1 /* mpn_mul_n -- Multiply two natural numbers of length n.
3 Copyright (C) 1991-2015 Free Software Foundation, Inc.
5 This file is part of the GNU MP Library.
7 The GNU MP Library is free software; you can redistribute it and/or modify
8 it under the terms of the GNU Lesser General Public License as published by
9 the Free Software Foundation; either version 2.1 of the License, or (at your
10 option) any later version.
12 The GNU MP Library is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
15 License for more details.
17 You should have received a copy of the GNU Lesser General Public License
18 along with the GNU MP Library; see the file COPYING.LIB. If not, see
19 <http://www.gnu.org/licenses/>. */
24 /* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
25 both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
26 always stored. Return the most significant limb.
29 1. PRODP != UP and PRODP != VP, i.e. the destination
30 must be distinct from the multiplier and the multiplicand. */
32 /* If KARATSUBA_THRESHOLD is not already defined, define it to a
33 value which is good on most machines. */
34 #ifndef KARATSUBA_THRESHOLD
35 #define KARATSUBA_THRESHOLD 32
38 /* The code can't handle KARATSUBA_THRESHOLD smaller than 2. */
39 #if KARATSUBA_THRESHOLD < 2
40 #undef KARATSUBA_THRESHOLD
41 #define KARATSUBA_THRESHOLD 2
44 /* Handle simple cases with traditional multiplication.
46 This is the most critical code of multiplication. All multiplies rely
47 on this, both small and huge. Small ones arrive here immediately. Huge
48 ones arrive here as this is the base case for Karatsuba's recursive
53 impn_mul_n_basecase (mp_ptr prodp
, mp_srcptr up
, mp_srcptr vp
, mp_size_t size
)
55 impn_mul_n_basecase (prodp
, up
, vp
, size
)
66 /* Multiply by the first limb in V separately, as the result can be
67 stored (not added) to PROD. We also avoid a loop for zeroing. */
72 MPN_COPY (prodp
, up
, size
);
74 MPN_ZERO (prodp
, size
);
78 cy_limb
= mpn_mul_1 (prodp
, up
, size
, v_limb
);
80 prodp
[size
] = cy_limb
;
83 /* For each iteration in the outer loop, multiply one limb from
84 U with one limb from V, and add it to PROD. */
85 for (i
= 1; i
< size
; i
++)
92 cy_limb
= mpn_add_n (prodp
, prodp
, up
, size
);
95 cy_limb
= mpn_addmul_1 (prodp
, up
, size
, v_limb
);
97 prodp
[size
] = cy_limb
;
104 impn_mul_n (mp_ptr prodp
,
105 mp_srcptr up
, mp_srcptr vp
, mp_size_t size
, mp_ptr tspace
)
107 impn_mul_n (prodp
, up
, vp
, size
, tspace
)
117 /* The size is odd, the code code below doesn't handle that.
118 Multiply the least significant (size - 1) limbs with a recursive
119 call, and handle the most significant limb of S1 and S2
121 /* A slightly faster way to do this would be to make the Karatsuba
122 code below behave as if the size were even, and let it check for
123 odd size in the end. I.e., in essence move this code to the end.
