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Befaco/pffft/pffft.c

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  1. /* Copyright (c) 2013  Julien Pommier ( pommier@modartt.com )

  2. 

  3.    Based on original fortran 77 code from FFTPACKv4 from NETLIB

  4.    (http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber

  5.    of NCAR, in 1985.

  6. 

  7.    As confirmed by the NCAR fftpack software curators, the following

  8.    FFTPACKv5 license applies to FFTPACKv4 sources. My changes are

  9.    released under the same terms.

  10. 

  11.    FFTPACK license:

  12. 

  13.    http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html

  14. 

  15.    Copyright (c) 2004 the University Corporation for Atmospheric

  16.    Research ("UCAR"). All rights reserved. Developed by NCAR's

  17.    Computational and Information Systems Laboratory, UCAR,

  18.    www.cisl.ucar.edu.

  19. 

  20.    Redistribution and use of the Software in source and binary forms,

  21.    with or without modification, is permitted provided that the

  22.    following conditions are met:

  23. 

  24.    - Neither the names of NCAR's Computational and Information Systems

  25.    Laboratory, the University Corporation for Atmospheric Research,

  26.    nor the names of its sponsors or contributors may be used to

  27.    endorse or promote products derived from this Software without

  28.    specific prior written permission.  

  29. 

  30.    - Redistributions of source code must retain the above copyright

  31.    notices, this list of conditions, and the disclaimer below.

  32. 

  33.    - Redistributions in binary form must reproduce the above copyright

  34.    notice, this list of conditions, and the disclaimer below in the

  35.    documentation and/or other materials provided with the

  36.    distribution.

  37. 

  38.    THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,

  39.    EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF

  40.    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND

  41.    NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT

  42.    HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,

  43.    EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN

  44.    ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN

  45.    CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE

  46.    SOFTWARE.

  47. 

  48. 

  49.    PFFFT : a Pretty Fast FFT.

  50. 

  51.    This file is largerly based on the original FFTPACK implementation, modified in

  52.    order to take advantage of SIMD instructions of modern CPUs.

  53. */

  54. 

  55. /*

  56.   ChangeLog: 

  57.   - 2011/10/02, version 1: This is the very first release of this file.

  58. */

  59. 

  60. #include "pffft.h"

  61. #include <stdlib.h>

  62. #include <stdio.h>

  63. #include <math.h>

  64. #include <assert.h>

  65. 

  66. /* detect compiler flavour */

  67. #if defined(_MSC_VER)

  68. #  define COMPILER_MSVC

  69. #elif defined(__GNUC__)

  70. #  define COMPILER_GCC

  71. #endif

  72. 

  73. #if defined(COMPILER_GCC)

  74. #  define ALWAYS_INLINE(return_type) inline return_type __attribute__ ((always_inline))

  75. #  define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))

  76. #  define RESTRICT __restrict

  77. #  define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ varname__[size__];

  78. #elif defined(COMPILER_MSVC)

  79. #  define ALWAYS_INLINE(return_type) __forceinline return_type

  80. #  define NEVER_INLINE(return_type) __declspec(noinline) return_type

  81. #  define RESTRICT __restrict

  82. #  define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (type__*)_alloca(size__ * sizeof(type__))

  83. #endif

  84. 

  85. 

  86. /* 

  87.    vector support macros: the rest of the code is independant of

  88.    SSE/Altivec/NEON -- adding support for other platforms with 4-element

  89.    vectors should be limited to these macros 

  90. */

  91. 

  92. 

  93. // define PFFFT_SIMD_DISABLE if you want to use scalar code instead of simd code

  94. //#define PFFFT_SIMD_DISABLE

  95. 

  96. /*

  97.    Altivec support macros 

  98. */

  99. #if !defined(PFFFT_SIMD_DISABLE) && (defined(__ppc__) || defined(__ppc64__))

  100. typedef vector float v4sf;

  101. #  define SIMD_SZ 4

  102. #  define VZERO() ((vector float) vec_splat_u8(0))

  103. #  define VMUL(a,b) vec_madd(a,b, VZERO())

  104. #  define VADD(a,b) vec_add(a,b)

  105. #  define VMADD(a,b,c) vec_madd(a,b,c)

  106. #  define VSUB(a,b) vec_sub(a,b)

  107. 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); }

  108. #  define LD_PS1(p) ld_ps1(&p)

  109. #  define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = vec_mergeh(in1, in2); out2 = vec_mergel(in1, in2); out1 = tmp__; }

  110. #  define UNINTERLEAVE2(in1, in2, out1, out2) {                           \

  111.     vector unsigned char vperm1 =  (vector unsigned char)(0,1,2,3,8,9,10,11,16,17,18,19,24,25,26,27); \

  112.     vector unsigned char vperm2 =  (vector unsigned char)(4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31); \

  113.     v4sf tmp__ = vec_perm(in1, in2, vperm1); out2 = vec_perm(in1, in2, vperm2); out1 = tmp__; \

  114.   }

  115. #  define VTRANSPOSE4(x0,x1,x2,x3) {              \

  116.     v4sf y0 = vec_mergeh(x0, x2);               \

  117.     v4sf y1 = vec_mergel(x0, x2);               \

  118.     v4sf y2 = vec_mergeh(x1, x3);               \

  119.     v4sf y3 = vec_mergel(x1, x3);               \

  120.     x0 = vec_mergeh(y0, y2);                    \

  121.     x1 = vec_mergel(y0, y2);                    \

  122.     x2 = vec_mergeh(y1, y3);                    \

  123.     x3 = vec_mergel(y1, y3);                    \

  124.   }

  125. #  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))

  126. #  define VALIGNED(ptr) ((((long)(ptr)) & 0xF) == 0)

  127. 

  128. /*

  129.   SSE1 support macros

  130. */

  131. #elif !defined(PFFFT_SIMD_DISABLE) && (defined(__x86_64__) || defined(_M_X64) || defined(i386) || defined(_M_IX86))

  132. 

  133. #include <xmmintrin.h>

  134. typedef __m128 v4sf;

  135. #  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.

  136. #  define VZERO() _mm_setzero_ps()

  137. #  define VMUL(a,b) _mm_mul_ps(a,b)

  138. #  define VADD(a,b) _mm_add_ps(a,b)

  139. #  define VMADD(a,b,c) _mm_add_ps(_mm_mul_ps(a,b), c)

  140. #  define VSUB(a,b) _mm_sub_ps(a,b)

  141. #  define LD_PS1(p) _mm_set1_ps(p)

  142. #  define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_unpacklo_ps(in1, in2); out2 = _mm_unpackhi_ps(in1, in2); out1 = tmp__; }

  143. #  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__; }

  144. #  define VTRANSPOSE4(x0,x1,x2,x3) _MM_TRANSPOSE4_PS(x0,x1,x2,x3)

  145. #  define VSWAPHL(a,b) _mm_shuffle_ps(b, a, _MM_SHUFFLE(3,2,1,0))

  146. #  define VALIGNED(ptr) ((((long)(ptr)) & 0xF) == 0)

  147. 

  148. /*

  149.   ARM NEON support macros

  150. */

  151. #elif !defined(PFFFT_SIMD_DISABLE) && (defined(__arm__) || defined(__aarch64__) || defined(__arm64__))

  152. #  include <arm_neon.h>

  153. typedef float32x4_t v4sf;

  154. #  define SIMD_SZ 4

  155. #  define VZERO() vdupq_n_f32(0)

  156. #  define VMUL(a,b) vmulq_f32(a,b)

  157. #  define VADD(a,b) vaddq_f32(a,b)

  158. #  define VMADD(a,b,c) vmlaq_f32(c,a,b)

  159. #  define VSUB(a,b) vsubq_f32(a,b)

  160. #  define LD_PS1(p) vld1q_dup_f32(&(p))

  161. #  define INTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vzipq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }

  162. #  define UNINTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vuzpq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }

  163. #  define VTRANSPOSE4(x0,x1,x2,x3) {                                    \

  164.     float32x4x2_t t0_ = vzipq_f32(x0, x2);                              \

  165.     float32x4x2_t t1_ = vzipq_f32(x1, x3);                              \

  166.     float32x4x2_t u0_ = vzipq_f32(t0_.val[0], t1_.val[0]);              \

  167.     float32x4x2_t u1_ = vzipq_f32(t0_.val[1], t1_.val[1]);              \

  168.     x0 = u0_.val[0]; x1 = u0_.val[1]; x2 = u1_.val[0]; x3 = u1_.val[1]; \

  169.   }

  170. // marginally faster version

  171. //#  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)::); }

  172. #  define VSWAPHL(a,b) vcombine_f32(vget_low_f32(b), vget_high_f32(a))

  173. #  define VALIGNED(ptr) ((((long)(ptr)) & 0x3) == 0)

  174. #else

  175. #  if !defined(PFFFT_SIMD_DISABLE)

  176. #    warning "building with simd disabled !\n";

  177. #    define PFFFT_SIMD_DISABLE // fallback to scalar code

  178. #  endif

  179. #endif

  180. 

  181. // fallback mode for situations where SSE/Altivec are not available, use scalar mode instead

  182. #ifdef PFFFT_SIMD_DISABLE

  183. typedef float v4sf;

  184. #  define SIMD_SZ 1

  185. #  define VZERO() 0.f

  186. #  define VMUL(a,b) ((a)*(b))

  187. #  define VADD(a,b) ((a)+(b))

  188. #  define VMADD(a,b,c) ((a)*(b)+(c))

  189. #  define VSUB(a,b) ((a)-(b))

  190. #  define LD_PS1(p) (p)

  191. #  define VALIGNED(ptr) ((((long)(ptr)) & 0x3) == 0)

  192. #endif

  193. 

  194. // shortcuts for complex multiplcations

  195. #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); }

  196. #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); }

  197. #ifndef SVMUL

  198. // multiply a scalar with a vector

  199. #define SVMUL(f,v) VMUL(LD_PS1(f),v)

  200. #endif

  201. 

  202. #if !defined(PFFFT_SIMD_DISABLE)

  203. typedef union v4sf_union {

  204.   v4sf  v;

  205.   float f[4];

  206. } v4sf_union;

  207. 

  208. #include <string.h>

  209. 

  210. #define assertv4(v,f0,f1,f2,f3) assert(v.f[0] == (f0) && v.f[1] == (f1) && v.f[2] == (f2) && v.f[3] == (f3))

  211. 

  212. /* detect bugs with the vector support macros */

  213. void validate_pffft_simd() {

  214.   float f[16] = { 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 };

  215.   v4sf_union a0, a1, a2, a3, t, u; 

  216.   memcpy(a0.f, f, 4*sizeof(float));

  217.   memcpy(a1.f, f+4, 4*sizeof(float));

  218.   memcpy(a2.f, f+8, 4*sizeof(float));

  219.   memcpy(a3.f, f+12, 4*sizeof(float));

  220. 

  221.   t = a0; u = a1; t.v = VZERO();

  222.   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);

  223.   t.v = VADD(a1.v, a2.v);

  224.   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);

  225.   t.v = VMUL(a1.v, a2.v);

  226.   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);

  227.   t.v = VMADD(a1.v, a2.v,a0.v);

  228.   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);

  229. 

  230.   INTERLEAVE2(a1.v,a2.v,t.v,u.v);

  231.   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]);

  232.   assertv4(t, 4, 8, 5, 9); assertv4(u, 6, 10, 7, 11);

  233.   UNINTERLEAVE2(a1.v,a2.v,t.v,u.v);

  234.   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]);

  235.   assertv4(t, 4, 6, 8, 10); assertv4(u, 5, 7, 9, 11);

  236. 

  237.   t.v=LD_PS1(f[15]);

  238.   printf("LD_PS1(15)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);

  239.   assertv4(t, 15, 15, 15, 15);

  240.   t.v = VSWAPHL(a1.v, a2.v);

  241.   printf("VSWAPHL(4:7,8:11)=[%2g %2g %2g %2g]\n", t.f[0], t.f[1], t.f[2], t.f[3]);

  242.   assertv4(t, 8, 9, 6, 7);

  243.   VTRANSPOSE4(a0.v, a1.v, a2.v, a3.v);

  244.   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", 

  245.          a0.f[0], a0.f[1], a0.f[2], a0.f[3], a1.f[0], a1.f[1], a1.f[2], a1.f[3], 

  246.          a2.f[0], a2.f[1], a2.f[2], a2.f[3], a3.f[0], a3.f[1], a3.f[2], a3.f[3]); 

  247.   assertv4(a0, 0, 4, 8, 12); assertv4(a1, 1, 5, 9, 13); assertv4(a2, 2, 6, 10, 14); assertv4(a3, 3, 7, 11, 15);

  248. }

  249. #endif //!PFFFT_SIMD_DISABLE

  250. 

  251. /* SSE and co like 16-bytes aligned pointers */

  252. #define MALLOC_V4SF_ALIGNMENT 64 // with a 64-byte alignment, we are even aligned on L2 cache lines...

  253. void *pffft_aligned_malloc(size_t nb_bytes) {

  254.   void *p, *p0 = malloc(nb_bytes + MALLOC_V4SF_ALIGNMENT);

  255.   if (!p0) return (void *) 0;

  256.   p = (void *) (((size_t) p0 + MALLOC_V4SF_ALIGNMENT) & (~((size_t) (MALLOC_V4SF_ALIGNMENT-1))));

  257.   *((void **) p - 1) = p0;

  258.   return p;

  259. }

  260. 

