mpn/generic/div_qr_1u_pi2.c - gmp - Git at Google

 /* mpn_div_qr_1u_pi2.

    THIS FILE CONTAINS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE.  IT IS
    ONLY SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
    GUARANTEED THAT IT'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

 Copyright 2013, 2017 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/.  */

 /* ISSUES:

    * Can we really use the high pi2 inverse limb for udiv_qrnnd_preinv?

    * Are there any problems with generating n quotient limbs in the q area?  It
      surely simplifies things.

    * Not yet adequately tested.
 */

 #include "gmp-impl.h"
 #include "longlong.h"

 /* Define some longlong.h-style macros, but for wider operations.
    * add_sssaaaa is like longlong.h's add_ssaaaa but propagating carry-out into
      an additional sum operand.
 */
 #if defined (__GNUC__)  && ! defined (__INTEL_COMPILER) && ! defined (NO_ASM)

 #if HAVE_HOST_CPU_FAMILY_x86 && W_TYPE_SIZE == 32
 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
   __asm__ ("add\t%7, %k2\n\tadc\t%5, %k1\n\tadc\t$0, %k0"		\
 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
 	   : "0"  ((USItype)(s2)),					\
 	     "1"  ((USItype)(a1)), "g" ((USItype)(b1)),			\
 	     "%2" ((USItype)(a0)), "g" ((USItype)(b0)))
 #endif

 #if defined (__amd64__) && W_TYPE_SIZE == 64
 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
   __asm__ ("add\t%7, %q2\n\tadc\t%5, %q1\n\tadc\t$0, %q0"		\
 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
 	   : "0"  ((UDItype)(s2)),					\
 	     "1"  ((UDItype)(a1)), "rme" ((UDItype)(b1)),		\
 	     "%2" ((UDItype)(a0)), "rme" ((UDItype)(b0)))
 #endif

 #if defined (__aarch64__) && W_TYPE_SIZE == 64
 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
   __asm__ ("adds\t%2, %x6, %7\n\tadcs\t%1, %x4, %x5\n\tadc\t%0, %x3, xzr"\
 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
 	   : "rZ" (s2), "%rZ"  (a1), "rZ" (b1), "%rZ" (a0), "rI" (b0)	\
 	     __CLOBBER_CC)
 #endif

 #if HAVE_HOST_CPU_FAMILY_powerpc && !defined (_LONG_LONG_LIMB)
 /* This works fine for 32-bit and 64-bit limbs, except for 64-bit limbs with a
    processor running in 32-bit mode, since the carry flag then gets the 32-bit
    carry.  */
 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
   __asm__ ("add%I7c\t%2,%6,%7\n\tadde\t%1,%4,%5\n\taddze\t%0,%3"	\
 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
 	   : "r"  (s2), "r"  (a1), "r" (b1), "%r" (a0), "rI" (b0)	\
 	     __CLOBBER_CC)
 #endif

 #endif /* __GNUC__ */

 #ifndef add_sssaaaa
 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
   do {									\
     UWtype __s0, __s1, __c0, __c1;					\
     __s0 = (a0) + (b0);							\
     __s1 = (a1) + (b1);							\
     __c0 = __s0 < (a0);							\
     __c1 = __s1 < (a1);							\
     (s0) = __s0;							\
     __s1 = __s1 + __c0;							\
     (s1) = __s1;							\
     (s2) += __c1 + (__s1 < __c0);					\
   } while (0)
 #endif

 struct precomp_div_1_pi2
 {
   mp_limb_t dip[2];
   mp_limb_t d;
   int norm_cnt;
 };

 mp_limb_t
 mpn_div_qr_1u_pi2 (mp_ptr qp,
 		   mp_srcptr up, mp_size_t un,
 		   struct precomp_div_1_pi2 *pd)
 {
   mp_size_t i;
   mp_limb_t r, u2, u1, u0;
   mp_limb_t d0, di1, di0;
   mp_limb_t q3a, q2a, q2b, q1b, q2c, q1c, q1d, q0d;
   mp_limb_t cnd;
   int cnt;

   ASSERT (un >= 2);
   ASSERT ((pd->d & GMP_NUMB_HIGHBIT) == 0);
   ASSERT (! MPN_OVERLAP_P (qp, un-2, up, un) || qp+2 >= up);
   ASSERT_MPN (up, un);

 #define q3 q3a
 #define q2 q2b
 #define q1 q1b

   up += un - 3;
   cnt = pd->norm_cnt;
   r = up[2] >> (GMP_NUMB_BITS - cnt);
   d0 = pd->d << cnt;

   qp += un - 2;

   di1 = pd->dip[1];
   di0 = pd->dip[0];

   for (i = un - 3; i >= 0; i -= 2)
     {
       u2 = r;
       u1 = (up[2] << cnt) | (up[1] >> (GMP_NUMB_BITS - cnt));
       u0 = (up[1] << cnt) | (up[0] >> (GMP_NUMB_BITS - cnt));

