[PATCH] D13994: Optimization for pow(x, n) where n is some constant

[Mandeep Singh Grang via llvm-commits]

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In order to avoid calling pow function we generate repeated fmul when n is a
positive or negative whole number. The idea here is that:
  x^(2^i) = x^(2^(i/2)) * x^(2^(i/2))

For eg:
  pow(x, 4.0) ==> y = fmul x, x
                  x = fmul y, y
                  ret x

For exponents which are not powers of 2, we generate fmul as follows:
  pow(x, 5.0) ==> y = fmul x, x
                  z = fmul y, y
                  x = fmul z, x
                  ret x

For negative exponents we simply divide the final result by 1.0 thus generating
an fdiv instruction.

The max no. of fmul generated = ceil(log2 n)
where, log2 is log to the base 2
       n = the exponent of x

By default, fmul would be generated only when exponent <= 32.
For exponents greater than 32 we generate pow instruction.
We provide a new flag:
  -mllvm -power-opt-threshold=<limit>
which can be set to override the default behavior.

Note: The above behavior is enabled only when -ffast-math is enabled (this is
similar to GCC's behavior).

Repository:
  rL LLVM

http://reviews.llvm.org/D13994

Files:
  lib/Transforms/Utils/SimplifyLibCalls.cpp
  test/Transforms/InstCombine/pow-4.ll

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