/* flonum_mult.c - multiply two flonums
|
/* flonum_mult.c - multiply two flonums
|
Copyright 1987, 1990, 1991, 1992, 1995, 2000, 2002, 2003, 2007
|
Copyright 1987, 1990, 1991, 1992, 1995, 2000, 2002, 2003, 2007
|
Free Software Foundation, Inc.
|
Free Software Foundation, Inc.
|
|
|
This file is part of GAS, the GNU Assembler.
|
This file is part of GAS, the GNU Assembler.
|
|
|
GAS is free software; you can redistribute it and/or modify
|
GAS is free software; you can redistribute it and/or modify
|
it under the terms of the GNU General Public License as published by
|
it under the terms of the GNU General Public License as published by
|
the Free Software Foundation; either version 3, or (at your option)
|
the Free Software Foundation; either version 3, or (at your option)
|
any later version.
|
any later version.
|
|
|
GAS is distributed in the hope that it will be useful, but WITHOUT
|
GAS is distributed in the hope that it will be useful, but WITHOUT
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
|
License for more details.
|
License for more details.
|
|
|
You should have received a copy of the GNU General Public License
|
You should have received a copy of the GNU General Public License
|
along with GAS; see the file COPYING. If not, write to the Free
|
along with GAS; see the file COPYING. If not, write to the Free
|
Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
|
Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
|
02110-1301, USA. */
|
02110-1301, USA. */
|
|
|
#include "ansidecl.h"
|
#include "ansidecl.h"
|
#include "flonum.h"
|
#include "flonum.h"
|
|
|
/* plan for a . b => p(roduct)
|
/* plan for a . b => p(roduct)
|
|
|
+-------+-------+-/ /-+-------+-------+
|
+-------+-------+-/ /-+-------+-------+
|
| a | a | ... | a | a |
|
| a | a | ... | a | a |
|
| A | A-1 | | 1 | 0 |
|
| A | A-1 | | 1 | 0 |
|
+-------+-------+-/ /-+-------+-------+
|
+-------+-------+-/ /-+-------+-------+
|
|
|
+-------+-------+-/ /-+-------+-------+
|
+-------+-------+-/ /-+-------+-------+
|
| b | b | ... | b | b |
|
| b | b | ... | b | b |
|
| B | B-1 | | 1 | 0 |
|
| B | B-1 | | 1 | 0 |
|
+-------+-------+-/ /-+-------+-------+
|
+-------+-------+-/ /-+-------+-------+
|
|
|
+-------+-------+-/ /-+-------+-/ /-+-------+-------+
|
+-------+-------+-/ /-+-------+-/ /-+-------+-------+
|
| p | p | ... | p | ... | p | p |
|
| p | p | ... | p | ... | p | p |
|
| A+B+1| A+B | | N | | 1 | 0 |
|
| A+B+1| A+B | | N | | 1 | 0 |
|
+-------+-------+-/ /-+-------+-/ /-+-------+-------+
|
+-------+-------+-/ /-+-------+-/ /-+-------+-------+
|
|
|
/^\
|
/^\
|
(carry) a .b ... | ... a .b a .b
|
(carry) a .b ... | ... a .b a .b
|
A B | 0 1 0 0
|
A B | 0 1 0 0
|
|
|
|
|
... | ... a .b
|
... | ... a .b
|
| 1 0
|
| 1 0
|
|
|
|
|
| ...
|
| ...
|
|
|
|
|
|
|
|
|
|
|
|
|
| ___
|
| ___
|
| \
|
| \
|
+----- P = > a .b
|
+----- P = > a .b
|
N /__ i j
|
N /__ i j
|
|
|
N = 0 ... A+B
|
N = 0 ... A+B
|
|
|
for all i,j where i+j=N
|
for all i,j where i+j=N
|
[i,j integers > 0]
|
[i,j integers > 0]
|
|
|
a[], b[], p[] may not intersect.
|
a[], b[], p[] may not intersect.
