[libc-commits] [libc] [llvm] [libc][math] Refactor pow to Header Only. (PR #176529)
via libc-commits
libc-commits at lists.llvm.org
Fri Jan 16 17:39:15 PST 2026
https://github.com/AnonMiraj created https://github.com/llvm/llvm-project/pull/176529
@bassiounix
closes : #176516
>From 99aef88611d074be801ae01dc875583c78410191 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 17 Jan 2026 03:38:16 +0200
Subject: [PATCH] [libc][math] Refactor pow to Header Only.
---
libc/shared/math.h | 1 +
libc/shared/math/pow.h | 22 +
libc/src/__support/math/CMakeLists.txt | 19 +
libc/src/__support/math/pow.h | 544 ++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 13 +-
libc/src/math/generic/pow.cpp | 523 +----------------
libc/test/shared/CMakeLists.txt | 1 +
libc/test/shared/shared_math_test.cpp | 1 +
.../llvm-project-overlay/libc/BUILD.bazel | 26 +-
9 files changed, 612 insertions(+), 538 deletions(-)
create mode 100644 libc/shared/math/pow.h
create mode 100644 libc/src/__support/math/pow.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 017c94f8ad54a..5ebadfb530682 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -74,6 +74,7 @@
#include "math/logbf.h"
#include "math/logbf128.h"
#include "math/logbf16.h"
+#include "math/pow.h"
#include "math/rsqrtf.h"
#include "math/rsqrtf16.h"
#include "math/sin.h"
diff --git a/libc/shared/math/pow.h b/libc/shared/math/pow.h
new file mode 100644
index 0000000000000..a5a31d70ed0ca
--- /dev/null
+++ b/libc/shared/math/pow.h
@@ -0,0 +1,22 @@
+//===-- Shared pow function -------------------------------------*- 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_SHARED_MATH_POW_H
+#define LLVM_LIBC_SHARED_MATH_POW_H
+#include "shared/libc_common.h"
+#include "src/__support/math/pow.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::pow;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_POW_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index cb03b18678145..05d0ee2c4561c 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -1139,6 +1139,25 @@ add_header_library(
libc.src.__support.uint128
)
+add_header_library(
+ pow
+ HDRS
+ pow.h
+ DEPENDS
+ libc.src.__support.CPP.bit
+ libc.src.__support.FPUtil.fenv_impl
+ 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.sqrt
+ libc.src.__support.FPUtil.triple_double
+ libc.src.__support.macros.optimization
+ libc.src.__support.math.common_constants
+ libc.src.__support.math.exp10f
+ libc.src.__support.math.exp2f
+)
+
add_header_library(
sin
HDRS
diff --git a/libc/src/__support/math/pow.h b/libc/src/__support/math/pow.h
new file mode 100644
index 0000000000000..8e4507cf0242f
--- /dev/null
+++ b/libc/src/__support/math/pow.h
@@ -0,0 +1,544 @@
+//===-- Implementation header for pow ------------------------*- 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___SUPPORT_MATH_POW_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_POW_H
+
+#include "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/CPP/bit.h"
+#include "src/__support/FPUtil/FEnvImpl.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/sqrt.h" // Speedup for pow(x, 1/2) = sqrt(x)
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
+#include "src/__support/math/exp_constants.h" // Lookup tables EXP_M1 and EXP_M2.
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+using fputil::DoubleDouble;
+
+namespace {
+
+using namespace common_constants_internal;
+
+// Constants for log2(x) range reduction, generated by Sollya with:
+// > for i from 0 to 127 do {
+// r = 2^-8 * ceil( 2^8 * (1 - 2^(-8)) / (1 + i*2^-7) );
+// b = nearestint(log2(r) * 2^41) * 2^-41;
+// c = round(log2(r) - b, D, RN);
+// print("{", -c, ",", -b, "},");
+// };
+// This is the same as -log2(RD[i]), with the least significant bits of the
+// high part set to be 2^-41, so that the sum of high parts + e_x is exact in
+// double precision.
+// We also replace the first and the last ones to be 0.
+constexpr DoubleDouble LOG2_R_DD[128] = {
+ {0.0, 0.0},
+ {-0x1.19b14945cf6bap-44, 0x1.72c7ba21p-7},
+ {-0x1.95539356f93dcp-43, 0x1.743ee862p-6},
+ {0x1.abe0a48f83604p-43, 0x1.184b8e4c5p-5},
+ {0x1.635577970e04p-43, 0x1.77394c9d9p-5},
+ {-0x1.401fbaaa67e3cp-45, 0x1.d6ebd1f2p-5},
+ {-0x1.5b1799ceaeb51p-43, 0x1.1bb32a6008p-4},
