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|
/* ntt_gfp.c - low-level radix-2 dif/dit ntt routines over GF(p)
Copyright 2005, 2006, 2007, 2008, 2009 Dave Newman, Jason Papadopoulos,
Brian Gladman, Alexander Kruppa, Paul Zimmermann.
The SP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The SP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the SP Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include "sp.h"
#include "ecm-impl.h"
/*--------------------------- FORWARD NTT --------------------------------*/
static void bfly_dif(spv_t x0, spv_t x1, spv_t w,
spv_size_t len, sp_t p, sp_t d)
{
spv_size_t i = 0;
#if (defined(__GNUC__) || defined(__ICL)) && \
defined(__i386__) && defined(HAVE_SSE2)
asm volatile (
"movd %6, %%xmm6 \n\t"
"pshufd $0x44, %%xmm6, %%xmm5 \n\t"
"pshufd $0, %%xmm6, %%xmm6 \n\t"
"movd %7, %%xmm7 \n\t"
"pshufd $0, %%xmm7, %%xmm7 \n\t"
"0: \n\t"
"movdqa (%1,%4,4), %%xmm0 \n\t"
"movdqa (%2,%4,4), %%xmm1 \n\t"
"movdqa %%xmm1, %%xmm2 \n\t"
"paddd %%xmm0, %%xmm1 \n\t"
"psubd %%xmm2, %%xmm0 \n\t"
"psubd %%xmm6, %%xmm1 \n\t"
"pxor %%xmm2, %%xmm2 \n\t"
"pcmpgtd %%xmm1, %%xmm2 \n\t"
"pand %%xmm6, %%xmm2 \n\t"
"paddd %%xmm2, %%xmm1 \n\t"
"movdqa %%xmm1, (%1,%4,4) \n\t"
"pxor %%xmm2, %%xmm2 \n\t"
"pcmpgtd %%xmm0, %%xmm2 \n\t"
"pand %%xmm6, %%xmm2 \n\t"
"paddd %%xmm2, %%xmm0 \n\t"
"movdqa (%3,%4,4), %%xmm2 \n\t"
"addl $4, %4 \n\t" /* INC */
"pshufd $0x31, %%xmm0, %%xmm1\n\t"
"pshufd $0x31, %%xmm2, %%xmm3\n\t"
"pmuludq %%xmm2, %%xmm0 \n\t"
"pmuludq %%xmm3, %%xmm1 \n\t"
"movdqa %%xmm0, %%xmm2 \n\t"
"movdqa %%xmm1, %%xmm3 \n\t"
"psrlq $" STRING((2*SP_NUMB_BITS - W_TYPE_SIZE)) ", %%xmm2 \n\t"
"pmuludq %%xmm7, %%xmm2 \n\t"
"psrlq $" STRING((2*SP_NUMB_BITS - W_TYPE_SIZE)) ", %%xmm3 \n\t"
"pmuludq %%xmm7, %%xmm3 \n\t"
#if SP_NUMB_BITS < W_TYPE_SIZE - 1
"psrlq $33, %%xmm2 \n\t"
"pmuludq %%xmm6, %%xmm2 \n\t"
"psrlq $33, %%xmm3 \n\t"
"pmuludq %%xmm6, %%xmm3 \n\t"
"psubq %%xmm2, %%xmm0 \n\t"
"psubq %%xmm3, %%xmm1 \n\t"
#else
"pshufd $0xf5, %%xmm2, %%xmm2 \n\t"
"pmuludq %%xmm6, %%xmm2 \n\t"
"pshufd $0xf5, %%xmm3, %%xmm3 \n\t"
"pmuludq %%xmm6, %%xmm3 \n\t"
"psubq %%xmm2, %%xmm0 \n\t"
"psubq %%xmm3, %%xmm1 \n\t"
"psubq %%xmm5, %%xmm0 \n\t"
"psubq %%xmm5, %%xmm1 \n\t"
"pshufd $0xf5, %%xmm0, %%xmm2 \n\t"
"pshufd $0xf5, %%xmm1, %%xmm3 \n\t"
"pand %%xmm5, %%xmm2 \n\t"
