditions are met:
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- Neither the names of NCAR's Computational and Information Systems
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Laboratory, the University Corporation for Atmospheric Research,
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nor the names of its sponsors or contributors may be used to
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endorse or promote products derived from this Software without
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specific prior written permission.
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- Redistributions of source code must retain the above copyright
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notices, this list of conditions, and the disclaimer below.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions, and the disclaimer below in the
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documentation and/or other materials provided with the
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distribution.
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THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
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HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
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SOFTWARE.
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PFFFT : a Pretty Fast FFT.
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This file is largerly based on the original FFTPACK implementation, modified in
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order to take advantage of SIMD instructions of modern CPUs.
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*/
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/*
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ChangeLog:
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- 2011/10/02, version 1: This is the very first release of this file.
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*/
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#if !defined PFFT_MACROS_ONLY
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#include "pffft.h"
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#include "simd.h"
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#include <string.h>
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#include <stdlib.h>
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#include <math.h>
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#include <assert.h>
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#define pffft_aligned_free _soxr_simd_aligned_free
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#define pffft_aligned_malloc _soxr_simd_aligned_malloc
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#define pffft_aligned_calloc _soxr_simd_aligned_calloc
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#endif
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/*
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vector support macros: the rest of the code is independant of
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SSE/Altivec/NEON -- adding support for other platforms with 4-element
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vectors should be limited to these macros
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*/
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/* define PFFFT_SIMD_DISABLE if you want to use scalar code instead of simd code */
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/*#define PFFFT_SIMD_DISABLE */
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/* detect compiler flavour */
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#if defined(_MSC_VER)
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# define COMPILER_MSVC
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#elif defined(__GNUC__)
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# define COMPILER_GCC
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#endif
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#if defined(COMPILER_GCC)
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# define ALWAYS_INLINE(return_type) return_type __attribute__ ((always_inline))
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# define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))
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# define RESTRICT __restrict
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/*# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ varname__[size__]; */
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#elif defined(COMPILER_MSVC)
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# define ALWAYS_INLINE(return_type) __forceinline return_type
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# define NEVER_INLINE(return_type) __declspec(noinline) return_type
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# define RESTRICT __restrict
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/*# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (v4sf*)_alloca(size__ * sizeof(type__)) */
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#endif
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/*
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Altivec support macros
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*/
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#if !defined(PFFFT_SIMD_DISABLE) && (defined(__ppc__) || defined(__ppc64__))
