[libc] [llvm] [libc][math][c23] Implement higher math function `cbrtf16` in LLVM libc (PR #132484)

[Krishna Pandey via llvm-commits]

krishna2803 wrote:

| x (dec)              | x (hex) | cbrtf16(x) | mpfr::Operation::Cbrt(x)| Error (ULP) | Rounding Mode |
|--------------------------|-----------------|-----------------------|------------------------------------|-------------|---------------|
| 0.000096499919891357421875 | 0x0653          | 0.0458984375          | 0.045867919921875                  | 1           | Upward        |
| 0.000771999359130859375    | 0x1253          | 0.091796875           | 0.09173583984375                   | 1           | Upward        |
| 0.006175994873046875       | 0x1E53          | 0.18359375            | 0.1834716796875                    | 1           | Upward        |
| 0.049407958984375          | 0x2A53          | 0.3671875             | 0.366943359375                     | 1           | Upward        |
| 0.395263671875             | 0x3653          | 0.734375              | 0.73388671875                      | 1           | Upward        |
| 3.162109375                | 0x4253          | 1.46875               | 1.4677734375                       | 1           | Upward        |
| 25.296875                  | 0x4E53          | 2.9375                | 2.935546875                        | 1           | Upward        |
| 202.375                    | 0x5A53          | 5.875                 | 5.87109375                         | 1           | Upward        |
| 1619                       | 0x6653          | 11.75                 | 11.7421875                        | 1           | Upward        |
| 12952                      | 0x7253          | 23.5                  | 23.484375                         | 1           | Upward        |
| -0.000096499919891357421875| 0x8653          | -0.045867919921875     | -0.04583740234375                  | 1           | Upward        |
| -0.000771999359130859375   | 0x9253          | -0.09173583984375      | -0.0916748046875                   | 1           | Upward        |
| -0.006175994873046875      | 0x9E53          | -0.1834716796875       | -0.183349609375                    | 1           | Upward        |
| -0.049407958984375         | 0xAA53          | -0.366943359375        | -0.36669921875                     | 1           | Upward        |
| -0.395263671875            | 0xB653          | -0.73388671875         | -0.7333984375                      | 1           | Upward        |
| -3.162109375               | 0xC253          | -1.4677734375          | -1.466796875                       | 1           | Upward        |
| -25.296875                 | 0xCE53          | -2.935546875           | -2.93359375                        | 1           | Upward        |
| -202.375                   | 0xDA53          | -5.87109375            | -5.8671875                         | 1           | Upward        |
| -1619                     | 0xE653          | -11.7421875           | -11.734375                         | 1           | Upward        |
| -12952                    | 0xF253          | -23.484375            | -23.46875                          | 1           | Upward        |


(same is for negative values just add a negative sign)

after a bit of investigation, i found out that these errors occur when the rounding mode is upward. the result of cbrtf16 function doesn't match with mpfr. and interestingly this occurs when the last byte of the input is `0x53`.

https://github.com/llvm/llvm-project/pull/132484