124 Doing so would save us a recursive call, and potentially make the
125 stack grow a lot less. */
127 mp_size_t esize
= size
- 1; /* even size */
130 MPN_MUL_N_RECURSE (prodp
, up
, vp
, esize
, tspace
);
131 cy_limb
= mpn_addmul_1 (prodp
+ esize
, up
, esize
, vp
[esize
]);
132 prodp
[esize
+ esize
] = cy_limb
;
133 cy_limb
= mpn_addmul_1 (prodp
+ esize
, vp
, size
, up
[esize
]);
135 prodp
[esize
+ size
] = cy_limb
;
139 /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
141 Split U in two pieces, U1 and U0, such that
143 and V in V1 and V0, such that
146 UV is then computed recursively using the identity
149 UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
152 Where B = 2**BITS_PER_MP_LIMB. */
154 mp_size_t hsize
= size
>> 1;
158 /*** Product H. ________________ ________________
159 |_____U1 x V1____||____U0 x V0_____| */
160 /* Put result in upper part of PROD and pass low part of TSPACE
162 MPN_MUL_N_RECURSE (prodp
+ size
, up
+ hsize
, vp
+ hsize
, hsize
, tspace
);
164 /*** Product M. ________________
165 |_(U1-U0)(V0-V1)_| */
166 if (mpn_cmp (up
+ hsize
, up
, hsize
) >= 0)
168 mpn_sub_n (prodp
, up
+ hsize
, up
, hsize
);
173 mpn_sub_n (prodp
, up
, up
+ hsize
, hsize
);
176 if (mpn_cmp (vp
+ hsize
, vp
, hsize
) >= 0)
178 mpn_sub_n (prodp
+ hsize
, vp
+ hsize
, vp
, hsize
);
183 mpn_sub_n (prodp
+ hsize
, vp
, vp
+ hsize
, hsize
);
184 /* No change of NEGFLG. */
186 /* Read temporary operands from low part of PROD.
187 Put result in low part of TSPACE using upper part of TSPACE
189 MPN_MUL_N_RECURSE (tspace
, prodp
, prodp
+ hsize
, hsize
, tspace
+ size
);
191 /*** Add/copy product H. */
192 MPN_COPY (prodp
+ hsize
, prodp
+ size
, hsize
);
193 cy
= mpn_add_n (prodp
+ size
, prodp
+ size
, prodp
+ size
+ hsize
, hsize
);
195 /*** Add product M (if NEGFLG M is a negative number). */
197 cy
-= mpn_sub_n (prodp
+ hsize
, prodp
+ hsize
, tspace
, size
);
199 cy
+= mpn_add_n (prodp
+ hsize
, prodp
+ hsize
, tspace
, size
);
201 /*** Product L. ________________ ________________
202 |________________||____U0 x V0_____| */
203 /* Read temporary operands from low part of PROD.
204 Put result in low part of TSPACE using upper part of TSPACE
206 MPN_MUL_N_RECURSE (tspace
, up
, vp
, hsize
, tspace
+ size
);
208 /*** Add/copy Product L (twice). */
210 cy
+= mpn_add_n (prodp
+ hsize
, prodp
+ hsize
, tspace
, size
);
212 mpn_add_1 (prodp
+ hsize
+ size
, prodp
+ hsize
+ size
, hsize
, cy
);
214 MPN_COPY (prodp
, tspace
, hsize
);
215 cy
= mpn_add_n (prodp
+ hsize
, prodp
+ hsize
, tspace
+ hsize
, hsize
);
217 mpn_add_1 (prodp
+ size
, prodp
+ size
, size
, 1);
223 impn_sqr_n_basecase (mp_ptr prodp
, mp_srcptr up
, mp_size_t size
)
225 impn_sqr_n_basecase (prodp
, up
, size
)
235 /* Multiply by the first limb in V separately, as the result can be
236 stored (not added) to PROD. We also avoid a loop for zeroing. */
241 MPN_COPY (prodp
, up
, size
);
243 MPN_ZERO (prodp
, size
);
247 cy_limb
= mpn_mul_1 (prodp
, up
, size
, v_limb
);
249 prodp
[size
] = cy_limb
;
252 /* For each iteration in the outer loop, multiply one limb from
253 U with one limb from V, and add it to PROD. */
254 for (i
= 1; i
< size
; i
++)
261 cy_limb
= mpn_add_n (prodp
, prodp
, up
, size
);
264 cy_limb
= mpn_addmul_1 (prodp
, up
, size
, v_limb
);
266 prodp
[size
] = cy_limb
;
273 impn_sqr_n (mp_ptr prodp
,
274 mp_srcptr up
, mp_size_t size
, mp_ptr tspace
)
276 impn_sqr_n (prodp
, up
, size
, tspace
)
285 /* The size is odd, the code code below doesn't handle that.
