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-rw-r--r--libc/src/math/generic/atan2f128.cpp189
1 files changed, 2 insertions, 187 deletions
diff --git a/libc/src/math/generic/atan2f128.cpp b/libc/src/math/generic/atan2f128.cpp
index a3aba0b..ec051dd 100644
--- a/libc/src/math/generic/atan2f128.cpp
+++ b/libc/src/math/generic/atan2f128.cpp
@@ -7,197 +7,12 @@
//===----------------------------------------------------------------------===//
#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"
+#include "src/__support/math/atan2f128.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);
+ return math::atan2f128(y, x);
}
} // namespace LIBC_NAMESPACE_DECL
generated by cgit v1.1 at 2025-08-02 08:38:55 +0000