/src/libgmp/mpn/toom63_mul.c

Source (jump to first uncovered line)
/* Implementation of the algorithm for Toom-Cook 4.5-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, 2012 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 either:

  * 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.

or

  * the GNU General Public License as published by the Free Software
    Foundation; either version 2 of the License, or (at your option) any
    later version.

or both in parallel, as here.

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 General Public License
for more details.

You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library.  If not,
see https://www.gnu.org/licenses/.  */


#include "gmp-impl.h"

/* Stores |{ap,n}-{bp,n}| in {rp,n}. */
/* It returns 0 or ~0, depending on the sign of the result. */
static unsigned
abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
{
  mp_limb_t  x, y;
  while (--n >= 0)
    {
      x = ap[n];
      y = bp[n];
      if (x != y)
  {
    n++;
    if (x > y)
      {
        mpn_sub_n (rp, ap, bp, n);
        return 0;
      }
    else
      {
        mpn_sub_n (rp, bp, ap, n);
        return ~ (unsigned) 0;
      }
  }
      rp[n] = 0;
    }
  return 0;
}

/* It returns 0 or ~0, depending on the sign of the result rm. */
static unsigned
abs_sub_add_n (mp_ptr rm, mp_ptr rp, mp_srcptr rs, mp_size_t n) {
  unsigned result;
  result = abs_sub_n (rm, rp, rs, n);
  ASSERT_NOCARRY(mpn_add_n (rp, rp, rs, n));
  return result;
}


/* Toom-4.5, the splitting 6x3 unbalanced version.
   Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.

  <--s-><--n--><--n--><--n--><--n--><--n-->
   ____ ______ ______ ______ ______ ______
  |_a5_|__a4__|__a3__|__a2__|__a1__|__a0__|
      |b2_|__b1__|__b0__|
      <-t-><--n--><--n-->

*/
#define TOOM_63_MUL_N_REC(p, a, b, n, ws)   \
  do { mpn_mul_n (p, a, b, n);        \
  } while (0)

#define TOOM_63_MUL_REC(p, a, na, b, nb, ws)    \
  do { mpn_mul (p, a, na, b, nb);     \
  } while (0)

void
mpn_toom63_mul (mp_ptr pp,
    mp_srcptr ap, mp_size_t an,
    mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
{
  mp_size_t n, s, t;
  mp_limb_t cy;
  unsigned sign;

  /***************************** decomposition *******************************/
#define a5  (ap + 5 * n)
#define b0  (bp + 0 * n)
#define b1  (bp + 1 * n)
#define b2  (bp + 2 * n)

  ASSERT (an >= bn);
  n = 1 + (an >= 2 * bn ? (an - 1) / (size_t) 6 : (bn - 1) / (size_t) 3);

  s = an - 5 * n;
  t = bn - 2 * n;

  ASSERT (0 < s && s <= n);
  ASSERT (0 < t && t <= n);
  /* WARNING! it assumes s+t>=n */
  ASSERT ( s + t >= n );
  ASSERT ( s + t > 4);
  /* WARNING! it assumes n>1 */
  ASSERT ( n > 2);

#define   r8    pp        /* 2n   */
#define   r7    scratch        /* 3n+1 */
#define   r5    (pp + 3*n)      /* 3n+1 */
#define   v0    (pp + 3*n)      /* n+1 */
#define   v1    (pp + 4*n+1)      /* n+1 */
#define   v2    (pp + 5*n+2)      /* n+1 */
#define   v3    (pp + 6*n+3)      /* n+1 */
#define   r3    (scratch + 3 * n + 1)    /* 3n+1 */
#define   r1    (pp + 7*n)      /* s+t <= 2*n */
#define   ws    (scratch + 6 * n + 2)    /* ??? */

  /* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
     need all of them, when DO_mpn_sublsh_n usea a scratch  */
/*   if (scratch == NULL) scratch = TMP_SALLOC_LIMBS (9 * n + 3); */