+ {0x1.7c407050799bfp-43, 0x1.4c560fe688p-4},
+ {0x1.da6339da288fcp-43, 0x1.7d60496cf8p-4},
+ {0x1.be4f6f22dbbadp-43, 0x1.960caf9ab8p-4},
+ {-0x1.c760bc9b188c4p-45, 0x1.c7b528b71p-4},
+ {0x1.164e932b2d51cp-44, 0x1.f9c95dc1dp-4},
+ {0x1.924ae921f7ecap-45, 0x1.097e38ce6p-3},
+ {-0x1.6d25a5b8a19b2p-44, 0x1.22dadc2ab4p-3},
+ {0x1.e50a1644ac794p-43, 0x1.3c6fb650ccp-3},
+ {0x1.f34baa74a7942p-43, 0x1.494f863b8cp-3},
+ {-0x1.8f7aac147fdc1p-46, 0x1.633a8bf438p-3},
+ {0x1.f84be19cb9578p-43, 0x1.7046031c78p-3},
+ {-0x1.66cccab240e9p-46, 0x1.8a8980abfcp-3},
+ {-0x1.3f7a55cd2af4cp-47, 0x1.97c1cb13c8p-3},
+ {0x1.3458cde69308cp-43, 0x1.b2602497d4p-3},
+ {-0x1.667f21fa8423fp-44, 0x1.bfc67a8p-3},
+ {0x1.d2fe4574e09b9p-47, 0x1.dac22d3e44p-3},
+ {0x1.367bde40c5e6dp-43, 0x1.e857d3d36p-3},
+ {0x1.d45da26510033p-46, 0x1.01d9bbcfa6p-2},
+ {-0x1.7204f55bbf90dp-44, 0x1.08bce0d96p-2},
+ {-0x1.d4f1b95e0ff45p-43, 0x1.169c05364p-2},
+ {0x1.c20d74c0211bfp-44, 0x1.1d982c9d52p-2},
+ {0x1.ad89a083e072ap-43, 0x1.249cd2b13cp-2},
+ {0x1.cd0cb4492f1bcp-43, 0x1.32bfee370ep-2},
+ {-0x1.2101a9685c779p-47, 0x1.39de8e155ap-2},
+ {0x1.9451cd394fe8dp-43, 0x1.4106017c3ep-2},
+ {0x1.661e393a16b95p-44, 0x1.4f6fbb2cecp-2},
+ {-0x1.c6d8d86531d56p-44, 0x1.56b22e6b58p-2},
+ {0x1.c1c885adb21d3p-43, 0x1.5dfdcf1eeap-2},
+ {0x1.3bb5921006679p-45, 0x1.6552b49986p-2},
+ {0x1.1d406db502403p-43, 0x1.6cb0f6865cp-2},
+ {0x1.55a63e278bad5p-43, 0x1.7b89f02cf2p-2},
+ {-0x1.66ae2a7ada553p-49, 0x1.8304d90c12p-2},
+ {-0x1.66cccab240e9p-45, 0x1.8a8980abfcp-2},
+ {-0x1.62404772a151dp-45, 0x1.921800924ep-2},
+ {0x1.ac9bca36fd02ep-44, 0x1.99b072a96cp-2},
+ {0x1.4bc302ffa76fbp-43, 0x1.a8ff97181p-2},
+ {0x1.01fea1ec47c71p-43, 0x1.b0b67f4f46p-2},
+ {-0x1.f20203b3186a6p-43, 0x1.b877c57b1cp-2},
+ {-0x1.2642415d47384p-45, 0x1.c043859e3p-2},
+ {-0x1.bc76a2753b99bp-50, 0x1.c819dc2d46p-2},
+ {-0x1.da93ae3a5f451p-43, 0x1.cffae611aep-2},
+ {-0x1.50e785694a8c6p-43, 0x1.d7e6c0abc4p-2},
+ {0x1.c56138c894641p-43, 0x1.dfdd89d586p-2},
+ {0x1.5669df6a2b592p-43, 0x1.e7df5fe538p-2},
+ {-0x1.ea92d9e0e8ac2p-48, 0x1.efec61b012p-2},
+ {0x1.a0331af2e6feap-43, 0x1.f804ae8d0cp-2},
+ {0x1.9518ce032f41dp-48, 0x1.0014332bep-1},
+ {-0x1.b3b3864c60011p-44, 0x1.042bd4b9a8p-1},
+ {-0x1.103e8f00d41c8p-45, 0x1.08494c66b9p-1},
+ {0x1.65be75cc3da17p-43, 0x1.0c6caaf0c5p-1},
+ {0x1.3676289cd3dd4p-43, 0x1.1096015deep-1},
+ {-0x1.41dfc7d7c3321p-43, 0x1.14c560fe69p-1},
+ {0x1.e0cda8bd74461p-44, 0x1.18fadb6e2dp-1},
+ {0x1.2a606046ad444p-44, 0x1.1d368296b5p-1},
+ {0x1.f9ea977a639cp-43, 0x1.217868b0c3p-1},
+ {-0x1.50520a377c7ecp-45, 0x1.25c0a0463cp-1},
+ {0x1.6e3cb71b554e7p-47, 0x1.2a0f3c3407p-1},
+ {-0x1.4275f1035e5e8p-48, 0x1.2e644fac05p-1},
+ {-0x1.4275f1035e5e8p-48, 0x1.2e644fac05p-1},
+ {-0x1.979a5db68721dp-45, 0x1.32bfee370fp-1},
+ {0x1.1ee969a95f529p-43, 0x1.37222bb707p-1},
+ {0x1.bb4b69336b66ep-43, 0x1.3b8b1c68fap-1},
+ {0x1.d5e6a8a4fb059p-45, 0x1.3ffad4e74fp-1},
+ {0x1.3106e404cabb7p-44, 0x1.44716a2c08p-1},
+ {0x1.3106e404cabb7p-44, 0x1.44716a2c08p-1},
+ {-0x1.9bcaf1aa4168ap-43, 0x1.48eef19318p-1},
+ {0x1.1646b761c48dep-44, 0x1.4d7380dcc4p-1},
+ {0x1.2f0c0bfe9dbecp-43, 0x1.51ff2e3021p-1},
+ {0x1.29904613e33cp-43, 0x1.5692101d9bp-1},
+ {0x1.1d406db502403p-44, 0x1.5b2c3da197p-1},
+ {0x1.1d406db502403p-44, 0x1.5b2c3da197p-1},
+ {-0x1.125d6cbcd1095p-44, 0x1.5fcdce2728p-1},
+ {-0x1.bd9b32266d92cp-43, 0x1.6476d98adap-1},
+ {0x1.54243b21709cep-44, 0x1.6927781d93p-1},
+ {0x1.54243b21709cep-44, 0x1.6927781d93p-1},
+ {-0x1.ce60916e52e91p-44, 0x1.6ddfc2a79p-1},
+ {0x1.f1f5ae718f241p-43, 0x1.729fd26b7p-1},
+ {-0x1.6eb9612e0b4f3p-43, 0x1.7767c12968p-1},
+ {-0x1.6eb9612e0b4f3p-43, 0x1.7767c12968p-1},
+ {0x1.fed21f9cb2cc5p-43, 0x1.7c37a9227ep-1},
+ {0x1.7f5dc57266758p-43, 0x1.810fa51bf6p-1},
+ {0x1.7f5dc57266758p-43, 0x1.810fa51bf6p-1},
+ {0x1.5b338360c2ae2p-43, 0x1.85efd062c6p-1},
+ {-0x1.96fc8f4b56502p-43, 0x1.8ad846cf37p-1},
+ {-0x1.96fc8f4b56502p-43, 0x1.8ad846cf37p-1},
+ {-0x1.bdc81c4db3134p-44, 0x1.8fc924c89bp-1},
+ {0x1.36c101ee1344p-43, 0x1.94c287492cp-1},
+ {0x1.36c101ee1344p-43, 0x1.94c287492cp-1},
+ {0x1.e41fa0a62e6aep-44, 0x1.99c48be206p-1},
+ {-0x1.d97ee9124773bp-46, 0x1.9ecf50bf44p-1},
+ {-0x1.d97ee9124773bp-46, 0x1.9ecf50bf44p-1},