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typedef vector float v4sf;
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# define SIMD_SZ 4
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# define VZERO() ((vector float) vec_splat_u8(0))
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# define VMUL(a,b) vec_madd(a,b, VZERO())
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# define VADD(a,b) vec_add(a,b)
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# define VMADD(a,b,c) vec_madd(a,b,c)
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# define VSUB(a,b) vec_sub(a,b)
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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); }
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# define LD_PS1(p) ld_ps1(&p)
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# define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = vec_mergeh(in1, in2); out2 = vec_mergel(in1, in2); out1 = tmp__; }
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# define UNINTERLEAVE2(in1, in2, out1, out2) { \
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vector unsigned char vperm1 = (vector unsigned char)(0,1,2,3,8,9,10,11,16,17,18,19,24,25,26,27); \
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vector unsigned char vperm2 = (vector unsigned char)(4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31); \
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v4sf tmp__ = vec_perm(in1, in2, vperm1); out2 = vec_perm(in1, in2, vperm2); out1 = tmp__; \
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}
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# define VTRANSPOSE4(x0,x1,x2,x3) { \
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v4sf y0 = vec_mergeh(x0, x2); \
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v4sf y1 = vec_mergel(x0, x2); \
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v4sf y2 = vec_mergeh(x1, x3); \
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v4sf y3 = vec_mergel(x1, x3); \
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x0 = vec_mergeh(y0, y2); \
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x1 = vec_mergel(y0, y2); \
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x2 = vec_mergeh(y1, y3); \
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x3 = vec_mergel(y1, y3); \
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}
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# 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))
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# define VALIGNED(ptr) ((((long)(ptr)) & 0xF) == 0)
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/*
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SSE1 support macros
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*/
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#elif !defined(PFFFT_SIMD_DISABLE) && (defined(__x86_64__) || defined(_M_X64) || defined(i386) || defined(_M_IX86))
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#include <xmmintrin.h>
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typedef __m128 v4sf;
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# 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. */
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# define VZERO() _mm_setzero_ps()
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# define VMUL(a,b) _mm_mul_ps(a,b)
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# define VADD(a,b) _mm_add_ps(a,b)
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# define VMADD(a,b,c) _mm_add_ps(_mm_mul_ps(a,b), c)
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# define VSUB(a,b) _mm_sub_ps(a,b)
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# define LD_PS1(p) _mm_set1_ps(p)
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# define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_unpacklo_ps(in1, in2); out2 = _mm_unpackhi_ps(in1, in2); out1 = tmp__; }
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# 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__; }
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# define VTRANSPOSE4(x0,x1,x2,x3) _MM_TRANSPOSE4_PS(x0,x1,x2,x3)
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# define VSWAPHL(a,b) _mm_shuffle_ps(b, a, _MM_SHUFFLE(3,2,1,0))
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# define VALIGNED(ptr) ((((long)(ptr)) & 0xF) == 0)
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/*
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ARM NEON support macros
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*/
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#elif !defined(PFFFT_SIMD_DISABLE) && defined(__arm__)
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# include <arm_neon.h>
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typedef float32x4_t v4sf;
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# define SIMD_SZ 4
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# define VZERO() vdupq_n_f32(0)
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# define VMUL(a,b) vmulq_f32(a,b)
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# define VADD(a,b) vaddq_f32(a,b)
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# define VMADD(a,b,c) vmlaq_f32(c,a,b)
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# define VSUB(a,b) vsubq_f32(a,b)
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# define LD_PS1(p) vld1q_dup_f32(&(p))