  261. void pffft_aligned_free(void *p) {

  262.   if (p) free(*((void **) p - 1));

  263. }

  264. 

  265. int pffft_simd_size() { return SIMD_SZ; }

  266. 

  267. /*

  268.   passf2 and passb2 has been merged here, fsign = -1 for passf2, +1 for passb2

  269. */

  270. static NEVER_INLINE(void) passf2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1, float fsign) {

  271.   int k, i;

  272.   int l1ido = l1*ido;

  273.   if (ido <= 2) {

  274.     for (k=0; k < l1ido; k += ido, ch += ido, cc+= 2*ido) {

  275.       ch[0]         = VADD(cc[0], cc[ido+0]);

  276.       ch[l1ido]     = VSUB(cc[0], cc[ido+0]);

  277.       ch[1]         = VADD(cc[1], cc[ido+1]);

  278.       ch[l1ido + 1] = VSUB(cc[1], cc[ido+1]);

  279.     }

  280.   } else {

  281.     for (k=0; k < l1ido; k += ido, ch += ido, cc += 2*ido) {

  282.       for (i=0; i<ido-1; i+=2) {

  283.         v4sf tr2 = VSUB(cc[i+0], cc[i+ido+0]);

  284.         v4sf ti2 = VSUB(cc[i+1], cc[i+ido+1]);

  285.         v4sf wr = LD_PS1(wa1[i]), wi = VMUL(LD_PS1(fsign), LD_PS1(wa1[i+1]));

  286.         ch[i]   = VADD(cc[i+0], cc[i+ido+0]);

  287.         ch[i+1] = VADD(cc[i+1], cc[i+ido+1]);

  288.         VCPLXMUL(tr2, ti2, wr, wi);

  289.         ch[i+l1ido]   = tr2;

  290.         ch[i+l1ido+1] = ti2;

  291.       }

  292.     }

  293.   }

  294. }

  295. 

  296. /*

  297.   passf3 and passb3 has been merged here, fsign = -1 for passf3, +1 for passb3

  298. */

  299. static NEVER_INLINE(void) passf3_ps(int ido, int l1, const v4sf *cc, v4sf *ch,

  300.                                     const float *wa1, const float *wa2, float fsign) {

  301.   static const float taur = -0.5f;

  302.   float taui = 0.866025403784439f*fsign;

  303.   int i, k;

  304.   v4sf tr2, ti2, cr2, ci2, cr3, ci3, dr2, di2, dr3, di3;

  305.   int l1ido = l1*ido;

  306.   float wr1, wi1, wr2, wi2;

  307.   assert(ido > 2);

  308.   for (k=0; k< l1ido; k += ido, cc+= 3*ido, ch +=ido) {

  309.     for (i=0; i<ido-1; i+=2) {

  310.       tr2 = VADD(cc[i+ido], cc[i+2*ido]);

  311.       cr2 = VADD(cc[i], SVMUL(taur,tr2));

  312.       ch[i]    = VADD(cc[i], tr2);

  313.       ti2 = VADD(cc[i+ido+1], cc[i+2*ido+1]);

  314.       ci2 = VADD(cc[i    +1], SVMUL(taur,ti2));

  315.       ch[i+1]  = VADD(cc[i+1], ti2);

  316.       cr3 = SVMUL(taui, VSUB(cc[i+ido], cc[i+2*ido]));

  317.       ci3 = SVMUL(taui, VSUB(cc[i+ido+1], cc[i+2*ido+1]));

  318.       dr2 = VSUB(cr2, ci3);

  319.       dr3 = VADD(cr2, ci3);

  320.       di2 = VADD(ci2, cr3);

  321.       di3 = VSUB(ci2, cr3);

  322.       wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1]; 

  323.       VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));

  324.       ch[i+l1ido] = dr2; 

  325.       ch[i+l1ido + 1] = di2;

  326.       VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));

  327.       ch[i+2*l1ido] = dr3;

  328.       ch[i+2*l1ido+1] = di3;

  329.     }

  330.   }

  331. } /* passf3 */

  332. 

  333. static NEVER_INLINE(void) passf4_ps(int ido, int l1, const v4sf *cc, v4sf *ch,

  334.                                     const float *wa1, const float *wa2, const float *wa3, float fsign) {

  335.   /* isign == -1 for forward transform and +1 for backward transform */

  336. 

  337.   int i, k;

  338.   v4sf ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;

  339.   int l1ido = l1*ido;

  340.   if (ido == 2) {

  341.     for (k=0; k < l1ido; k += ido, ch += ido, cc += 4*ido) {

  342.       tr1 = VSUB(cc[0], cc[2*ido + 0]);

  343.       tr2 = VADD(cc[0], cc[2*ido + 0]);

  344.       ti1 = VSUB(cc[1], cc[2*ido + 1]);

  345.       ti2 = VADD(cc[1], cc[2*ido + 1]);

  346.       ti4 = VMUL(VSUB(cc[1*ido + 0], cc[3*ido + 0]), LD_PS1(fsign));

  347.       tr4 = VMUL(VSUB(cc[3*ido + 1], cc[1*ido + 1]), LD_PS1(fsign));

  348.       tr3 = VADD(cc[ido + 0], cc[3*ido + 0]);

  349.       ti3 = VADD(cc[ido + 1], cc[3*ido + 1]);

  350. 

  351.       ch[0*l1ido + 0] = VADD(tr2, tr3);

  352.       ch[0*l1ido + 1] = VADD(ti2, ti3);

  353.       ch[1*l1ido + 0] = VADD(tr1, tr4);

  354.       ch[1*l1ido + 1] = VADD(ti1, ti4);

  355.       ch[2*l1ido + 0] = VSUB(tr2, tr3);

  356.       ch[2*l1ido + 1] = VSUB(ti2, ti3);        

  357.       ch[3*l1ido + 0] = VSUB(tr1, tr4);

  358.       ch[3*l1ido + 1] = VSUB(ti1, ti4);

  359.     }

  360.   } else {

  361.     for (k=0; k < l1ido; k += ido, ch+=ido, cc += 4*ido) {

  362.       for (i=0; i<ido-1; i+=2) {

  363.         float wr1, wi1, wr2, wi2, wr3, wi3;

  364.         tr1 = VSUB(cc[i + 0], cc[i + 2*ido + 0]);

  365.         tr2 = VADD(cc[i + 0], cc[i + 2*ido + 0]);

  366.         ti1 = VSUB(cc[i + 1], cc[i + 2*ido + 1]);

  367.         ti2 = VADD(cc[i + 1], cc[i + 2*ido + 1]);

  368.         tr4 = VMUL(VSUB(cc[i + 3*ido + 1], cc[i + 1*ido + 1]), LD_PS1(fsign));

  369.         ti4 = VMUL(VSUB(cc[i + 1*ido + 0], cc[i + 3*ido + 0]), LD_PS1(fsign));

  370.         tr3 = VADD(cc[i + ido + 0], cc[i + 3*ido + 0]);

  371.         ti3 = VADD(cc[i + ido + 1], cc[i + 3*ido + 1]);

  372. 

  373.         ch[i] = VADD(tr2, tr3);

  374.         cr3    = VSUB(tr2, tr3);

  375.         ch[i + 1] = VADD(ti2, ti3);

  376.         ci3 = VSUB(ti2, ti3);

  377. 

  378.         cr2 = VADD(tr1, tr4);

  379.         cr4 = VSUB(tr1, tr4);

  380.         ci2 = VADD(ti1, ti4);

  381.         ci4 = VSUB(ti1, ti4);

  382.         wr1=wa1[i], wi1=fsign*wa1[i+1];

  383.         VCPLXMUL(cr2, ci2, LD_PS1(wr1), LD_PS1(wi1));

  384.         wr2=wa2[i], wi2=fsign*wa2[i+1]; 

  385.         ch[i + l1ido] = cr2;

  386.         ch[i + l1ido + 1] = ci2;

  387. 

  388.         VCPLXMUL(cr3, ci3, LD_PS1(wr2), LD_PS1(wi2));

  389.         wr3=wa3[i], wi3=fsign*wa3[i+1]; 

  390.         ch[i + 2*l1ido] = cr3;

  391.         ch[i + 2*l1ido + 1] = ci3;

  392. 

  393.         VCPLXMUL(cr4, ci4, LD_PS1(wr3), LD_PS1(wi3));

  394.         ch[i + 3*l1ido] = cr4;

  395.         ch[i + 3*l1ido + 1] = ci4;

  396.       }

  397.     }

  398.   }

  399. } /* passf4 */

  400. 

  401. /*

  402.   passf5 and passb5 has been merged here, fsign = -1 for passf5, +1 for passb5

  403. */

  404. static NEVER_INLINE(void) passf5_ps(int ido, int l1, const v4sf *cc, v4sf *ch,

  405.                                     const float *wa1, const float *wa2, 

  406.                                     const float *wa3, const float *wa4, float fsign) {  

  407.   static const float tr11 = .309016994374947f;

  408.   const float ti11 = .951056516295154f*fsign;

  409.   static const float tr12 = -.809016994374947f;

  410.   const float ti12 = .587785252292473f*fsign;

  411. 

  412.   /* Local variables */

  413.   int i, k;

  414.   v4sf ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,

  415.     ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;

  416. 

  417.   float wr1, wi1, wr2, wi2, wr3, wi3, wr4, wi4;

  418. 

  419. #define cc_ref(a_1,a_2) cc[(a_2-1)*ido + a_1 + 1]

  420. #define ch_ref(a_1,a_3) ch[(a_3-1)*l1*ido + a_1 + 1]

  421. 

  422.   assert(ido > 2);

  423.   for (k = 0; k < l1; ++k, cc += 5*ido, ch += ido) {

  424.     for (i = 0; i < ido-1; i += 2) {

  425.       ti5 = VSUB(cc_ref(i  , 2), cc_ref(i  , 5));

  426.       ti2 = VADD(cc_ref(i  , 2), cc_ref(i  , 5));

  427.       ti4 = VSUB(cc_ref(i  , 3), cc_ref(i  , 4));

  428.       ti3 = VADD(cc_ref(i  , 3), cc_ref(i  , 4));

  429.       tr5 = VSUB(cc_ref(i-1, 2), cc_ref(i-1, 5));

  430.       tr2 = VADD(cc_ref(i-1, 2), cc_ref(i-1, 5));

  431.       tr4 = VSUB(cc_ref(i-1, 3), cc_ref(i-1, 4));

  432.       tr3 = VADD(cc_ref(i-1, 3), cc_ref(i-1, 4));

  433.       ch_ref(i-1, 1) = VADD(cc_ref(i-1, 1), VADD(tr2, tr3));

  434.       ch_ref(i  , 1) = VADD(cc_ref(i  , 1), VADD(ti2, ti3));

  435.       cr2 = VADD(cc_ref(i-1, 1), VADD(SVMUL(tr11, tr2),SVMUL(tr12, tr3)));

  436.       ci2 = VADD(cc_ref(i  , 1), VADD(SVMUL(tr11, ti2),SVMUL(tr12, ti3)));

  437.       cr3 = VADD(cc_ref(i-1, 1), VADD(SVMUL(tr12, tr2),SVMUL(tr11, tr3)));

  438.       ci3 = VADD(cc_ref(i  , 1), VADD(SVMUL(tr12, ti2),SVMUL(tr11, ti3)));

  439.       cr5 = VADD(SVMUL(ti11, tr5), SVMUL(ti12, tr4));

  440.       ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));

  441.       cr4 = VSUB(SVMUL(ti12, tr5), SVMUL(ti11, tr4));

  442.       ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));

  443.       dr3 = VSUB(cr3, ci4);

  444.       dr4 = VADD(cr3, ci4);

  445.       di3 = VADD(ci3, cr4);

  446.       di4 = VSUB(ci3, cr4);

  447.       dr5 = VADD(cr2, ci5);

  448.       dr2 = VSUB(cr2, ci5);

  449.       di5 = VSUB(ci2, cr5);

  450.       di2 = VADD(ci2, cr5);

  451.       wr1=wa1[i], wi1=fsign*wa1[i+1], wr2=wa2[i], wi2=fsign*wa2[i+1]; 

  452.       wr3=wa3[i], wi3=fsign*wa3[i+1], wr4=wa4[i], wi4=fsign*wa4[i+1]; 

  453.       VCPLXMUL(dr2, di2, LD_PS1(wr1), LD_PS1(wi1));

  454.       ch_ref(i - 1, 2) = dr2;

  455.       ch_ref(i, 2)     = di2;

  456.       VCPLXMUL(dr3, di3, LD_PS1(wr2), LD_PS1(wi2));

  457.       ch_ref(i - 1, 3) = dr3;

  458.       ch_ref(i, 3)     = di3;

  459.       VCPLXMUL(dr4, di4, LD_PS1(wr3), LD_PS1(wi3));

  460.       ch_ref(i - 1, 4) = dr4;

  461.       ch_ref(i, 4)     = di4;

  462.       VCPLXMUL(dr5, di5, LD_PS1(wr4), LD_PS1(wi4));

  463.       ch_ref(i - 1, 5) = dr5;

  464.       ch_ref(i, 5)     = di5;

  465.     }

  466.   }

  467. #undef ch_ref

  468. #undef cc_ref

  469. }

  470. 