       /* Dividend in {r,u1,u0} */

       umul_ppmm (q1d,q0d, u1, di0);
       umul_ppmm (q2b,q1b, u1, di1);
       q2b++;				/* cannot spill */
       add_sssaaaa (r,q2b,q1b, q2b,q1b, u1,u0);

       umul_ppmm (q2c,q1c, u2,  di0);
       add_sssaaaa (r,q2b,q1b, q2b,q1b, q2c,q1c);
       umul_ppmm (q3a,q2a, u2, di1);

       add_sssaaaa (r,q2b,q1b, q2b,q1b, q2a,q1d);

       q3 += r;

       r = u0 - q2 * d0;

       cnd = (r >= q1);
       r += d0 & -cnd;
       sub_ddmmss (q3,q2,  q3,q2,  0,cnd);

       if (UNLIKELY (r >= d0))
 	{
 	  r -= d0;
 	  add_ssaaaa (q3,q2,  q3,q2,  0,1);
 	}

       qp[0] = q2;
       qp[1] = q3;

       up -= 2;
       qp -= 2;
     }

   if ((un & 1) != 0)
     {
       u2 = r;
       u1 = (up[2] << cnt);

       udiv_qrnnd_preinv (q3, r, u2, u1, d0, di1);
       qp[1] = q3;
     }
   else
     {
       u2 = r;
       u1 = (up[2] << cnt) | (up[1] >> (GMP_NUMB_BITS - cnt));
       u0 = (up[1] << cnt);

       /* Dividend in {r,u1,u0} */

       umul_ppmm (q1d,q0d, u1, di0);
       umul_ppmm (q2b,q1b, u1, di1);
       q2b++;				/* cannot spill */
       add_sssaaaa (r,q2b,q1b, q2b,q1b, u1,u0);

       umul_ppmm (q2c,q1c, u2,  di0);
       add_sssaaaa (r,q2b,q1b, q2b,q1b, q2c,q1c);
       umul_ppmm (q3a,q2a, u2, di1);

       add_sssaaaa (r,q2b,q1b, q2b,q1b, q2a,q1d);

       q3 += r;

       r = u0 - q2 * d0;

       cnd = (r >= q1);
       r += d0 & -cnd;
       sub_ddmmss (q3,q2,  q3,q2,  0,cnd);

       if (UNLIKELY (r >= d0))
 	{
 	  r -= d0;
 	  add_ssaaaa (q3,q2,  q3,q2,  0,1);
 	}

       qp[0] = q2;
       qp[1] = q3;
     }

   return r >> cnt;

 #undef q3
 #undef q2
 #undef q1
 }
	/* mpn_div_qr_1u_pi2.

	THIS FILE CONTAINS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE. IT IS
	ONLY SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
	GUARANTEED THAT IT'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

	Copyright 2013, 2017 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/. */

	/* ISSUES:

	* Can we really use the high pi2 inverse limb for udiv_qrnnd_preinv?

	* Are there any problems with generating n quotient limbs in the q area? It
	surely simplifies things.

	* Not yet adequately tested.
	*/

	#include "gmp-impl.h"
	#include "longlong.h"

	/* Define some longlong.h-style macros, but for wider operations.
	* add_sssaaaa is like longlong.h's add_ssaaaa but propagating carry-out into
	an additional sum operand.
	*/
	#if defined (__GNUC__) && ! defined (__INTEL_COMPILER) && ! defined (NO_ASM)

	#if HAVE_HOST_CPU_FAMILY_x86 && W_TYPE_SIZE == 32
	#define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0) \
	__asm__ ("add\t%7, %k2\n\tadc\t%5, %k1\n\tadc\t$0, %k0" \
	: "=r" (s2), "=&r" (s1), "=&r" (s0) \
	: "0" ((USItype)(s2)), \
	"1" ((USItype)(a1)), "g" ((USItype)(b1)), \
	"%2" ((USItype)(a0)), "g" ((USItype)(b0)))
	#endif

	#if defined (__amd64__) && W_TYPE_SIZE == 64
	#define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0) \
	__asm__ ("add\t%7, %q2\n\tadc\t%5, %q1\n\tadc\t$0, %q0" \
	: "=r" (s2), "=&r" (s1), "=&r" (s0) \
	: "0" ((UDItype)(s2)), \
	"1" ((UDItype)(a1)), "rme" ((UDItype)(b1)), \
	"%2" ((UDItype)(a0)), "rme" ((UDItype)(b0)))
	#endif

	#if defined (__aarch64__) && W_TYPE_SIZE == 64
	#define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0) \
	__asm__ ("adds\t%2, %x6, %7\n\tadcs\t%1, %x4, %x5\n\tadc\t%0, %x3, xzr"\
	: "=r" (s2), "=&r" (s1), "=&r" (s0) \
	: "rZ" (s2), "%rZ" (a1), "rZ" (b1), "%rZ" (a0), "rI" (b0) \
	__CLOBBER_CC)
	#endif