+ {-0x1.3f94e00e7d6bcp-46, 0x1.a3e2f4ac44p-1},
+ {-0x1.6879fa00b120ap-43, 0x1.a8ff971811p-1},
+ {-0x1.6879fa00b120ap-43, 0x1.a8ff971811p-1},
+ {0x1.1659d8e2d7d38p-44, 0x1.ae255819fp-1},
+ {0x1.1e5e0ae0d3f8ap-43, 0x1.b35458761dp-1},
+ {0x1.1e5e0ae0d3f8ap-43, 0x1.b35458761dp-1},
+ {0x1.484a15babcf88p-43, 0x1.b88cb9a2abp-1},
+ {0x1.484a15babcf88p-43, 0x1.b88cb9a2abp-1},
+ {0x1.871a7610e40bdp-45, 0x1.bdce9dcc96p-1},
+ {-0x1.2d90e5edaeceep-43, 0x1.c31a27dd01p-1},
+ {-0x1.2d90e5edaeceep-43, 0x1.c31a27dd01p-1},
+ {-0x1.5dd31d962d373p-43, 0x1.c86f7b7ea5p-1},
+ {-0x1.5dd31d962d373p-43, 0x1.c86f7b7ea5p-1},
+ {-0x1.9ad57391924a7p-43, 0x1.cdcebd2374p-1},
+ {-0x1.3167ccc538261p-44, 0x1.d338120a6ep-1},
+ {-0x1.3167ccc538261p-44, 0x1.d338120a6ep-1},
+ {0x1.c7a4ff65ddbc9p-45, 0x1.d8aba045bp-1},
+ {0x1.c7a4ff65ddbc9p-45, 0x1.d8aba045bp-1},
+ {-0x1.f9ab3cf74babap-44, 0x1.de298ec0bbp-1},
+ {-0x1.f9ab3cf74babap-44, 0x1.de298ec0bbp-1},
+ {0x1.52842c1c1e586p-43, 0x1.e3b20546f5p-1},
+ {0x1.52842c1c1e586p-43, 0x1.e3b20546f5p-1},
+ {0x1.3c6764fc87b4ap-48, 0x1.e9452c8a71p-1},
+ {0x1.3c6764fc87b4ap-48, 0x1.e9452c8a71p-1},
+ {-0x1.a0976c0a2827dp-44, 0x1.eee32e2aedp-1},
+ {-0x1.a0976c0a2827dp-44, 0x1.eee32e2aedp-1},
+ {-0x1.a45314dc4fc42p-43, 0x1.f48c34bd1fp-1},
+ {-0x1.a45314dc4fc42p-43, 0x1.f48c34bd1fp-1},
+ {0x1.ef5d00e390ap-44, 0x1.fa406bd244p-1},
+ {0.0, 1.0},
+};
+
+LIBC_INLINE static constexpr bool is_odd_integer(double x) {
+ using FPBits = fputil::FPBits<double>;
+ FPBits xbits(x);
+ uint64_t x_u = xbits.uintval();
+ unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
+ unsigned lsb =
+ static_cast<unsigned>(cpp::countr_zero(x_u | FPBits::EXP_MASK));
+ constexpr unsigned UNIT_EXPONENT =
+ static_cast<unsigned>(FPBits::EXP_BIAS + FPBits::FRACTION_LEN);
+ return (x_e + lsb == UNIT_EXPONENT);
+}
+
+LIBC_INLINE static constexpr bool is_integer(double x) {
+ using FPBits = fputil::FPBits<double>;
+ FPBits xbits(x);
+ uint64_t x_u = xbits.uintval();
+ unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
+ unsigned lsb =
+ static_cast<unsigned>(cpp::countr_zero(x_u | FPBits::EXP_MASK));
+ constexpr unsigned UNIT_EXPONENT =
+ static_cast<unsigned>(FPBits::EXP_BIAS + FPBits::FRACTION_LEN);
+ return (x_e + lsb >= UNIT_EXPONENT);
+}
+
+} // namespace
+
+LIBC_INLINE static constexpr double pow(double x, double y) {
+ using FPBits = fputil::FPBits<double>;
+
+ FPBits xbits(x), ybits(y);
+
+ bool x_sign = xbits.sign() == Sign::NEG;
+ bool y_sign = ybits.sign() == Sign::NEG;
+
+ FPBits x_abs = xbits.abs();
+ FPBits y_abs = ybits.abs();
+
+ uint64_t x_mant = xbits.get_mantissa();
+ uint64_t y_mant = ybits.get_mantissa();
+ uint64_t x_u = xbits.uintval();
+ uint64_t x_a = x_abs.uintval();
+ uint64_t y_a = y_abs.uintval();
+
+ double e_x = static_cast<double>(xbits.get_exponent());
+ uint64_t sign = 0;
+
+ ///////// BEGIN - Check exceptional cases ////////////////////////////////////
+ // If x or y is signaling NaN
+ if (x_abs.is_signaling_nan() || y_abs.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // The double precision number that is closest to 1 is (1 - 2^-53), which has
+ // log2(1 - 2^-53) ~ -1.715...p-53.
+ // So if |y| > |1075 / log2(1 - 2^-53)|, and x is finite:
+ // |y * log2(x)| = 0 or > 1075.
+ // Hence x^y will either overflow or underflow if x is not zero.
+ if (LIBC_UNLIKELY(y_mant == 0 || y_a > 0x43d7'4910'd52d'3052 ||
+ x_u == FPBits::one().uintval() ||
+ x_u >= FPBits::inf().uintval() ||
+ x_u < FPBits::min_normal().uintval())) {
+ // Exceptional exponents.
+ if (y == 0.0)
+ return 1.0;
+
+ switch (y_a) {
+ case 0x3fe0'0000'0000'0000: { // y = +-0.5
+ // TODO: speed up x^(-1/2) with rsqrt(x) when available.
+ if (LIBC_UNLIKELY(
+ (x == 0.0 || x_u == FPBits::inf(Sign::NEG).uintval()))) {
+ // pow(-0, 1/2) = +0
+ // pow(-inf, 1/2) = +inf
+ // Make sure it works correctly for FTZ/DAZ.
+ return y_sign ? 1.0 / (x * x) : (x * x);
+ }
+ return y_sign ? (1.0 / fputil::sqrt<double>(x)) : fputil::sqrt<double>(x);
+ }
+ case 0x3ff0'0000'0000'0000: // y = +-1.0
+ return y_sign ? (1.0 / x) : x;
+ case 0x4000'0000'0000'0000: // y = +-2.0;
+ return y_sign ? (1.0 / (x * x)) : (x * x);
+ }
+
+ // |y| > |1075 / log2(1 - 2^-53)|.