  471. static NEVER_INLINE(void) radf2_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch, const float *wa1) {

  472.   static const float minus_one = -1.f;

  473.   int i, k, l1ido = l1*ido;

  474.   for (k=0; k < l1ido; k += ido) {

  475.     v4sf a = cc[k], b = cc[k + l1ido];

  476.     ch[2*k] = VADD(a, b);

  477.     ch[2*(k+ido)-1] = VSUB(a, b);

  478.   }

  479.   if (ido < 2) return;

  480.   if (ido != 2) {

  481.     for (k=0; k < l1ido; k += ido) {

  482.       for (i=2; i<ido; i+=2) {

  483.         v4sf tr2 = cc[i - 1 + k + l1ido], ti2 = cc[i + k + l1ido];

  484.         v4sf br = cc[i - 1 + k], bi = cc[i + k];

  485.         VCPLXMULCONJ(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1])); 

  486.         ch[i + 2*k] = VADD(bi, ti2);

  487.         ch[2*(k+ido) - i] = VSUB(ti2, bi);

  488.         ch[i - 1 + 2*k] = VADD(br, tr2);

  489.         ch[2*(k+ido) - i -1] = VSUB(br, tr2);

  490.       }

  491.     }

  492.     if (ido % 2 == 1) return;

  493.   }

  494.   for (k=0; k < l1ido; k += ido) {

  495.     ch[2*k + ido] = SVMUL(minus_one, cc[ido-1 + k + l1ido]);

  496.     ch[2*k + ido-1] = cc[k + ido-1];

  497.   }

  498. } /* radf2 */

  499. 

  500. 

  501. static NEVER_INLINE(void) radb2_ps(int ido, int l1, const v4sf *cc, v4sf *ch, const float *wa1) {

  502.   static const float minus_two=-2;

  503.   int i, k, l1ido = l1*ido;

  504.   v4sf a,b,c,d, tr2, ti2;

  505.   for (k=0; k < l1ido; k += ido) {

  506.     a = cc[2*k]; b = cc[2*(k+ido) - 1];

  507.     ch[k] = VADD(a, b);

  508.     ch[k + l1ido] =VSUB(a, b);

  509.   }

  510.   if (ido < 2) return;

  511.   if (ido != 2) {

  512.     for (k = 0; k < l1ido; k += ido) {

  513.       for (i = 2; i < ido; i += 2) {

  514.         a = cc[i-1 + 2*k]; b = cc[2*(k + ido) - i - 1];

  515.         c = cc[i+0 + 2*k]; d = cc[2*(k + ido) - i + 0];

  516.         ch[i-1 + k] = VADD(a, b);

  517.         tr2 = VSUB(a, b);

  518.         ch[i+0 + k] = VSUB(c, d);

  519.         ti2 = VADD(c, d);

  520.         VCPLXMUL(tr2, ti2, LD_PS1(wa1[i - 2]), LD_PS1(wa1[i - 1]));

  521.         ch[i-1 + k + l1ido] = tr2;

  522.         ch[i+0 + k + l1ido] = ti2;

  523.       }

  524.     }

  525.     if (ido % 2 == 1) return;

  526.   }

  527.   for (k = 0; k < l1ido; k += ido) {

  528.     a = cc[2*k + ido-1]; b = cc[2*k + ido];

  529.     ch[k + ido-1] = VADD(a,a);

  530.     ch[k + ido-1 + l1ido] = SVMUL(minus_two, b);

  531.   }

  532. } /* radb2 */

  533. 

  534. static void radf3_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,

  535.                      const float *wa1, const float *wa2) {

  536.   static const float taur = -0.5f;

  537.   static const float taui = 0.866025403784439f;

  538.   int i, k, ic;

  539.   v4sf ci2, di2, di3, cr2, dr2, dr3, ti2, ti3, tr2, tr3, wr1, wi1, wr2, wi2;

  540.   for (k=0; k<l1; k++) {

  541.     cr2 = VADD(cc[(k + l1)*ido], cc[(k + 2*l1)*ido]);

  542.     ch[3*k*ido] = VADD(cc[k*ido], cr2);

  543.     ch[(3*k+2)*ido] = SVMUL(taui, VSUB(cc[(k + l1*2)*ido], cc[(k + l1)*ido]));

  544.     ch[ido-1 + (3*k + 1)*ido] = VADD(cc[k*ido], SVMUL(taur, cr2));

  545.   }

  546.   if (ido == 1) return;

  547.   for (k=0; k<l1; k++) {

  548.     for (i=2; i<ido; i+=2) {

  549.       ic = ido - i;

  550.       wr1 = LD_PS1(wa1[i - 2]); wi1 = LD_PS1(wa1[i - 1]);

  551.       dr2 = cc[i - 1 + (k + l1)*ido]; di2 = cc[i + (k + l1)*ido];

  552.       VCPLXMULCONJ(dr2, di2, wr1, wi1);

  553. 

  554.       wr2 = LD_PS1(wa2[i - 2]); wi2 = LD_PS1(wa2[i - 1]);

  555.       dr3 = cc[i - 1 + (k + l1*2)*ido]; di3 = cc[i + (k + l1*2)*ido];

  556.       VCPLXMULCONJ(dr3, di3, wr2, wi2);

  557.         

  558.       cr2 = VADD(dr2, dr3);

  559.       ci2 = VADD(di2, di3);

  560.       ch[i - 1 + 3*k*ido] = VADD(cc[i - 1 + k*ido], cr2);

  561.       ch[i + 3*k*ido] = VADD(cc[i + k*ido], ci2);

  562.       tr2 = VADD(cc[i - 1 + k*ido], SVMUL(taur, cr2));

  563.       ti2 = VADD(cc[i + k*ido], SVMUL(taur, ci2));

  564.       tr3 = SVMUL(taui, VSUB(di2, di3));

  565.       ti3 = SVMUL(taui, VSUB(dr3, dr2));

  566.       ch[i - 1 + (3*k + 2)*ido] = VADD(tr2, tr3);

  567.       ch[ic - 1 + (3*k + 1)*ido] = VSUB(tr2, tr3);

  568.       ch[i + (3*k + 2)*ido] = VADD(ti2, ti3);

  569.       ch[ic + (3*k + 1)*ido] = VSUB(ti3, ti2);

  570.     }

  571.   }

  572. } /* radf3 */

  573. 

  574. 

  575. static void radb3_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch,

  576.                      const float *wa1, const float *wa2)

  577. {

  578.   static const float taur = -0.5f;

  579.   static const float taui = 0.866025403784439f;

  580.   static const float taui_2 = 0.866025403784439f*2;

  581.   int i, k, ic;

  582.   v4sf ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;

  583.   for (k=0; k<l1; k++) {

  584.     tr2 = cc[ido-1 + (3*k + 1)*ido]; tr2 = VADD(tr2,tr2);

  585.     cr2 = VMADD(LD_PS1(taur), tr2, cc[3*k*ido]);

  586.     ch[k*ido] = VADD(cc[3*k*ido], tr2);

  587.     ci3 = SVMUL(taui_2, cc[(3*k + 2)*ido]);

  588.     ch[(k + l1)*ido] = VSUB(cr2, ci3);

  589.     ch[(k + 2*l1)*ido] = VADD(cr2, ci3);

  590.   }

  591.   if (ido == 1) return;

  592.   for (k=0; k<l1; k++) {

  593.     for (i=2; i<ido; i+=2) {

  594.       ic = ido - i;

  595.       tr2 = VADD(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]);

  596.       cr2 = VMADD(LD_PS1(taur), tr2, cc[i - 1 + 3*k*ido]);

  597.       ch[i - 1 + k*ido] = VADD(cc[i - 1 + 3*k*ido], tr2);

  598.       ti2 = VSUB(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]);

  599.       ci2 = VMADD(LD_PS1(taur), ti2, cc[i + 3*k*ido]);

  600.       ch[i + k*ido] = VADD(cc[i + 3*k*ido], ti2);

  601.       cr3 = SVMUL(taui, VSUB(cc[i - 1 + (3*k + 2)*ido], cc[ic - 1 + (3*k + 1)*ido]));

  602.       ci3 = SVMUL(taui, VADD(cc[i + (3*k + 2)*ido], cc[ic + (3*k + 1)*ido]));

  603.       dr2 = VSUB(cr2, ci3);

  604.       dr3 = VADD(cr2, ci3);

  605.       di2 = VADD(ci2, cr3);

  606.       di3 = VSUB(ci2, cr3);

  607.       VCPLXMUL(dr2, di2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));

  608.       ch[i - 1 + (k + l1)*ido] = dr2;

  609.       ch[i + (k + l1)*ido] = di2;

  610.       VCPLXMUL(dr3, di3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));

  611.       ch[i - 1 + (k + 2*l1)*ido] = dr3;

  612.       ch[i + (k + 2*l1)*ido] = di3;

  613.     }

  614.   }

  615. } /* radb3 */

  616. 

  617. static NEVER_INLINE(void) radf4_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf * RESTRICT ch,

  618.                                    const float * RESTRICT wa1, const float * RESTRICT wa2, const float * RESTRICT wa3)

  619. {

  620.   static const float minus_hsqt2 = (float)-0.7071067811865475;

  621.   int i, k, l1ido = l1*ido;

  622.   {

  623.     const v4sf *RESTRICT cc_ = cc, * RESTRICT cc_end = cc + l1ido; 

  624.     v4sf * RESTRICT ch_ = ch;

  625.     while (cc < cc_end) {

  626.       // this loop represents between 25% and 40% of total radf4_ps cost !

  627.       v4sf a0 = cc[0], a1 = cc[l1ido];

  628.       v4sf a2 = cc[2*l1ido], a3 = cc[3*l1ido];

  629.       v4sf tr1 = VADD(a1, a3);

  630.       v4sf tr2 = VADD(a0, a2);

  631.       ch[2*ido-1] = VSUB(a0, a2);

  632.       ch[2*ido  ] = VSUB(a3, a1);

  633.       ch[0      ] = VADD(tr1, tr2);

  634.       ch[4*ido-1] = VSUB(tr2, tr1);

  635.       cc += ido; ch += 4*ido;

  636.     }

  637.     cc = cc_; ch = ch_;

  638.   }

  639.   if (ido < 2) return;

  640.   if (ido != 2) {

  641.     for (k = 0; k < l1ido; k += ido) {

  642.       const v4sf * RESTRICT pc = (v4sf*)(cc + 1 + k);

  643.       for (i=2; i<ido; i += 2, pc += 2) {

  644.         int ic = ido - i;

  645.         v4sf wr, wi, cr2, ci2, cr3, ci3, cr4, ci4;

  646.         v4sf tr1, ti1, tr2, ti2, tr3, ti3, tr4, ti4;

  647. 

  648.         cr2 = pc[1*l1ido+0];

  649.         ci2 = pc[1*l1ido+1];

  650.         wr=LD_PS1(wa1[i - 2]);

  651.         wi=LD_PS1(wa1[i - 1]);

  652.         VCPLXMULCONJ(cr2,ci2,wr,wi);

  653. 

  654.         cr3 = pc[2*l1ido+0];

  655.         ci3 = pc[2*l1ido+1];

  656.         wr = LD_PS1(wa2[i-2]); 

  657.         wi = LD_PS1(wa2[i-1]);

  658.         VCPLXMULCONJ(cr3, ci3, wr, wi);

  659. 

  660.         cr4 = pc[3*l1ido];

  661.         ci4 = pc[3*l1ido+1];

  662.         wr = LD_PS1(wa3[i-2]); 

  663.         wi = LD_PS1(wa3[i-1]);

  664.         VCPLXMULCONJ(cr4, ci4, wr, wi);

  665. 

  666.         /* at this point, on SSE, five of "cr2 cr3 cr4 ci2 ci3 ci4" should be loaded in registers */

  667. 

  668.         tr1 = VADD(cr2,cr4);

  669.         tr4 = VSUB(cr4,cr2); 

  670.         tr2 = VADD(pc[0],cr3);

  671.         tr3 = VSUB(pc[0],cr3);

  672.         ch[i - 1 + 4*k] = VADD(tr1,tr2);

  673.         ch[ic - 1 + 4*k + 3*ido] = VSUB(tr2,tr1); // at this point tr1 and tr2 can be disposed

  674.         ti1 = VADD(ci2,ci4);

  675.         ti4 = VSUB(ci2,ci4);

  676.         ch[i - 1 + 4*k + 2*ido] = VADD(ti4,tr3);

  677.         ch[ic - 1 + 4*k + 1*ido] = VSUB(tr3,ti4); // dispose tr3, ti4

  678.         ti2 = VADD(pc[1],ci3);

  679.         ti3 = VSUB(pc[1],ci3);

  680.         ch[i + 4*k] = VADD(ti1, ti2);

  681.         ch[ic + 4*k + 3*ido] = VSUB(ti1, ti2);

  682.         ch[i + 4*k + 2*ido] = VADD(tr4, ti3);

  683.         ch[ic + 4*k + 1*ido] = VSUB(tr4, ti3);

  684.       }

  685.     }

  686.     if (ido % 2 == 1) return;

  687.   }

  688.   for (k=0; k<l1ido; k += ido) {

  689.     v4sf a = cc[ido-1 + k + l1ido], b = cc[ido-1 + k + 3*l1ido];

  690.     v4sf c = cc[ido-1 + k], d = cc[ido-1 + k + 2*l1ido];

  691.     v4sf ti1 = SVMUL(minus_hsqt2, VADD(a, b));

  692.     v4sf tr1 = SVMUL(minus_hsqt2, VSUB(b, a));

  693.     ch[ido-1 + 4*k] = VADD(tr1, c);

  694.     ch[ido-1 + 4*k + 2*ido] = VSUB(c, tr1);

  695.     ch[4*k + 1*ido] = VSUB(ti1, d); 

  696.     ch[4*k + 3*ido] = VADD(ti1, d); 

  697.   }

  698. } /* radf4 */

  699. 

