[libc-commits] [libc] ca8b14d - [libc][math] Implement fast pass for double precision atan2 with 1 ULP errors. (#100648)
via libc-commits
libc-commits at lists.llvm.org
Fri Jul 26 06:56:50 PDT 2024
Author: lntue
Date: 2024-07-26T09:56:46-04:00
New Revision: ca8b14de51fb15273b6697c87466dcd2661ebbc7
URL: https://github.com/llvm/llvm-project/commit/ca8b14de51fb15273b6697c87466dcd2661ebbc7
DIFF: https://github.com/llvm/llvm-project/commit/ca8b14de51fb15273b6697c87466dcd2661ebbc7.diff
LOG: [libc][math] Implement fast pass for double precision atan2 with 1 ULP errors. (#100648)
Added:
libc/src/math/generic/atan2.cpp
libc/test/src/math/atan2_test.cpp
libc/test/src/math/smoke/atan2_test.cpp
Modified:
libc/config/darwin/arm/entrypoints.txt
libc/config/linux/aarch64/entrypoints.txt
libc/config/linux/arm/entrypoints.txt
libc/config/linux/riscv/entrypoints.txt
libc/config/linux/x86_64/entrypoints.txt
libc/config/windows/entrypoints.txt
libc/docs/math/index.rst
libc/spec/stdc.td
libc/src/math/generic/CMakeLists.txt
libc/test/src/math/CMakeLists.txt
libc/test/src/math/smoke/CMakeLists.txt
Removed:
################################################################################
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index 3b50666b968e8..38eace26f10ab 100644
--- a/libc/config/darwin/arm/entrypoints.txt
+++ b/libc/config/darwin/arm/entrypoints.txt
@@ -120,6 +120,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acoshf
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.atan2
libc.src.math.atan2f
libc.src.math.atanf
libc.src.math.atanhf
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 2334fed773702..b2c5341b39d27 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -343,6 +343,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acoshf
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.atan2
libc.src.math.atan2f
libc.src.math.atanf
libc.src.math.atanhf
diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
index 61ee68ac66082..8e77105fdb13e 100644
--- a/libc/config/linux/arm/entrypoints.txt
+++ b/libc/config/linux/arm/entrypoints.txt
@@ -213,6 +213,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acoshf
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.atan2
libc.src.math.atan2f
libc.src.math.atanf
libc.src.math.atanhf
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 07466805b34cd..e3ed5a5988fed 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -365,6 +365,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acoshf
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.atan2
libc.src.math.atan2f
libc.src.math.atanf
libc.src.math.atanhf
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 035ceb8ca57bf..96f975520fe61 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -365,6 +365,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acoshf
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.atan2
libc.src.math.atan2f
libc.src.math.atanf
libc.src.math.atanhf