+ if (y_a > 0x43d7'4910'd52d'3052) {
+ if (y_a >= 0x7ff0'0000'0000'0000) {
+ // y is inf or nan
+ if (y_mant != 0) {
+ // y is NaN
+ // pow(1, NaN) = 1
+ // pow(x, NaN) = NaN
+ return (x_u == FPBits::one().uintval()) ? 1.0 : y;
+ }
+
+ // Now y is +-Inf
+ if (x_abs.is_nan()) {
+ // pow(NaN, +-Inf) = NaN
+ return x;
+ }
+
+ if (x_a == 0x3ff0'0000'0000'0000) {
+ // pow(+-1, +-Inf) = 1.0
+ return 1.0;
+ }
+
+ if (x == 0.0 && y_sign) {
+ // pow(+-0, -Inf) = +inf and raise FE_DIVBYZERO
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+ return FPBits::inf().get_val();
+ }
+ // pow (|x| < 1, -inf) = +inf
+ // pow (|x| < 1, +inf) = 0.0
+ // pow (|x| > 1, -inf) = 0.0
+ // pow (|x| > 1, +inf) = +inf
+ return ((x_a < FPBits::one().uintval()) == y_sign)
+ ? FPBits::inf().get_val()
+ : 0.0;
+ }
+ // x^y will overflow / underflow in double precision. Set y to a
+ // large enough exponent but not too large, so that the computations
+ // won't overflow in double precision.
+ y = y_sign ? -0x1.0p100 : 0x1.0p100;
+ }
+
+ // y is finite and non-zero.
+
+ if (x_u == FPBits::one().uintval()) {
+ // pow(1, y) = 1
+ return 1.0;
+ }
+
+ // TODO: Speed things up with pow(2, y) = exp2(y) and pow(10, y) = exp10(y).
+
+ if (x == 0.0) {
+ bool out_is_neg = x_sign && is_odd_integer(y);
+ if (y_sign) {
+ // pow(0, negative number) = inf
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+ return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
+ }
+ // pow(0, positive number) = 0
+ return out_is_neg ? -0.0 : 0.0;
+ }
+
+ if (x_a == FPBits::inf().uintval()) {
+ bool out_is_neg = x_sign && is_odd_integer(y);
+ if (y_sign)
+ return out_is_neg ? -0.0 : 0.0;
+ return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
+ }
+
+ if (x_a > FPBits::inf().uintval()) {
+ // x is NaN.
+ // pow (aNaN, 0) is already taken care above.
+ return x;
+ }
+
+ // Normalize denormal inputs.
+ if (x_a < FPBits::min_normal().uintval()) {
+ e_x -= 64.0;
+ x_mant = FPBits(x * 0x1.0p64).get_mantissa();
+ }
+
+ // x is finite and negative, and y is a finite integer.
+ if (x_sign) {
+ if (is_integer(y)) {
+ x = -x;
+ if (is_odd_integer(y))
+ // sign = -1.0;
+ sign = 0x8000'0000'0000'0000;
+ } else {
+ // pow( negative, non-integer ) = NaN
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+ }
+ }
+
+ ///////// END - Check exceptional cases //////////////////////////////////////
+
+ // x^y = 2^( y * log2(x) )
+ // = 2^( y * ( e_x + log2(m_x) ) )
+ // First we compute log2(x) = e_x + log2(m_x)
+
+ // Extract exponent field of x.
+
+ // Use the highest 7 fractional bits of m_x as the index for look up tables.
+ unsigned idx_x = static_cast<unsigned>(x_mant >> (FPBits::FRACTION_LEN - 7));
+ // Add the hidden bit to the mantissa.
+ // 1 <= m_x < 2
+ FPBits m_x = FPBits(x_mant | 0x3ff0'0000'0000'0000);
+
+ // Reduced argument for log2(m_x):
+ // dx = r * m_x - 1.
+ // The computation is exact, and -2^-8 <= dx < 2^-7.
+ // Then m_x = (1 + dx) / r, and
+ // log2(m_x) = log2( (1 + dx) / r )
+ // = log2(1 + dx) - log2(r).
+
+ // In order for the overall computations x^y = 2^(y * log2(x)) to have the
+ // relative errors < 2^-52 (1ULP), we will need to evaluate the exponent part
+ // y * log2(x) with absolute errors < 2^-52 (or better, 2^-53). Since the
+ // whole exponent range for double precision is bounded by
+ // |y * log2(x)| < 1076 ~ 2^10, we need to evaluate log2(x) with absolute
+ // errors < 2^-53 * 2^-10 = 2^-63.
+
+ // With that requirement, we use the following degree-6 polynomial
+ // approximation:
+ // P(dx) ~ log2(1 + dx) / dx
+ // Generated by Sollya with:
+ // > P = fpminimax(log2(1 + x)/x, 6, [|D...|], [-2^-8, 2^-7]); P;
+ // > dirtyinfnorm(log2(1 + x) - x*P, [-2^-8, 2^-7]);
+ // 0x1.d03cc...p-66
+ constexpr double COEFFS[] = {0x1.71547652b82fep0, -0x1.71547652b82e7p-1,
+ 0x1.ec709dc3b1fd5p-2, -0x1.7154766124215p-2,
+ 0x1.2776bd90259d8p-2, -0x1.ec586c6f3d311p-3,
+ 0x1.9c4775eccf524p-3};
+ // Error: ulp(dx^2) <= (2^-7)^2 * 2^-52 = 2^-66
+ // Extra errors from various computations and rounding directions, the overall
+ // errors we can be bounded by 2^-65.
+
+ DoubleDouble dx_c0;
+
+ // Perform exact range reduction and exact product dx * c0.
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double dx = fputil::multiply_add(RD[idx_x], m_x.get_val(), -1.0); // Exact
+ dx_c0 = fputil::exact_mult(COEFFS[0], dx);
+#else
+ double c = FPBits(m_x.uintval() & 0x3fff'e000'0000'0000).get_val();
+ double dx =
+ fputil::multiply_add(RD[idx_x], m_x.get_val() - c, CD[idx_x]); // Exact
+ dx_c0 = fputil::exact_mult<double, 28>(dx, COEFFS[0]); // Exact
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+ double dx2 = dx * dx;
+ double c0 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);
+ double c1 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);
+ double c2 = fputil::multiply_add(dx, COEFFS[6], COEFFS[5]);
+
+ double p = fputil::polyeval(dx2, c0, c1, c2);
+
+ // s = e_x - log2(r) + dx * P(dx)
+ // Absolute error bound:
+ // |log2(x) - log2_x.hi - log2_x.lo| < 2^-65.