  700. 

  701. static NEVER_INLINE(void) radb4_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch,

  702.                                    const float * RESTRICT wa1, const float * RESTRICT wa2, const float *RESTRICT wa3)

  703. {

  704.   static const float minus_sqrt2 = (float)-1.414213562373095;

  705.   static const float two = 2.f;

  706.   int i, k, l1ido = l1*ido;

  707.   v4sf ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;

  708.   {

  709.     const v4sf *RESTRICT cc_ = cc, * RESTRICT ch_end = ch + l1ido; 

  710.     v4sf *ch_ = ch;

  711.     while (ch < ch_end) {

  712.       v4sf a = cc[0], b = cc[4*ido-1];

  713.       v4sf c = cc[2*ido], d = cc[2*ido-1];

  714.       tr3 = SVMUL(two,d);

  715.       tr2 = VADD(a,b);

  716.       tr1 = VSUB(a,b);

  717.       tr4 = SVMUL(two,c);

  718.       ch[0*l1ido] = VADD(tr2, tr3);

  719.       ch[2*l1ido] = VSUB(tr2, tr3);

  720.       ch[1*l1ido] = VSUB(tr1, tr4);

  721.       ch[3*l1ido] = VADD(tr1, tr4);

  722.       

  723.       cc += 4*ido; ch += ido;

  724.     }

  725.     cc = cc_; ch = ch_;

  726.   }

  727.   if (ido < 2) return;

  728.   if (ido != 2) {

  729.     for (k = 0; k < l1ido; k += ido) {

  730.       const v4sf * RESTRICT pc = (v4sf*)(cc - 1 + 4*k);

  731.       v4sf * RESTRICT ph = (v4sf*)(ch + k + 1);

  732.       for (i = 2; i < ido; i += 2) {

  733. 

  734.         tr1 = VSUB(pc[i], pc[4*ido - i]);

  735.         tr2 = VADD(pc[i], pc[4*ido - i]);

  736.         ti4 = VSUB(pc[2*ido + i], pc[2*ido - i]);

  737.         tr3 = VADD(pc[2*ido + i], pc[2*ido - i]);

  738.         ph[0] = VADD(tr2, tr3);

  739.         cr3 = VSUB(tr2, tr3);

  740. 

  741.         ti3 = VSUB(pc[2*ido + i + 1], pc[2*ido - i + 1]);

  742.         tr4 = VADD(pc[2*ido + i + 1], pc[2*ido - i + 1]);

  743.         cr2 = VSUB(tr1, tr4);

  744.         cr4 = VADD(tr1, tr4);

  745. 

  746.         ti1 = VADD(pc[i + 1], pc[4*ido - i + 1]);

  747.         ti2 = VSUB(pc[i + 1], pc[4*ido - i + 1]);

  748. 

  749.         ph[1] = VADD(ti2, ti3); ph += l1ido;

  750.         ci3 = VSUB(ti2, ti3);

  751.         ci2 = VADD(ti1, ti4);

  752.         ci4 = VSUB(ti1, ti4);

  753.         VCPLXMUL(cr2, ci2, LD_PS1(wa1[i-2]), LD_PS1(wa1[i-1]));

  754.         ph[0] = cr2;

  755.         ph[1] = ci2; ph += l1ido;

  756.         VCPLXMUL(cr3, ci3, LD_PS1(wa2[i-2]), LD_PS1(wa2[i-1]));

  757.         ph[0] = cr3;

  758.         ph[1] = ci3; ph += l1ido;

  759.         VCPLXMUL(cr4, ci4, LD_PS1(wa3[i-2]), LD_PS1(wa3[i-1]));

  760.         ph[0] = cr4;

  761.         ph[1] = ci4; ph = ph - 3*l1ido + 2;

  762.       }

  763.     }

  764.     if (ido % 2 == 1) return;

  765.   }

  766.   for (k=0; k < l1ido; k+=ido) {

  767.     int i0 = 4*k + ido;

  768.     v4sf c = cc[i0-1], d = cc[i0 + 2*ido-1];

  769.     v4sf a = cc[i0+0], b = cc[i0 + 2*ido+0];

  770.     tr1 = VSUB(c,d);

  771.     tr2 = VADD(c,d);

  772.     ti1 = VADD(b,a);

  773.     ti2 = VSUB(b,a);

  774.     ch[ido-1 + k + 0*l1ido] = VADD(tr2,tr2);

  775.     ch[ido-1 + k + 1*l1ido] = SVMUL(minus_sqrt2, VSUB(ti1, tr1));

  776.     ch[ido-1 + k + 2*l1ido] = VADD(ti2, ti2);

  777.     ch[ido-1 + k + 3*l1ido] = SVMUL(minus_sqrt2, VADD(ti1, tr1));

  778.   }

  779. } /* radb4 */

  780. 

  781. static void radf5_ps(int ido, int l1, const v4sf * RESTRICT cc, v4sf * RESTRICT ch, 

  782.                      const float *wa1, const float *wa2, const float *wa3, const float *wa4)

  783. {

  784.   static const float tr11 = .309016994374947f;

  785.   static const float ti11 = .951056516295154f;

  786.   static const float tr12 = -.809016994374947f;

  787.   static const float ti12 = .587785252292473f;

  788. 

  789.   /* System generated locals */

  790.   int cc_offset, ch_offset;

  791. 

  792.   /* Local variables */

  793.   int i, k, ic;

  794.   v4sf ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3, dr4, dr5,

  795.     cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5;

  796.   int idp2;

  797. 

  798. 

  799. #define cc_ref(a_1,a_2,a_3) cc[((a_3)*l1 + (a_2))*ido + a_1]

  800. #define ch_ref(a_1,a_2,a_3) ch[((a_3)*5 + (a_2))*ido + a_1]

  801. 

  802.   /* Parameter adjustments */

  803.   ch_offset = 1 + ido * 6;

  804.   ch -= ch_offset;

  805.   cc_offset = 1 + ido * (1 + l1);

  806.   cc -= cc_offset;

  807. 

  808.   /* Function Body */

  809.   for (k = 1; k <= l1; ++k) {

  810.     cr2 = VADD(cc_ref(1, k, 5), cc_ref(1, k, 2));

  811.     ci5 = VSUB(cc_ref(1, k, 5), cc_ref(1, k, 2));

  812.     cr3 = VADD(cc_ref(1, k, 4), cc_ref(1, k, 3));

  813.     ci4 = VSUB(cc_ref(1, k, 4), cc_ref(1, k, 3));

  814.     ch_ref(1, 1, k) = VADD(cc_ref(1, k, 1), VADD(cr2, cr3));

  815.     ch_ref(ido, 2, k) = VADD(cc_ref(1, k, 1), VADD(SVMUL(tr11, cr2), SVMUL(tr12, cr3)));

  816.     ch_ref(1, 3, k) = VADD(SVMUL(ti11, ci5), SVMUL(ti12, ci4));

  817.     ch_ref(ido, 4, k) = VADD(cc_ref(1, k, 1), VADD(SVMUL(tr12, cr2), SVMUL(tr11, cr3)));

  818.     ch_ref(1, 5, k) = VSUB(SVMUL(ti12, ci5), SVMUL(ti11, ci4));

  819.     //printf("pffft: radf5, k=%d ch_ref=%f, ci4=%f\n", k, ch_ref(1, 5, k), ci4);

  820.   }

  821.   if (ido == 1) {

  822.     return;

  823.   }

  824.   idp2 = ido + 2;

  825.   for (k = 1; k <= l1; ++k) {

  826.     for (i = 3; i <= ido; i += 2) {

  827.       ic = idp2 - i;

  828.       dr2 = LD_PS1(wa1[i-3]); di2 = LD_PS1(wa1[i-2]);

  829.       dr3 = LD_PS1(wa2[i-3]); di3 = LD_PS1(wa2[i-2]);

  830.       dr4 = LD_PS1(wa3[i-3]); di4 = LD_PS1(wa3[i-2]);

  831.       dr5 = LD_PS1(wa4[i-3]); di5 = LD_PS1(wa4[i-2]);

  832.       VCPLXMULCONJ(dr2, di2, cc_ref(i-1, k, 2), cc_ref(i, k, 2));

  833.       VCPLXMULCONJ(dr3, di3, cc_ref(i-1, k, 3), cc_ref(i, k, 3));

  834.       VCPLXMULCONJ(dr4, di4, cc_ref(i-1, k, 4), cc_ref(i, k, 4));

  835.       VCPLXMULCONJ(dr5, di5, cc_ref(i-1, k, 5), cc_ref(i, k, 5));

  836.       cr2 = VADD(dr2, dr5);

  837.       ci5 = VSUB(dr5, dr2);

  838.       cr5 = VSUB(di2, di5);

  839.       ci2 = VADD(di2, di5);

  840.       cr3 = VADD(dr3, dr4);

  841.       ci4 = VSUB(dr4, dr3);

  842.       cr4 = VSUB(di3, di4);

  843.       ci3 = VADD(di3, di4);

  844.       ch_ref(i - 1, 1, k) = VADD(cc_ref(i - 1, k, 1), VADD(cr2, cr3));

  845.       ch_ref(i, 1, k) = VSUB(cc_ref(i, k, 1), VADD(ci2, ci3));//

  846.       tr2 = VADD(cc_ref(i - 1, k, 1), VADD(SVMUL(tr11, cr2), SVMUL(tr12, cr3)));

  847.       ti2 = VSUB(cc_ref(i, k, 1), VADD(SVMUL(tr11, ci2), SVMUL(tr12, ci3)));//

  848.       tr3 = VADD(cc_ref(i - 1, k, 1), VADD(SVMUL(tr12, cr2), SVMUL(tr11, cr3)));

  849.       ti3 = VSUB(cc_ref(i, k, 1), VADD(SVMUL(tr12, ci2), SVMUL(tr11, ci3)));//

  850.       tr5 = VADD(SVMUL(ti11, cr5), SVMUL(ti12, cr4));

  851.       ti5 = VADD(SVMUL(ti11, ci5), SVMUL(ti12, ci4));

  852.       tr4 = VSUB(SVMUL(ti12, cr5), SVMUL(ti11, cr4));

  853.       ti4 = VSUB(SVMUL(ti12, ci5), SVMUL(ti11, ci4));

  854.       ch_ref(i - 1, 3, k) = VSUB(tr2, tr5);

  855.       ch_ref(ic - 1, 2, k) = VADD(tr2, tr5);

  856.       ch_ref(i, 3, k) = VADD(ti2, ti5);

  857.       ch_ref(ic, 2, k) = VSUB(ti5, ti2);

  858.       ch_ref(i - 1, 5, k) = VSUB(tr3, tr4);

  859.       ch_ref(ic - 1, 4, k) = VADD(tr3, tr4);

  860.       ch_ref(i, 5, k) = VADD(ti3, ti4);

  861.       ch_ref(ic, 4, k) = VSUB(ti4, ti3);

  862.     }

  863.   }

  864. #undef cc_ref

  865. #undef ch_ref

  866. } /* radf5 */

  867. 

  868. static void radb5_ps(int ido, int l1, const v4sf *RESTRICT cc, v4sf *RESTRICT ch, 

  869.                   const float *wa1, const float *wa2, const float *wa3, const float *wa4)

  870. {

  871.   static const float tr11 = .309016994374947f;

  872.   static const float ti11 = .951056516295154f;

  873.   static const float tr12 = -.809016994374947f;

  874.   static const float ti12 = .587785252292473f;

  875. 

  876.   int cc_offset, ch_offset;

  877. 

  878.   /* Local variables */

  879.   int i, k, ic;

  880.   v4sf ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,

  881.     ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;

  882.   int idp2;

  883. 

  884. #define cc_ref(a_1,a_2,a_3) cc[((a_3)*5 + (a_2))*ido + a_1]

  885. #define ch_ref(a_1,a_2,a_3) ch[((a_3)*l1 + (a_2))*ido + a_1]

  886. 

  887.   /* Parameter adjustments */

  888.   ch_offset = 1 + ido * (1 + l1);

  889.   ch -= ch_offset;

  890.   cc_offset = 1 + ido * 6;

  891.   cc -= cc_offset;

  892. 