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index b6aced83c5815..06c3682255c45 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -118,6 +118,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.acoshf
libc.src.math.asinf
libc.src.math.asinhf
+ libc.src.math.atan2
libc.src.math.atan2f
libc.src.math.atanf
libc.src.math.atanhf
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index e7db07f071a8c..9f88b4d9a44b3 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -260,7 +260,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan | |check| | | | | | 7.12.4.3 | F.10.1.3 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| atan2 | |check| | | | | | 7.12.4.4 | F.10.1.4 |
+| atan2 | |check| | 1 ULP | | | | 7.12.4.4 | F.10.1.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| atan2pi | | | | | | 7.12.4.11 | F.10.1.11 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index d5a5cb6fedb4b..9c84accd72cff 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -692,6 +692,7 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"atanf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+ FunctionSpec<"atan2", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
FunctionSpec<"atan2f", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
FunctionSpec<"acoshf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 53155c6bbd84b..27b5b945e278c 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3848,6 +3848,26 @@ add_entrypoint_object(
libc.src.__support.macros.optimization
)
+add_entrypoint_object(
+ atan2
+ SRCS
+ atan2.cpp
+ HDRS
+ ../atan2.h
+ COMPILE_OPTIONS
+ -O3
+ DEPENDS
+ .inv_trigf_utils
+ libc.src.__support.FPUtil.double_double
+ 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.FPUtil.polyeval
+ libc.src.__support.FPUtil.rounding_mode
+ libc.src.__support.macros.optimization
+)
+
add_entrypoint_object(
scalblnf16
SRCS
diff --git a/libc/src/math/generic/atan2.cpp b/libc/src/math/generic/atan2.cpp
new file mode 100644
index 0000000000000..c39deebca4d40
--- /dev/null
+++ b/libc/src/math/generic/atan2.cpp
@@ -0,0 +1,313 @@
+//===-- Double-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/atan2.h"
+#include "inv_trigf_utils.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace {
+
+using DoubleDouble = fputil::DoubleDouble;
+
+// atan(i/64) with i = 0..64, generated by Sollya with:
+// > for i from 0 to 64 do {
+// a = round(atan(i/64), D, RN);
+// b = round(atan(i/64) - a, D, RN);
+// print("{", b, ",", a, "},");
+// };
+constexpr fputil::DoubleDouble ATAN_I[65] = {
+ {0.0, 0.0},
+ {-0x1.220c39d4dff5p-61, 0x1.fff555bbb729bp-7},
+ {-0x1.5ec431444912cp-60, 0x1.ffd55bba97625p-6},
+ {-0x1.86ef8f794f105p-63, 0x1.7fb818430da2ap-5},
+ {-0x1.c934d86d23f1dp-60, 0x1.ff55bb72cfdeap-5},
+ {0x1.ac4ce285df847p-58, 0x1.3f59f0e7c559dp-4},
+ {-0x1.cfb654c0c3d98p-58, 0x1.7ee182602f10fp-4},
+ {0x1.f7b8f29a05987p-58, 0x1.be39ebe6f07c3p-4},
+ {-0x1.cd37686760c17p-59, 0x1.fd5ba9aac2f6ep-4},
+ {-0x1.b485914dacf8cp-59, 0x1.1e1fafb043727p-3},
+ {0x1.61a3b0ce9281bp-57, 0x1.3d6eee8c6626cp-3},
