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Optimized mp multiplication

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Don't bother multiplying zeroes since that only wastes cycles.
This commit is contained in:
Siddhesh Poyarekar 2013-02-13 14:16:23 +05:30
parent bdf028142e
commit 909279a5cf
2 changed files with 51 additions and 8 deletions
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3
ChangeLog
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@ -1,5 +1,8 @@
2013-02-13 Siddhesh Poyarekar <siddhesh@redhat.com>
* sysdeps/ieee754/dbl-64/mpa.c (__mul): Don't bother with zero
values in the mantissa.
* sysdeps/ieee754/dbl-64/mpa.c (add_magnitudes): Use ZK to
minimize writes to Z.
(sub_magnitudes): Simplify code a bit.

56
sysdeps/ieee754/dbl-64/mpa.c
View File

@ -610,7 +610,7 @@ void
SECTION
__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int i, j, k, k2;
int i, j, k, ip, ip2;
double u, zk;
/* Is z=0? */
@ -620,11 +620,51 @@ __mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
return;
}
/* Multiply, add and carry. */
k2 = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
zk = Z[k2] = ZERO;
/* We need not iterate through all X's and Y's since it's pointless to
multiply zeroes. Here, both are zero... */
for (ip2 = p; ip2 > 0; ip2--)
if (X[ip2] != ZERO || Y[ip2] != ZERO)
break;
for (k = k2; k > p; k--)
/* ... and here, at least one of them is still zero. */
for (ip = ip2; ip > 0; ip--)
if (X[ip] * Y[ip] != ZERO)
break;
/* The product looks like this for p = 3 (as an example):
a1 a2 a3
x b1 b2 b3
-----------------------------
a1*b3 a2*b3 a3*b3
a1*b2 a2*b2 a3*b2
a1*b1 a2*b1 a3*b1
So our K needs to ideally be P*2, but we're limiting ourselves to P + 3
for P >= 3. We compute the above digits in two parts; the last P-1
digits and then the first P digits. The last P-1 digits are a sum of
products of the input digits from P to P-k where K is 0 for the least
significant digit and increases as we go towards the left. The product
term is of the form X[k]*X[P-k] as can be seen in the above example.
The first P digits are also a sum of products with the same product term,
except that the sum is from 1 to k. This is also evident from the above
example.
Another thing that becomes evident is that only the most significant
ip+ip2 digits of the result are non-zero, where ip and ip2 are the
'internal precision' of the input numbers, i.e. digits after ip and ip2
are all ZERO. */
k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
while (k > ip + ip2 + 1)
Z[k--] = ZERO;
zk = Z[k] = ZERO;
while (k > p)
{
for (i = k - p, j = p; i < p + 1; i++, j--)
zk += X[i] * Y[j];
@ -632,10 +672,11 @@ __mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
u = (zk + CUTTER) - CUTTER;
if (u > zk)
u -= RADIX;
Z[k] = zk - u;
Z[k--] = zk - u;
zk = u * RADIXI;
}
/* The real deal. */
while (k > 1)
{
for (i = 1, j = k - 1; i < k; i++, j--)
@ -644,9 +685,8 @@ __mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
u = (zk + CUTTER) - CUTTER;
if (u > zk)
u -= RADIX;
Z[k] = zk - u;
Z[k--] = zk - u;
zk = u * RADIXI;
k--;
}
Z[k] = zk;