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[libc][math] Implement a fast pass for atan2f128 with 1ULP error using DyadicFloat<128>. (#133150)

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Part of https://github.com/llvm/llvm-project/issues/131642.
This commit is contained in:
lntue
2025-04-01 10:57:32 -04:00
committed by GitHub
parent 664745cf38
commit 8741412bdf
15 changed files with 514 additions and 4 deletions
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1
libc/config/linux/aarch64/entrypoints.txt
View File

@@ -759,6 +759,7 @@ endif()
if(LIBC_TYPES_HAS_FLOAT128)
list(APPEND TARGET_LIBM_ENTRYPOINTS
# math.h C23 _Float128 entrypoints
libc.src.math.atan2f128
libc.src.math.canonicalizef128
libc.src.math.ceilf128
libc.src.math.copysignf128

1
libc/config/linux/riscv/entrypoints.txt
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@@ -640,6 +640,7 @@ endif()
if(LIBC_TYPES_HAS_FLOAT128)
list(APPEND TARGET_LIBM_ENTRYPOINTS
# math.h C23 _Float128 entrypoints
libc.src.math.atan2f128
libc.src.math.canonicalizef128
libc.src.math.ceilf128
libc.src.math.copysignf128

1
libc/config/linux/x86_64/entrypoints.txt
View File

@@ -776,6 +776,7 @@ endif()
if(LIBC_TYPES_HAS_FLOAT128)
list(APPEND TARGET_LIBM_ENTRYPOINTS
# math.h C23 _Float128 entrypoints
libc.src.math.atan2f128
libc.src.math.canonicalizef128
libc.src.math.ceilf128
libc.src.math.copysignf128

2
libc/docs/headers/math/index.rst
View File

@@ -263,7 +263,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan | |check| | 1 ULP | | | | 7.12.4.3 | F.10.1.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan2 | |check| | 1 ULP | | | | 7.12.4.4 | F.10.1.4 |
| atan2 | |check| | 1 ULP | | | 1 ULP | 7.12.4.4 | F.10.1.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan2pi | | | | | | 7.12.4.11 | F.10.1.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

8
libc/include/math.yaml
View File

@@ -93,6 +93,14 @@ functions:
arguments:
- type: long double
- type: long double
- name: atan2f128
standards:
- stdc
return_type: float128
arguments:
- type: float128
- type: float128
guard: LIBC_TYPES_HAS_FLOAT128
- name: atanf
standards:
- stdc

2
libc/src/__support/FPUtil/dyadic_float.h
View File

@@ -104,7 +104,7 @@ template <size_t Bits> struct DyadicFloat {
normalize();
}
LIBC_INLINE constexpr DyadicFloat(Sign s, int e, MantissaType m)
LIBC_INLINE constexpr DyadicFloat(Sign s, int e, const MantissaType &m)
: sign(s), exponent(e), mantissa(m) {
normalize();
}

1
libc/src/math/CMakeLists.txt
View File

@@ -62,6 +62,7 @@ add_math_entrypoint_object(atanf)
add_math_entrypoint_object(atan2)
add_math_entrypoint_object(atan2f)
add_math_entrypoint_object(atan2l)
add_math_entrypoint_object(atan2f128)
add_math_entrypoint_object(atanh)
add_math_entrypoint_object(atanhf)

21
libc/src/math/atan2f128.h Normal file
View File

@@ -0,0 +1,21 @@
//===-- Implementation header for atan2f128 ---------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_LIBC_SRC_MATH_ATAN2F128_H
#define LLVM_LIBC_SRC_MATH_ATAN2F128_H
#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/types.h"
namespace LIBC_NAMESPACE_DECL {
float128 atan2f128(float128 x, float128 y);
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_ATAN2F128_H

21
libc/src/math/generic/CMakeLists.txt
View File

@@ -4117,8 +4117,11 @@ add_header_library(
HDRS
atan_utils.h
DEPENDS
libc.src.__support.integer_literals
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.macros.optimization
)
@@ -4200,6 +4203,24 @@ add_entrypoint_object(
.atan2
)
add_entrypoint_object(
atan2f128
SRCS
atan2f128.cpp
HDRS
../atan2f128.h
DEPENDS
.atan_utils
libc.src.__support.integer_literals
libc.src.__support.uint128
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.macros.optimization
libc.src.__support.macros.properties.types
)
add_entrypoint_object(
scalbln
SRCS

