Skip to content

[libc][math] Implement correctly rounded double precision tan #97489

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 3 commits into from
Jul 3, 2024
Merged

[libc][math] Implement correctly rounded double precision tan #97489

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
41fcdc8
[libc][math] Implement correctly roudned double precision tan.
lntue Jul 2, 2024
248dcae
Fix smoke test.
lntue Jul 3, 2024
3813b44
Address comments
lntue Jul 3, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
1 change: 1 addition & 0 deletions libc/config/darwin/arm/entrypoints.txt
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -234,6 +234,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.sqrt
libc.src.math.sqrtf
libc.src.math.sqrtl
libc.src.math.tan
libc.src.math.tanf
libc.src.math.tanhf
libc.src.math.trunc
Expand Down
1 change: 1 addition & 0 deletions libc/config/linux/aarch64/entrypoints.txt
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -489,6 +489,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.sqrt
libc.src.math.sqrtf
libc.src.math.sqrtl
libc.src.math.tan
libc.src.math.tanf
libc.src.math.tanhf
libc.src.math.trunc
Expand Down
1 change: 1 addition & 0 deletions libc/config/linux/arm/entrypoints.txt
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -366,6 +366,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.sqrt
libc.src.math.sqrtf
libc.src.math.sqrtl
libc.src.math.tan
libc.src.math.tanf
libc.src.math.tanhf
libc.src.math.trunc
Expand Down
1 change: 1 addition & 0 deletions libc/config/linux/riscv/entrypoints.txt
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -497,6 +497,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.sqrt
libc.src.math.sqrtf
libc.src.math.sqrtl
libc.src.math.tan
libc.src.math.tanf
libc.src.math.tanhf
libc.src.math.trunc
Expand Down
2 changes: 1 addition & 1 deletion libc/docs/math/index.rst
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -338,7 +338,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sqrt | |check| | |check| | |check| | | |check| | 7.12.7.10 | F.10.4.10 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| tan | |check| | | | | | 7.12.4.7 | F.10.1.7 |
| tan | |check| | |check| | | | | 7.12.4.7 | F.10.1.7 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| tanh | |check| | | | | | 7.12.5.6 | F.10.2.6 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
Expand Down
36 changes: 36 additions & 0 deletions libc/src/__support/FPUtil/double_double.h
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -129,6 +129,42 @@ LIBC_INLINE DoubleDouble multiply_add<DoubleDouble>(const DoubleDouble &a,
return add(c, quick_mult(a, b));
}

// Accurate double-double division, following Karp-Markstein's trick for
// division, implemented in the CORE-MATH project at:
// https://gitlab.inria.fr/core-math/core-math/-/blob/master/src/binary64/tan/tan.c#L1855
//
// Error bounds:
// Let a = ah + al, b = bh + bl.
// Let r = rh + rl be the approximation of (ah + al) / (bh + bl).
// Then:
// (ah + al) / (bh + bl) - rh =
// = ((ah - bh * rh) + (al - bl * rh)) / (bh + bl)
// = (1 + O(bl/bh)) * ((ah - bh * rh) + (al - bl * rh)) / bh
// Let q = round(1/bh), then the above expressions are approximately:
// = (1 + O(bl / bh)) * (1 + O(2^-52)) * q * ((ah - bh * rh) + (al - bl * rh))
// So we can compute:
// rl = q * (ah - bh * rh) + q * (al - bl * rh)
// as accurate as possible, then the error is bounded by:
// |(ah + al) / (bh + bl) - (rh + rl)| < O(bl/bh) * (2^-52 + al/ah + bl/bh)
LIBC_INLINE DoubleDouble div(const DoubleDouble &a, const DoubleDouble &b) {
DoubleDouble r;
double q = 1.0 / b.hi;
r.hi = a.hi * q;

#ifdef LIBC_TARGET_CPU_HAS_FMA
double e_hi = fputil::multiply_add(b.hi, -r.hi, a.hi);
double e_lo = fputil::multiply_add(b.lo, -r.hi, a.lo);
#else
DoubleDouble b_hi_r_hi = fputil::exact_mult</*NO_FMA=*/true>(b.hi, -r.hi);
DoubleDouble b_lo_r_hi = fputil::exact_mult</*NO_FMA=*/true>(b.lo, -r.hi);
double e_hi = (a.hi + b_hi_r_hi.hi) + b_hi_r_hi.lo;
double e_lo = (a.lo + b_lo_r_hi.hi) + b_lo_r_hi.lo;
#endif // LIBC_TARGET_CPU_HAS_FMA

r.lo = q * (e_hi + e_lo);
return r;
}

} // namespace LIBC_NAMESPACE::fputil

#endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_DOUBLE_DOUBLE_H
21 changes: 21 additions & 0 deletions libc/src/math/generic/CMakeLists.txt
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -323,6 +323,27 @@ add_entrypoint_object(
-O3
)

add_entrypoint_object(
tan
SRCS
tan.cpp
HDRS
../tan.h
DEPENDS
.range_reduction_double
libc.hdr.errno_macros
libc.src.errno.errno
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.macros.optimization
COMPILE_OPTIONS
-O3
Comment on lines +343 to +344
Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

We don't do debug builds at all for math, right? I think normally a release build is O2 so it makes sense to override to O3 in that case.

)

add_entrypoint_object(
tanf
SRCS
Expand Down
Loading
Loading