  893.   /* Function Body */

  894.   for (k = 1; k <= l1; ++k) {

  895.     ti5 = VADD(cc_ref(1, 3, k), cc_ref(1, 3, k));

  896.     ti4 = VADD(cc_ref(1, 5, k), cc_ref(1, 5, k));

  897.     tr2 = VADD(cc_ref(ido, 2, k), cc_ref(ido, 2, k));

  898.     tr3 = VADD(cc_ref(ido, 4, k), cc_ref(ido, 4, k));

  899.     ch_ref(1, k, 1) = VADD(cc_ref(1, 1, k), VADD(tr2, tr3));

  900.     cr2 = VADD(cc_ref(1, 1, k), VADD(SVMUL(tr11, tr2), SVMUL(tr12, tr3)));

  901.     cr3 = VADD(cc_ref(1, 1, k), VADD(SVMUL(tr12, tr2), SVMUL(tr11, tr3)));

  902.     ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));

  903.     ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));

  904.     ch_ref(1, k, 2) = VSUB(cr2, ci5);

  905.     ch_ref(1, k, 3) = VSUB(cr3, ci4);

  906.     ch_ref(1, k, 4) = VADD(cr3, ci4);

  907.     ch_ref(1, k, 5) = VADD(cr2, ci5);

  908.   }

  909.   if (ido == 1) {

  910.     return;

  911.   }

  912.   idp2 = ido + 2;

  913.   for (k = 1; k <= l1; ++k) {

  914.     for (i = 3; i <= ido; i += 2) {

  915.       ic = idp2 - i;

  916.       ti5 = VADD(cc_ref(i  , 3, k), cc_ref(ic  , 2, k));

  917.       ti2 = VSUB(cc_ref(i  , 3, k), cc_ref(ic  , 2, k));

  918.       ti4 = VADD(cc_ref(i  , 5, k), cc_ref(ic  , 4, k));

  919.       ti3 = VSUB(cc_ref(i  , 5, k), cc_ref(ic  , 4, k));

  920.       tr5 = VSUB(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k));

  921.       tr2 = VADD(cc_ref(i-1, 3, k), cc_ref(ic-1, 2, k));

  922.       tr4 = VSUB(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k));

  923.       tr3 = VADD(cc_ref(i-1, 5, k), cc_ref(ic-1, 4, k));

  924.       ch_ref(i - 1, k, 1) = VADD(cc_ref(i-1, 1, k), VADD(tr2, tr3));

  925.       ch_ref(i, k, 1) = VADD(cc_ref(i, 1, k), VADD(ti2, ti3));

  926.       cr2 = VADD(cc_ref(i-1, 1, k), VADD(SVMUL(tr11, tr2), SVMUL(tr12, tr3)));

  927.       ci2 = VADD(cc_ref(i  , 1, k), VADD(SVMUL(tr11, ti2), SVMUL(tr12, ti3)));

  928.       cr3 = VADD(cc_ref(i-1, 1, k), VADD(SVMUL(tr12, tr2), SVMUL(tr11, tr3)));

  929.       ci3 = VADD(cc_ref(i  , 1, k), VADD(SVMUL(tr12, ti2), SVMUL(tr11, ti3)));

  930.       cr5 = VADD(SVMUL(ti11, tr5), SVMUL(ti12, tr4));

  931.       ci5 = VADD(SVMUL(ti11, ti5), SVMUL(ti12, ti4));

  932.       cr4 = VSUB(SVMUL(ti12, tr5), SVMUL(ti11, tr4));

  933.       ci4 = VSUB(SVMUL(ti12, ti5), SVMUL(ti11, ti4));

  934.       dr3 = VSUB(cr3, ci4);

  935.       dr4 = VADD(cr3, ci4);

  936.       di3 = VADD(ci3, cr4);

  937.       di4 = VSUB(ci3, cr4);

  938.       dr5 = VADD(cr2, ci5);

  939.       dr2 = VSUB(cr2, ci5);

  940.       di5 = VSUB(ci2, cr5);

  941.       di2 = VADD(ci2, cr5);

  942.       VCPLXMUL(dr2, di2, LD_PS1(wa1[i-3]), LD_PS1(wa1[i-2]));

  943.       VCPLXMUL(dr3, di3, LD_PS1(wa2[i-3]), LD_PS1(wa2[i-2]));

  944.       VCPLXMUL(dr4, di4, LD_PS1(wa3[i-3]), LD_PS1(wa3[i-2]));

  945.       VCPLXMUL(dr5, di5, LD_PS1(wa4[i-3]), LD_PS1(wa4[i-2]));

  946. 

  947.       ch_ref(i-1, k, 2) = dr2; ch_ref(i, k, 2) = di2;

  948.       ch_ref(i-1, k, 3) = dr3; ch_ref(i, k, 3) = di3;

  949.       ch_ref(i-1, k, 4) = dr4; ch_ref(i, k, 4) = di4;

  950.       ch_ref(i-1, k, 5) = dr5; ch_ref(i, k, 5) = di5;

  951.     }

  952.   }

  953. #undef cc_ref

  954. #undef ch_ref

  955. } /* radb5 */

  956. 

  957. static NEVER_INLINE(v4sf *) rfftf1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2, 

  958.                                       const float *wa, const int *ifac) {  

  959.   v4sf *in  = (v4sf*)input_readonly;

  960.   v4sf *out = (in == work2 ? work1 : work2);

  961.   int nf = ifac[1], k1;

  962.   int l2 = n;

  963.   int iw = n-1;

  964.   assert(in != out && work1 != work2);

  965.   for (k1 = 1; k1 <= nf; ++k1) {

  966.     int kh = nf - k1;

  967.     int ip = ifac[kh + 2];

  968.     int l1 = l2 / ip;

  969.     int ido = n / l2;

  970.     iw -= (ip - 1)*ido;

  971.     switch (ip) {

  972.       case 5: {

  973.         int ix2 = iw + ido;

  974.         int ix3 = ix2 + ido;

  975.         int ix4 = ix3 + ido;

  976.         radf5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);

  977.       } break;

  978.       case 4: {

  979.         int ix2 = iw + ido;

  980.         int ix3 = ix2 + ido;

  981.         radf4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);

  982.       } break;

  983.       case 3: {

  984.         int ix2 = iw + ido;

  985.         radf3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);

  986.       } break;

  987.       case 2:

  988.         radf2_ps(ido, l1, in, out, &wa[iw]);

  989.         break;

  990.       default:

  991.         assert(0);

  992.         break;

  993.     }

  994.     l2 = l1;

  995.     if (out == work2) {

  996.       out = work1; in = work2;

  997.     } else {

  998.       out = work2; in = work1;

  999.     }

  1000.   }

  1001.   return in; /* this is in fact the output .. */

  1002. } /* rfftf1 */

  1003. 

  1004. static NEVER_INLINE(v4sf *) rfftb1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2, 

  1005.                                       const float *wa, const int *ifac) {  

  1006.   v4sf *in  = (v4sf*)input_readonly;

  1007.   v4sf *out = (in == work2 ? work1 : work2);

  1008.   int nf = ifac[1], k1;

  1009.   int l1 = 1;

  1010.   int iw = 0;

  1011.   assert(in != out);

  1012.   for (k1=1; k1<=nf; k1++) {

  1013.     int ip = ifac[k1 + 1];

  1014.     int l2 = ip*l1;

  1015.     int ido = n / l2;

  1016.     switch (ip) {

  1017.       case 5: {

  1018.         int ix2 = iw + ido;

  1019.         int ix3 = ix2 + ido;

  1020.         int ix4 = ix3 + ido;

  1021.         radb5_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);

  1022.       } break;

  1023.       case 4: {

  1024.         int ix2 = iw + ido;

  1025.         int ix3 = ix2 + ido;

  1026.         radb4_ps(ido, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3]);

  1027.       } break;

  1028.       case 3: {

  1029.         int ix2 = iw + ido;

  1030.         radb3_ps(ido, l1, in, out, &wa[iw], &wa[ix2]);

  1031.       } break;

  1032.       case 2:

  1033.         radb2_ps(ido, l1, in, out, &wa[iw]);

  1034.         break;

  1035.       default:

  1036.         assert(0);

  1037.         break;

  1038.     }

  1039.     l1 = l2;

  1040.     iw += (ip - 1)*ido;

  1041. 

  1042.     if (out == work2) {

  1043.       out = work1; in = work2;

  1044.     } else {

  1045.       out = work2; in = work1;

  1046.     }

  1047.   }

  1048.   return in; /* this is in fact the output .. */

  1049. }

  1050. 

  1051. static int decompose(int n, int *ifac, const int *ntryh) {

  1052.   int nl = n, nf = 0, i, j = 0;

  1053.   for (j=0; ntryh[j]; ++j) {

  1054.     int ntry = ntryh[j];

  1055.     while (nl != 1) {

  1056.       int nq = nl / ntry;

  1057.       int nr = nl - ntry * nq;

  1058.       if (nr == 0) {

  1059.         ifac[2+nf++] = ntry;

  1060.         nl = nq;

  1061.         if (ntry == 2 && nf != 1) {

  1062.           for (i = 2; i <= nf; ++i) {

  1063.             int ib = nf - i + 2;

  1064.             ifac[ib + 1] = ifac[ib];

  1065.           }

  1066.           ifac[2] = 2;

  1067.         }

  1068.       } else break;

  1069.     }

  1070.   }

  1071.   ifac[0] = n;

  1072.   ifac[1] = nf;  

  1073.   return nf;

  1074. }

  1075. 

  1076. 

  1077. 

  1078. static void rffti1_ps(int n, float *wa, int *ifac)

  1079. {

  1080.   static const int ntryh[] = { 4,2,3,5,0 };

  1081.   int k1, j, ii;

  1082. 

  1083.   int nf = decompose(n,ifac,ntryh);

  1084.   float argh = (2*M_PI) / n;

  1085.   int is = 0;

  1086.   int nfm1 = nf - 1;

  1087.   int l1 = 1;

  1088.   for (k1 = 1; k1 <= nfm1; k1++) {

  1089.     int ip = ifac[k1 + 1];

  1090.     int ld = 0;

  1091.     int l2 = l1*ip;

  1092.     int ido = n / l2;

  1093.     int ipm = ip - 1;

  1094.     for (j = 1; j <= ipm; ++j) {

  1095.       float argld;

  1096.       int i = is, fi=0;

  1097.       ld += l1;

  1098.       argld = ld*argh;

  1099.       for (ii = 3; ii <= ido; ii += 2) {

  1100.         i += 2;

  1101.         fi += 1;

  1102.         wa[i - 2] = cos(fi*argld);

  1103.         wa[i - 1] = sin(fi*argld);

  1104.       }

  1105.       is += ido;

  1106.     }

  1107.     l1 = l2;

  1108.   }

  1109. } /* rffti1 */

  1110. 

  1111. void cffti1_ps(int n, float *wa, int *ifac)

  1112. {

  1113.   static const int ntryh[] = { 5,3,4,2,0 };

  1114.   int k1, j, ii;

  1115. 

  1116.   int nf = decompose(n,ifac,ntryh);

  1117.   float argh = (2*M_PI)/(float)n;

  1118.   int i = 1;

  1119.   int l1 = 1;

  1120.   for (k1=1; k1<=nf; k1++) {

  1121.     int ip = ifac[k1+1];

  1122.     int ld = 0;

  1123.     int l2 = l1*ip;

  1124.     int ido = n / l2;

  1125.     int idot = ido + ido + 2;

  1126.     int ipm = ip - 1;

  1127.     for (j=1; j<=ipm; j++) {

  1128.       float argld;

  1129.       int i1 = i, fi = 0;

  1130.       wa[i-1] = 1;

  1131.       wa[i] = 0;

  1132.       ld += l1;

  1133.       argld = ld*argh;

  1134.       for (ii = 4; ii <= idot; ii += 2) {

  1135.         i += 2;

  1136.         fi += 1;

  1137.         wa[i-1] = cos(fi*argld);

  1138.         wa[i] = sin(fi*argld);

  1139.       }

  1140.       if (ip > 5) {

  1141.         wa[i1-1] = wa[i-1];

  1142.         wa[i1] = wa[i];

  1143.       }

  1144.     }

  1145.     l1 = l2;

  1146.   }

  1147. } /* cffti1 */

  1148. 

  1149. 

  1150. v4sf *cfftf1_ps(int n, const v4sf *input_readonly, v4sf *work1, v4sf *work2, const float *wa, const int *ifac, int isign) {

  1151.   v4sf *in  = (v4sf*)input_readonly;

  1152.   v4sf *out = (in == work2 ? work1 : work2); 

  1153.   int nf = ifac[1], k1;

  1154.   int l1 = 1;

  1155.   int iw = 0;

  1156.   assert(in != out && work1 != work2);

  1157.   for (k1=2; k1<=nf+1; k1++) {

  1158.     int ip = ifac[k1];

  1159.     int l2 = ip*l1;

  1160.     int ido = n / l2;

  1161.     int idot = ido + ido;

  1162.     switch (ip) {

  1163.       case 5: {

  1164.         int ix2 = iw + idot;

  1165.         int ix3 = ix2 + idot;

  1166.         int ix4 = ix3 + idot;

  1167.         passf5_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);

  1168.       } break;

  1169.       case 4: {

  1170.         int ix2 = iw + idot;

  1171.         int ix3 = ix2 + idot;

  1172.         passf4_ps(idot, l1, in, out, &wa[iw], &wa[ix2], &wa[ix3], isign);

  1173.       } break;

  1174.       case 2: {

  1175.         passf2_ps(idot, l1, in, out, &wa[iw], isign);

  1176.       } break;

  1177.       case 3: {

  1178.         int ix2 = iw + idot;

  1179.         passf3_ps(idot, l1, in, out, &wa[iw], &wa[ix2], isign);

  1180.       } break;

  1181.       default:

  1182.         assert(0);

  1183.     }

  1184.     l1 = l2;

  1185.     iw += (ip - 1)*idot;

  1186.     if (out == work2) {

  1187.       out = work1; in = work2;

  1188.     } else {

  1189.       out = work2; in = work1;

  1190.     }

  1191.   }

  1192. 

  1193.   return in; /* this is in fact the output .. */

  1194. }

  1195. 

  1196. 

  1197. struct PFFFT_Setup {

  1198.   int     N;

  1199.   int     Ncvec; // nb of complex simd vectors (N/4 if PFFFT_COMPLEX, N/8 if PFFFT_REAL)

  1200.   int ifac[15];

  1201.   pffft_transform_t transform;

  1202.   v4sf *data; // allocated room for twiddle coefs

  1203.   float *e;    // points into 'data' , N/4*3 elements

  1204.   float *twiddle; // points into 'data', N/4 elements

  1205. };

  1206. 