203
libc/src/math/generic/atan2f128.cpp Normal file
View File

@@ -0,0 +1,203 @@
//===-- Quad-precision atan2 function -------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/atan2f128.h"
#include "atan_utils.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/integer_literals.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/types.h"
#include "src/__support/uint128.h"
namespace LIBC_NAMESPACE_DECL {
namespace {
using Float128 = fputil::DyadicFloat<128>;
static constexpr Float128 ZERO = {Sign::POS, 0, 0_u128};
static constexpr Float128 MZERO = {Sign::NEG, 0, 0_u128};
static constexpr Float128 PI = {Sign::POS, -126,
0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
static constexpr Float128 MPI = {Sign::NEG, -126,
0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
static constexpr Float128 PI_OVER_2 = {
Sign::POS, -127, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
static constexpr Float128 MPI_OVER_2 = {
Sign::NEG, -127, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
static constexpr Float128 PI_OVER_4 = {
Sign::POS, -128, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
static constexpr Float128 THREE_PI_OVER_4 = {
Sign::POS, -128, 0x96cbe3f9'990e91a7'9394c9e8'a0a5159d_u128};
// Adjustment for constant term:
// CONST_ADJ[x_sign][y_sign][recip]
static constexpr Float128 CONST_ADJ[2][2][2] = {
{{ZERO, MPI_OVER_2}, {MZERO, MPI_OVER_2}},
{{MPI, PI_OVER_2}, {MPI, PI_OVER_2}}};
} // anonymous namespace
// There are several range reduction steps we can take for atan2(y, x) as
// follow:
// * Range reduction 1: signness
// atan2(y, x) will return a number between -PI and PI representing the angle
// forming by the 0x axis and the vector (x, y) on the 0xy-plane.
// In particular, we have that:
// atan2(y, x) = atan( y/x ) if x >= 0 and y >= 0 (I-quadrant)
// = pi + atan( y/x ) if x < 0 and y >= 0 (II-quadrant)
// = -pi + atan( y/x ) if x < 0 and y < 0 (III-quadrant)
// = atan( y/x ) if x >= 0 and y < 0 (IV-quadrant)
// Since atan function is odd, we can use the formula:
// atan(-u) = -atan(u)
// to adjust the above conditions a bit further:
// atan2(y, x) = atan( |y|/|x| ) if x >= 0 and y >= 0 (I-quadrant)
// = pi - atan( |y|/|x| ) if x < 0 and y >= 0 (II-quadrant)
// = -pi + atan( |y|/|x| ) if x < 0 and y < 0 (III-quadrant)
// = -atan( |y|/|x| ) if x >= 0 and y < 0 (IV-quadrant)
// Which can be simplified to:
// atan2(y, x) = sign(y) * atan( |y|/|x| ) if x >= 0
// = sign(y) * (pi - atan( |y|/|x| )) if x < 0
// * Range reduction 2: reciprocal
// Now that the argument inside atan is positive, we can use the formula:
// atan(1/x) = pi/2 - atan(x)
// to make the argument inside atan <= 1 as follow:
// atan2(y, x) = sign(y) * atan( |y|/|x|) if 0 <= |y| <= x
// = sign(y) * (pi/2 - atan( |x|/|y| ) if 0 <= x < |y|
// = sign(y) * (pi - atan( |y|/|x| )) if 0 <= |y| <= -x
// = sign(y) * (pi/2 + atan( |x|/|y| )) if 0 <= -x < |y|
// * Range reduction 3: look up table.
// After the previous two range reduction steps, we reduce the problem to
// compute atan(u) with 0 <= u <= 1, or to be precise:
// atan( n / d ) where n = min(|x|, |y|) and d = max(|x|, |y|).
// An accurate polynomial approximation for the whole [0, 1] input range will
// require a very large degree. To make it more efficient, we reduce the input
// range further by finding an integer idx such that:
// | n/d - idx/64 | <= 1/128.
// In particular,
// idx := round(2^6 * n/d)
// Then for the fast pass, we find a polynomial approximation for:
// atan( n/d ) ~ atan( idx/64 ) + (n/d - idx/64) * Q(n/d - idx/64)
// For the accurate pass, we use the addition formula:
// atan( n/d ) - atan( idx/64 ) = atan( (n/d - idx/64)/(1 + (n*idx)/(64*d)) )