+ {-0x1.054ab2c010f3dp-58, 0x1.5c9811e3ec26ap-3},
+ {0x1.347b0b4f881cap-58, 0x1.7b97b4bce5b02p-3},
+ {0x1.cf601e7b4348ep-59, 0x1.9a6a8e96c8626p-3},
+ {0x1.17b10d2e0e5abp-61, 0x1.b90d7529260a2p-3},
+ {0x1.c648d1534597ep-57, 0x1.d77d5df205736p-3},
+ {0x1.8ab6e3cf7afbdp-57, 0x1.f5b75f92c80ddp-3},
+ {0x1.62e47390cb865p-56, 0x1.09dc597d86362p-2},
+ {0x1.30ca4748b1bf9p-57, 0x1.18bf5a30bf178p-2},
+ {-0x1.077cdd36dfc81p-56, 0x1.278372057ef46p-2},
+ {-0x1.963a544b672d8p-57, 0x1.362773707ebccp-2},
+ {-0x1.5d5e43c55b3bap-56, 0x1.44aa436c2af0ap-2},
+ {-0x1.2566480884082p-57, 0x1.530ad9951cd4ap-2},
+ {-0x1.a725715711fp-56, 0x1.614840309cfe2p-2},
+ {-0x1.c63aae6f6e918p-56, 0x1.6f61941e4def1p-2},
+ {0x1.69c885c2b249ap-56, 0x1.7d5604b63b3f7p-2},
+ {0x1.b6d0ba3748fa8p-56, 0x1.8b24d394a1b25p-2},
+ {0x1.9e6c988fd0a77p-56, 0x1.98cd5454d6b18p-2},
+ {-0x1.24dec1b50b7ffp-56, 0x1.a64eec3cc23fdp-2},
+ {0x1.ae187b1ca504p-56, 0x1.b3a911da65c6cp-2},
+ {-0x1.cc1ce70934c34p-56, 0x1.c0db4c94ec9fp-2},
+ {-0x1.a2cfa4418f1adp-56, 0x1.cde53432c1351p-2},
+ {0x1.a2b7f222f65e2p-56, 0x1.dac670561bb4fp-2},
+ {0x1.0e53dc1bf3435p-56, 0x1.e77eb7f175a34p-2},
+ {-0x1.a3992dc382a23p-57, 0x1.f40dd0b541418p-2},
+ {-0x1.b32c949c9d593p-55, 0x1.0039c73c1a40cp-1},
+ {-0x1.d5b495f6349e6p-56, 0x1.0657e94db30dp-1},
+ {0x1.974fa13b5404fp-58, 0x1.0c6145b5b43dap-1},
+ {-0x1.2bdaee1c0ee35p-58, 0x1.1255d9bfbd2a9p-1},
+ {0x1.c621cec00c301p-55, 0x1.1835a88be7c13p-1},
+ {-0x1.928df287a668fp-58, 0x1.1e00babdefeb4p-1},
+ {0x1.c421c9f38224ep-57, 0x1.23b71e2cc9e6ap-1},
+ {-0x1.09e73b0c6c087p-56, 0x1.2958e59308e31p-1},
+ {0x1.c5d5e9ff0cf8dp-55, 0x1.2ee628406cbcap-1},
+ {0x1.1021137c71102p-55, 0x1.345f01cce37bbp-1},
+ {-0x1.2304331d8bf46p-55, 0x1.39c391cd4171ap-1},
+ {0x1.ecf8b492644fp-56, 0x1.3f13fb89e96f4p-1},
+ {-0x1.f76d0163f79c8p-56, 0x1.445065b795b56p-1},
+ {0x1.2419a87f2a458p-56, 0x1.4978fa3269ee1p-1},
+ {0x1.4a33dbeb3796cp-55, 0x1.4e8de5bb6ec04p-1},
+ {-0x1.1bb74abda520cp-55, 0x1.538f57b89061fp-1},
+ {-0x1.5e5c9d8c5a95p-56, 0x1.587d81f732fbbp-1},
+ {0x1.0028e4bc5e7cap-57, 0x1.5d58987169b18p-1},
+ {-0x1.2b785350ee8c1p-57, 0x1.6220d115d7b8ep-1},
+ {-0x1.6ea6febe8bbbap-56, 0x1.66d663923e087p-1},
+ {-0x1.a80386188c50ep-55, 0x1.6b798920b3d99p-1},
+ {-0x1.8c34d25aadef6p-56, 0x1.700a7c5784634p-1},
+ {0x1.7b2a6165884a1p-59, 0x1.748978fba8e0fp-1},
+ {0x1.406a08980374p-55, 0x1.78f6bbd5d315ep-1},
+ {0x1.560821e2f3aa9p-55, 0x1.7d528289fa093p-1},
+ {-0x1.bf76229d3b917p-56, 0x1.819d0b7158a4dp-1},
+ {0x1.6b66e7fc8b8c3p-57, 0x1.85d69576cc2c5p-1},
+ {-0x1.55b9a5e177a1bp-55, 0x1.89ff5ff57f1f8p-1},
+ {-0x1.ec182ab042f61p-56, 0x1.8e17aa99cc05ep-1},
+ {0x1.1a62633145c07p-55, 0x1.921fb54442d18p-1},
+};
+
+// Approximate atan(x) for |x| <= 2^-7.
+// Using degree-9 Taylor polynomial:
+// P = x - x^3/3 + x^5/5 -x^7/7 + x^9/9;
+// Then the absolute error is bounded by:
+// |atan(x) - P(x)| < |x|^11/11 < 2^(-7*11) / 11 < 2^-80.
+// And the relative error is bounded by:
+// |(atan(x) - P(x))/atan(x)| < |x|^10 / 10 < 2^-73.