  /********************** evaluation and recursive calls *********************/
  /* $\pm4$ */
  sign = mpn_toom_eval_pm2exp (v2, v0, 5, ap, n, s, 2, pp);
  pp[n] = mpn_lshift (pp, b1, n, 2); /* 4b1 */
  /* FIXME: use addlsh */
  v3[t] = mpn_lshift (v3, b2, t, 4);/* 16b2 */
  if ( n == t )
    v3[n]+= mpn_add_n (v3, v3, b0, n); /* 16b2+b0 */
  else
    v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 16b2+b0 */
  sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
  TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)*B(-4) */
  TOOM_63_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)*B(+4) */
  mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);

  /* $\pm1$ */
  sign = mpn_toom_eval_pm1 (v2, v0, 5, ap, n, s,    pp);
  /* Compute bs1 and bsm1. Code taken from toom33 */
  cy = mpn_add (ws, b0, n, b2, t);
#if HAVE_NATIVE_mpn_add_n_sub_n
  if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
    {
      cy = mpn_add_n_sub_n (v3, v1, b1, ws, n);
      v3[n] = cy >> 1;
      v1[n] = 0;
      sign = ~sign;
    }
  else
    {
      mp_limb_t cy2;
      cy2 = mpn_add_n_sub_n (v3, v1, ws, b1, n);
      v3[n] = cy + (cy2 >> 1);
      v1[n] = cy - (cy2 & 1);
    }
#else
  v3[n] = cy + mpn_add_n (v3, ws, b1, n);
  if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
    {
      mpn_sub_n (v1, b1, ws, n);
      v1[n] = 0;
      sign = ~sign;
    }
  else
    {
      cy -= mpn_sub_n (v1, ws, b1, n);
      v1[n] = cy;
    }
#endif
  TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)*B(-1) */
  TOOM_63_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)*B(1) */
  mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);

  /* $\pm2$ */
  sign = mpn_toom_eval_pm2 (v2, v0, 5, ap, n, s, pp);
  pp[n] = mpn_lshift (pp, b1, n, 1); /* 2b1 */
  /* FIXME: use addlsh or addlsh2 */
  v3[t] = mpn_lshift (v3, b2, t, 2);/* 4b2 */
  if ( n == t )
    v3[n]+= mpn_add_n (v3, v3, b0, n); /* 4b2+b0 */
  else
    v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 4b2+b0 */
  sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
  TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)*B(-2) */
  TOOM_63_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)*B(+2) */
  mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);

  /* A(0)*B(0) */
  TOOM_63_MUL_N_REC(pp, ap, bp, n, ws);

  /* Infinity */
  if (s > t) {
    TOOM_63_MUL_REC(r1, a5, s, b2, t, ws);
  } else {
    TOOM_63_MUL_REC(r1, b2, t, a5, s, ws);
  };

  mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);

#undef a5
#undef b0
#undef b1
#undef b2
#undef r1
#undef r3
#undef r5
#undef v0
#undef v1
#undef v2
#undef v3
#undef r7
#undef r8
#undef ws
}