// = atan( (n - d*(idx/64))/(d + n*(idx/64)) )
// And for the fast pass, we use degree-13 minimax polynomial to compute the
// RHS:
// atan(u) ~ P(u) = u - c_3 * u^3 + c_5 * u^5 - c_7 * u^7 + c_9 *u^9 -
// - c_11 * u^11 + c_13 * u^13
// with absolute errors bounded by:
// |atan(u) - P(u)| < 2^-121
// and relative errors bounded by:
// |(atan(u) - P(u)) / P(u)| < 2^-114.
LLVM_LIBC_FUNCTION(float128, atan2f128, (float128 y, float128 x)) {
using FPBits = fputil::FPBits<float128>;
using Float128 = fputil::DyadicFloat<128>;
FPBits x_bits(x), y_bits(y);
bool x_sign = x_bits.sign().is_neg();
bool y_sign = y_bits.sign().is_neg();
x_bits = x_bits.abs();
y_bits = y_bits.abs();
UInt128 x_abs = x_bits.uintval();
UInt128 y_abs = y_bits.uintval();
bool recip = x_abs < y_abs;
UInt128 min_abs = recip ? x_abs : y_abs;
UInt128 max_abs = !recip ? x_abs : y_abs;
unsigned min_exp = static_cast<unsigned>(min_abs >> FPBits::FRACTION_LEN);
unsigned max_exp = static_cast<unsigned>(max_abs >> FPBits::FRACTION_LEN);
Float128 num(FPBits(min_abs).get_val());
Float128 den(FPBits(max_abs).get_val());
// Check for exceptional cases, whether inputs are 0, inf, nan, or close to
// overflow, or close to underflow.
if (LIBC_UNLIKELY(max_exp >= 0x7fffU || min_exp == 0U)) {
if (x_bits.is_nan() || y_bits.is_nan())
return FPBits::quiet_nan().get_val();
unsigned x_except = x == 0 ? 0 : (FPBits(x_abs).is_inf() ? 2 : 1);
unsigned y_except = y == 0 ? 0 : (FPBits(y_abs).is_inf() ? 2 : 1);
// Exceptional cases:
// EXCEPT[y_except][x_except][x_is_neg]
// with x_except & y_except:
// 0: zero
// 1: finite, non-zero
// 2: infinity
constexpr Float128 EXCEPTS[3][3][2] = {
{{ZERO, PI}, {ZERO, PI}, {ZERO, PI}},
{{PI_OVER_2, PI_OVER_2}, {ZERO, ZERO}, {ZERO, PI}},
{{PI_OVER_2, PI_OVER_2},
{PI_OVER_2, PI_OVER_2},
{PI_OVER_4, THREE_PI_OVER_4}},
};
if ((x_except != 1) || (y_except != 1)) {
Float128 r = EXCEPTS[y_except][x_except][x_sign];
if (y_sign)
r.sign = r.sign.negate();
return static_cast<float128>(r);
}
}
bool final_sign = ((x_sign != y_sign) != recip);
Float128 const_term = CONST_ADJ[x_sign][y_sign][recip];
int exp_diff = den.exponent - num.exponent;
// We have the following bound for normalized n and d:
// 2^(-exp_diff - 1) < n/d < 2^(-exp_diff + 1).
if (LIBC_UNLIKELY(exp_diff > FPBits::FRACTION_LEN + 2)) {
if (final_sign)
const_term.sign = const_term.sign.negate();
return static_cast<float128>(const_term);
}
// Take 24 leading bits of num and den to convert to float for fast division.
// We also multiply the numerator by 64 using integer addition directly to the
// exponent field.
float num_f =
cpp::bit_cast<float>(static_cast<uint32_t>(num.mantissa >> 104) +
(6U << fputil::FPBits<float>::FRACTION_LEN));
float den_f = cpp::bit_cast<float>(
static_cast<uint32_t>(den.mantissa >> 104) +
(static_cast<uint32_t>(exp_diff) << fputil::FPBits<float>::FRACTION_LEN));
float k = fputil::nearest_integer(num_f / den_f);
unsigned idx = static_cast<unsigned>(k);
// k_f128 = idx / 64
Float128 k_f128(Sign::POS, -6, Float128::MantissaType(idx));
// Range reduction:
// atan(n/d) - atan(k) = atan((n/d - k/64) / (1 + (n/d) * (k/64)))
// = atan((n - d * k/64)) / (d + n * k/64))
// num_f128 = n - d * k/64
Float128 num_f128 = fputil::multiply_add(den, -k_f128, num);
// den_f128 = d + n * k/64
Float128 den_f128 = fputil::multiply_add(num, k_f128, den);
// q = (n - d * k) / (d + n * k)
Float128 q = fputil::quick_mul(num_f128, fputil::approx_reciprocal(den_f128));
// p ~ atan(q)
Float128 p = atan_eval(q);
Float128 r =
fputil::quick_add(const_term, fputil::quick_add(ATAN_I_F128[idx], p));
if (final_sign)
r.sign = r.sign.negate();
return static_cast<float128>(r);
}
} // namespace LIBC_NAMESPACE_DECL

