/* flonum_mult.c - multiply two flonums
Copyright (C) 1987-2024 Free Software Foundation, Inc.
This file is part of GAS, the GNU Assembler.
GAS is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3, or (at your option)
any later version.
GAS 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 a copy of the GNU General Public License
along with GAS; see the file COPYING. If not, write to the Free
Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
02110-1301, USA. */
#include "ansidecl.h"
#include "flonum.h"
/* plan for a . b => p(roduct)
+-------+-------+-/ /-+-------+-------+
| a | a | ... | a | a |
| A | A-1 | | 1 | 0 |
+-------+-------+-/ /-+-------+-------+
+-------+-------+-/ /-+-------+-------+
| b | b | ... | b | b |
| B | B-1 | | 1 | 0 |
+-------+-------+-/ /-+-------+-------+
+-------+-------+-/ /-+-------+-/ /-+-------+-------+
| p | p | ... | p | ... | p | p |
| A+B+1| A+B | | N | | 1 | 0 |
+-------+-------+-/ /-+-------+-/ /-+-------+-------+
/^\
(carry) a .b ... | ... a .b a .b
A B | 0 1 0 0
|
... | ... a .b
| 1 0
|
| ...
|
|
|
| ___
| \
+----- P = > a .b
N /__ i j
N = 0 ... A+B
for all i,j where i+j=N
[i,j integers > 0]
a[], b[], p[] may not intersect.
Zero length factors signify 0 significant bits: treat as 0.0.
0.0 factors do the right thing.
Zero length product OK.
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
probably yield better code on most C compilers. Dean Elsner.
(C style also gives deeper insight [to me] ... oh well ...) */
void
flonum_multip (const FLONUM_TYPE *a, const FLONUM_TYPE *b,
FLONUM_TYPE *product)
{
int size_of_a; /* 0 origin */
int size_of_b; /* 0 origin */
int size_of_product; /* 0 origin */
int size_of_sum; /* 0 origin */
int extra_product_positions; /* 1 origin */
unsigned long work;
unsigned long carry;
long exponent;
LITTLENUM_TYPE *q;
long significant; /* TRUE when we emit a non-0 littlenum */
/* ForTran accent follows. */
int P; /* Scan product low-order -> high. */
int N; /* As in sum above. */
int A; /* Which [] of a? */
int B; /* Which [] of b? */
if ((a->sign != '-' && a->sign != '+')
|| (b->sign != '-' && b->sign != '+'))
{
/* Got to fail somehow. Any suggestions? */
product->sign = 0;
return;
}
product->sign = (a->sign == b->sign) ? '+' : '-';
size_of_a = a->leader - a->low;
size_of_b = b->leader - b->low;
exponent = a->exponent + b->exponent;
size_of_product = product->high - product->low;
size_of_sum = size_of_a + size_of_b;
extra_product_positions = size_of_product - size_of_sum;
if (extra_product_positions < 0)
{
P = extra_product_positions; /* P < 0 */
exponent -= extra_product_positions; /* Increases exponent. */
}
else
{
P = 0;
}
carry = 0;
significant = 0;
for (N = 0; N <= size_of_sum; N++)
{
work = carry;
carry = 0;
for (A = 0; A <= N; A++)
{
B = N - A;
if (A <= size_of_a && B <= size_of_b && B >= 0)
{
#ifdef TRACE
printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
A, a->low[A], B, b->low[B], work);
#endif
/* Watch out for sign extension! Without the casts, on
the DEC Alpha, the multiplication result is *signed*
int, which gets sign-extended to convert to the
unsigned long! */
work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
carry += work >> LITTLENUM_NUMBER_OF_BITS;
work &= LITTLENUM_MASK;
#ifdef TRACE
printf ("work=%08x carry=%04x\n", work, carry);
#endif
}
}
significant |= work;
if (significant || P < 0)
{
if (P >= 0)
{
product->low[P] = work;
#ifdef TRACE
printf ("P=%d. work[p]:=%04x\n", P, work);
#endif
}
P++;
}
else
{
extra_product_positions++;
exponent++;
}
}
/* [P]-> position # size_of_sum + 1.
This is where 'carry' should go. */
#ifdef TRACE
printf ("final carry =%04x\n", carry);
#endif
if (carry)
{
if (extra_product_positions > 0)
product->low[P] = carry;
else
{
/* No room at high order for carry littlenum. */
/* Shift right 1 to make room for most significant littlenum. */
exponent++;
P--;
for (q = product->low + P; q >= product->low; q--)
{
work = *q;
*q = carry;
carry = work;
}
}
}
else
P--;
product->leader = product->low + P;
product->exponent = exponent;
}
