8373480: Optimize multiplication by constant multiplier using LEA instructions

[jatin-bhateja]

Emulate multiplier using LEA addressing scheme, where effective address = BASE + INDEX * SCALE + OFFSET
Refer to section "3.5.1.2 Using LEA" of Intel's optimization manual for details reagarding slow vs fast lea instructions.
Given that latency of IMUL with register operands is 3 cycles, a combination of two fast LEAs each with 1 cycle latency to emulate multipler is performant.

Consider X as the multiplicand, by variying the scale of first LEA instruction we can generate 4 input i.e.

    X + X * 1 = 2X
    X + X * 2 = 3X
    X + X * 4 = 5X
    X + X * 8 = 9X

Following table list downs various multiplier combinations for output of first LEA at BASE and/or INDEX by varying the
scale of second fast LEA instruction. We will only handle the cases which cannot be handled by just shift + add.

      BASE   INDEX   SCALE  MULTIPLER
        X      X       1       2       (Terminal)
        X      X       2       3       (Terminal)
        X      X       4       5       (Terminal)
        X      X       8       9       (Terminal)
       3X     3X       1       6
        X     3X       2       7
       5X     5X       1      10
        X     5X       2      11
        X     3X       4      13
       5X     5X       2      15
        X     2X       8      17
       9X     9X       1      18
        X     9X       2      19
        X     5X       4      21
       5X     5X       4      25
       9X     9X       2      27
        X     9X       4      37
        X     5X       8      41
       9X     9X       4      45
        X     9X       8      73
       9X     9X       8      81

All the non-unity inputs tied to BASE / INDEX are derived out of terminal cases which represent first FAST LEA. Thus, all the multipliers can be computed using just two LEA instructions.

Preliminary benchmarking shows around 15% improvments on latest x86 servers.

TODO:

• Functional validation jtreg.
• JMH micro benchmark.

Best Regards,
Jatin

---

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Issue

• JDK-8373480: Optimize multiplication by constant multiplier using LEA instructions (Enhancement - P4)

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