"pand %%xmm5, %%xmm3 \n\t"
"paddq %%xmm2, %%xmm0 \n\t"
"paddq %%xmm3, %%xmm1 \n\t"
#endif
"pshufd $0x8, %%xmm0, %%xmm0 \n\t"
"pshufd $0x8, %%xmm1, %%xmm1 \n\t"
"punpckldq %%xmm1, %%xmm0 \n\t"
"psubd %%xmm6, %%xmm0 \n\t"
"pxor %%xmm1, %%xmm1 \n\t"
"pcmpgtd %%xmm0, %%xmm1 \n\t"
"pand %%xmm6, %%xmm1 \n\t"
"paddd %%xmm1, %%xmm0 \n\t"
"movdqa %%xmm0, -16(%2,%4,4) \n\t"
"cmpl %5, %4 \n\t"
"jne 0b \n\t"
:"=r"(i)
:"r"(x0), "r"(x1), "r"(w), "0"(i), "g"(len), "g"(p), "g"(d)
:"%xmm0", "%xmm1", "%xmm2", "%xmm3",
"%xmm5", "%xmm6", "%xmm7", "cc", "memory");
#elif defined( _MSC_VER ) && defined( SSE2)
__asm
{ push esi
push edi
mov edi, x0
mov esi, x1
mov edx, w
xor ecx, ecx
mov eax, len
movd xmm6, p
pshufd xmm5, xmm6, 0x44
pshufd xmm6, xmm6, 0
movd xmm7, d
pshufd xmm7, xmm7, 0
L0: movdqa xmm0, [edi+ecx*4]
movdqa xmm1, [esi+ecx*4]
movdqa xmm2, xmm1
paddd xmm1, xmm0
psubd xmm0, xmm2
psubd xmm1, xmm6
pxor xmm2, xmm2
pcmpgtd xmm2, xmm1
pand xmm2, xmm6
paddd xmm1, xmm2
movdqa [edi+ecx*4], xmm1
pxor xmm2, xmm2
pcmpgtd xmm2, xmm0
pand xmm2, xmm6
paddd xmm0, xmm2
movdqa xmm2, [edx+ecx*4]
add ecx, 4
pshufd xmm1, xmm0, 0x31
pshufd xmm3, xmm2, 0x31
pmuludq xmm0, xmm2
pmuludq xmm1, xmm3
movdqa xmm2, xmm0
movdqa xmm3, xmm1
psrlq xmm2, 2*SP_NUMB_BITS - W_TYPE_SIZE
pmuludq xmm2, xmm7
psrlq xmm3, 2*SP_NUMB_BITS - W_TYPE_SIZE
pmuludq xmm3, xmm7
#if SP_NUMB_BITS < W_TYPE_SIZE - 1
psrlq xmm2, 33
pmuludq xmm2, xmm6
psrlq xmm3, 33
pmuludq xmm3, xmm6
psubq xmm0, xmm2
psubq xmm1, xmm3
#else
pshufd xmm2, xmm2, 0xf5
pmuludq xmm2, xmm6
pshufd xmm3, xmm3, 0xf5
pmuludq xmm3, xmm6
psubq xmm0, xmm2
psubq xmm1, xmm3
psubq xmm0, xmm5
psubq xmm1, xmm5
pshufd xmm2, xmm0, 0xf5
pshufd xmm3, xmm1, 0xf5
pand xmm2, xmm5
pand xmm3, xmm5
paddq xmm0, xmm2
paddq xmm1, xmm3
#endif
pshufd xmm0, xmm0, 0x8
pshufd xmm1, xmm1, 0x8
punpckldq xmm0, xmm1
psubd xmm0, xmm6
pxor xmm1, xmm1
pcmpgtd xmm1, xmm0
pand xmm1, xmm6
paddd xmm0, xmm1
movdqa [esi+ecx*4-16], xmm0
cmp eax, ecx
jne L0
pop edi
pop esi
}
#else
for (i = 0; i < len; i++)
{
sp_t w0 = w[i];
sp_t t0 = x0[i];
sp_t t1 = x1[i];
sp_t t2, t3;
t2 = sp_add (t0, t1, p);
t3 = sp_sub (t0, t1, p);
t3 = sp_mul (t3, w0, p, d);
x0[i] = t2;
x1[i] = t3;
}
#endif
}
static void
spv_ntt_dif_core (spv_t x, spv_t w,
spv_size_t log2_len, sp_t p, sp_t d)
{
spv_size_t len;
spv_t x0, x1;
/* handle small transforms immediately */