Coverage Report

Created: 2024-11-21 07:03

Line	Count	Source (jump to first uncovered line)
1		/* Implementation of the algorithm for Toom-Cook 4.5-way.
2
3		Contributed to the GNU project by Marco Bodrato.
4
5		THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
6		SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
7		GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
8
9		Copyright 2009, 2012 Free Software Foundation, Inc.
10
11		This file is part of the GNU MP Library.
12
13		The GNU MP Library is free software; you can redistribute it and/or modify
14		it under the terms of either:
15
16		* the GNU Lesser General Public License as published by the Free
17		Software Foundation; either version 3 of the License, or (at your
18		option) any later version.
19
20		or
21
22		* the GNU General Public License as published by the Free Software
23		Foundation; either version 2 of the License, or (at your option) any
24		later version.
25
26		or both in parallel, as here.
27
28		The GNU MP Library is distributed in the hope that it will be useful, but
29		WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
30		or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
31		for more details.
32
33		You should have received copies of the GNU General Public License and the
34		GNU Lesser General Public License along with the GNU MP Library. If not,
35		see https://www.gnu.org/licenses/. */
36
37
38		#include "gmp-impl.h"
39
40		/* Stores \|{ap,n}-{bp,n}\| in {rp,n}. */
41		/* It returns 0 or ~0, depending on the sign of the result. */
42		static unsigned
43		abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
44	308	{
45	308	mp_limb_t x, y;
46	389	while (--n >= 0)
47	389	{
48	389	x = ap[n];
49	389	y = bp[n];
50	389	if (x != y)
51	308	{
52	308	n++;
53	308	if (x > y)
54	33	{
55	33	mpn_sub_n (rp, ap, bp, n);
56	33	return 0;
57	33	}
58	275	else
59	275	{
60	275	mpn_sub_n (rp, bp, ap, n);
61	275	return ~ (unsigned) 0;
62	275	}
63	308	}
64	81	rp[n] = 0;
65	81	}
66	0	return 0;
67	308	}
68
69		/* It returns 0 or ~0, depending on the sign of the result rm. */
70		static unsigned
71	308	abs_sub_add_n (mp_ptr rm, mp_ptr rp, mp_srcptr rs, mp_size_t n) {
72	308	unsigned result;
73	308	result = abs_sub_n (rm, rp, rs, n);
74	308	ASSERT_NOCARRY(mpn_add_n (rp, rp, rs, n));
75	308	return result;
76	308	}
77
78
79		/* Toom-4.5, the splitting 6x3 unbalanced version.
80		Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.
81
82		<--s-><--n--><--n--><--n--><--n--><--n-->
83		____ ______ ______ ______ ______ ______
84		\|_a5_\|__a4__\|__a3__\|__a2__\|__a1__\|__a0__\|
85		\|b2_\|__b1__\|__b0__\|
86		<-t-><--n--><--n-->
87
88		*/
89		#define TOOM_63_MUL_N_REC(p, a, b, n, ws) \
90	1.07k	do { mpn_mul_n (p, a, b, n); \
91	1.07k	} while (0)
92
93		#define TOOM_63_MUL_REC(p, a, na, b, nb, ws) \
94	154	do { mpn_mul (p, a, na, b, nb); \
95	154	} while (0)
96
97		void
98		mpn_toom63_mul (mp_ptr pp,
99		mp_srcptr ap, mp_size_t an,
100		mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
101	154	{
102	154	mp_size_t n, s, t;
103	154	mp_limb_t cy;
104	154	unsigned sign;
105
106		/*************************** decomposition *****************************/
107	154	#define a5 (ap + 5 * n)
108	462	#define b0 (bp + 0 * n)
109	770	#define b1 (bp + 1 * n)
110	462	#define b2 (bp + 2 * n)
111
112	154	ASSERT (an >= bn);
113	154	n = 1 + (an >= 2 * bn ? (an - 1) / (size_t) 6 : (bn - 1) / (size_t) 3);
114
115	154	s = an - 5 * n;
116	154	t = bn - 2 * n;
117
118	154	ASSERT (0 < s && s <= n);
119	154	ASSERT (0 < t && t <= n);
120		/* WARNING! it assumes s+t>=n */
121	154	ASSERT ( s + t >= n );
122	154	ASSERT ( s + t > 4);
123		/* WARNING! it assumes n>1 */