+
+ // Notice that e_x - log2(r).hi is exact, so we perform an exact sum of
+ // e_x - log2(r).hi and the high part of the product dx * c0:
+ // log2_x_hi.hi + log2_x_hi.lo = e_x - log2(r).hi + (dx * c0).hi
+ DoubleDouble log2_x_hi =
+ fputil::exact_add(e_x + LOG2_R_DD[idx_x].hi, dx_c0.hi);
+ // The low part is dx^2 * p + low part of (dx * c0) + low part of -log2(r).
+ double log2_x_lo =
+ fputil::multiply_add(dx2, p, dx_c0.lo + LOG2_R_DD[idx_x].lo);
+ // Perform accurate sums.
+ DoubleDouble log2_x = fputil::exact_add(log2_x_hi.hi, log2_x_lo);
+ log2_x.lo += log2_x_hi.lo;
+
+ // To compute 2^(y * log2(x)), we break the exponent into 3 parts:
+ // y * log(2) = hi + mid + lo, where
+ // hi is an integer
+ // mid * 2^6 is an integer
+ // |lo| <= 2^-7
+ // Then:
+ // x^y = 2^(y * log2(x)) = 2^hi * 2^mid * 2^lo,
+ // In which 2^mid is obtained from a look-up table of size 2^6 = 64 elements,
+ // and 2^lo ~ 1 + lo * P(lo).
+ // Thus, we have:
+ // hi + mid = 2^-6 * round( 2^6 * y * log2(x) )
+ // If we restrict the output such that |hi| < 150, (hi + mid) uses (8 + 6)
+ // bits, hence, if we use double precision to perform
+ // round( 2^6 * y * log2(x))
+ // the lo part is bounded by 2^-7 + 2^(-(52 - 14)) = 2^-7 + 2^-38
+
+ // In the following computations:
+ // y6 = 2^6 * y
+ // hm = 2^6 * (hi + mid) = round(2^6 * y * log2(x)) ~ round(y6 * s)
+ // lo6 = 2^6 * lo = 2^6 * (y - (hi + mid)) = y6 * log2(x) - hm.
+ double y6 = y * 0x1.0p6; // Exact.
+
+ DoubleDouble y6_log2_x = fputil::exact_mult(y6, log2_x.hi);
+ y6_log2_x.lo = fputil::multiply_add(y6, log2_x.lo, y6_log2_x.lo);
+
+ // Check overflow/underflow.
+ double scale = 1.0;
+
+ // |2^(hi + mid) - exp2_hi_mid| <= ulp(exp2_hi_mid) / 2
+ // Clamp the exponent part into smaller range that fits double precision.
+ // For those exponents that are out of range, the final conversion will round
+ // them correctly to inf/max float or 0/min float accordingly.
+ constexpr double UPPER_EXP_BOUND = 512.0 * 0x1.0p6;
+ if (LIBC_UNLIKELY(FPBits(y6_log2_x.hi).abs().get_val() >= UPPER_EXP_BOUND)) {
+ if (FPBits(y6_log2_x.hi).sign() == Sign::POS) {
+ scale = 0x1.0p512;
+ y6_log2_x.hi -= 512.0 * 64.0;
+ if (y6_log2_x.hi > 513.0 * 64.0)
+ y6_log2_x.hi = 513.0 * 64.0;
+ } else {
+ scale = 0x1.0p-512;
+ y6_log2_x.hi += 512.0 * 64.0;
+ if (y6_log2_x.hi < (-1076.0 + 512.0) * 64.0)
+ y6_log2_x.hi = -564.0 * 64.0;
+ }
+ }
+
+ double hm = fputil::nearest_integer(y6_log2_x.hi);
+
+ // lo6 = 2^6 * lo.
+ double lo6_hi = y6_log2_x.hi - hm;
+ double lo6 = lo6_hi + y6_log2_x.lo;
+
+ int hm_i = static_cast<int>(hm);
+ unsigned idx_y = static_cast<unsigned>(hm_i) & 0x3f;
+
+ // 2^hi
+ int64_t exp2_hi_i = static_cast<int64_t>(
+ static_cast<uint64_t>(static_cast<int64_t>(hm_i >> 6))
+ << FPBits::FRACTION_LEN);
+ // 2^mid
+ int64_t exp2_mid_hi_i =
+ static_cast<int64_t>(FPBits(EXP2_MID1[idx_y].hi).uintval());
+ int64_t exp2_mid_lo_i =
+ static_cast<int64_t>(FPBits(EXP2_MID1[idx_y].mid).uintval());
+ // (-1)^sign * 2^hi * 2^mid
+ // Error <= 2^hi * 2^-53
+ uint64_t exp2_hm_hi_i =
+ static_cast<uint64_t>(exp2_hi_i + exp2_mid_hi_i) + sign;
+ // The low part could be 0.
+ uint64_t exp2_hm_lo_i =
+ idx_y != 0 ? static_cast<uint64_t>(exp2_hi_i + exp2_mid_lo_i) + sign
+ : sign;
+ double exp2_hm_hi = FPBits(exp2_hm_hi_i).get_val();
+ double exp2_hm_lo = FPBits(exp2_hm_lo_i).get_val();
+
+ // Degree-5 polynomial approximation P(lo6) ~ 2^(lo6 / 2^6) = 2^(lo).
+ // Generated by Sollya with:
+ // > P = fpminimax(2^(x/64), 5, [|1, D...|], [-2^-1, 2^-1]);
+ // > dirtyinfnorm(2^(x/64) - P, [-0.5, 0.5]);
+ // 0x1.a2b77e618f5c4c176fd11b7659016cde5de83cb72p-60
+ constexpr double EXP2_COEFFS[] = {0x1p0,
+ 0x1.62e42fefa39efp-7,
+ 0x1.ebfbdff82a23ap-15,
+ 0x1.c6b08d7076268p-23,
+ 0x1.3b2ad33f8b48bp-31,
+ 0x1.5d870c4d84445p-40};
+
+ double lo6_sqr = lo6 * lo6;
+
+ double d0 = fputil::multiply_add(lo6, EXP2_COEFFS[2], EXP2_COEFFS[1]);
+ double d1 = fputil::multiply_add(lo6, EXP2_COEFFS[4], EXP2_COEFFS[3]);
+ double pp = fputil::polyeval(lo6_sqr, d0, d1, EXP2_COEFFS[5]);
+
+ double r = fputil::multiply_add(exp2_hm_hi * lo6, pp, exp2_hm_lo);
+ r += exp2_hm_hi;
+
+ return r * scale;
+}
+
+} // namespace math
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_POW_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index e4ad6fcafeaf0..e947496f68962 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1581,18 +1581,7 @@ add_entrypoint_object(
HDRS
../powf.h
DEPENDS
- libc.src.__support.math.exp10f
- libc.src.__support.math.exp2f
- libc.src.__support.CPP.bit
- libc.src.__support.FPUtil.fenv_impl
- 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.sqrt
- libc.src.__support.FPUtil.triple_double
- libc.src.__support.macros.optimization
- libc.src.__support.math.common_constants
+ libc.src.__support.math.pow
libc.src.errno.errno
)
diff --git a/libc/src/math/generic/pow.cpp b/libc/src/math/generic/pow.cpp
index c9f685b82fcb5..5fbd7f5441add 100644
--- a/libc/src/math/generic/pow.cpp
+++ b/libc/src/math/generic/pow.cpp
@@ -7,531 +7,12 @@
//===----------------------------------------------------------------------===//
#include "src/math/pow.h"
-#include "hdr/errno_macros.h"
-#include "hdr/fenv_macros.h"
-#include "src/__support/CPP/bit.h"
-#include "src/__support/FPUtil/FEnvImpl.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/sqrt.h" // Speedup for pow(x, 1/2) = sqrt(x)
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-#include "src/__support/math/common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
-#include "src/__support/math/exp_constants.h" // Lookup tables EXP_M1 and EXP_M2.