switch (log2_len) {
case 0:
return;
case 1:
{
sp_t t0 = x[0];
sp_t t1 = x[1];
x[0] = sp_add (t0, t1, p);
x[1] = sp_sub (t0, t1, p);
return;
}
case 2:
{
sp_t t0 = x[0];
sp_t t1 = x[1];
sp_t t2 = x[2];
sp_t t3 = x[3];
sp_t t4, t5, t6, t7;
t4 = sp_add (t0, t2, p);
t6 = sp_sub (t0, t2, p);
t5 = sp_add (t1, t3, p);
t7 = sp_sub (t1, t3, p);
x[0] = sp_add (t4, t5, p);
x[1] = sp_sub (t4, t5, p);
t7 = sp_mul (t7, w[1], p, d);
x[2] = sp_add (t6, t7, p);
x[3] = sp_sub (t6, t7, p);
return;
}
case 3:
{
sp_t t0 = x[0];
sp_t t1 = x[1];
sp_t t2 = x[2];
sp_t t3 = x[3];
sp_t t4 = x[4];
sp_t t5 = x[5];
sp_t t6 = x[6];
sp_t t7 = x[7];
sp_t t8, t9, t10, t11, t12, t13, t14, t15;
t8 = sp_add (t0, t4, p);
t12 = sp_sub (t0, t4, p);
t9 = sp_add (t1, t5, p);
t13 = sp_sub (t1, t5, p);
t13 = sp_mul (t13, w[1], p, d);
t10 = sp_add (t2, t6, p);
t14 = sp_sub (t2, t6, p);
t14 = sp_mul (t14, w[2], p, d);
t11 = sp_add (t3, t7, p);
t15 = sp_sub (t3, t7, p);
t15 = sp_mul (t15, w[3], p, d);
t0 = sp_add (t8, t10, p);
t2 = sp_sub (t8, t10, p);
t1 = sp_add (t9, t11, p);
t3 = sp_sub (t9, t11, p);
t3 = sp_mul (t3, w[2], p, d);
x[0] = sp_add (t0, t1, p);
x[1] = sp_sub (t0, t1, p);
x[2] = sp_add (t2, t3, p);
x[3] = sp_sub (t2, t3, p);
t0 = sp_add (t12, t14, p);
t2 = sp_sub (t12, t14, p);
t1 = sp_add (t13, t15, p);
t3 = sp_sub (t13, t15, p);
t3 = sp_mul (t3, w[2], p, d);
x[4] = sp_add (t0, t1, p);
x[5] = sp_sub (t0, t1, p);
x[6] = sp_add (t2, t3, p);
x[7] = sp_sub (t2, t3, p);
return;
}
}
len = 1 << (log2_len - 1);
x0 = x;
x1 = x + len;
bfly_dif (x0, x1, w, len, p, d);
spv_ntt_dif_core (x0, w + len, log2_len - 1, p, d);
spv_ntt_dif_core (x1, w + len, log2_len - 1, p, d);
}
void
spv_ntt_gfp_dif (spv_t x, spv_size_t log2_len, spm_t data)
{
sp_t p = data->sp;
sp_t d = data->mul_c;
if (log2_len <= NTT_GFP_TWIDDLE_DIF_BREAKOVER)
{
spv_t w = data->nttdata->twiddle +
data->nttdata->twiddle_size - (1 << log2_len);
spv_ntt_dif_core (x, w, log2_len, p, d);
}
else
{
/* recursive version for data that
doesn't fit in the L1 cache */
spv_size_t len = 1 << (log2_len - 1);
spv_t x0 = x;
spv_t x1 = x + len;
spv_t roots = data->nttdata->ntt_roots;
{
spv_size_t i;
spv_size_t block_size = MIN(len, MAX_NTT_BLOCK_SIZE);
sp_t root = roots[log2_len];
spv_t w = data->scratch;
w[0] = 1;
for (i = 1; i < block_size; i++)
w[i] = sp_mul (w[i-1], root, p, d);