  1207. PFFFT_Setup *pffft_new_setup(int N, pffft_transform_t transform) {

  1208.   PFFFT_Setup *s = (PFFFT_Setup*)malloc(sizeof(PFFFT_Setup));

  1209.   int k, m;

  1210.   /* unfortunately, the fft size must be a multiple of 16 for complex FFTs 

  1211.      and 32 for real FFTs -- a lot of stuff would need to be rewritten to

  1212.      handle other cases (or maybe just switch to a scalar fft, I don't know..) */

  1213.   if (transform == PFFFT_REAL) { assert((N%(2*SIMD_SZ*SIMD_SZ))==0 && N>0); }

  1214.   if (transform == PFFFT_COMPLEX) { assert((N%(SIMD_SZ*SIMD_SZ))==0 && N>0); }

  1215.   //assert((N % 32) == 0);

  1216.   s->N = N;

  1217.   s->transform = transform;  

  1218.   /* nb of complex simd vectors */

  1219.   s->Ncvec = (transform == PFFFT_REAL ? N/2 : N)/SIMD_SZ;

  1220.   s->data = (v4sf*)pffft_aligned_malloc(2*s->Ncvec * sizeof(v4sf));

  1221.   s->e = (float*)s->data;

  1222.   s->twiddle = (float*)(s->data + (2*s->Ncvec*(SIMD_SZ-1))/SIMD_SZ);  

  1223. 

  1224.   if (transform == PFFFT_REAL) {

  1225.     for (k=0; k < s->Ncvec; ++k) {

  1226.       int i = k/SIMD_SZ;

  1227.       int j = k%SIMD_SZ;

  1228.       for (m=0; m < SIMD_SZ-1; ++m) {

  1229.         float A = -2*M_PI*(m+1)*k / N;

  1230.         s->e[(2*(i*3 + m) + 0) * SIMD_SZ + j] = cos(A);

  1231.         s->e[(2*(i*3 + m) + 1) * SIMD_SZ + j] = sin(A);

  1232.       }

  1233.     }

  1234.     rffti1_ps(N/SIMD_SZ, s->twiddle, s->ifac);

  1235.   } else {

  1236.     for (k=0; k < s->Ncvec; ++k) {

  1237.       int i = k/SIMD_SZ;

  1238.       int j = k%SIMD_SZ;

  1239.       for (m=0; m < SIMD_SZ-1; ++m) {

  1240.         float A = -2*M_PI*(m+1)*k / N;

  1241.         s->e[(2*(i*3 + m) + 0)*SIMD_SZ + j] = cos(A);

  1242.         s->e[(2*(i*3 + m) + 1)*SIMD_SZ + j] = sin(A);

  1243.       }

  1244.     }

  1245.     cffti1_ps(N/SIMD_SZ, s->twiddle, s->ifac);

  1246.   }

  1247. 

  1248.   /* check that N is decomposable with allowed prime factors */

  1249.   for (k=0, m=1; k < s->ifac[1]; ++k) { m *= s->ifac[2+k]; }

  1250.   if (m != N/SIMD_SZ) {

  1251.     pffft_destroy_setup(s); s = 0;

  1252.   }

  1253. 

  1254.   return s;

  1255. }

  1256. 

  1257. 

  1258. void pffft_destroy_setup(PFFFT_Setup *s) {

  1259.   pffft_aligned_free(s->data);

  1260.   free(s);

  1261. }

  1262. 

  1263. #if !defined(PFFFT_SIMD_DISABLE)

  1264. 

  1265. /* [0 0 1 2 3 4 5 6 7 8] -> [0 8 7 6 5 4 3 2 1] */

  1266. static void reversed_copy(int N, const v4sf *in, int in_stride, v4sf *out) {

  1267.   v4sf g0, g1;

  1268.   int k;

  1269.   INTERLEAVE2(in[0], in[1], g0, g1); in += in_stride;

  1270.   

  1271.   *--out = VSWAPHL(g0, g1); // [g0l, g0h], [g1l g1h] -> [g1l, g0h]

  1272.   for (k=1; k < N; ++k) {

  1273.     v4sf h0, h1;

  1274.     INTERLEAVE2(in[0], in[1], h0, h1); in += in_stride;

  1275.     *--out = VSWAPHL(g1, h0);

  1276.     *--out = VSWAPHL(h0, h1);

  1277.     g1 = h1;

  1278.   }

  1279.   *--out = VSWAPHL(g1, g0);

  1280. }

  1281. 

  1282. static void unreversed_copy(int N, const v4sf *in, v4sf *out, int out_stride) {

  1283.   v4sf g0, g1, h0, h1;

  1284.   int k;

  1285.   g0 = g1 = in[0]; ++in;

  1286.   for (k=1; k < N; ++k) {

  1287.     h0 = *in++; h1 = *in++;

  1288.     g1 = VSWAPHL(g1, h0);

  1289.     h0 = VSWAPHL(h0, h1);

  1290.     UNINTERLEAVE2(h0, g1, out[0], out[1]); out += out_stride;

  1291.     g1 = h1;

  1292.   }

  1293.   h0 = *in++; h1 = g0;

  1294.   g1 = VSWAPHL(g1, h0);

  1295.   h0 = VSWAPHL(h0, h1);

  1296.   UNINTERLEAVE2(h0, g1, out[0], out[1]);

  1297. }

  1298. 

  1299. void pffft_zreorder(PFFFT_Setup *setup, const float *in, float *out, pffft_direction_t direction) {

  1300.   int k, N = setup->N, Ncvec = setup->Ncvec;

  1301.   const v4sf *vin = (const v4sf*)in;

  1302.   v4sf *vout = (v4sf*)out;

  1303.   assert(in != out);

  1304.   if (setup->transform == PFFFT_REAL) {

  1305.     int k, dk = N/32;

  1306.     if (direction == PFFFT_FORWARD) {

  1307.       for (k=0; k < dk; ++k) {

  1308.         INTERLEAVE2(vin[k*8 + 0], vin[k*8 + 1], vout[2*(0*dk + k) + 0], vout[2*(0*dk + k) + 1]);

  1309.         INTERLEAVE2(vin[k*8 + 4], vin[k*8 + 5], vout[2*(2*dk + k) + 0], vout[2*(2*dk + k) + 1]);

  1310.       }

  1311.       reversed_copy(dk, vin+2, 8, (v4sf*)(out + N/2));

  1312.       reversed_copy(dk, vin+6, 8, (v4sf*)(out + N));

  1313.     } else {

  1314.       for (k=0; k < dk; ++k) {

  1315.         UNINTERLEAVE2(vin[2*(0*dk + k) + 0], vin[2*(0*dk + k) + 1], vout[k*8 + 0], vout[k*8 + 1]);

  1316.         UNINTERLEAVE2(vin[2*(2*dk + k) + 0], vin[2*(2*dk + k) + 1], vout[k*8 + 4], vout[k*8 + 5]);

  1317.       }

  1318.       unreversed_copy(dk, (v4sf*)(in + N/4), (v4sf*)(out + N - 6*SIMD_SZ), -8);

  1319.       unreversed_copy(dk, (v4sf*)(in + 3*N/4), (v4sf*)(out + N - 2*SIMD_SZ), -8);

  1320.     }

  1321.   } else {

  1322.     if (direction == PFFFT_FORWARD) {

  1323.       for (k=0; k < Ncvec; ++k) { 

  1324.         int kk = (k/4) + (k%4)*(Ncvec/4);

  1325.         INTERLEAVE2(vin[k*2], vin[k*2+1], vout[kk*2], vout[kk*2+1]);

  1326.       }

  1327.     } else {

  1328.       for (k=0; k < Ncvec; ++k) { 

  1329.         int kk = (k/4) + (k%4)*(Ncvec/4);

  1330.         UNINTERLEAVE2(vin[kk*2], vin[kk*2+1], vout[k*2], vout[k*2+1]);

  1331.       }

  1332.     }

  1333.   }

  1334. }

  1335. 

  1336. void pffft_cplx_finalize(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {

  1337.   int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks

  1338.   v4sf r0, i0, r1, i1, r2, i2, r3, i3;

  1339.   v4sf sr0, dr0, sr1, dr1, si0, di0, si1, di1;

  1340.   assert(in != out);

  1341.   for (k=0; k < dk; ++k) {    

  1342.     r0 = in[8*k+0]; i0 = in[8*k+1];

  1343.     r1 = in[8*k+2]; i1 = in[8*k+3];

  1344.     r2 = in[8*k+4]; i2 = in[8*k+5];

  1345.     r3 = in[8*k+6]; i3 = in[8*k+7];

  1346.     VTRANSPOSE4(r0,r1,r2,r3);

  1347.     VTRANSPOSE4(i0,i1,i2,i3);

  1348.     VCPLXMUL(r1,i1,e[k*6+0],e[k*6+1]);

  1349.     VCPLXMUL(r2,i2,e[k*6+2],e[k*6+3]);

  1350.     VCPLXMUL(r3,i3,e[k*6+4],e[k*6+5]);

  1351. 

  1352.     sr0 = VADD(r0,r2); dr0 = VSUB(r0, r2);

  1353.     sr1 = VADD(r1,r3); dr1 = VSUB(r1, r3);

  1354.     si0 = VADD(i0,i2); di0 = VSUB(i0, i2);

  1355.     si1 = VADD(i1,i3); di1 = VSUB(i1, i3);

  1356. 

  1357.     /*

  1358.       transformation for each column is:

  1359.       

  1360.       [1   1   1   1   0   0   0   0]   [r0]

  1361.       [1   0  -1   0   0  -1   0   1]   [r1]

  1362.       [1  -1   1  -1   0   0   0   0]   [r2]

  1363.       [1   0  -1   0   0   1   0  -1]   [r3]

  1364.       [0   0   0   0   1   1   1   1] * [i0]

  1365.       [0   1   0  -1   1   0  -1   0]   [i1]

  1366.       [0   0   0   0   1  -1   1  -1]   [i2]

  1367.       [0  -1   0   1   1   0  -1   0]   [i3]    

  1368.     */

  1369.     

  1370.     r0 = VADD(sr0, sr1); i0 = VADD(si0, si1);

  1371.     r1 = VADD(dr0, di1); i1 = VSUB(di0, dr1);

  1372.     r2 = VSUB(sr0, sr1); i2 = VSUB(si0, si1);

  1373.     r3 = VSUB(dr0, di1); i3 = VADD(di0, dr1);

  1374.   

  1375.     *out++ = r0; *out++ = i0; *out++ = r1; *out++ = i1;

  1376.     *out++ = r2; *out++ = i2; *out++ = r3; *out++ = i3;

  1377.   }

  1378. }

  1379. 

  1380. void pffft_cplx_preprocess(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {

  1381.   int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks

  1382.   v4sf r0, i0, r1, i1, r2, i2, r3, i3;

  1383.   v4sf sr0, dr0, sr1, dr1, si0, di0, si1, di1;

  1384.   assert(in != out);

  1385.   for (k=0; k < dk; ++k) {    

  1386.     r0 = in[8*k+0]; i0 = in[8*k+1];

  1387.     r1 = in[8*k+2]; i1 = in[8*k+3];

  1388.     r2 = in[8*k+4]; i2 = in[8*k+5];

  1389.     r3 = in[8*k+6]; i3 = in[8*k+7];

  1390. 

  1391.     sr0 = VADD(r0,r2); dr0 = VSUB(r0, r2);

  1392.     sr1 = VADD(r1,r3); dr1 = VSUB(r1, r3);

  1393.     si0 = VADD(i0,i2); di0 = VSUB(i0, i2);

  1394.     si1 = VADD(i1,i3); di1 = VSUB(i1, i3);

  1395. 

  1396.     r0 = VADD(sr0, sr1); i0 = VADD(si0, si1);

  1397.     r1 = VSUB(dr0, di1); i1 = VADD(di0, dr1);

  1398.     r2 = VSUB(sr0, sr1); i2 = VSUB(si0, si1);

  1399.     r3 = VADD(dr0, di1); i3 = VSUB(di0, dr1);

  1400. 

  1401.     VCPLXMULCONJ(r1,i1,e[k*6+0],e[k*6+1]);

  1402.     VCPLXMULCONJ(r2,i2,e[k*6+2],e[k*6+3]);

  1403.     VCPLXMULCONJ(r3,i3,e[k*6+4],e[k*6+5]);

  1404. 

  1405.     VTRANSPOSE4(r0,r1,r2,r3);

  1406.     VTRANSPOSE4(i0,i1,i2,i3);

  1407. 

  1408.     *out++ = r0; *out++ = i0; *out++ = r1; *out++ = i1;

  1409.     *out++ = r2; *out++ = i2; *out++ = r3; *out++ = i3;

  1410.   }

  1411. }

  1412. 

  1413. 

  1414. static ALWAYS_INLINE(void) pffft_real_finalize_4x4(const v4sf *in0, const v4sf *in1, const v4sf *in,

  1415.                             const v4sf *e, v4sf *out) {

  1416.   v4sf r0, i0, r1, i1, r2, i2, r3, i3;

  1417.   v4sf sr0, dr0, sr1, dr1, si0, di0, si1, di1;

  1418.   r0 = *in0; i0 = *in1;

  1419.   r1 = *in++; i1 = *in++; r2 = *in++; i2 = *in++; r3 = *in++; i3 = *in++;

  1420.   VTRANSPOSE4(r0,r1,r2,r3);

  1421.   VTRANSPOSE4(i0,i1,i2,i3);

  1422.  