124	154	ASSERT ( n > 2);
125
126	154	#define r8 pp /* 2n */
127	308	#define r7 scratch /* 3n+1 */
128	154	#define r5 (pp + 3n) / 3n+1 */
129	462	#define v0 (pp + 3n) / n+1 */
130	616	#define v1 (pp + 4n+1) / n+1 */
131	462	#define v2 (pp + 5n+2) / n+1 */
132	2.15k	#define v3 (pp + 6n+3) / n+1 */
133	308	#define r3 (scratch + 3 * n + 1) /* 3n+1 */
134	154	#define r1 (pp + 7n) / s+t <= 2n /
135	770	#define ws (scratch + 6 * n + 2) /* ??? */
136
137		/* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
138		need all of them, when DO_mpn_sublsh_n usea a scratch */
139		/* if (scratch == NULL) scratch = TMP_SALLOC_LIMBS (9 * n + 3); */
140
141		/******************** evaluation and recursive calls *******************/
142		/* $\pm4$ */
143	154	sign = mpn_toom_eval_pm2exp (v2, v0, 5, ap, n, s, 2, pp);
144	154	pp[n] = mpn_lshift (pp, b1, n, 2); /* 4b1 */
145		/* FIXME: use addlsh */
146	154	v3[t] = mpn_lshift (v3, b2, t, 4);/* 16b2 */
147	154	if ( n == t )
148	4	v3[n]+= mpn_add_n (v3, v3, b0, n); /* 16b2+b0 */
149	150	else
150	150	v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 16b2+b0 */
151	154	sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
152	154	TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)B(-4) /
153	154	TOOM_63_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)B(+4) /
154	154	mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);
155
156		/* $\pm1$ */
157	154	sign = mpn_toom_eval_pm1 (v2, v0, 5, ap, n, s, pp);
158		/* Compute bs1 and bsm1. Code taken from toom33 */
159	154	cy = mpn_add (ws, b0, n, b2, t);
160		#if HAVE_NATIVE_mpn_add_n_sub_n
161		if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
162		{
163		cy = mpn_add_n_sub_n (v3, v1, b1, ws, n);
164		v3[n] = cy >> 1;
165		v1[n] = 0;
166		sign = ~sign;
167		}
168		else
169		{
170		mp_limb_t cy2;
171		cy2 = mpn_add_n_sub_n (v3, v1, ws, b1, n);
172		v3[n] = cy + (cy2 >> 1);
173		v1[n] = cy - (cy2 & 1);
174		}
175		#else
176	154	v3[n] = cy + mpn_add_n (v3, ws, b1, n);
177	154	if (cy == 0 && mpn_cmp (ws, b1, n) < 0)
178	64	{
179	64	mpn_sub_n (v1, b1, ws, n);
180	64	v1[n] = 0;
181	64	sign = ~sign;
182	64	}
183	90	else
184	90	{
185	90	cy -= mpn_sub_n (v1, ws, b1, n);
186	90	v1[n] = cy;
187	90	}
188	154	#endif
189	154	TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)B(-1) /
190	154	TOOM_63_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)B(1) /
191	154	mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);
192
193		/* $\pm2$ */
194	154	sign = mpn_toom_eval_pm2 (v2, v0, 5, ap, n, s, pp);
195	154	pp[n] = mpn_lshift (pp, b1, n, 1); /* 2b1 */
196		/* FIXME: use addlsh or addlsh2 */
197	154	v3[t] = mpn_lshift (v3, b2, t, 2);/* 4b2 */
198	154	if ( n == t )
199	4	v3[n]+= mpn_add_n (v3, v3, b0, n); /* 4b2+b0 */
200	150	else
201	150	v3[n] = mpn_add (v3, b0, n, v3, t+1); /* 4b2+b0 */
202	154	sign ^= abs_sub_add_n (v1, v3, pp, n + 1);
203	154	TOOM_63_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)B(-2) /
204	154	TOOM_63_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)B(+2) /
205	154	mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);
206
207		/* A(0)B(0) /
208	154	TOOM_63_MUL_N_REC(pp, ap, bp, n, ws);
209
210		/* Infinity */
211	154	if (s > t) {
212	1	TOOM_63_MUL_REC(r1, a5, s, b2, t, ws);
213	153	} else {
214	153	TOOM_63_MUL_REC(r1, b2, t, a5, s, ws);
215	153	};
216
217	154	mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);
218
219	154	#undef a5
220	154	#undef b0
221	154	#undef b1
222	154	#undef b2
223	154	#undef r1
224	154	#undef r3
225	154	#undef r5
226	154	#undef v0
227	154	#undef v1
228	154	#undef v2
229	154	#undef v3
230	154	#undef r7
231	154	#undef r8
232	154	#undef ws
233	154	}