root = sp_pow (root, block_size, p, d);
for (i = 0; i < len; i += block_size)
{
if (i)
spv_mul_sp (w, w, root, block_size, p, d);
bfly_dif (x0 + i, x1 + i, w, block_size, p, d);
}
}
spv_ntt_gfp_dif (x0, log2_len - 1, data);
spv_ntt_gfp_dif (x1, log2_len - 1, data);
}
}
/*--------------------------- INVERSE NTT --------------------------------*/
static inline void bfly_dit(spv_t x0, spv_t x1, spv_t w,
spv_size_t len, sp_t p, sp_t d)
{
spv_size_t i = 0;
#if (defined(__GNUC__) || defined(__ICL)) && \
defined(__i386__) && defined(HAVE_SSE2)
asm volatile (
"movd %6, %%xmm6 \n\t"
"pshufd $0x44, %%xmm6, %%xmm5 \n\t"
"pshufd $0, %%xmm6, %%xmm6 \n\t"
"movd %7, %%xmm7 \n\t"
"pshufd $0, %%xmm7, %%xmm7 \n\t"
"0: \n\t"
"movdqa (%2,%4,4), %%xmm0 \n\t"
"movdqa (%3,%4,4), %%xmm2 \n\t"
"pshufd $0x31, %%xmm0, %%xmm1\n\t"
"pshufd $0x31, %%xmm2, %%xmm3\n\t"
"pmuludq %%xmm2, %%xmm0 \n\t"
"pmuludq %%xmm3, %%xmm1 \n\t"
"movdqa %%xmm0, %%xmm2 \n\t"
"movdqa %%xmm1, %%xmm3 \n\t"
"psrlq $" STRING((2*SP_NUMB_BITS - W_TYPE_SIZE)) ", %%xmm2 \n\t"
"pmuludq %%xmm7, %%xmm2 \n\t"
"psrlq $" STRING((2*SP_NUMB_BITS - W_TYPE_SIZE)) ", %%xmm3 \n\t"
"pmuludq %%xmm7, %%xmm3 \n\t"
#if SP_NUMB_BITS < W_TYPE_SIZE - 1
"psrlq $33, %%xmm2 \n\t"
"pmuludq %%xmm6, %%xmm2 \n\t"
"psrlq $33, %%xmm3 \n\t"
"pmuludq %%xmm6, %%xmm3 \n\t"
"psubq %%xmm2, %%xmm0 \n\t"
"psubq %%xmm3, %%xmm1 \n\t"
#else
"pshufd $0xf5, %%xmm2, %%xmm2 \n\t"
"pmuludq %%xmm6, %%xmm2 \n\t"
"pshufd $0xf5, %%xmm3, %%xmm3 \n\t"
"pmuludq %%xmm6, %%xmm3 \n\t"
"psubq %%xmm2, %%xmm0 \n\t"
"psubq %%xmm3, %%xmm1 \n\t"
"psubq %%xmm5, %%xmm0 \n\t"
"psubq %%xmm5, %%xmm1 \n\t"
"pshufd $0xf5, %%xmm0, %%xmm2 \n\t"
"pshufd $0xf5, %%xmm1, %%xmm3 \n\t"
"pand %%xmm5, %%xmm2 \n\t"
"pand %%xmm5, %%xmm3 \n\t"
"paddq %%xmm2, %%xmm0 \n\t"
"paddq %%xmm3, %%xmm1 \n\t"
#endif
"pshufd $0x8, %%xmm0, %%xmm0 \n\t"
"pshufd $0x8, %%xmm1, %%xmm1 \n\t"
"punpckldq %%xmm1, %%xmm0 \n\t"
"psubd %%xmm6, %%xmm0 \n\t"
"pxor %%xmm1, %%xmm1 \n\t"
"pcmpgtd %%xmm0, %%xmm1 \n\t"
"pand %%xmm6, %%xmm1 \n\t"
"paddd %%xmm0, %%xmm1 \n\t"
"movdqa (%1,%4,4), %%xmm0 \n\t"
"movdqa %%xmm1, %%xmm2 \n\t"
"paddd %%xmm0, %%xmm1 \n\t"
"psubd %%xmm2, %%xmm0 \n\t"
"psubd %%xmm6, %%xmm1 \n\t"
"pxor %%xmm2, %%xmm2 \n\t"
"pcmpgtd %%xmm1, %%xmm2 \n\t"
"pand %%xmm6, %%xmm2 \n\t"
"paddd %%xmm2, %%xmm1 \n\t"
"movdqa %%xmm1, (%1,%4,4) \n\t"
