Page 222 - ARM 64 Bit Assembly Language

210 Chapter 7

Listing 7.5 AArch64 assembly code for division by constant 193.

1 // The following code will calculate w2/193
2 // It will leave the quotient in x0 and
3 // the remainder in x1
4 ldr x3, =0x54E42524 // x3 = (1/193 << 38)
5 smull x4, w2, w3 //x*m
6 asr x0, x4, #38
7 sub x0, x0, x4, asr #63 // subtract sign of dividend
8 // calculate remainder in x1
9 mov x1, #193 // x1 = divisor
10 mul x1, x1, x0 // multiply divisor by product
11 sub x1, x2, x1 // subtract that from numerator

Example 17 shows how to calculate m and n for division by 193. On the AArch64 processor,
division by a constant can be performed very efficiently. Listing 7.5 shows how division by
193 can be implemented using only a few lines of code. In the listing, the numbers are 32 bits
in length, so the constant m is much larger than in the example that was multiplied by hand,
but otherwise the method is the same.
If we wish to divide by 23 using 32 bits of precision, we compute the multiplier as

2 32+4−1 2 35
m = + 1 = + 1 = 1493901669.17 ≈ 1493901669 = 590B2165 16 .
23 23
That is 01011001000010110010000101100101 2 . Note that there are only 12 non-zero bits,
and the pattern 1011001 appears three times in the 32-bit multiplier. The multiply can be im-
24 6 4 3 0 13 6 4 3 0 2 6 4
plemented as 2 (2 x + 2 x + 2 x + 2 x) + 2 (2 x + 2 x + 2 x + 2 x) + 2 (2 x + 2 x +
0
3
0
2 x + 2 x) + 2 x. So the following code sequence can be used on processors that do not have
the multiply instruction:
Listing 7.6 AArch64 assembly code for division of a variable by a constant without using
a multiply instruction.

1 // The following code will calculate w2/23
2 // It will leave the quotient in x0 and does
3 // not calculate a remainder
4 sxtw x2, w2 // Sign extend w2
5 mov x0, x2 // Copy into x0
6 // calculate 2^6x+2^4x+2^3x+2^0x
7 add x3, x2, x0, lsl #3
8 add x3, x3, x0, lsl #4
9 add x3, x3, x0, lsl #6
10 // now perform three 64-bit shift-add operations
11 lsl x3, x3, #2