toom8_sqr.c
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上传日期：2022-08-06
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- /* Implementation of the squaring algorithm with Toom-Cook 8.5-way.
- Contributed to the GNU project by Marco Bodrato.
- THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
- SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
- GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
- Copyright 2009 Free Software Foundation, Inc.
- This file is part of the GNU MP Library.
- The GNU MP 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 GNU MP 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 GNU MP Library. If not, see http://www.gnu.org/licenses/. */
- #include "gmp.h"
- #include "gmp-impl.h"
- #if GMP_NUMB_BITS < 29
- #error Not implemented.
- #endif
- #if GMP_NUMB_BITS < 43
- #define BIT_CORRECTION 1
- #define CORRECTION_BITS GMP_NUMB_BITS
- #else
- #define BIT_CORRECTION 0
- #define CORRECTION_BITS 0
- #endif
- #ifndef SQR_TOOM8_THRESHOLD
- #define SQR_TOOM8_THRESHOLD MUL_TOOM8H_THRESHOLD
- #endif
- #ifndef SQR_TOOM6_THRESHOLD
- #define SQR_TOOM6_THRESHOLD MUL_TOOM6H_THRESHOLD
- #endif
- #if TUNE_PROGRAM_BUILD
- #define MAYBE_sqr_basecase 1
- #define MAYBE_sqr_above_basecase 1
- #define MAYBE_sqr_toom2 1
- #define MAYBE_sqr_above_toom2 1
- #define MAYBE_sqr_toom3 1
- #define MAYBE_sqr_above_toom3 1
- #define MAYBE_sqr_toom4 1
- #define MAYBE_sqr_above_toom4 1
- #define MAYBE_sqr_above_toom6 1
- #else
- #define SQR_TOOM8_MAX
- ((SQR_FFT_THRESHOLD <= MP_SIZE_T_MAX - (8*2-1+7)) ?
- ((SQR_FFT_THRESHOLD+8*2-1+7)/8)
- : MP_SIZE_T_MAX )
- #define MAYBE_sqr_basecase
- (SQR_TOOM8_THRESHOLD < 8 * SQR_TOOM2_THRESHOLD)
- #define MAYBE_sqr_above_basecase
- (SQR_TOOM8_MAX >= SQR_TOOM2_THRESHOLD)
- #define MAYBE_sqr_toom2
- (SQR_TOOM8_THRESHOLD < 8 * SQR_TOOM3_THRESHOLD)
- #define MAYBE_sqr_above_toom2
- (SQR_TOOM8_MAX >= SQR_TOOM3_THRESHOLD)
- #define MAYBE_sqr_toom3
- (SQR_TOOM8_THRESHOLD < 8 * SQR_TOOM4_THRESHOLD)
- #define MAYBE_sqr_above_toom3
- (SQR_TOOM8_MAX >= SQR_TOOM4_THRESHOLD)
- #define MAYBE_sqr_toom4
- (SQR_TOOM8_THRESHOLD < 8 * SQR_TOOM6_THRESHOLD)
- #define MAYBE_sqr_above_toom4
- (SQR_TOOM8_MAX >= SQR_TOOM6_THRESHOLD)
- #define MAYBE_sqr_above_toom6
- (SQR_TOOM8_MAX >= SQR_TOOM8_THRESHOLD)
- #endif
- #define TOOM8_SQR_REC(p, a, n, ws)
- do {
- if (MAYBE_sqr_basecase && ( !MAYBE_sqr_above_basecase
- || BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD)))
- mpn_sqr_basecase (p, a, n);
- else if (MAYBE_sqr_toom2 && ( !MAYBE_sqr_above_toom2
- || BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)))
- mpn_toom2_sqr (p, a, n, ws);
- else if (MAYBE_sqr_toom3 && ( !MAYBE_sqr_above_toom3
- || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD)))
- mpn_toom3_sqr (p, a, n, ws);
- else if (MAYBE_sqr_toom4 && ( !MAYBE_sqr_above_toom4
- || BELOW_THRESHOLD (n, SQR_TOOM6_THRESHOLD)))
- mpn_toom4_sqr (p, a, n, ws);
- else if (! MAYBE_sqr_above_toom6
- || BELOW_THRESHOLD (n, SQR_TOOM8_THRESHOLD))
- mpn_toom6_sqr (p, a, n, ws);
- else
- mpn_toom8_sqr (p, a, n, ws);
- } while (0)
- void
- mpn_toom8_sqr (mp_ptr pp, mp_srcptr ap, mp_size_t an, mp_ptr scratch)
- {
- mp_size_t n, s;