"pxor %%xmm2, %%xmm2 \n\t"
"pcmpgtd %%xmm0, %%xmm2 \n\t"
"pand %%xmm6, %%xmm2 \n\t"
"paddd %%xmm2, %%xmm0 \n\t"
"movdqa %%xmm0, (%2,%4,4) \n\t"
"addl $4, %4 \n\t" /* INC */
"cmpl %5, %4 \n\t"
"jne 0b \n\t"
:"=r"(i)
:"r"(x0), "r"(x1), "r"(w), "0"(i), "g"(len), "g"(p), "g"(d)
:"%xmm0", "%xmm1", "%xmm2", "%xmm3",
"%xmm5", "%xmm6", "%xmm7", "cc", "memory");
#elif defined( _MSC_VER ) && defined( SSE2)
__asm
{ push esi
push edi
mov edi, x0
mov esi, x1
mov edx, w
xor ecx, ecx
mov eax, len
movd xmm6, p
pshufd xmm5, xmm6, 0x44
pshufd xmm6, xmm6, 0
movd xmm7, d
pshufd xmm7, xmm7, 0
L0: movdqa xmm0, [esi+ecx*4]
movdqa xmm2, [edx+ecx*4]
pshufd xmm1, xmm0, 0x31
pshufd xmm3, xmm2, 0x31
pmuludq xmm0, xmm2
pmuludq xmm1, xmm3
movdqa xmm2, xmm0
movdqa xmm3, xmm1
psrlq xmm2, 2*SP_NUMB_BITS - W_TYPE_SIZE
pmuludq xmm2, xmm7
psrlq xmm3, 2*SP_NUMB_BITS - W_TYPE_SIZE
pmuludq xmm3, xmm7
#if SP_NUMB_BITS < W_TYPE_SIZE - 1
psrlq xmm2, 33
pmuludq xmm2, xmm6
psrlq xmm3, 33
pmuludq xmm3, xmm6
psubq xmm0, xmm2
psubq xmm1, xmm3
#else
pshufd xmm2, xmm2, 0xf5
pmuludq xmm2, xmm6
pshufd xmm3, xmm3, 0xf5
pmuludq xmm3, xmm6
psubq xmm0, xmm2
psubq xmm1, xmm3
psubq xmm0, xmm5
psubq xmm1, xmm5
pshufd xmm2, xmm0, 0xf5
pshufd xmm3, xmm1, 0xf5
pand xmm2, xmm5
pand xmm3, xmm5
paddq xmm0, xmm2
paddq xmm1, xmm3
#endif
pshufd xmm0, xmm0, 0x8
pshufd xmm1, xmm1, 0x8
punpckldq xmm0, xmm1
psubd xmm0, xmm6
pxor xmm1, xmm1
pcmpgtd xmm1, xmm0
pand xmm1, xmm6
paddd xmm1, xmm0
movdqa xmm0, [edi+ecx*4]
movdqa xmm2, xmm1
paddd xmm1, xmm0
psubd xmm0, xmm2
psubd xmm1, xmm6
pxor xmm2, xmm2
pcmpgtd xmm2, xmm1
pand xmm2, xmm6
paddd xmm1, xmm2
movdqa [edi+ecx*4], xmm1
pxor xmm2, xmm2
pcmpgtd xmm2, xmm0
pand xmm2, xmm6
paddd xmm0, xmm2
movdqa [esi+ecx*4], xmm0
add ecx, 4
cmp eax, ecx
jne L0
pop edi
pop esi
}
#else
for (i = 0; i < len; i++)
{
sp_t w0 = w[i];
sp_t t0 = x0[i];
sp_t t1 = x1[i];
t1 = sp_mul (t1, w0, p, d);
x0[i] = sp_add (t0, t1, p);
x1[i] = sp_sub (t0, t1, p);
}
#endif
}
static void
spv_ntt_dit_core (spv_t x, spv_t w,
spv_size_t log2_len, sp_t p, sp_t d)
{
spv_size_t len;
spv_t x0, x1;
/* handle small transforms immediately */
switch (log2_len) {
case 0:
return;
case 1:
{
sp_t t0 = x[0];
sp_t t1 = x[1];
x[0] = sp_add (t0, t1, p);
x[1] = sp_sub (t0, t1, p);
return;
}
case 2:
{
sp_t t0 = x[0];
sp_t t1 = x[1];
sp_t t2 = x[2];