|
Zero length factors signify 0 significant bits: treat as 0.0.
|
Zero length factors signify 0 significant bits: treat as 0.0.
|
0.0 factors do the right thing.
|
0.0 factors do the right thing.
|
Zero length product OK.
|
Zero length product OK.
|
|
|
I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
|
I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
|
because I felt the ForTran way was more intuitive. The C way would
|
because I felt the ForTran way was more intuitive. The C way would
|
probably yield better code on most C compilers. Dean Elsner.
|
probably yield better code on most C compilers. Dean Elsner.
|
(C style also gives deeper insight [to me] ... oh well ...) */
|
(C style also gives deeper insight [to me] ... oh well ...) */
|
|
|
void
|
void
|
flonum_multip (const FLONUM_TYPE *a, const FLONUM_TYPE *b,
|
flonum_multip (const FLONUM_TYPE *a, const FLONUM_TYPE *b,
|
FLONUM_TYPE *product)
|
FLONUM_TYPE *product)
|
{
|
{
|
int size_of_a; /* 0 origin */
|
int size_of_a; /* 0 origin */
|
int size_of_b; /* 0 origin */
|
int size_of_b; /* 0 origin */
|
int size_of_product; /* 0 origin */
|
int size_of_product; /* 0 origin */
|
int size_of_sum; /* 0 origin */
|
int size_of_sum; /* 0 origin */
|
int extra_product_positions; /* 1 origin */
|
int extra_product_positions; /* 1 origin */
|
unsigned long work;
|
unsigned long work;
|
unsigned long carry;
|
unsigned long carry;
|
long exponent;
|
long exponent;
|
LITTLENUM_TYPE *q;
|
LITTLENUM_TYPE *q;
|
long significant; /* TRUE when we emit a non-0 littlenum */
|
long significant; /* TRUE when we emit a non-0 littlenum */
|
/* ForTran accent follows. */
|
/* ForTran accent follows. */
|
int P; /* Scan product low-order -> high. */
|
int P; /* Scan product low-order -> high. */
|
int N; /* As in sum above. */
|
int N; /* As in sum above. */
|
int A; /* Which [] of a? */
|
int A; /* Which [] of a? */
|
int B; /* Which [] of b? */
|
int B; /* Which [] of b? */
|
|
|
if ((a->sign != '-' && a->sign != '+')
|
if ((a->sign != '-' && a->sign != '+')
|
|| (b->sign != '-' && b->sign != '+'))
|
|| (b->sign != '-' && b->sign != '+'))
|
{
|
{
|
/* Got to fail somehow. Any suggestions? */
|
/* Got to fail somehow. Any suggestions? */
|
product->sign = 0;
|
product->sign = 0;
|
return;
|
return;
|
}
|
}
|
product->sign = (a->sign == b->sign) ? '+' : '-';
|
product->sign = (a->sign == b->sign) ? '+' : '-';
|
size_of_a = a->leader - a->low;
|
size_of_a = a->leader - a->low;
|
size_of_b = b->leader - b->low;
|
size_of_b = b->leader - b->low;
|
exponent = a->exponent + b->exponent;
|
exponent = a->exponent + b->exponent;
|
size_of_product = product->high - product->low;
|
size_of_product = product->high - product->low;
|
size_of_sum = size_of_a + size_of_b;
|
size_of_sum = size_of_a + size_of_b;
|
extra_product_positions = size_of_product - size_of_sum;
|
extra_product_positions = size_of_product - size_of_sum;
|
if (extra_product_positions < 0)
|
if (extra_product_positions < 0)
|
{
|
{
|
P = extra_product_positions; /* P < 0 */
|
P = extra_product_positions; /* P < 0 */
|
exponent -= extra_product_positions; /* Increases exponent. */
|