	#if HAVE_HOST_CPU_FAMILY_powerpc && !defined (_LONG_LONG_LIMB)
	/* This works fine for 32-bit and 64-bit limbs, except for 64-bit limbs with a
	processor running in 32-bit mode, since the carry flag then gets the 32-bit
	carry. */
	#define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0) \
	__asm__ ("add%I7c\t%2,%6,%7\n\tadde\t%1,%4,%5\n\taddze\t%0,%3" \
	: "=r" (s2), "=&r" (s1), "=&r" (s0) \
	: "r" (s2), "r" (a1), "r" (b1), "%r" (a0), "rI" (b0) \
	__CLOBBER_CC)
	#endif

	#endif /* __GNUC__ */

	#ifndef add_sssaaaa
	#define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0) \
	do { \
	UWtype __s0, __s1, __c0, __c1; \
	__s0 = (a0) + (b0); \
	__s1 = (a1) + (b1); \
	__c0 = __s0 < (a0); \
	__c1 = __s1 < (a1); \
	(s0) = __s0; \
	__s1 = __s1 + __c0; \
	(s1) = __s1; \
	(s2) += __c1 + (__s1 < __c0); \
	} while (0)
	#endif

	struct precomp_div_1_pi2
	{
	mp_limb_t dip[2];
	mp_limb_t d;
	int norm_cnt;
	};

	mp_limb_t
	mpn_div_qr_1u_pi2 (mp_ptr qp,
	mp_srcptr up, mp_size_t un,
	struct precomp_div_1_pi2 *pd)
	{
	mp_size_t i;
	mp_limb_t r, u2, u1, u0;
	mp_limb_t d0, di1, di0;
	mp_limb_t q3a, q2a, q2b, q1b, q2c, q1c, q1d, q0d;
	mp_limb_t cnd;
	int cnt;

	ASSERT (un >= 2);
	ASSERT ((pd->d & GMP_NUMB_HIGHBIT) == 0);
	ASSERT (! MPN_OVERLAP_P (qp, un-2, up, un) \|\| qp+2 >= up);
	ASSERT_MPN (up, un);

	#define q3 q3a
	#define q2 q2b
	#define q1 q1b

	up += un - 3;
	cnt = pd->norm_cnt;
	r = up[2] >> (GMP_NUMB_BITS - cnt);
	d0 = pd->d << cnt;

	qp += un - 2;

	di1 = pd->dip[1];
	di0 = pd->dip[0];

	for (i = un - 3; i >= 0; i -= 2)
	{
	u2 = r;
	u1 = (up[2] << cnt) \| (up[1] >> (GMP_NUMB_BITS - cnt));
	u0 = (up[1] << cnt) \| (up[0] >> (GMP_NUMB_BITS - cnt));

	/* Dividend in {r,u1,u0} */

	umul_ppmm (q1d,q0d, u1, di0);
	umul_ppmm (q2b,q1b, u1, di1);
	q2b++; /* cannot spill */
	add_sssaaaa (r,q2b,q1b, q2b,q1b, u1,u0);

	umul_ppmm (q2c,q1c, u2, di0);
	add_sssaaaa (r,q2b,q1b, q2b,q1b, q2c,q1c);
	umul_ppmm (q3a,q2a, u2, di1);

	add_sssaaaa (r,q2b,q1b, q2b,q1b, q2a,q1d);

	q3 += r;

	r = u0 - q2 * d0;

	cnd = (r >= q1);
	r += d0 & -cnd;
	sub_ddmmss (q3,q2, q3,q2, 0,cnd);

	if (UNLIKELY (r >= d0))
	{
	r -= d0;
	add_ssaaaa (q3,q2, q3,q2, 0,1);
	}

	qp[0] = q2;
	qp[1] = q3;

	up -= 2;
	qp -= 2;
	}

	if ((un & 1) != 0)
	{
	u2 = r;
	u1 = (up[2] << cnt);

	udiv_qrnnd_preinv (q3, r, u2, u1, d0, di1);
	qp[1] = q3;
	}
	else
	{
	u2 = r;
	u1 = (up[2] << cnt) \| (up[1] >> (GMP_NUMB_BITS - cnt));
	u0 = (up[1] << cnt);

	/* Dividend in {r,u1,u0} */

	umul_ppmm (q1d,q0d, u1, di0);
	umul_ppmm (q2b,q1b, u1, di1);
	q2b++; /* cannot spill */
	add_sssaaaa (r,q2b,q1b, q2b,q1b, u1,u0);

	umul_ppmm (q2c,q1c, u2, di0);
	add_sssaaaa (r,q2b,q1b, q2b,q1b, q2c,q1c);
	umul_ppmm (q3a,q2a, u2, di1);

	add_sssaaaa (r,q2b,q1b, q2b,q1b, q2a,q1d);

	q3 += r;

	r = u0 - q2 * d0;

	cnd = (r >= q1);
	r += d0 & -cnd;
	sub_ddmmss (q3,q2, q3,q2, 0,cnd);

	if (UNLIKELY (r >= d0))
	{
	r -= d0;
	add_ssaaaa (q3,q2, q3,q2, 0,1);
	}

	qp[0] = q2;
	qp[1] = q3;
	}

	return r >> cnt;

	#undef q3
	#undef q2
	#undef q1
	}