108
libc/src/math/generic/atan_utils.h
View File

@@ -9,8 +9,11 @@
#ifndef LLVM_LIBC_SRC_MATH_GENERIC_ATAN_UTILS_H
#define LLVM_LIBC_SRC_MATH_GENERIC_ATAN_UTILS_H
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/double_double.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/integer_literals.h"
#include "src/__support/macros/config.h"
namespace LIBC_NAMESPACE_DECL {
@@ -18,6 +21,7 @@ namespace LIBC_NAMESPACE_DECL {
namespace {
using DoubleDouble = fputil::DoubleDouble;
using Float128 = fputil::DyadicFloat<128>;
// atan(i/64) with i = 0..64, generated by Sollya with:
// > for i from 0 to 64 do {
@@ -25,7 +29,7 @@ using DoubleDouble = fputil::DoubleDouble;
// b = round(atan(i/64) - a, D, RN);
// print("{", b, ",", a, "},");
// };
constexpr fputil::DoubleDouble ATAN_I[65] = {
constexpr DoubleDouble ATAN_I[65] = {
{0.0, 0.0},
{-0x1.220c39d4dff5p-61, 0x1.fff555bbb729bp-7},
{-0x1.5ec431444912cp-60, 0x1.ffd55bba97625p-6},
@@ -106,7 +110,7 @@ constexpr fputil::DoubleDouble ATAN_I[65] = {
// + x_lo * (1 - x_hi^2 + x_hi^4)
// Since p.lo is ~ x^3/3, the relative error from rounding is bounded by:
// |(atan(x) - P(x))/atan(x)| < ulp(x^2) <= 2^(-14-52) = 2^-66.
DoubleDouble atan_eval(const DoubleDouble &x) {
[[maybe_unused]] DoubleDouble atan_eval(const DoubleDouble &x) {
DoubleDouble p;
p.hi = x.hi;
double x_hi_sq = x.hi * x.hi;
@@ -130,6 +134,106 @@ DoubleDouble atan_eval(const DoubleDouble &x) {
return p;
}
// Float128 versions.
// atan(i/64) with i = 0..64, generated by Sollya with:
// > for i from 1 to 64 do {
// a = round(atan(i/64), 128, RN);
// ll = ceil(log2(a));
// b = 2^ll + a;
// print("{Sign::POS, ", 2^(ll - 128), ",", b, "},");
// };
constexpr Float128 ATAN_I_F128[65] = {
{Sign::POS, 0, 0_u128},
{Sign::POS, -134, 0xfffaaadd'db94d5bb'e78c5640'15f76048_u128},
{Sign::POS, -133, 0xffeaaddd'4bb12542'779d776d'da8c6214_u128},
{Sign::POS, -132, 0xbfdc0c21'86d14fcf'220e10d6'1df56ec7_u128},
{Sign::POS, -132, 0xffaaddb9'67ef4e36'cb2792dc'0e2e0d51_u128},
{Sign::POS, -131, 0x9facf873'e2aceb58'99c50bbf'08e6cdf6_u128},
{Sign::POS, -131, 0xbf70c130'17887460'93567e78'4cf83676_u128},
{Sign::POS, -131, 0xdf1cf5f3'783e1bef'71e5340b'30e5d9ef_u128},
{Sign::POS, -131, 0xfeadd4d5'617b6e32'c897989f'3e888ef8_u128},
{Sign::POS, -130, 0x8f0fd7d8'21b93725'bd375929'83a0af9a_u128},