sp_t t3 = x[3];
sp_t t4, t5, t6, t7;
t4 = sp_add (t0, t1, p);
t5 = sp_sub (t0, t1, p);
t6 = sp_add (t2, t3, p);
t7 = sp_sub (t2, t3, p);
x[0] = sp_add (t4, t6, p);
x[2] = sp_sub (t4, t6, p);
t7 = sp_mul (t7, w[1], p, d);
x[1] = sp_add (t5, t7, p);
x[3] = sp_sub (t5, t7, p);
return;
}
case 3:
{
sp_t t0 = x[0];
sp_t t1 = x[1];
sp_t t2 = x[2];
sp_t t3 = x[3];
sp_t t4 = x[4];
sp_t t5 = x[5];
sp_t t6 = x[6];
sp_t t7 = x[7];
sp_t t8, t9, t10, t11;
t8 = sp_add(t0, t1, p);
t9 = sp_sub(t0, t1, p);
t10 = sp_add(t2, t3, p);
t11 = sp_sub(t2, t3, p);
t0 = sp_add(t8, t10, p);
t2 = sp_sub(t8, t10, p);
t11 = sp_mul (t11, w[2], p, d);
t1 = sp_add(t9, t11, p);
t3 = sp_sub(t9, t11, p);
t8 = sp_add(t4, t5, p);
t9 = sp_sub(t4, t5, p);
t10 = sp_add(t6, t7, p);
t11 = sp_sub(t6, t7, p);
t4 = sp_add(t8, t10, p);
t6 = sp_sub(t8, t10, p);
t11 = sp_mul (t11, w[2], p, d);
t5 = sp_add(t9, t11, p);
t7 = sp_sub(t9, t11, p);
x[0] = sp_add(t0, t4, p);
x[4] = sp_sub(t0, t4, p);
t5 = sp_mul (t5, w[1], p, d);
x[1] = sp_add(t1, t5, p);
x[5] = sp_sub(t1, t5, p);
t6 = sp_mul (t6, w[2], p, d);
x[2] = sp_add(t2, t6, p);
x[6] = sp_sub(t2, t6, p);
t7 = sp_mul (t7, w[3], p, d);
x[3] = sp_add(t3, t7, p);
x[7] = sp_sub(t3, t7, p);
return;
}
}
len = 1 << (log2_len - 1);
x0 = x;
x1 = x + len;
spv_ntt_dit_core (x0, w + len, log2_len - 1, p, d);
spv_ntt_dit_core (x1, w + len, log2_len - 1, p, d);
bfly_dit (x0, x1, w, len, p, d);
}
void
spv_ntt_gfp_dit (spv_t x, spv_size_t log2_len, spm_t data)
{
sp_t p = data->sp;
sp_t d = data->mul_c;
if (log2_len <= NTT_GFP_TWIDDLE_DIT_BREAKOVER)
{
spv_t w = data->inttdata->twiddle +
data->inttdata->twiddle_size - (1 << log2_len);
spv_ntt_dit_core (x, w, log2_len, p, d);
}
else
{
spv_size_t len = 1 << (log2_len - 1);
spv_t x0 = x;
spv_t x1 = x + len;
spv_t roots = data->inttdata->ntt_roots;
spv_ntt_gfp_dit (x0, log2_len - 1, data);
spv_ntt_gfp_dit (x1, log2_len - 1, data);
{
spv_size_t i;
spv_size_t block_size = MIN(len, MAX_NTT_BLOCK_SIZE);
sp_t root = roots[log2_len];
spv_t w = data->scratch;
w[0] = 1;
for (i = 1; i < block_size; i++)
w[i] = sp_mul (w[i-1], root, p, d);
root = sp_pow (root, block_size, p, d);
for (i = 0; i < len; i += block_size)
{
if (i)
spv_mul_sp (w, w, root, block_size, p, d);
bfly_dit (x0 + i, x1 + i, w, block_size, p, d);
}
}
}
}
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