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# define INTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vzipq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }
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# define UNINTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vuzpq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }
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# define VTRANSPOSE4_(x0,x1,x2,x3) { \
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float32x4x2_t t0_ = vzipq_f32(x0, x2); \
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float32x4x2_t t1_ = vzipq_f32(x1, x3); \
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float32x4x2_t u0_ = vzipq_f32(t0_.val[0], t1_.val[0]); \
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float32x4x2_t u1_ = vzipq_f32(t0_.val[1], t1_.val[1]); \
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x0 = u0_.val[0]; x1 = u0_.val[1]; x2 = u1_.val[0]; x3 = u1_.val[1]; \
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}
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/* marginally faster version */
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# 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)::); }
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# define VSWAPHL(a,b) vcombine_f32(vget_low_f32(b), vget_high_f32(a))
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# define VALIGNED(ptr) ((((long)(ptr)) & 0x3) == 0)
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#else
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# if !defined(PFFFT_SIMD_DISABLE)
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# warning "building with simd disabled !\n";
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# define PFFFT_SIMD_DISABLE /* fallback to scalar code */
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# endif
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#endif
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/* fallback mode for situations where SSE/Altivec are not available, use scalar mode instead */
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#ifdef PFFFT_SIMD_DISABLE
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typedef float v4sf;
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# define SIMD_SZ 1
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# define VZERO() 0.f
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# define VMUL(a,b) ((a)*(b))
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# define VADD(a,b) ((a)+(b))
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# define VMADD(a,b,c) ((a)*(b)+(c))
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# define VSUB(a,b) ((a)-(b))
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# define LD_PS1(p) (p)
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# define VALIGNED(ptr) ((((long)(ptr)) & 0x3) == 0)
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#endif
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/* shortcuts for complex multiplcations */
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#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); }
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#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); }
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#if !defined(PFFFT_SIMD_DISABLE)
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typedef union v4sf_union {
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v4sf v;
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float f[4];
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} v4sf_union;
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#if 0
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#include <string.h>
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#define assertv4(v,f0,f1,f2,f3) assert(v.f[0] == (f0) && v.f[1] == (f1) && v.f[2] == (f2) && v.f[3] == (f3))
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/* detect bugs with the vector support macros */
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void validate_pffft_simd() {
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float f[16] = { 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 };
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v4sf_union a0, a1, a2, a3, t, u;
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memcpy(a0.f, f, 4*sizeof(float));
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memcpy(a1.f, f+4, 4*sizeof(float));
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memcpy(a2.f, f+8, 4*sizeof(float));
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memcpy(a3.f, f+12, 4*sizeof(float));
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t = a0; u = a1; t.v = VZERO();
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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);
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t.v = VADD(a1.v, a2.v);
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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);
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t.v = VMUL(a1.v, a2.v);
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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);
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t.v = VMADD(a1.v, a2.v,a0.v);
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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);
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INTERLEAVE2(a1.v,a2.v,t.v,u.v);
