X=X+Y*Z
All 32*32 matrices, 64-bit double-precision elements
C code
void mm(double x[][], double y[][], double z[][]){
int i, j, k;
for (i = 0; i != 32; i = i + 1)
for (j = 0; j != 32; j = j + 1)
for (k = 0; k != 32; k = k + 1)
x[i][j] = x[i][j] + y[i][k] * z[k][j];
}
Compiled MIPS code
li $t1, 32 # $t1 = 32 -> li : load immediate
li $s0, 0 # i = 0
li $s1, 0 # j = 0
li $s2, 0 # k = 0
sll $t2, $s0, 5 # $t2 = i * 32 (size of row of x)
addu $t2 $t2, $s1 # $t2 = i * size(row) + j
sll $t2, $t2, 3 # $t2 = byte offset of [i][j]
addu $t2, $a0, $t2 # $t2 = byet address of x[i][j]
l.d $f4, 0($t2) # $f4 = 8 bytes of x[i][j] -> $f4, $f5에 모두 저장됨
L3: sll $t0, $s2, 5 # $t0 = k * 32 (size of row of z)
addu $t0, $t0, $s1 # $t0 = k * size(row) + j
sll $t0, $t0, 3 # $t0 = byte offset of [k][j]
addu $t0, $a2, $t0 # $t0 = byte address of z[k][j]
l.d $f16, 0($t0) # $f16 = 8 bytes of z[k][j]
sll $t0, $s0, 5 # $t0 = i * 32 (size of row of y)
addu $t0 $t0, $s2 # $t0 = i * size(row) + k
sll $t0, $t0, 3 # $t0 = byte offset of [i][k]
addu $t0, $a1, $t0 # $t0 = byte address of y[i][k]
l.d $f18, 0($t0) # $f18 = 8 bytes of y[i][k]
**mul.d $f16, $f18, $f16 # $f16 = y[i][k] * z[k][j]
add.d $f4, $f4, $f16 # $f4 = x[i][j] + y[i][k] * z[k][j]**
addiu $s2, $s2, 1 # $k = k + 1
bne $s2, $t1, L3 # if (k != 32) go to L3
**s.d $f4, 0($t2) # x[i][j] = $f4**
addiu $s1, $s1, 1 # $j = j + 1
bne $s1, $t1, L2 # if (j != 32) go to L2
addiu $s0, $s0, 1 # $i = i + 1
bne $s0, $t1, L1 # if (i != 32) go to L1
Extra bits of precision(guard, round, sticky)
Choice of rounding modes
round up : 올림
round down : 내림
truncate : 버림
round to nearest even : 가장 가까운 짝수로 반올림 ⇒ 정확도가 유지됨.
ex) 0.5 → 0 // 1.5 → 2 // 2.5 → 2 // 3.5 → 4
| Binary | +0001.01 | -0001.01 | +0101.10 | +0100.10 | -0011.10 |
|---|---|---|---|---|---|
| Round up | +0010 | -0001 | +0.0110 | +0101 | -0011 |
| Round down | +0.001 | -0010 | +0101 | +0100 | -0100 |
| Truncate | +0001 | -0001 | +0101 | +0100 | -0011 |
| Round to nearest even | +0001 | +0001 | +0110 | +0100 | -0100 |