+#include "src/__support/math/pow.h"
namespace LIBC_NAMESPACE_DECL {
-using fputil::DoubleDouble;
-
-namespace {
-
-using namespace common_constants_internal;
-
-// Constants for log2(x) range reduction, generated by Sollya with:
-// > for i from 0 to 127 do {
-// r = 2^-8 * ceil( 2^8 * (1 - 2^(-8)) / (1 + i*2^-7) );
-// b = nearestint(log2(r) * 2^41) * 2^-41;
-// c = round(log2(r) - b, D, RN);
-// print("{", -c, ",", -b, "},");
-// };
-// This is the same as -log2(RD[i]), with the least significant bits of the
-// high part set to be 2^-41, so that the sum of high parts + e_x is exact in
-// double precision.
-// We also replace the first and the last ones to be 0.
-constexpr DoubleDouble LOG2_R_DD[128] = {
- {0.0, 0.0},
- {-0x1.19b14945cf6bap-44, 0x1.72c7ba21p-7},
- {-0x1.95539356f93dcp-43, 0x1.743ee862p-6},
- {0x1.abe0a48f83604p-43, 0x1.184b8e4c5p-5},
- {0x1.635577970e04p-43, 0x1.77394c9d9p-5},
- {-0x1.401fbaaa67e3cp-45, 0x1.d6ebd1f2p-5},
- {-0x1.5b1799ceaeb51p-43, 0x1.1bb32a6008p-4},
- {0x1.7c407050799bfp-43, 0x1.4c560fe688p-4},
- {0x1.da6339da288fcp-43, 0x1.7d60496cf8p-4},
- {0x1.be4f6f22dbbadp-43, 0x1.960caf9ab8p-4},
- {-0x1.c760bc9b188c4p-45, 0x1.c7b528b71p-4},
- {0x1.164e932b2d51cp-44, 0x1.f9c95dc1dp-4},
- {0x1.924ae921f7ecap-45, 0x1.097e38ce6p-3},
- {-0x1.6d25a5b8a19b2p-44, 0x1.22dadc2ab4p-3},
- {0x1.e50a1644ac794p-43, 0x1.3c6fb650ccp-3},
- {0x1.f34baa74a7942p-43, 0x1.494f863b8cp-3},
- {-0x1.8f7aac147fdc1p-46, 0x1.633a8bf438p-3},
- {0x1.f84be19cb9578p-43, 0x1.7046031c78p-3},
- {-0x1.66cccab240e9p-46, 0x1.8a8980abfcp-3},
- {-0x1.3f7a55cd2af4cp-47, 0x1.97c1cb13c8p-3},
- {0x1.3458cde69308cp-43, 0x1.b2602497d4p-3},
- {-0x1.667f21fa8423fp-44, 0x1.bfc67a8p-3},
- {0x1.d2fe4574e09b9p-47, 0x1.dac22d3e44p-3},
- {0x1.367bde40c5e6dp-43, 0x1.e857d3d36p-3},
- {0x1.d45da26510033p-46, 0x1.01d9bbcfa6p-2},
- {-0x1.7204f55bbf90dp-44, 0x1.08bce0d96p-2},
- {-0x1.d4f1b95e0ff45p-43, 0x1.169c05364p-2},
- {0x1.c20d74c0211bfp-44, 0x1.1d982c9d52p-2},
- {0x1.ad89a083e072ap-43, 0x1.249cd2b13cp-2},
- {0x1.cd0cb4492f1bcp-43, 0x1.32bfee370ep-2},
- {-0x1.2101a9685c779p-47, 0x1.39de8e155ap-2},
- {0x1.9451cd394fe8dp-43, 0x1.4106017c3ep-2},
- {0x1.661e393a16b95p-44, 0x1.4f6fbb2cecp-2},
- {-0x1.c6d8d86531d56p-44, 0x1.56b22e6b58p-2},
- {0x1.c1c885adb21d3p-43, 0x1.5dfdcf1eeap-2},
- {0x1.3bb5921006679p-45, 0x1.6552b49986p-2},
- {0x1.1d406db502403p-43, 0x1.6cb0f6865cp-2},
- {0x1.55a63e278bad5p-43, 0x1.7b89f02cf2p-2},
- {-0x1.66ae2a7ada553p-49, 0x1.8304d90c12p-2},
- {-0x1.66cccab240e9p-45, 0x1.8a8980abfcp-2},
- {-0x1.62404772a151dp-45, 0x1.921800924ep-2},
- {0x1.ac9bca36fd02ep-44, 0x1.99b072a96cp-2},
- {0x1.4bc302ffa76fbp-43, 0x1.a8ff97181p-2},
- {0x1.01fea1ec47c71p-43, 0x1.b0b67f4f46p-2},
- {-0x1.f20203b3186a6p-43, 0x1.b877c57b1cp-2},
- {-0x1.2642415d47384p-45, 0x1.c043859e3p-2},
- {-0x1.bc76a2753b99bp-50, 0x1.c819dc2d46p-2},
- {-0x1.da93ae3a5f451p-43, 0x1.cffae611aep-2},
- {-0x1.50e785694a8c6p-43, 0x1.d7e6c0abc4p-2},
- {0x1.c56138c894641p-43, 0x1.dfdd89d586p-2},
- {0x1.5669df6a2b592p-43, 0x1.e7df5fe538p-2},
- {-0x1.ea92d9e0e8ac2p-48, 0x1.efec61b012p-2},
- {0x1.a0331af2e6feap-43, 0x1.f804ae8d0cp-2},
- {0x1.9518ce032f41dp-48, 0x1.0014332bep-1},
- {-0x1.b3b3864c60011p-44, 0x1.042bd4b9a8p-1},
- {-0x1.103e8f00d41c8p-45, 0x1.08494c66b9p-1},
- {0x1.65be75cc3da17p-43, 0x1.0c6caaf0c5p-1},
- {0x1.3676289cd3dd4p-43, 0x1.1096015deep-1},
- {-0x1.41dfc7d7c3321p-43, 0x1.14c560fe69p-1},
- {0x1.e0cda8bd74461p-44, 0x1.18fadb6e2dp-1},
- {0x1.2a606046ad444p-44, 0x1.1d368296b5p-1},
- {0x1.f9ea977a639cp-43, 0x1.217868b0c3p-1},
- {-0x1.50520a377c7ecp-45, 0x1.25c0a0463cp-1},
- {0x1.6e3cb71b554e7p-47, 0x1.2a0f3c3407p-1},
- {-0x1.4275f1035e5e8p-48, 0x1.2e644fac05p-1},
- {-0x1.4275f1035e5e8p-48, 0x1.2e644fac05p-1},
- {-0x1.979a5db68721dp-45, 0x1.32bfee370fp-1},
- {0x1.1ee969a95f529p-43, 0x1.37222bb707p-1},