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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]);
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assertv4(t, 4, 8, 5, 9); assertv4(u, 6, 10, 7, 11);
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UNINTERLEAVE2(a1.v,a2.v,t.v,u.v);
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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]);
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assertv4(t, 4, 6, 8, 10); assertv4(u, 5, 7, 9, 11);
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t.v=LD_PS1(f[15]);
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printf("LD_PS1(15)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
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assertv4(t, 15, 15, 15, 15);
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t.v = VSWAPHL(a1.v, a2.v);
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printf("VSWAPHL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);
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assertv4(t, 8, 9, 6, 7);
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VTRANSPOSE4(a0.v, a1.v, a2.v, a3.v);
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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",
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a0.f[0], a0.f[1], a0.f[2], a0.f[3], a1.f[0], a1.f[1], a1.f[2], a1.f[3],
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a2.f[0], a2.f[1], a2.f[2], a2.f[3], a3.f[0], a3.f[1], a3.f[2], a3.f[3]);
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assertv4(a0, 0, 4, 8, 12); assertv4(a1, 1, 5, 9, 13); assertv4(a2, 2, 6, 10, 14); assertv4(a3, 3, 7, 11, 15);
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}
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#endif
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#endif /*!PFFFT_SIMD_DISABLE */
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#if !defined PFFT_MACROS_ONLY
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#if defined (COMPILER_MSVC)
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#define sin (float)sin
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#define cos (float)cos
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#else
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#define sin sinf
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#define cos cosf
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#endif
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/*
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int pffft_simd_size() { return SIMD_SZ; }
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*/
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/*
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passf2 and passb2 has been merged here, fsign = -1 for passf2, +1 for passb2
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*/
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static NEVER_INLINE(void) passf2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1, float fsign) {
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int k, i;
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int l1ido = l1*ido;
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if (ido <= 2) {
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for (k=0; k < l1ido; k += ido, ch += ido, cc+= 2*ido) {
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ch[0] = VADD(cc[0], cc[ido+0]);
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ch[l1ido] = VSUB(cc[0], cc[ido+0]);
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ch[1] = VADD(cc[1], cc[ido+1]);
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ch[l1ido + 1] = VSUB(cc[1], cc[ido+1]);
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}
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} else {
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for (k=0; k < l1ido; k += ido, ch += ido, cc += 2*ido) {
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for (i=0; i<ido-1; i+=2) {
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v4sf tr2 = VSUB(cc[i+0], cc[i+ido+0]);
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v4sf ti2 = VSUB(cc[i+1], cc[i+ido+1]);
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v4sf wr = LD_PS1(wa1[i]), wi = VMUL(LD_PS1(fsign), LD_PS1(wa1[i+1]));
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ch[i] = VADD(cc[i+0], cc[i+ido+0]);
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ch[i+1] = VADD(cc[i+1], cc[i+ido+1]);
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VCPLXMUL(tr2, ti2, wr, wi);
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ch[i+l1ido] = tr2;
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ch[i+l1ido+1] = ti2;
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}
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}
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}
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}
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/*
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passf3 and passb3 has been merged here, fsign = -1 for passf3, +1 for passb3
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*/
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static NEVER_INLINE(void) passf3_ps(int ido, int l1, const v4sf *cc, v4sf *ch,
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const float *wa1, const float *wa2, float fsign) {
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static const float taur = -0.5f;