{Sign::POS, -130, 0x9eb77746'331362c3'47619d25'0360fe85_u128},
{Sign::POS, -130, 0xae4c08f1'f6134efa'b54d3fef'0c2de994_u128},
{Sign::POS, -130, 0xbdcbda5e'72d81134'7b0b4f88'1c9c7488_u128},
{Sign::POS, -130, 0xcd35474b'643130e7'b00f3da1'a46eeb3b_u128},
{Sign::POS, -130, 0xdc86ba94'93051022'f621a5c1'cb552f03_u128},
{Sign::POS, -130, 0xebbeaef9'02b9b38c'91a2a68b'2fbd78e8_u128},
{Sign::POS, -130, 0xfadbafc9'6406eb15'6dc79ef5'f7a217e6_u128},
{Sign::POS, -129, 0x84ee2cbe'c31b12c5'c8e72197'0cabd3a3_u128},
{Sign::POS, -129, 0x8c5fad18'5f8bc130'ca4748b1'bf88298d_u128},
{Sign::POS, -129, 0x93c1b902'bf7a2df1'06459240'6fe1447a_u128},
{Sign::POS, -129, 0x9b13b9b8'3f5e5e69'c5abb498'd27af328_u128},
{Sign::POS, -129, 0xa25521b6'15784d45'43787549'88b8d9e3_u128},
{Sign::POS, -129, 0xa9856cca'8e6a4eda'99b7f77b'f7d9e8c1_u128},
{Sign::POS, -129, 0xb0a42018'4e7f0cb1'b51d51dc'200a0fc3_u128},
{Sign::POS, -129, 0xb7b0ca0f'26f78473'8aa32122'dcfe4483_u128},
{Sign::POS, -129, 0xbeab025b'1d9fbad3'910b8564'93411026_u128},
{Sign::POS, -129, 0xc59269ca'50d92b6d'a1746e91'f50a28de_u128},
{Sign::POS, -129, 0xcc66aa2a'6b58c33c'd9311fa1'4ed9b7c4_u128},
{Sign::POS, -129, 0xd327761e'611fe5b6'427c95e9'001e7136_u128},
{Sign::POS, -129, 0xd9d488ed'32e3635c'30f6394a'0806345d_u128},
{Sign::POS, -129, 0xe06da64a'764f7c67'c631ed96'798cb804_u128},
{Sign::POS, -129, 0xe6f29a19'609a84ba'60b77ce1'ca6dc2c8_u128},
{Sign::POS, -129, 0xed63382b'0dda7b45'6fe445ec'bc3a8d03_u128},
{Sign::POS, -129, 0xf3bf5bf8'bad1a21c'a7b837e6'86adf3fa_u128},
{Sign::POS, -129, 0xfa06e85a'a0a0be5c'66d23c7d'5dc8ecc2_u128},
{Sign::POS, -128, 0x801ce39e'0d205c99'a6d6c6c5'4d938596_u128},
{Sign::POS, -128, 0x832bf4a6'd9867e2a'4b6a09cb'61a515c1_u128},
{Sign::POS, -128, 0x8630a2da'da1ed065'd3e84ed5'013ca37e_u128},
{Sign::POS, -128, 0x892aecdf'de9547b5'094478fc'472b4afc_u128},
{Sign::POS, -128, 0x8c1ad445'f3e09b8c'439d8018'60205921_u128},
{Sign::POS, -128, 0x8f005d5e'f7f59f9b'5c835e16'65c43748_u128},
{Sign::POS, -128, 0x91db8f16'64f350e2'10e4f9c1'126e0220_u128},
{Sign::POS, -128, 0x94ac72c9'847186f6'18c4f393'f78a32f9_u128},
{Sign::POS, -128, 0x97731420'365e538b'abd3fe19'f1aeb6b3_u128},
{Sign::POS, -128, 0x9a2f80e6'71bdda20'4226f8e2'204ff3bd_u128},
{Sign::POS, -128, 0x9ce1c8e6'a0b8cdb9'f799c4e8'174cf11c_u128},