- {0x1.bb4b69336b66ep-43, 0x1.3b8b1c68fap-1},
- {0x1.d5e6a8a4fb059p-45, 0x1.3ffad4e74fp-1},
- {0x1.3106e404cabb7p-44, 0x1.44716a2c08p-1},
- {0x1.3106e404cabb7p-44, 0x1.44716a2c08p-1},
- {-0x1.9bcaf1aa4168ap-43, 0x1.48eef19318p-1},
- {0x1.1646b761c48dep-44, 0x1.4d7380dcc4p-1},
- {0x1.2f0c0bfe9dbecp-43, 0x1.51ff2e3021p-1},
- {0x1.29904613e33cp-43, 0x1.5692101d9bp-1},
- {0x1.1d406db502403p-44, 0x1.5b2c3da197p-1},
- {0x1.1d406db502403p-44, 0x1.5b2c3da197p-1},
- {-0x1.125d6cbcd1095p-44, 0x1.5fcdce2728p-1},
- {-0x1.bd9b32266d92cp-43, 0x1.6476d98adap-1},
- {0x1.54243b21709cep-44, 0x1.6927781d93p-1},
- {0x1.54243b21709cep-44, 0x1.6927781d93p-1},
- {-0x1.ce60916e52e91p-44, 0x1.6ddfc2a79p-1},
- {0x1.f1f5ae718f241p-43, 0x1.729fd26b7p-1},
- {-0x1.6eb9612e0b4f3p-43, 0x1.7767c12968p-1},
- {-0x1.6eb9612e0b4f3p-43, 0x1.7767c12968p-1},
- {0x1.fed21f9cb2cc5p-43, 0x1.7c37a9227ep-1},
- {0x1.7f5dc57266758p-43, 0x1.810fa51bf6p-1},
- {0x1.7f5dc57266758p-43, 0x1.810fa51bf6p-1},
- {0x1.5b338360c2ae2p-43, 0x1.85efd062c6p-1},
- {-0x1.96fc8f4b56502p-43, 0x1.8ad846cf37p-1},
- {-0x1.96fc8f4b56502p-43, 0x1.8ad846cf37p-1},
- {-0x1.bdc81c4db3134p-44, 0x1.8fc924c89bp-1},
- {0x1.36c101ee1344p-43, 0x1.94c287492cp-1},
- {0x1.36c101ee1344p-43, 0x1.94c287492cp-1},
- {0x1.e41fa0a62e6aep-44, 0x1.99c48be206p-1},
- {-0x1.d97ee9124773bp-46, 0x1.9ecf50bf44p-1},
- {-0x1.d97ee9124773bp-46, 0x1.9ecf50bf44p-1},
- {-0x1.3f94e00e7d6bcp-46, 0x1.a3e2f4ac44p-1},
- {-0x1.6879fa00b120ap-43, 0x1.a8ff971811p-1},
- {-0x1.6879fa00b120ap-43, 0x1.a8ff971811p-1},
- {0x1.1659d8e2d7d38p-44, 0x1.ae255819fp-1},
- {0x1.1e5e0ae0d3f8ap-43, 0x1.b35458761dp-1},
- {0x1.1e5e0ae0d3f8ap-43, 0x1.b35458761dp-1},
- {0x1.484a15babcf88p-43, 0x1.b88cb9a2abp-1},
- {0x1.484a15babcf88p-43, 0x1.b88cb9a2abp-1},
- {0x1.871a7610e40bdp-45, 0x1.bdce9dcc96p-1},
- {-0x1.2d90e5edaeceep-43, 0x1.c31a27dd01p-1},
- {-0x1.2d90e5edaeceep-43, 0x1.c31a27dd01p-1},
- {-0x1.5dd31d962d373p-43, 0x1.c86f7b7ea5p-1},
- {-0x1.5dd31d962d373p-43, 0x1.c86f7b7ea5p-1},
- {-0x1.9ad57391924a7p-43, 0x1.cdcebd2374p-1},
- {-0x1.3167ccc538261p-44, 0x1.d338120a6ep-1},
- {-0x1.3167ccc538261p-44, 0x1.d338120a6ep-1},
- {0x1.c7a4ff65ddbc9p-45, 0x1.d8aba045bp-1},
- {0x1.c7a4ff65ddbc9p-45, 0x1.d8aba045bp-1},
- {-0x1.f9ab3cf74babap-44, 0x1.de298ec0bbp-1},
- {-0x1.f9ab3cf74babap-44, 0x1.de298ec0bbp-1},
- {0x1.52842c1c1e586p-43, 0x1.e3b20546f5p-1},
- {0x1.52842c1c1e586p-43, 0x1.e3b20546f5p-1},
- {0x1.3c6764fc87b4ap-48, 0x1.e9452c8a71p-1},
- {0x1.3c6764fc87b4ap-48, 0x1.e9452c8a71p-1},
- {-0x1.a0976c0a2827dp-44, 0x1.eee32e2aedp-1},
- {-0x1.a0976c0a2827dp-44, 0x1.eee32e2aedp-1},
- {-0x1.a45314dc4fc42p-43, 0x1.f48c34bd1fp-1},
- {-0x1.a45314dc4fc42p-43, 0x1.f48c34bd1fp-1},
- {0x1.ef5d00e390ap-44, 0x1.fa406bd244p-1},
- {0.0, 1.0},
-};
-
-bool is_odd_integer(double x) {
- using FPBits = fputil::FPBits<double>;
- FPBits xbits(x);
- uint64_t x_u = xbits.uintval();
- unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
- unsigned lsb =
- static_cast<unsigned>(cpp::countr_zero(x_u | FPBits::EXP_MASK));
- constexpr unsigned UNIT_EXPONENT =
- static_cast<unsigned>(FPBits::EXP_BIAS + FPBits::FRACTION_LEN);
- return (x_e + lsb == UNIT_EXPONENT);
-}
-
-bool is_integer(double x) {
- using FPBits = fputil::FPBits<double>;
- FPBits xbits(x);
- uint64_t x_u = xbits.uintval();
- unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
- unsigned lsb =
- static_cast<unsigned>(cpp::countr_zero(x_u | FPBits::EXP_MASK));
- constexpr unsigned UNIT_EXPONENT =
- static_cast<unsigned>(FPBits::EXP_BIAS + FPBits::FRACTION_LEN);
- return (x_e + lsb >= UNIT_EXPONENT);
-}
-
-} // namespace
-
LLVM_LIBC_FUNCTION(double, pow, (double x, double y)) {
- using FPBits = fputil::FPBits<double>;
-
- FPBits xbits(x), ybits(y);
-
- bool x_sign = xbits.sign() == Sign::NEG;
- bool y_sign = ybits.sign() == Sign::NEG;
-
- FPBits x_abs = xbits.abs();