  1423.   /*

  1424.     transformation for each column is:

  1425. 

  1426.     [1   1   1   1   0   0   0   0]   [r0]

  1427.     [1   0  -1   0   0  -1   0   1]   [r1]

  1428.     [1   0  -1   0   0   1   0  -1]   [r2]

  1429.     [1  -1   1  -1   0   0   0   0]   [r3]

  1430.     [0   0   0   0   1   1   1   1] * [i0]

  1431.     [0  -1   0   1  -1   0   1   0]   [i1]

  1432.     [0  -1   0   1   1   0  -1   0]   [i2]

  1433.     [0   0   0   0  -1   1  -1   1]   [i3]    

  1434.   */

  1435.   

  1436.   //cerr << "matrix initial, before e , REAL:\n 1: " << r0 << "\n 1: " << r1 << "\n 1: " << r2 << "\n 1: " << r3 << "\n";

  1437.   //cerr << "matrix initial, before e, IMAG :\n 1: " << i0 << "\n 1: " << i1 << "\n 1: " << i2 << "\n 1: " << i3 << "\n";

  1438. 

  1439.   VCPLXMUL(r1,i1,e[0],e[1]);

  1440.   VCPLXMUL(r2,i2,e[2],e[3]);

  1441.   VCPLXMUL(r3,i3,e[4],e[5]);

  1442. 

  1443.   //cerr << "matrix initial, real part:\n 1: " << r0 << "\n 1: " << r1 << "\n 1: " << r2 << "\n 1: " << r3 << "\n";

  1444.   //cerr << "matrix initial, imag part:\n 1: " << i0 << "\n 1: " << i1 << "\n 1: " << i2 << "\n 1: " << i3 << "\n";

  1445. 

  1446.   sr0 = VADD(r0,r2); dr0 = VSUB(r0,r2); 

  1447.   sr1 = VADD(r1,r3); dr1 = VSUB(r3,r1);

  1448.   si0 = VADD(i0,i2); di0 = VSUB(i0,i2); 

  1449.   si1 = VADD(i1,i3); di1 = VSUB(i3,i1);

  1450. 

  1451.   r0 = VADD(sr0, sr1);

  1452.   r3 = VSUB(sr0, sr1);

  1453.   i0 = VADD(si0, si1);

  1454.   i3 = VSUB(si1, si0);

  1455.   r1 = VADD(dr0, di1);

  1456.   r2 = VSUB(dr0, di1);

  1457.   i1 = VSUB(dr1, di0);

  1458.   i2 = VADD(dr1, di0);

  1459. 

  1460.   *out++ = r0;

  1461.   *out++ = i0;

  1462.   *out++ = r1;

  1463.   *out++ = i1;

  1464.   *out++ = r2;

  1465.   *out++ = i2;

  1466.   *out++ = r3;

  1467.   *out++ = i3;

  1468. 

  1469. }

  1470. 

  1471. static NEVER_INLINE(void) pffft_real_finalize(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {

  1472.   int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks

  1473.   /* fftpack order is f0r f1r f1i f2r f2i ... f(n-1)r f(n-1)i f(n)r */

  1474. 

  1475.   v4sf_union cr, ci, *uout = (v4sf_union*)out;

  1476.   v4sf save = in[7], zero=VZERO();

  1477.   float xr0, xi0, xr1, xi1, xr2, xi2, xr3, xi3;

  1478.   static const float s = M_SQRT2/2;

  1479. 

  1480.   cr.v = in[0]; ci.v = in[Ncvec*2-1];

  1481.   assert(in != out);

  1482.   pffft_real_finalize_4x4(&zero, &zero, in+1, e, out);

  1483. 

  1484.   /*

  1485.     [cr0 cr1 cr2 cr3 ci0 ci1 ci2 ci3]

  1486. 

  1487.     [Xr(1)]  ] [1   1   1   1   0   0   0   0]

  1488.     [Xr(N/4) ] [0   0   0   0   1   s   0  -s]

  1489.     [Xr(N/2) ] [1   0  -1   0   0   0   0   0]

  1490.     [Xr(3N/4)] [0   0   0   0   1  -s   0   s]

  1491.     [Xi(1)   ] [1  -1   1  -1   0   0   0   0]

  1492.     [Xi(N/4) ] [0   0   0   0   0  -s  -1  -s]

  1493.     [Xi(N/2) ] [0  -1   0   1   0   0   0   0]

  1494.     [Xi(3N/4)] [0   0   0   0   0  -s   1  -s]

  1495.   */

  1496. 

  1497.   xr0=(cr.f[0]+cr.f[2]) + (cr.f[1]+cr.f[3]); uout[0].f[0] = xr0;

  1498.   xi0=(cr.f[0]+cr.f[2]) - (cr.f[1]+cr.f[3]); uout[1].f[0] = xi0;

  1499.   xr2=(cr.f[0]-cr.f[2]);                     uout[4].f[0] = xr2;

  1500.   xi2=(cr.f[3]-cr.f[1]);                     uout[5].f[0] = xi2;

  1501.   xr1= ci.f[0] + s*(ci.f[1]-ci.f[3]);        uout[2].f[0] = xr1;

  1502.   xi1=-ci.f[2] - s*(ci.f[1]+ci.f[3]);        uout[3].f[0] = xi1;

  1503.   xr3= ci.f[0] - s*(ci.f[1]-ci.f[3]);        uout[6].f[0] = xr3;

  1504.   xi3= ci.f[2] - s*(ci.f[1]+ci.f[3]);        uout[7].f[0] = xi3; 

  1505. 

  1506.   for (k=1; k < dk; ++k) {

  1507.     v4sf save_next = in[8*k+7];

  1508.     pffft_real_finalize_4x4(&save, &in[8*k+0], in + 8*k+1,

  1509.                            e + k*6, out + k*8);

  1510.     save = save_next;

  1511.   }

  1512. 

  1513. }

  1514. 

  1515. static ALWAYS_INLINE(void) pffft_real_preprocess_4x4(const v4sf *in, 

  1516.                                              const v4sf *e, v4sf *out, int first) {

  1517.   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];

  1518.   /*

  1519.     transformation for each column is:

  1520. 

  1521.     [1   1   1   1   0   0   0   0]   [r0]

  1522.     [1   0   0  -1   0  -1  -1   0]   [r1]

  1523.     [1  -1  -1   1   0   0   0   0]   [r2]

  1524.     [1   0   0  -1   0   1   1   0]   [r3]

  1525.     [0   0   0   0   1  -1   1  -1] * [i0]

  1526.     [0  -1   1   0   1   0   0   1]   [i1]

  1527.     [0   0   0   0   1   1  -1  -1]   [i2]

  1528.     [0   1  -1   0   1   0   0   1]   [i3]    

  1529.   */

  1530. 

  1531.   v4sf sr0 = VADD(r0,r3), dr0 = VSUB(r0,r3); 

  1532.   v4sf sr1 = VADD(r1,r2), dr1 = VSUB(r1,r2);

  1533.   v4sf si0 = VADD(i0,i3), di0 = VSUB(i0,i3); 

  1534.   v4sf si1 = VADD(i1,i2), di1 = VSUB(i1,i2);

  1535. 

  1536.   r0 = VADD(sr0, sr1);

  1537.   r2 = VSUB(sr0, sr1);

  1538.   r1 = VSUB(dr0, si1);

  1539.   r3 = VADD(dr0, si1);

  1540.   i0 = VSUB(di0, di1);

  1541.   i2 = VADD(di0, di1);

  1542.   i1 = VSUB(si0, dr1);

  1543.   i3 = VADD(si0, dr1);

  1544. 

  1545.   VCPLXMULCONJ(r1,i1,e[0],e[1]);

  1546.   VCPLXMULCONJ(r2,i2,e[2],e[3]);

  1547.   VCPLXMULCONJ(r3,i3,e[4],e[5]);

  1548. 

  1549.   VTRANSPOSE4(r0,r1,r2,r3);

  1550.   VTRANSPOSE4(i0,i1,i2,i3);

  1551. 

  1552.   if (!first) {

  1553.     *out++ = r0;

  1554.     *out++ = i0;

  1555.   }

  1556.   *out++ = r1;

  1557.   *out++ = i1;

  1558.   *out++ = r2;

  1559.   *out++ = i2;

  1560.   *out++ = r3;

  1561.   *out++ = i3;

  1562. }

  1563. 

  1564. static NEVER_INLINE(void) pffft_real_preprocess(int Ncvec, const v4sf *in, v4sf *out, const v4sf *e) {

  1565.   int k, dk = Ncvec/SIMD_SZ; // number of 4x4 matrix blocks

  1566.   /* fftpack order is f0r f1r f1i f2r f2i ... f(n-1)r f(n-1)i f(n)r */

  1567. 

  1568.   v4sf_union Xr, Xi, *uout = (v4sf_union*)out;

  1569.   float cr0, ci0, cr1, ci1, cr2, ci2, cr3, ci3;

  1570.   static const float s = M_SQRT2;

  1571.   assert(in != out);

  1572.   for (k=0; k < 4; ++k) {

  1573.     Xr.f[k] = ((float*)in)[8*k];

  1574.     Xi.f[k] = ((float*)in)[8*k+4];

  1575.   }

  1576. 

  1577.   pffft_real_preprocess_4x4(in, e, out+1, 1); // will write only 6 values

  1578. 

  1579.   /*

  1580.     [Xr0 Xr1 Xr2 Xr3 Xi0 Xi1 Xi2 Xi3]

  1581. 

  1582.     [cr0] [1   0   2   0   1   0   0   0]

  1583.     [cr1] [1   0   0   0  -1   0  -2   0]

  1584.     [cr2] [1   0  -2   0   1   0   0   0]

  1585.     [cr3] [1   0   0   0  -1   0   2   0]

  1586.     [ci0] [0   2   0   2   0   0   0   0]

  1587.     [ci1] [0   s   0  -s   0  -s   0  -s]

  1588.     [ci2] [0   0   0   0   0  -2   0   2]

  1589.     [ci3] [0  -s   0   s   0  -s   0  -s]

  1590.   */

  1591.   for (k=1; k < dk; ++k) {    

  1592.     pffft_real_preprocess_4x4(in+8*k, e + k*6, out-1+k*8, 0);

  1593.   }

  1594. 

  1595.   cr0=(Xr.f[0]+Xi.f[0]) + 2*Xr.f[2]; uout[0].f[0] = cr0;

  1596.   cr1=(Xr.f[0]-Xi.f[0]) - 2*Xi.f[2]; uout[0].f[1] = cr1;

  1597.   cr2=(Xr.f[0]+Xi.f[0]) - 2*Xr.f[2]; uout[0].f[2] = cr2;

  1598.   cr3=(Xr.f[0]-Xi.f[0]) + 2*Xi.f[2]; uout[0].f[3] = cr3;

  1599.   ci0= 2*(Xr.f[1]+Xr.f[3]);                       uout[2*Ncvec-1].f[0] = ci0;

  1600.   ci1= s*(Xr.f[1]-Xr.f[3]) - s*(Xi.f[1]+Xi.f[3]); uout[2*Ncvec-1].f[1] = ci1;

  1601.   ci2= 2*(Xi.f[3]-Xi.f[1]);                       uout[2*Ncvec-1].f[2] = ci2;

  1602.   ci3=-s*(Xr.f[1]-Xr.f[3]) - s*(Xi.f[1]+Xi.f[3]); uout[2*Ncvec-1].f[3] = ci3;

  1603. }

  1604. 

  1605. 

  1606. void pffft_transform_internal(PFFFT_Setup *setup, const float *finput, float *foutput, v4sf *scratch,

  1607.                              pffft_direction_t direction, int ordered) {

  1608.   int k, Ncvec   = setup->Ncvec;

  1609.   int nf_odd = (setup->ifac[1] & 1);

  1610. 

  1611.   // temporary buffer is allocated on the stack if the scratch pointer is NULL

  1612.   int stack_allocate = (scratch == 0 ? Ncvec*2 : 1);

  1613.   VLA_ARRAY_ON_STACK(v4sf, scratch_on_stack, stack_allocate);

  1614. 

  1615.   const v4sf *vinput = (const v4sf*)finput;

  1616.   v4sf *voutput      = (v4sf*)foutput;

  1617.   v4sf *buff[2]      = { voutput, scratch ? scratch : scratch_on_stack };

  1618.   int ib = (nf_odd ^ ordered ? 1 : 0);

  1619. 

  1620.   assert(VALIGNED(finput) && VALIGNED(foutput));

  1621. 