+// For x = x_hi + x_lo, fully expand the polynomial and drop any terms less than
+// ulp(x_hi^3 / 3) gives us:
+// P(x) ~ x_hi - x_hi^3/3 + x_hi^5/5 - x_hi^7/7 + x_hi^9/9 +
+// + x_lo * (1 - x_hi^2 + x_hi^4)
+DoubleDouble atan_eval(const DoubleDouble &x) {
+ DoubleDouble p;
+ p.hi = x.hi;
+ double x_hi_sq = x.hi * x.hi;
+ // c0 ~ x_hi^2 * 1/5 - 1/3
+ double c0 = fputil::multiply_add(x_hi_sq, 0x1.999999999999ap-3,
+ -0x1.5555555555555p-2);
+ // c1 ~ x_hi^2 * 1/9 - 1/7
+ double c1 = fputil::multiply_add(x_hi_sq, 0x1.c71c71c71c71cp-4,
+ -0x1.2492492492492p-3);
+ // x_hi^3
+ double x_hi_3 = x_hi_sq * x.hi;
+ // x_hi^4
+ double x_hi_4 = x_hi_sq * x_hi_sq;
+ // d0 ~ 1/3 - x_hi^2 / 5 + x_hi^4 / 7 - x_hi^6 / 9
+ double d0 = fputil::multiply_add(x_hi_4, c1, c0);
+ // x_lo - x_lo * x_hi^2 + x_lo * x_hi^4
+ double d1 = fputil::multiply_add(x_hi_4 - x_hi_sq, x.lo, x.lo);
+ // p.lo ~ -x_hi^3/3 + x_hi^5/5 - x_hi^7/7 + x_hi^9/9 +
+ // + x_lo * (1 - x_hi^2 + x_hi^4)
+ p.lo = fputil::multiply_add(x_hi_3, d0, d1);
+ return p;
+}
+
+} // 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-9 Taylor polynomial to compute the RHS:
+// atan(u) ~ P(u) = u - u^3/3 + u^5/5 - u^7/7 + u^9/9
+// with absolute errors bounded by:
+// |atan(u) - P(u)| < |u|^11 / 11 < 2^-80
+// and relative errors bounded by:
+// |(atan(u) - P(u)) / P(u)| < u^10 / 11 < 2^-73.
+
+LLVM_LIBC_FUNCTION(double, atan2, (double y, double x)) {
+ using FPBits = fputil::FPBits<double>;
+
+ constexpr double IS_NEG[2] = {1.0, -1.0};
+ constexpr DoubleDouble ZERO = {0.0, 0.0};
+ constexpr DoubleDouble MZERO = {-0.0, -0.0};
+ constexpr DoubleDouble PI = {0x1.1a62633145c07p-53, 0x1.921fb54442d18p+1};
+ constexpr DoubleDouble MPI = {-0x1.1a62633145c07p-53, -0x1.921fb54442d18p+1};
+ constexpr DoubleDouble PI_OVER_2 = {0x1.1a62633145c07p-54,
+ 0x1.921fb54442d18p0};
+ constexpr DoubleDouble MPI_OVER_2 = {-0x1.1a62633145c07p-54,
+ -0x1.921fb54442d18p0};
+ constexpr DoubleDouble PI_OVER_4 = {0x1.1a62633145c07p-55,
+ 0x1.921fb54442d18p-1};
+ constexpr DoubleDouble THREE_PI_OVER_4 = {0x1.a79394c9e8a0ap-54,
+ 0x1.2d97c7f3321d2p+1};
+ // Adjustment for constant term:
+ // CONST_ADJ[x_sign][y_sign][recip]
+ constexpr DoubleDouble CONST_ADJ[2][2][2] = {
+ {{ZERO, MPI_OVER_2}, {MZERO, MPI_OVER_2}},
+ {{MPI, PI_OVER_2}, {MPI, PI_OVER_2}}};
+
+ 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();
+ uint64_t x_abs = x_bits.uintval();
+ uint64_t y_abs = y_bits.uintval();
+ bool recip = x_abs < y_abs;
+ uint64_t min_abs = recip ? x_abs : y_abs;
+ uint64_t 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);
+
+ double num = FPBits(min_abs).get_val();
+ double 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 > 0x7ffU - 128U || min_exp < 128U)) {
+ if (x_bits.is_nan() || y_bits.is_nan())
+ return FPBits::quiet_nan().get_val();
+ unsigned x_except = x_abs == 0 ? 0 : (FPBits(x_abs).is_inf() ? 2 : 1);
+ unsigned y_except = y_abs == 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 DoubleDouble 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)) {
+ DoubleDouble r = EXCEPTS[y_except][x_except][x_sign];
+ return fputil::multiply_add(IS_NEG[y_sign], r.hi, IS_NEG[y_sign] * r.lo);
+ }
+ bool scale_up = min_exp < 128U;
+ bool scale_down = max_exp > 0x7ffU - 128U;
+ // At least one input is denormal, multiply both numerator and denominator
+ // by some large enough power of 2 to normalize denormal inputs.