{Sign::POS, -128, 0x9f89fdc4'f4b7a1ec'f8b49264'4f0701e0_u128},
{Sign::POS, -128, 0xa22832db'cadaae08'92fe9c08'637af0e6_u128},
{Sign::POS, -128, 0xa4bc7d19'34f70924'19a87f2a'457dac9f_u128},
{Sign::POS, -128, 0xa746f2dd'b7602294'67b7d66f'2d74e019_u128},
{Sign::POS, -128, 0xa9c7abdc'4830f5c8'916a84b5'be7933f6_u128},
{Sign::POS, -128, 0xac3ec0fb'997dd6a1'a36273a5'6afa8ef4_u128},
{Sign::POS, -128, 0xaeac4c38'b4d8c080'14725e2f'3e52070a_u128},
{Sign::POS, -128, 0xb110688a'ebdc6f6a'43d65788'b9f6a7b5_u128},
{Sign::POS, -128, 0xb36b31c9'1f043691'59014174'4462f93a_u128},
{Sign::POS, -128, 0xb5bcc490'59ecc4af'f8f3cee7'5e3907d5_u128},
{Sign::POS, -128, 0xb8053e2b'c2319e73'cb2da552'10a4443d_u128},
{Sign::POS, -128, 0xba44bc7d'd470782f'654c2cb1'0942e386_u128},
{Sign::POS, -128, 0xbc7b5dea'e98af280'd4113006'e80fb290_u128},
{Sign::POS, -128, 0xbea94144'fd049aac'1043c5e7'55282e7d_u128},
{Sign::POS, -128, 0xc0ce85b8'ac526640'89dd62c4'6e92fa25_u128},
{Sign::POS, -128, 0xc2eb4abb'661628b5'b373fe45'c61bb9fb_u128},
{Sign::POS, -128, 0xc4ffaffa'bf8fbd54'8cb43d10'bc9e0221_u128},
{Sign::POS, -128, 0xc70bd54c'e602ee13'e7d54fbd'09f2be38_u128},
{Sign::POS, -128, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128},
};
// Degree-13 minimax polynomial generated by Sollya with:
// > P = fpminimax(atan(x), [|1, 3, 5, 7, 9, 11, 13|], [|1, 128...|],
// [0, 2^-7]);
// > dirtyinfnorm(atan(x) - P, [0, 2^-7]);
// 0x1.26016ad97f323875760f869684c0898d7b7bb8bep-122
constexpr Float128 ATAN_POLY_F128[] = {
{Sign::NEG, -129, 0xaaaaaaaa'aaaaaaaa'aaaaaaa6'003c5d1d_u128},
{Sign::POS, -130, 0xcccccccc'cccccccc'cca00232'8776b063_u128},
{Sign::NEG, -130, 0x92492492'49249201'27f5268a'cb24aec0_u128},
{Sign::POS, -131, 0xe38e38e3'8dce3d96'626a1643'f8eb68f3_u128},
{Sign::NEG, -131, 0xba2e8b7a'ea4ad00f'005a35c7'6ef609b1_u128},
{Sign::POS, -131, 0x9d82765e'd22a7d92'ac09c405'c0a69214_u128},
};
// Approximate atan for |x| <= 2^-7.
[[maybe_unused]] Float128 atan_eval(const Float128 &x) {
Float128 x_sq = fputil::quick_mul(x, x);
Float128 x3 = fputil::quick_mul(x, x_sq);
Float128 p = fputil::polyeval(x_sq, ATAN_POLY_F128[0], ATAN_POLY_F128[1],
ATAN_POLY_F128[2], ATAN_POLY_F128[3],
ATAN_POLY_F128[4], ATAN_POLY_F128[5]);
return fputil::multiply_add(x3, p, x);
}
} // anonymous namespace
} // namespace LIBC_NAMESPACE_DECL