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float taui = 0.866025403784439f*fsign;
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int i, k;
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v4sf tr2, ti2, cr2, ci2, cr3, ci3, dr2, di2, dr3, di3;
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int l1ido = l1*ido;
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float wr1, wi1, wr2, wi2;
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assert(ido > 2);
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for (k=0; k< l1ido; k += ido, cc+= 3*ido, ch +=ido) {
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for (i=0; i<ido-1; i+=2) {
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tr2 = VADD(cc[i+ido], cc[i+2*ido]);
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cr2 = VADD(cc[i], VMUL(LD_PS1(taur),tr2));
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ch[i] = VADD(cc[i], tr2);
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ti2 = VADD(cc[i+ido+1], cc[i+2*ido+1]);
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ci2 = VADD(cc[i +1], VMUL(LD_PS1(taur),ti2));
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ch[i+1] = VADD(cc[i+1], ti2);
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cr3 = VMUL(LD_PS1(taui), VSUB(cc[i+ido], cc[i+2*ido]));
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ci3 = VMUL(LD_PS1(taui), VSUB(cc[i+ido+1], cc[i+2*ido+1]));
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dr2 = VSUB(cr2, ci3);
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dr3 = VADD(cr2, ci3);
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di2 = VADD(ci2, cr3);
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di3 = VSUB(ci2, cr3);
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wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1];
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VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));
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ch[i+l1ido] = dr2;
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ch[i+l1ido + 1] = di2;
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VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));
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ch[i+2*l1ido] = dr3;
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ch[i+2*l1ido+1] = di3;
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}
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}
|
|
} /* 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 */
|
|
|
|
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] = VMUL(LD_PS1(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] = VMUL(LD_PS1(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] = VMUL(LD_PS1(taui), VSUB(cc[(k + l1*2)*ido], cc[(k + l1)*ido]));
|
|
ch[ido-1 + (3*k + 1)*ido] = VADD(cc[k*ido], VMUL(LD_PS1(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], VMUL(LD_PS1(taur), cr2));
|
|
ti2 = VADD(cc[i + k*ido], VMUL(LD_PS1(taur), ci2));
|
|
tr3 = VMUL(LD_PS1(taui), VSUB(di2, di3));
|
|
ti3 = VMUL(LD_PS1(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 = VMUL(LD_PS1(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 = VMUL(LD_PS1(taui), VSUB(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]));
|
|
ci3 = VMUL(LD_PS1(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 = VMUL(LD_PS1(minus_hsqt2), VADD(a, b));
|
|
v4sf tr1 = VMUL(LD_PS1(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 = VMUL(LD_PS1(two),d);
|
|
tr2 = VADD(a,b);
|
|
tr1 = VSUB(a,b);
|
|
tr4 = VMUL(LD_PS1(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] = VMUL(LD_PS1(minus_sqrt2), VSUB(ti1, tr1));
|
|
ch[ido-1 + k + 2*l1ido] = VADD(ti2, ti2);
|
|
ch[ido-1 + k + 3*l1ido] = VMUL(LD_PS1(minus_sqrt2), VADD(ti1, tr1));
|
|
}
|
|
} /* radb4 */
|
|
|
|
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 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 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[3]) {
|
|
int nl = n, nf = 0, i, j = 0;
|
|
for (j=0; j < 3; ++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[3] = { 4,2,3 };
|
|
int k1, j, ii;
|
|
|
|
int nf = decompose(n,ifac,ntryh);
|
|
float argh = (float)((2*M_PI) / n);
|
|
int is = 0;
|
|
int nfm1 = nf - 1;
|
|
int l1 = 1;
|
|
if (nfm1 == 0) return;
|
|
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 = (float)ld*argh;
|
|
for (ii = 3; ii <= ido; ii += 2) {
|
|
i += 2;
|
|
fi += 1;
|
|
wa[i - 2] = cos((float)fi*argld);
|
|
wa[i - 1] = sin((float)fi*argld);
|
|
}
|
|
is += ido;
|
|
}
|
|
l1 = l2;
|
|
}
|
|
} /* rffti1 */
|
|
|
|
static void cffti1_ps(int n, float *wa, int *ifac)
|
|
{
|
|
static const int ntryh[3] = { 3,4,2 };
|
|
int k1, j, ii;
|
|
|
|
int nf = decompose(n,ifac,ntryh);
|
|
float argh = (float)((2*M_PI)/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 = (float)ld*argh;
|
|
for (ii = 4; ii <= idot; ii += 2) {
|
|
i += 2;
|
|
fi += 1;
|
|
wa[i-1] = cos((float)fi*argld);
|
|
wa[i] = sin((float)fi*argld);
|
|
}
|
|
if (ip > 5) {
|
|
wa[i1-1] = wa[i-1];
|
|
wa[i1] = wa[i];
|
|
}
|
|
}
|
|
l1 = l2;
|
|
}
|
|
} /* cffti1 */
|
|
|
|
|
|
static 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 4: {
|
|
int ix2 = iw + idot;
|
|
int ix3 = ix2 + idot;
|
|
passf4_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], (float)isign);
|
|
} break;
|
|
case 2: {
|
|
passf2_ps(idot, l1, in, out, &wa[iw], (float)isign);
|
|
} break;
|
|
case 3: {
|
|
int ix2 = iw + idot;
|
|
passf3_ps(idot, l1, in, out, &wa[iw], &wa[ix2], (float)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) {