+ if (scale_up) {
+ num *= 0x1.0p64;
+ if (!scale_down)
+ den *= 0x1.0p64;
+ } else if (scale_down) {
+ den *= 0x1.0p-64;
+ if (!scale_up)
+ num *= 0x1.0p-64;
+ }
+
+ min_abs = FPBits(num).uintval();
+ max_abs = FPBits(den).uintval();
+ min_exp = static_cast<unsigned>(min_abs >> FPBits::FRACTION_LEN);
+ max_exp = static_cast<unsigned>(max_abs >> FPBits::FRACTION_LEN);
+ }
+
+ double final_sign = IS_NEG[(x_sign != y_sign) != recip];
+ DoubleDouble const_term = CONST_ADJ[x_sign][y_sign][recip];
+ unsigned exp_
diff = max_exp - min_exp;
+ // 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 > 54)) {
+ return fputil::multiply_add(final_sign, const_term.hi,
+ final_sign * (const_term.lo + num / den));
+ }
+
+ double k = fputil::nearest_integer(64.0 * num / den);
+ unsigned idx = static_cast<unsigned>(k);
+ // k = idx / 64
+ k *= 0x1.0p-6;
+
+ // Range reduction:
+ // atan(n/d) - atan(k/64) = atan((n/d - k/64) / (1 + (n/d) * (k/64)))
+ // = atan((n - d * k/64)) / (d + n * k/64))
+ DoubleDouble num_k = fputil::exact_mult(num, k);
+ DoubleDouble den_k = fputil::exact_mult(den, k);
+
+ // num_dd = n - d * k
+ DoubleDouble num_dd = fputil::exact_add(num - den_k.hi, -den_k.lo);
+ // den_dd = d + n * k
+ DoubleDouble den_dd = fputil::exact_add(den, num_k.hi);
+ den_dd.lo += num_k.lo;
+
+ // q = (n - d * k) / (d + n * k)
+ DoubleDouble q = fputil::div(num_dd, den_dd);
+ // p ~ atan(q)
+ DoubleDouble p = atan_eval(q);
+
+ DoubleDouble r = fputil::add(const_term, fputil::add(ATAN_I[idx], p));
+ r.hi *= final_sign;
+ r.lo *= final_sign;
+
+ return r.hi + r.lo;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 3ad5d98858165..380d283763afa 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2044,6 +2044,18 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ atan2_test
+ NEED_MPFR
+ SUITE
+ libc-math-unittests
+ SRCS
+ atan2_test.cpp
+ DEPENDS
+ libc.src.math.atan2
+ libc.src.__support.FPUtil.fp_bits
+)
+
add_fp_unittest(
f16add_test
NEED_MPFR
diff --git a/libc/test/src/math/atan2_test.cpp b/libc/test/src/math/atan2_test.cpp
new file mode 100644
index 0000000000000..637ac8928a2bc
--- /dev/null
+++ b/libc/test/src/math/atan2_test.cpp
@@ -0,0 +1,125 @@
+//===-- Unittests for atan2 -----------------------------------------------===//
+//
+// 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/__support/FPUtil/FPBits.h"
+#include "src/math/atan2.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcAtan2Test = LIBC_NAMESPACE::testing::FPTest<double>;
+using LIBC_NAMESPACE::testing::tlog;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+TEST_F(LlvmLibcAtan2Test, TrickyInputs) {
+ mpfr::BinaryInput<double> inputs[] = {
+ {0x1.0853408534085p-2, 0x1.e7b54166c6126p-2},
+ {FPBits::inf().get_val(), 0x0.0000000000001p-1022},
+ };
+
+ for (mpfr::BinaryInput<double> &input : inputs) {
+ double x = input.x;
+ double y = input.y;
+ mpfr::RoundingMode rm = mpfr::RoundingMode::Downward;
+ mpfr::ForceRoundingMode rr(rm);
+ ASSERT_MPFR_MATCH(mpfr::Operation::Atan2, input,
+ LIBC_NAMESPACE::atan2(x, y), 0.5, rm);
