[all-commits] [llvm/llvm-project] aa3f93: [libc][math] Add float-only implementation for ata...

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: aa3f930931e65b02bacac0c7dfa52a181a0fd5bb
      https://github.com/llvm/llvm-project/commit/aa3f930931e65b02bacac0c7dfa52a181a0fd5bb
  Author: lntue <lntue at google.com>
  Date:   2025-11-20 (Thu, 20 Nov 2025)

  Changed paths:
    M libc/src/__support/math/CMakeLists.txt
    M libc/src/__support/math/atanf.h
    A libc/src/__support/math/atanf_float.h
    M libc/test/src/math/atanf_test.cpp
    M libc/test/src/math/exhaustive/CMakeLists.txt
    A libc/test/src/math/exhaustive/atanf_float_test.cpp

  Log Message:
  -----------
  [libc][math] Add float-only implementation for atanf. (#167004)

Algorithm:
```
  1)  atan(x) = sign(x) * atan(|x|)

  2)  If |x| > 1 + 1/32, atan(|x|) = pi/2 - atan(1/|x|)

  3)  For 1/16 < |x| < 1 + 1/32, we find k such that: | |x| - k/16 | <= 1/32.
      Let y = |x| - k/16, then using the angle summation formula, we have:
    atan(|x|) = atan(k/16) + atan( (|x| - k/16) / (1 + |x| * k/16) )
              = atan(k/16) + atan( y / (1 + (y + k/16) * k/16 )
              = atan(k/16) + atan( y / ((1 + k^2/256) + y * k/16) )

  4)  Let u = y / (1 + k^2/256), then we can rewritten the above as:
    atan(|x|) = atan(k/16) + atan( u / (1 + u * k/16) )
              ~ atan(k/16) + (u - k/16 * u^2 + (k^2/256 - 1/3) * u^3 +
                              + (k/16 - (k/16)^3) * u^4) + O(u^5)
```

With all the computations are done in single precision (float), the
total of approximation errors and rounding errors is bounded by 4 ULPs.



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