llvm-project.git/libc/test/src/math/cbrtf_test.cpp, branch users/nico/python-1 Unnamed repository; edit this file 'description' to name the repository. [libc][math] Implement cbrtf function correctly rounded to all rounding modes. (#97936) 2024-07-08T14:02:12+00:00 lntue 35648136+lntue@users.noreply.github.com 2024-07-08T14:02:12+00:00 c9ee6b1977e7dc88e3bd89b5e361c703721711fd Fixes https://github.com/llvm/llvm-project/issues/92874 Algorithm: Let `x = (-1)^s * 2^e * (1 + m)`. - Step 1: Range reduction: reduce the exponent with: ``` y = cbrt(x) = (-1)^s * 2^(floor(e/3)) * 2^((e % 3)/3) * (1 + m)^(1/3) ``` - Step 2: Use the first 4 bit fractional bits of `m` to look up for a degree-7 polynomial approximation to: ``` (1 + m)^(1/3) ~ 1 + m * P(m). ``` - Step 3: Perform the multiplication: ``` 2^((e % 3)/3) * (1 + m)^(1/3). ``` - Step 4: Check for exact cases to prevent rounding and clear `FE_INEXACT` floating point exception. - Step 5: Combine with the exponent and sign before converting down to `float` and return. 
Fixes https://github.com/llvm/llvm-project/issues/92874

Algorithm: Let `x = (-1)^s * 2^e * (1 + m)`.
- Step 1: Range reduction: reduce the exponent with:
```
  y = cbrt(x) = (-1)^s * 2^(floor(e/3)) * 2^((e % 3)/3) * (1 + m)^(1/3)
```
- Step 2: Use the first 4 bit fractional bits of `m` to look up for a
degree-7 polynomial approximation to:
```
  (1 + m)^(1/3) ~ 1 + m * P(m).
```
- Step 3: Perform the multiplication:
```
  2^((e % 3)/3) * (1 + m)^(1/3).
```
- Step 4: Check for exact cases to prevent rounding and clear
`FE_INEXACT` floating point exception.
- Step 5: Combine with the exponent and sign before converting down to
`float` and return.