+ input.x = -input.x;
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atan2, input,
+ LIBC_NAMESPACE::atan2(-x, y), 0.5);
+ input.y = -input.y;
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atan2, input,
+ LIBC_NAMESPACE::atan2(-x, -y), 0.5);
+ input.x = -input.x;
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atan2, input,
+ LIBC_NAMESPACE::atan2(x, -y), 0.5);
+ }
+}
+
+TEST_F(LlvmLibcAtan2Test, InDoubleRange) {
+ constexpr uint64_t X_COUNT = 123;
+ constexpr uint64_t X_START = FPBits(0.25).uintval();
+ constexpr uint64_t X_STOP = FPBits(4.0).uintval();
+ constexpr uint64_t X_STEP = (X_STOP - X_START) / X_COUNT;
+
+ constexpr uint64_t Y_COUNT = 137;
+ constexpr uint64_t Y_START = FPBits(0.25).uintval();
+ constexpr uint64_t Y_STOP = FPBits(4.0).uintval();
+ constexpr uint64_t 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;
+ double failed_x = 0.0, failed_y = 0.0, failed_r = 0.0;
+ double tol = 0.5;
+
+ for (uint64_t i = 0, v = X_START; i <= X_COUNT; ++i, v += X_STEP) {
+ double x = FPBits(v).get_val();
+ if (FPBits(x).is_inf_or_nan() || x < 0.0)
+ continue;
+
+ for (uint64_t j = 0, w = Y_START; j <= Y_COUNT; ++j, w += Y_STEP) {
+ double y = FPBits(w).get_val();
+ if (FPBits(y).is_inf_or_nan())
+ continue;
+
+ double result = LIBC_NAMESPACE::atan2(x, y);
+ ++total_count;
+ if (FPBits(result).is_inf_or_nan())
+ continue;
+
+ ++finite_count;
+ mpfr::BinaryInput<double> inputs{x, y};
+
+ if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Atan2, inputs,
+ result, 0.5, 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<double> 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);
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index 5ddc88a38eb64..8b2942343409d 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -3531,6 +3531,16 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ atan2_test
+ SUITE
+ libc-math-smoke-tests
+ SRCS
+ atan2_test.cpp
+ DEPENDS
+ libc.src.math.atan2
+)
+
add_fp_unittest(
scalblnf16_test
SUITE
diff --git a/libc/test/src/math/smoke/atan2_test.cpp b/libc/test/src/math/smoke/atan2_test.cpp
new file mode 100644
index 0000000000000..61dd6cab1049f
--- /dev/null
+++ b/libc/test/src/math/smoke/atan2_test.cpp
@@ -0,0 +1,22 @@
+//===-- Unittests for atan2 -----------------------------------------------===//
+//
+// 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/atan2.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcAtan2Test = LIBC_NAMESPACE::testing::FPTest<double>;
+
+TEST_F(LlvmLibcAtan2Test, SpecialNumbers) {
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::atan2(aNaN, zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::atan2(1.0, aNaN));
+ EXPECT_FP_EQ_ALL_ROUNDING(0.0, LIBC_NAMESPACE::atan2(zero, zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(-0.0, LIBC_NAMESPACE::atan2(-0.0, zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(0.0, LIBC_NAMESPACE::atan2(1.0, inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(-0.0, LIBC_NAMESPACE::atan2(-1.0, inf));
+}
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