|
|
int k, m;
|
|
PFFFT_Setup *s = (PFFFT_Setup*)malloc(sizeof(PFFFT_Setup));
|
|
if (!s)
|
|
return s;
|
|
if (transform == PFFFT_REAL) { assert(N >= 32); }
|
|
if (transform == PFFFT_COMPLEX) { assert(N >= 16); }
|
|
/*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*(size_t)s->Ncvec * sizeof(v4sf));
|
|
if (!s->data) {
|
|
free(s);
|
|
return 0;
|
|
}
|
|
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 = (float)(-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 = (float)(-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);
|
|
}
|
|
return s;
|
|
}
|
|
|
|
|
|
static void pffft_destroy_setup(PFFFT_Setup *s) {
|
|
if(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]);
|
|
}
|
|
|
|
static 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]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
static 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;
|
|
}
|
|
}
|
|
|
|
static 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 = (float)(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 = (float)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;
|
|
}
|
|
|
|
|
|
static 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); */
|
|
|
|
int ib = (nf_odd ^ ordered ? 1 : 0);
|
|
const v4sf *vinput = (const v4sf*)finput;
|
|
v4sf *voutput = (v4sf*)foutput;
|
|
v4sf *buff[2];
|
|
buff[0] = voutput, buff[1] = scratch /*? scratch : scratch_on_stack*/;
|
|
|
|
/*if (scratch == 0) scratch = scratch_on_stack; */
|
|
|
|
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);
|
|
}
|
|
|
|
#if 0
|
|
static void pffft_zconvolve_accumulate(PFFFT_Setup *s, const float *a, const float *b, float *ab, float scaling) {
|
|
int i, 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);
|
|
#endif
|
|
|
|
float ar, ai, br, bi, abr, abi;
|
|
v4sf vscal = LD_PS1(scaling);
|
|
|
|
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 __arm__
|
|
# if 1 /* inline asm version */
|
|
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 /* neon instrinsics version, 30% slower that the asm one with gcc 4.6 */
|
|
v4sf a1r, a1i, b1r, b1i;
|
|
v4sf a2r, a2i, b2r, b2i;
|
|
v4sf ab1r, ab1i, ab2r, ab2i;
|
|
for (i=0; i < Ncvec; i += 2) {
|
|
__builtin_prefetch(va+8);
|
|
__builtin_prefetch(va+10);
|
|
|
|
a1r = *va++; a1i = *va++;
|
|
a2r = *va++; a2i = *va++;
|
|
b1r = *vb++; b1i = *vb++;
|
|
b2r = *vb++; b2i = *vb++;
|
|
ab1r = vab[0]; ab1i = vab[1];
|
|
ab2r = vab[2]; ab2i = vab[3];
|
|
|
|
v4sf z1r = VMUL(a1r, b1r);
|
|
v4sf z2r = VMUL(a2r, b2r);
|
|
v4sf z1i = VMUL(a1r, b1i);
|
|
v4sf z2i = VMUL(a2r, b2i);
|
|
|
|
__builtin_prefetch(vb+4);
|
|
__builtin_prefetch(vb+6);
|
|
|
|
z1r = vmlsq_f32(z1r, a1i, b1i);
|
|
z2r = vmlsq_f32(z2r, a2i, b2i);
|
|
z1i = vmlaq_f32(z1i, a1i, b1r);
|
|
z2i = vmlaq_f32(z2i, a2i, b2r);
|
|
|
|
__builtin_prefetch(vab+4);
|
|
__builtin_prefetch(vab+6);
|
|
|
|
ab1r = vmlaq_f32(ab1r, z1r, vscal);
|
|
ab2r = vmlaq_f32(ab2r, z2r, vscal);
|
|
ab1i = vmlaq_f32(ab1i, z1i, vscal);
|
|
ab2i = vmlaq_f32(ab2i, z2i, vscal);
|
|
|
|
*vab++ = ab1r; *vab++ = ab1i;
|
|
*vab++ = ab2r; *vab++ = ab2i;
|
|
}
|
|
# endif
|
|
|
|
#else /* not ARM, no need to use a special routine */
|
|
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;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
static void pffft_zconvolve(PFFFT_Setup *s, const float *a, const float *b, float *ab) {
|
|
int i, Ncvec = s->Ncvec;
|
|
const v4sf * /*RESTRICT*/ va = (const v4sf*)a;
|
|
const v4sf * RESTRICT vb = (const v4sf*)b;
|
|
v4sf * /*RESTRICT*/ vab = (v4sf*)ab;
|
|
|
|
float ar, ai, br, bi;
|
|
|
|
#ifdef __arm__
|
|
#error
|
|
#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];
|
|
|
|
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] = ar;
|
|
vab[2*i+1] = ai;
|
|
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] = ar;
|
|
vab[2*i+3] = ai;
|
|
}
|
|
if (s->transform == PFFFT_REAL) {
|
|
((v4sf_union*)vab)[0].f[0] = ar*br;
|
|
((v4sf_union*)vab)[1].f[0] = ai*bi;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
#else /* defined(PFFFT_SIMD_DISABLE) */
|
|
|
|
/* standard routine using scalar floats, without SIMD stuff. */
|
|
|
|
#define pffft_zreorder_nosimd pffft_zreorder
|
|
static 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
|
|
static 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); */
|
|
/*if (scratch == 0) scratch = scratch_on_stack; */
|
|
|
|
int ib;
|
|
float *buff[2];
|
|
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);
|
|
}
|
|
|
|
#if 0
|
|
#define pffft_zconvolve_accumulate_nosimd pffft_zconvolve_accumulate
|
|
static 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
|
|
|
|
#define pffft_zconvolve_nosimd pffft_zconvolve
|
|
static void pffft_zconvolve_nosimd(PFFFT_Setup *s, const float *a, const float *b, float *ab) {
|
|
int i, Ncvec = s->Ncvec;
|
|
|
|
if (s->transform == PFFFT_REAL) {
|
|
/* take care of the fftpack ordering */
|
|
ab[0] = a[0]*b[0];
|
|
ab[2*Ncvec-1] = a[2*Ncvec-1]*b[2*Ncvec-1];
|
|
++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;
|
|
ab[2*i+1] = ai;
|
|
}
|
|
}
|
|
|
|
#endif /* defined(PFFFT_SIMD_DISABLE) */
|
|
|
|
static 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);
|
|
}
|
|
|
|
static 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);
|
|
}
|
|
|
|
|
|
static void pffft_reorder_back(int length, void * setup, float * data, float * work)
|
|
{
|
|
memcpy(work, data, (unsigned)length * sizeof(*work));
|
|
pffft_zreorder(setup, work, data, PFFFT_BACKWARD);
|
|
}
|
|
#endif
|