  1622.   //assert(finput != foutput);

  1623.   if (direction == PFFFT_FORWARD) {

  1624.     ib = !ib;

  1625.     if (setup->transform == PFFFT_REAL) { 

  1626.       ib = (rfftf1_ps(Ncvec*2, vinput, buff[ib], buff[!ib],

  1627.                       setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);      

  1628.       pffft_real_finalize(Ncvec, buff[ib], buff[!ib], (v4sf*)setup->e);

  1629.     } else {

  1630.       v4sf *tmp = buff[ib];

  1631.       for (k=0; k < Ncvec; ++k) {

  1632.         UNINTERLEAVE2(vinput[k*2], vinput[k*2+1], tmp[k*2], tmp[k*2+1]);

  1633.       }

  1634.       ib = (cfftf1_ps(Ncvec, buff[ib], buff[!ib], buff[ib], 

  1635.                       setup->twiddle, &setup->ifac[0], -1) == buff[0] ? 0 : 1);

  1636.       pffft_cplx_finalize(Ncvec, buff[ib], buff[!ib], (v4sf*)setup->e);

  1637.     }

  1638.     if (ordered) {

  1639.       pffft_zreorder(setup, (float*)buff[!ib], (float*)buff[ib], PFFFT_FORWARD);       

  1640.     } else ib = !ib;

  1641.   } else {

  1642.     if (vinput == buff[ib]) { 

  1643.       ib = !ib; // may happen when finput == foutput

  1644.     }

  1645.     if (ordered) {

  1646.       pffft_zreorder(setup, (float*)vinput, (float*)buff[ib], PFFFT_BACKWARD); 

  1647.       vinput = buff[ib]; ib = !ib;

  1648.     }

  1649.     if (setup->transform == PFFFT_REAL) {

  1650.       pffft_real_preprocess(Ncvec, vinput, buff[ib], (v4sf*)setup->e);

  1651.       ib = (rfftb1_ps(Ncvec*2, buff[ib], buff[0], buff[1], 

  1652.                       setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);

  1653.     } else {

  1654.       pffft_cplx_preprocess(Ncvec, vinput, buff[ib], (v4sf*)setup->e);

  1655.       ib = (cfftf1_ps(Ncvec, buff[ib], buff[0], buff[1], 

  1656.                       setup->twiddle, &setup->ifac[0], +1) == buff[0] ? 0 : 1);

  1657.       for (k=0; k < Ncvec; ++k) {

  1658.         INTERLEAVE2(buff[ib][k*2], buff[ib][k*2+1], buff[ib][k*2], buff[ib][k*2+1]);

  1659.       }

  1660.     }

  1661.   }

  1662.   

  1663.   if (buff[ib] != voutput) {

  1664.     /* extra copy required -- this situation should only happen when finput == foutput */

  1665.     assert(finput==foutput);

  1666.     for (k=0; k < Ncvec; ++k) {

  1667.       v4sf a = buff[ib][2*k], b = buff[ib][2*k+1];

  1668.       voutput[2*k] = a; voutput[2*k+1] = b;

  1669.     }

  1670.     ib = !ib;

  1671.   }

  1672.   assert(buff[ib] == voutput);

  1673. }

  1674. 

  1675. void pffft_zconvolve_accumulate(PFFFT_Setup *s, const float *a, const float *b, float *ab, float scaling) {

  1676.   int Ncvec = s->Ncvec;

  1677.   const v4sf * RESTRICT va = (const v4sf*)a;

  1678.   const v4sf * RESTRICT vb = (const v4sf*)b;

  1679.   v4sf * RESTRICT vab = (v4sf*)ab;

  1680. 

  1681. #ifdef __arm__

  1682.   __builtin_prefetch(va);

  1683.   __builtin_prefetch(vb);

  1684.   __builtin_prefetch(vab);

  1685.   __builtin_prefetch(va+2);

  1686.   __builtin_prefetch(vb+2);

  1687.   __builtin_prefetch(vab+2);

  1688.   __builtin_prefetch(va+4);

  1689.   __builtin_prefetch(vb+4);

  1690.   __builtin_prefetch(vab+4);

  1691.   __builtin_prefetch(va+6);

  1692.   __builtin_prefetch(vb+6);

  1693.   __builtin_prefetch(vab+6);

  1694. # ifndef __clang__

  1695. #   define ZCONVOLVE_USING_INLINE_NEON_ASM

  1696. # endif

  1697. #endif

  1698. 

  1699.   float ar, ai, br, bi, abr, abi;

  1700. #ifndef ZCONVOLVE_USING_INLINE_ASM

  1701.   v4sf vscal = LD_PS1(scaling);

  1702.   int i;

  1703. #endif

  1704. 

  1705.   assert(VALIGNED(a) && VALIGNED(b) && VALIGNED(ab));

  1706.   ar = ((v4sf_union*)va)[0].f[0];

  1707.   ai = ((v4sf_union*)va)[1].f[0];

  1708.   br = ((v4sf_union*)vb)[0].f[0];

  1709.   bi = ((v4sf_union*)vb)[1].f[0];

  1710.   abr = ((v4sf_union*)vab)[0].f[0];

  1711.   abi = ((v4sf_union*)vab)[1].f[0];

  1712.  

  1713. #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

  1714.   const float *a_ = a, *b_ = b; float *ab_ = ab;

  1715.   int N = Ncvec;

  1716.   asm volatile("mov         r8, %2                  \n"

  1717.                "vdup.f32    q15, %4                 \n"

  1718.                "1:                                  \n"

  1719.                "pld         [%0,#64]                \n"

  1720.                "pld         [%1,#64]                \n"

  1721.                "pld         [%2,#64]                \n"

  1722.                "pld         [%0,#96]                \n"

  1723.                "pld         [%1,#96]                \n"

  1724.                "pld         [%2,#96]                \n"

  1725.                "vld1.f32    {q0,q1},   [%0,:128]!         \n"

  1726.                "vld1.f32    {q4,q5},   [%1,:128]!         \n"

  1727.                "vld1.f32    {q2,q3},   [%0,:128]!         \n"

  1728.                "vld1.f32    {q6,q7},   [%1,:128]!         \n"

  1729.                "vld1.f32    {q8,q9},   [r8,:128]!          \n"

  1730.                

  1731.                "vmul.f32    q10, q0, q4             \n"

  1732.                "vmul.f32    q11, q0, q5             \n"

  1733.                "vmul.f32    q12, q2, q6             \n" 

  1734.                "vmul.f32    q13, q2, q7             \n"                 

  1735.                "vmls.f32    q10, q1, q5             \n"

  1736.                "vmla.f32    q11, q1, q4             \n"

  1737.                "vld1.f32    {q0,q1}, [r8,:128]!     \n"

  1738.                "vmls.f32    q12, q3, q7             \n"

  1739.                "vmla.f32    q13, q3, q6             \n"

  1740.                "vmla.f32    q8, q10, q15            \n"

  1741.                "vmla.f32    q9, q11, q15            \n"

  1742.                "vmla.f32    q0, q12, q15            \n"

  1743.                "vmla.f32    q1, q13, q15            \n"

  1744.                "vst1.f32    {q8,q9},[%2,:128]!    \n"

  1745.                "vst1.f32    {q0,q1},[%2,:128]!    \n"

  1746.                "subs        %3, #2                  \n"

  1747.                "bne         1b                      \n"

  1748.                : "+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");

  1749. #else // default routine, works fine for non-arm cpus with current compilers

  1750.   for (i=0; i < Ncvec; i += 2) {

  1751.     v4sf ar, ai, br, bi;

  1752.     ar = va[2*i+0]; ai = va[2*i+1];

  1753.     br = vb[2*i+0]; bi = vb[2*i+1];

  1754.     VCPLXMUL(ar, ai, br, bi);

  1755.     vab[2*i+0] = VMADD(ar, vscal, vab[2*i+0]);

  1756.     vab[2*i+1] = VMADD(ai, vscal, vab[2*i+1]);

  1757.     ar = va[2*i+2]; ai = va[2*i+3];

  1758.     br = vb[2*i+2]; bi = vb[2*i+3];

  1759.     VCPLXMUL(ar, ai, br, bi);

  1760.     vab[2*i+2] = VMADD(ar, vscal, vab[2*i+2]);

  1761.     vab[2*i+3] = VMADD(ai, vscal, vab[2*i+3]);

  1762.   }

  1763. #endif

  1764.   if (s->transform == PFFFT_REAL) {

  1765.     ((v4sf_union*)vab)[0].f[0] = abr + ar*br*scaling;

  1766.     ((v4sf_union*)vab)[1].f[0] = abi + ai*bi*scaling;

  1767.   }

  1768. }

  1769. 

  1770. 

  1771. #else // defined(PFFFT_SIMD_DISABLE)

  1772. 

  1773. // standard routine using scalar floats, without SIMD stuff.

  1774. 

  1775. #define pffft_zreorder_nosimd pffft_zreorder

  1776. void pffft_zreorder_nosimd(PFFFT_Setup *setup, const float *in, float *out, pffft_direction_t direction) {

  1777.   int k, N = setup->N;

  1778.   if (setup->transform == PFFFT_COMPLEX) {

  1779.     for (k=0; k < 2*N; ++k) out[k] = in[k];

  1780.     return;

  1781.   }

  1782.   else if (direction == PFFFT_FORWARD) {

  1783.     float x_N = in[N-1];

  1784.     for (k=N-1; k > 1; --k) out[k] = in[k-1]; 

  1785.     out[0] = in[0];

  1786.     out[1] = x_N;

  1787.   } else {

  1788.     float x_N = in[1];

  1789.     for (k=1; k < N-1; ++k) out[k] = in[k+1]; 

  1790.     out[0] = in[0];

  1791.     out[N-1] = x_N;

  1792.   }

  1793. }

  1794. 

  1795. #define pffft_transform_internal_nosimd pffft_transform_internal

  1796. void pffft_transform_internal_nosimd(PFFFT_Setup *setup, const float *input, float *output, float *scratch,

  1797.                                     pffft_direction_t direction, int ordered) {

  1798.   int Ncvec   = setup->Ncvec;

  1799.   int nf_odd = (setup->ifac[1] & 1);

  1800. 

  1801.   // temporary buffer is allocated on the stack if the scratch pointer is NULL

  1802.   int stack_allocate = (scratch == 0 ? Ncvec*2 : 1);

  1803.   VLA_ARRAY_ON_STACK(v4sf, scratch_on_stack, stack_allocate);

  1804.   float *buff[2];

  1805.   int ib;

  1806.   if (scratch == 0) scratch = scratch_on_stack;

  1807.   buff[0] = output; buff[1] = scratch;

  1808. 

  1809.   if (setup->transform == PFFFT_COMPLEX) ordered = 0; // it is always ordered.

  1810.   ib = (nf_odd ^ ordered ? 1 : 0);

  1811. 

  1812.   if (direction == PFFFT_FORWARD) {

  1813.     if (setup->transform == PFFFT_REAL) { 

  1814.       ib = (rfftf1_ps(Ncvec*2, input, buff[ib], buff[!ib],

  1815.                       setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);      

  1816.     } else {

  1817.       ib = (cfftf1_ps(Ncvec, input, buff[ib], buff[!ib], 

  1818.                       setup->twiddle, &setup->ifac[0], -1) == buff[0] ? 0 : 1);

  1819.     }

  1820.     if (ordered) {

  1821.       pffft_zreorder(setup, buff[ib], buff[!ib], PFFFT_FORWARD); ib = !ib;

  1822.     }

  1823.   } else {    

  1824.     if (input == buff[ib]) { 

  1825.       ib = !ib; // may happen when finput == foutput

  1826.     }

  1827.     if (ordered) {

  1828.       pffft_zreorder(setup, input, buff[!ib], PFFFT_BACKWARD); 

  1829.       input = buff[!ib];

  1830.     }

  1831.     if (setup->transform == PFFFT_REAL) {

  1832.       ib = (rfftb1_ps(Ncvec*2, input, buff[ib], buff[!ib], 

  1833.                       setup->twiddle, &setup->ifac[0]) == buff[0] ? 0 : 1);

  1834.     } else {

  1835.       ib = (cfftf1_ps(Ncvec, input, buff[ib], buff[!ib], 

  1836.                       setup->twiddle, &setup->ifac[0], +1) == buff[0] ? 0 : 1);

  1837.     }

  1838.   }

  1839.   if (buff[ib] != output) {

  1840.     int k;

  1841.     // extra copy required -- this situation should happens only when finput == foutput

  1842.     assert(input==output);

  1843.     for (k=0; k < Ncvec; ++k) {

  1844.       float a = buff[ib][2*k], b = buff[ib][2*k+1];

  1845.       output[2*k] = a; output[2*k+1] = b;

  1846.     }

  1847.     ib = !ib;

  1848.   }

  1849.   assert(buff[ib] == output);

  1850. }

  1851. 

  1852. #define pffft_zconvolve_accumulate_nosimd pffft_zconvolve_accumulate

  1853. void pffft_zconvolve_accumulate_nosimd(PFFFT_Setup *s, const float *a, const float *b,

  1854.                                        float *ab, float scaling) {

  1855.   int i, Ncvec = s->Ncvec;

  1856. 

  1857.   if (s->transform == PFFFT_REAL) {

  1858.     // take care of the fftpack ordering

  1859.     ab[0] += a[0]*b[0]*scaling;

  1860.     ab[2*Ncvec-1] += a[2*Ncvec-1]*b[2*Ncvec-1]*scaling;

  1861.     ++ab; ++a; ++b; --Ncvec;

  1862.   }

  1863.   for (i=0; i < Ncvec; ++i) {

  1864.     float ar, ai, br, bi;

  1865.     ar = a[2*i+0]; ai = a[2*i+1];

  1866.     br = b[2*i+0]; bi = b[2*i+1];

  1867.     VCPLXMUL(ar, ai, br, bi);

  1868.     ab[2*i+0] += ar*scaling;

  1869.     ab[2*i+1] += ai*scaling;

  1870.   }

  1871. }

  1872. 

  1873. #endif // defined(PFFFT_SIMD_DISABLE)

  1874. 

  1875. void pffft_transform(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction) {

  1876.   pffft_transform_internal(setup, input, output, (v4sf*)work, direction, 0);

  1877. }

  1878. 

  1879. void pffft_transform_ordered(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction) {

  1880.   pffft_transform_internal(setup, input, output, (v4sf*)work, direction, 1);

  1881. }