286 Multiply the least significant (size - 1) limbs with a recursive
287 call, and handle the most significant limb of S1 and S2
289 /* A slightly faster way to do this would be to make the Karatsuba
290 code below behave as if the size were even, and let it check for
291 odd size in the end. I.e., in essence move this code to the end.
292 Doing so would save us a recursive call, and potentially make the
293 stack grow a lot less. */
295 mp_size_t esize
= size
- 1; /* even size */
298 MPN_SQR_N_RECURSE (prodp
, up
, esize
, tspace
);
299 cy_limb
= mpn_addmul_1 (prodp
+ esize
, up
, esize
, up
[esize
]);
300 prodp
[esize
+ esize
] = cy_limb
;
301 cy_limb
= mpn_addmul_1 (prodp
+ esize
, up
, size
, up
[esize
]);
303 prodp
[esize
+ size
] = cy_limb
;
307 mp_size_t hsize
= size
>> 1;
310 /*** Product H. ________________ ________________
311 |_____U1 x U1____||____U0 x U0_____| */
312 /* Put result in upper part of PROD and pass low part of TSPACE
314 MPN_SQR_N_RECURSE (prodp
+ size
, up
+ hsize
, hsize
, tspace
);
316 /*** Product M. ________________
317 |_(U1-U0)(U0-U1)_| */
318 if (mpn_cmp (up
+ hsize
, up
, hsize
) >= 0)
320 mpn_sub_n (prodp
, up
+ hsize
, up
, hsize
);
324 mpn_sub_n (prodp
, up
, up
+ hsize
, hsize
);
327 /* Read temporary operands from low part of PROD.
328 Put result in low part of TSPACE using upper part of TSPACE
330 MPN_SQR_N_RECURSE (tspace
, prodp
, hsize
, tspace
+ size
);
332 /*** Add/copy product H. */
333 MPN_COPY (prodp
+ hsize
, prodp
+ size
, hsize
);
334 cy
= mpn_add_n (prodp
+ size
, prodp
+ size
, prodp
+ size
+ hsize
, hsize
);
336 /*** Add product M (if NEGFLG M is a negative number). */
337 cy
-= mpn_sub_n (prodp
+ hsize
, prodp
+ hsize
, tspace
, size
);
339 /*** Product L. ________________ ________________
340 |________________||____U0 x U0_____| */
341 /* Read temporary operands from low part of PROD.
342 Put result in low part of TSPACE using upper part of TSPACE
344 MPN_SQR_N_RECURSE (tspace
, up
, hsize
, tspace
+ size
);
346 /*** Add/copy Product L (twice). */
348 cy
+= mpn_add_n (prodp
+ hsize
, prodp
+ hsize
, tspace
, size
);
350 mpn_add_1 (prodp
+ hsize
+ size
, prodp
+ hsize
+ size
, hsize
, cy
);
352 MPN_COPY (prodp
, tspace
, hsize
);
353 cy
= mpn_add_n (prodp
+ hsize
, prodp
+ hsize
, tspace
+ hsize
, hsize
);
355 mpn_add_1 (prodp
+ size
, prodp
+ size
, size
, 1);
359 /* This should be made into an inline function in gmp.h. */
362 mpn_mul_n (mp_ptr prodp
, mp_srcptr up
, mp_srcptr vp
, mp_size_t size
)
364 mpn_mul_n (prodp
, up
, vp
, size
)
375 if (size
< KARATSUBA_THRESHOLD
)
377 impn_sqr_n_basecase (prodp
, up
, size
);
382 tspace
= (mp_ptr
) TMP_ALLOC (2 * size
* BYTES_PER_MP_LIMB
);
383 impn_sqr_n (prodp
, up
, size
, tspace
);
388 if (size
< KARATSUBA_THRESHOLD
)
390 impn_mul_n_basecase (prodp
, up
, vp
, size
);
395 tspace
= (mp_ptr
) TMP_ALLOC (2 * size
* BYTES_PER_MP_LIMB
);
396 impn_mul_n (prodp
, up
, vp
, size
, tspace
);