exponent -= extra_product_positions; /* Increases exponent. */
|
}
|
}
|
else
|
else
|
{
|
{
|
P = 0;
|
P = 0;
|
}
|
}
|
carry = 0;
|
carry = 0;
|
significant = 0;
|
significant = 0;
|
for (N = 0; N <= size_of_sum; N++)
|
for (N = 0; N <= size_of_sum; N++)
|
{
|
{
|
work = carry;
|
work = carry;
|
carry = 0;
|
carry = 0;
|
for (A = 0; A <= N; A++)
|
for (A = 0; A <= N; A++)
|
{
|
{
|
B = N - A;
|
B = N - A;
|
if (A <= size_of_a && B <= size_of_b && B >= 0)
|
if (A <= size_of_a && B <= size_of_b && B >= 0)
|
{
|
{
|
#ifdef TRACE
|
#ifdef TRACE
|
printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
|
printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
|
A, a->low[A], B, b->low[B], work);
|
A, a->low[A], B, b->low[B], work);
|
#endif
|
#endif
|
/* Watch out for sign extension! Without the casts, on
|
/* Watch out for sign extension! Without the casts, on
|
the DEC Alpha, the multiplication result is *signed*
|
the DEC Alpha, the multiplication result is *signed*
|
int, which gets sign-extended to convert to the
|
int, which gets sign-extended to convert to the
|
unsigned long! */
|
unsigned long! */
|
work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
|
work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
|
carry += work >> LITTLENUM_NUMBER_OF_BITS;
|
carry += work >> LITTLENUM_NUMBER_OF_BITS;
|
work &= LITTLENUM_MASK;
|
work &= LITTLENUM_MASK;
|
#ifdef TRACE
|
#ifdef TRACE
|
printf ("work=%08x carry=%04x\n", work, carry);
|
printf ("work=%08x carry=%04x\n", work, carry);
|
#endif
|
#endif
|
}
|
}
|
}
|
}
|
significant |= work;
|
significant |= work;
|
if (significant || P < 0)
|
if (significant || P < 0)
|
{
|
{
|
if (P >= 0)
|
if (P >= 0)
|
{
|
{
|
product->low[P] = work;
|
product->low[P] = work;
|
#ifdef TRACE
|
#ifdef TRACE
|
printf ("P=%d. work[p]:=%04x\n", P, work);
|
printf ("P=%d. work[p]:=%04x\n", P, work);
|
#endif
|
#endif
|
}
|
}
|
P++;
|
P++;
|
}
|
}
|
else
|
else
|
{
|
{
|
extra_product_positions++;
|
extra_product_positions++;
|
exponent++;
|
exponent++;
|
}
|
}
|
}
|
}
|
/* [P]-> position # size_of_sum + 1.
|
/* [P]-> position # size_of_sum + 1.
|
This is where 'carry' should go. */
|
This is where 'carry' should go. */
|
#ifdef TRACE
|
#ifdef TRACE
|
printf ("final carry =%04x\n", carry);
|
printf ("final carry =%04x\n", carry);
|
#endif
|
#endif
|
if (carry)
|
if (carry)
|
{
|
{
|
if (extra_product_positions > 0)
|
if (extra_product_positions > 0)
|
product->low[P] = carry;
|
product->low[P] = carry;
|
else
|
else
|
{
|
{
|
/* No room at high order for carry littlenum. */
|
/* No room at high order for carry littlenum. */
|
/* Shift right 1 to make room for most significant littlenum. */
|
/* Shift right 1 to make room for most significant littlenum. */
|
exponent++;
|
exponent++;
|
P--;
|
P--;
|
for (q = product->low + P; q >= product->low; q--)
|
for (q = product->low + P; q >= product->low; q--)
|
{
|
{
|
work = *q;
|
work = *q;
|
*q = carry;
|
*q = carry;
|
carry = work;
|
carry = work;
|
}
|
}
|
}
|
}
|
}
|
}
|
else
|
else
|
P--;
|
P--;
|
product->leader = product->low + P;
|
product->leader = product->low + P;
|
product->exponent = exponent;
|
product->exponent = exponent;
|
}
|
}
|
|
|