12
libc/test/src/math/CMakeLists.txt
View File

@@ -2413,6 +2413,18 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
add_fp_unittest(
atan2f128_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
atan2f128_test.cpp
DEPENDS
libc.src.math.atan2f128
libc.src.__support.FPUtil.fp_bits
)
add_fp_unittest(
f16add_test
NEED_MPFR

99
libc/test/src/math/atan2f128_test.cpp Normal file
View File

@@ -0,0 +1,99 @@
//===-- Unittests for atan2f128 -------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/atan2f128.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
using LlvmLibcAtan2f128Test = LIBC_NAMESPACE::testing::FPTest<float128>;
using LIBC_NAMESPACE::testing::tlog;
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
TEST_F(LlvmLibcAtan2f128Test, InQuadRange) {
constexpr StorageType X_COUNT = 123;
constexpr StorageType X_START = FPBits(0.25q).uintval();
constexpr StorageType X_STOP = FPBits(4.0q).uintval();
constexpr StorageType X_STEP = (X_STOP - X_START) / X_COUNT;
constexpr StorageType Y_COUNT = 137;
constexpr StorageType Y_START = FPBits(0.25q).uintval();
constexpr StorageType Y_STOP = FPBits(4.0q).uintval();
constexpr StorageType Y_STEP = (Y_STOP - Y_START) / Y_COUNT;
auto test = [&](mpfr::RoundingMode rounding_mode) {
mpfr::ForceRoundingMode __r(rounding_mode);
if (!__r.success)
return;
uint64_t fails = 0;
uint64_t finite_count = 0;
uint64_t total_count = 0;
float128 failed_x = 0.0, failed_y = 0.0, failed_r = 0.0;
double tol = 0.5;
for (StorageType i = 0, v = X_START; i <= X_COUNT; ++i, v += X_STEP) {
float128 x = FPBits(v).get_val();
if (FPBits(x).is_inf_or_nan() || x < 0.0q)
continue;
for (StorageType j = 0, w = Y_START; j <= Y_COUNT; ++j, w += Y_STEP) {
float128 y = FPBits(w).get_val();
if (FPBits(y).is_inf_or_nan())
continue;
float128 result = LIBC_NAMESPACE::atan2f128(x, y);
++total_count;
if (FPBits(result).is_inf_or_nan())
continue;
++finite_count;
mpfr::BinaryInput<float128> inputs{x, y};
if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Atan2, inputs,
result, 2.0, rounding_mode)) {
++fails;
while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(
mpfr::Operation::Atan2, inputs, result, tol, rounding_mode)) {
failed_x = x;
failed_y = y;
failed_r = result;
if (tol > 1000.0)
break;
tol *= 2.0;
}
}
}
}
if (fails || (finite_count < total_count)) {
tlog << " Atan2 failed: " << fails << "/" << finite_count << "/"
<< total_count << " tests.\n"
<< " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
}
if (fails) {
mpfr::BinaryInput<float128> inputs{failed_x, failed_y};
EXPECT_MPFR_MATCH(mpfr::Operation::Atan2, inputs, failed_r, 0.5,
rounding_mode);
}
};
tlog << " Test Rounding To Nearest...\n";
test(mpfr::RoundingMode::Nearest);
tlog << " Test Rounding Downward...\n";
test(mpfr::RoundingMode::Downward);
tlog << " Test Rounding Upward...\n";
test(mpfr::RoundingMode::Upward);
tlog << " Test Rounding Toward Zero...\n";
test(mpfr::RoundingMode::TowardZero);
}

10
libc/test/src/math/smoke/CMakeLists.txt
View File

@@ -4084,6 +4084,16 @@ add_fp_unittest(
libc.src.math.atan2
)
add_fp_unittest(
atan2f128_test
SUITE
libc-math-smoke-tests
SRCS
atan2f128_test.cpp
DEPENDS
libc.src.math.atan2f128
)
add_fp_unittest(
scalbln_test
SUITE

28
libc/test/src/math/smoke/atan2f128_test.cpp Normal file
View File

@@ -0,0 +1,28 @@
//===-- Unittests for atan2f128 -------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/atan2f128.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
using LlvmLibcAtan2f128Test = LIBC_NAMESPACE::testing::FPTest<float128>;
TEST_F(LlvmLibcAtan2f128Test, SpecialNumbers) {
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::atan2f128(aNaN, zero));
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::atan2f128(1.0, aNaN));
EXPECT_FP_EQ_ALL_ROUNDING(zero, LIBC_NAMESPACE::atan2f128(zero, zero));
EXPECT_FP_EQ_ALL_ROUNDING(neg_zero,
LIBC_NAMESPACE::atan2f128(neg_zero, zero));
EXPECT_FP_EQ_ALL_ROUNDING(zero, LIBC_NAMESPACE::atan2f128(1.0, inf));
EXPECT_FP_EQ_ALL_ROUNDING(neg_zero, LIBC_NAMESPACE::atan2f128(-1.0, inf));
float128 x = 0x1.ffffffffffffffffffffffffffe7p1q;
float128 y = 0x1.fffffffffffffffffffffffffff2p1q;
float128 r = 0x1.921fb54442d18469898cc51701b3p-1q;
EXPECT_FP_EQ(r, LIBC_NAMESPACE::atan2f128(x, y));
}