- /***************************** decomposition *******************************/
- ASSERT ( an >= 40 );
- n = 1 + ((an - 1)>>3);
- s = an - 7 * n;
- ASSERT (0 < s && s <= n);
- ASSERT ( s + s > 3 );
- #define r6 (pp + 3 * n) /* 3n+1 */
- #define r4 (pp + 7 * n) /* 3n+1 */
- #define r2 (pp +11 * n) /* 3n+1 */
- #define r0 (pp +15 * n) /* s+t <= 2*n */
- #define r7 (scratch) /* 3n+1 */
- #define r5 (scratch + 3 * n + 1) /* 3n+1 */
- #define r3 (scratch + 6 * n + 2) /* 3n+1 */
- #define r1 (scratch + 9 * n + 3) /* 3n+1 */
- #define v0 (pp +11 * n) /* n+1 */
- #define v2 (pp +13 * n+2) /* n+1 */
- #define wse (scratch +12 * n + 4) /* 3n+1 */
- /* Alloc also 3n+1 limbs for ws... toom_interpolate_16pts may
- need all of them, when DO_mpn_sublsh_n usea a scratch */
- /* if (scratch == NULL) */
- /* scratch = TMP_SALLOC_LIMBS (30 * n + 6); */
- /********************** evaluation and recursive calls *********************/
- /* $pm1/8$ */
- mpn_toom_eval_pm2rexp (v2, v0, 7, ap, n, s, 3, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-1/8)*B(-1/8)*8^. */
- TOOM8_SQR_REC(r7, v2, n + 1, wse); /* A(+1/8)*B(+1/8)*8^. */
- mpn_toom_couple_handling (r7, 2 * n + 1 + BIT_CORRECTION, pp, 0, n, 3, 0);
- /* $pm1/4$ */
- mpn_toom_eval_pm2rexp (v2, v0, 7, ap, n, s, 2, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-1/4)*B(-1/4)*4^. */
- TOOM8_SQR_REC(r5, v2, n + 1, wse); /* A(+1/4)*B(+1/4)*4^. */
- mpn_toom_couple_handling (r5, 2 * n + 1, pp, 0, n, 2, 0);
- /* $pm2$ */
- mpn_toom_eval_pm2 (v2, v0, 7, ap, n, s, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-2)*B(-2) */
- TOOM8_SQR_REC(r3, v2, n + 1, wse); /* A(+2)*B(+2) */
- mpn_toom_couple_handling (r3, 2 * n + 1, pp, 0, n, 1, 2);
- /* $pm8$ */
- mpn_toom_eval_pm2exp (v2, v0, 7, ap, n, s, 3, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-8)*B(-8) */
- TOOM8_SQR_REC(r1, v2, n + 1, wse); /* A(+8)*B(+8) */
- mpn_toom_couple_handling (r1, 2 * n + 1 + BIT_CORRECTION, pp, 0, n, 3, 6);
- /* $pm1/2$ */
- mpn_toom_eval_pm2rexp (v2, v0, 7, ap, n, s, 1, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-1/2)*B(-1/2)*2^. */
- TOOM8_SQR_REC(r6, v2, n + 1, wse); /* A(+1/2)*B(+1/2)*2^. */
- mpn_toom_couple_handling (r6, 2 * n + 1, pp, 0, n, 1, 0);
- /* $pm1$ */
- mpn_toom_eval_pm1 (v2, v0, 7, ap, n, s, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-1)*B(-1) */
- TOOM8_SQR_REC(r4, v2, n + 1, wse); /* A(1)*B(1) */
- mpn_toom_couple_handling (r4, 2 * n + 1, pp, 0, n, 0, 0);
- /* $pm4$ */
- mpn_toom_eval_pm2exp (v2, v0, 7, ap, n, s, 2, pp);
- TOOM8_SQR_REC(pp, v0, n + 1, wse); /* A(-4)*B(-4) */
- TOOM8_SQR_REC(r2, v2, n + 1, wse); /* A(+4)*B(+4) */
- mpn_toom_couple_handling (r2, 2 * n + 1, pp, 0, n, 2, 4);
- #undef v0
- #undef v2
- /* A(0)*B(0) */
- TOOM8_SQR_REC(pp, ap, n, wse);
- mpn_toom_interpolate_16pts (pp, r1, r3, r5, r7, n, 2 * s, 0, wse);
- #undef r0
- #undef r1
- #undef r2
- #undef r3
- #undef r4
- #undef r5
- #undef r6
- #undef wse
- }
- #undef TOOM8_SQR_REC
- #undef MAYBE_sqr_basecase
- #undef MAYBE_sqr_above_basecase
- #undef MAYBE_sqr_toom2
- #undef MAYBE_sqr_above_toom2
- #undef MAYBE_sqr_toom3
- #undef MAYBE_sqr_above_toom3
- #undef MAYBE_sqr_above_toom4
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