- FPBits y_abs = ybits.abs();
-
- uint64_t x_mant = xbits.get_mantissa();
- uint64_t y_mant = ybits.get_mantissa();
- uint64_t x_u = xbits.uintval();
- uint64_t x_a = x_abs.uintval();
- uint64_t y_a = y_abs.uintval();
-
- double e_x = static_cast<double>(xbits.get_exponent());
- uint64_t sign = 0;
-
- ///////// BEGIN - Check exceptional cases ////////////////////////////////////
- // If x or y is signaling NaN
- if (x_abs.is_signaling_nan() || y_abs.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- // The double precision number that is closest to 1 is (1 - 2^-53), which has
- // log2(1 - 2^-53) ~ -1.715...p-53.
- // So if |y| > |1075 / log2(1 - 2^-53)|, and x is finite:
- // |y * log2(x)| = 0 or > 1075.
- // Hence x^y will either overflow or underflow if x is not zero.
- if (LIBC_UNLIKELY(y_mant == 0 || y_a > 0x43d7'4910'd52d'3052 ||
- x_u == FPBits::one().uintval() ||
- x_u >= FPBits::inf().uintval() ||
- x_u < FPBits::min_normal().uintval())) {
- // Exceptional exponents.
- if (y == 0.0)
- return 1.0;
-
- switch (y_a) {
- case 0x3fe0'0000'0000'0000: { // y = +-0.5
- // TODO: speed up x^(-1/2) with rsqrt(x) when available.
- if (LIBC_UNLIKELY(
- (x == 0.0 || x_u == FPBits::inf(Sign::NEG).uintval()))) {
- // pow(-0, 1/2) = +0
- // pow(-inf, 1/2) = +inf
- // Make sure it works correctly for FTZ/DAZ.
- return y_sign ? 1.0 / (x * x) : (x * x);
- }
- return y_sign ? (1.0 / fputil::sqrt<double>(x)) : fputil::sqrt<double>(x);
- }
- case 0x3ff0'0000'0000'0000: // y = +-1.0
- return y_sign ? (1.0 / x) : x;
- case 0x4000'0000'0000'0000: // y = +-2.0;
- return y_sign ? (1.0 / (x * x)) : (x * x);
- }
-
- // |y| > |1075 / log2(1 - 2^-53)|.
- if (y_a > 0x43d7'4910'd52d'3052) {
- if (y_a >= 0x7ff0'0000'0000'0000) {
- // y is inf or nan
- if (y_mant != 0) {
- // y is NaN
- // pow(1, NaN) = 1
- // pow(x, NaN) = NaN
- return (x_u == FPBits::one().uintval()) ? 1.0 : y;
- }
-
- // Now y is +-Inf
- if (x_abs.is_nan()) {
- // pow(NaN, +-Inf) = NaN
- return x;
- }
-
- if (x_a == 0x3ff0'0000'0000'0000) {
- // pow(+-1, +-Inf) = 1.0
- return 1.0;
- }
-
- if (x == 0.0 && y_sign) {
- // pow(+-0, -Inf) = +inf and raise FE_DIVBYZERO
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_DIVBYZERO);
- return FPBits::inf().get_val();
- }
- // pow (|x| < 1, -inf) = +inf
- // pow (|x| < 1, +inf) = 0.0
- // pow (|x| > 1, -inf) = 0.0
- // pow (|x| > 1, +inf) = +inf
- return ((x_a < FPBits::one().uintval()) == y_sign)
- ? FPBits::inf().get_val()
- : 0.0;
- }
- // x^y will overflow / underflow in double precision. Set y to a
- // large enough exponent but not too large, so that the computations
- // won't overflow in double precision.
- y = y_sign ? -0x1.0p100 : 0x1.0p100;
- }
-
- // y is finite and non-zero.
-
- if (x_u == FPBits::one().uintval()) {
- // pow(1, y) = 1
- return 1.0;
- }
-
- // TODO: Speed things up with pow(2, y) = exp2(y) and pow(10, y) = exp10(y).
-
- if (x == 0.0) {
- bool out_is_neg = x_sign && is_odd_integer(y);
- if (y_sign) {
- // pow(0, negative number) = inf
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_DIVBYZERO);
- return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
- }
- // pow(0, positive number) = 0
- return out_is_neg ? -0.0 : 0.0;
- }
-
- if (x_a == FPBits::inf().uintval()) {
- bool out_is_neg = x_sign && is_odd_integer(y);
- if (y_sign)
- return out_is_neg ? -0.0 : 0.0;
- return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
- }
-
- if (x_a > FPBits::inf().uintval()) {
- // x is NaN.
- // pow (aNaN, 0) is already taken care above.
- return x;
- }
-
- // Normalize denormal inputs.
- if (x_a < FPBits::min_normal().uintval()) {
- e_x -= 64.0;
- x_mant = FPBits(x * 0x1.0p64).get_mantissa();
- }
-
- // x is finite and negative, and y is a finite integer.
- if (x_sign) {
- if (is_integer(y)) {
- x = -x;
- if (is_odd_integer(y))
- // sign = -1.0;
- sign = 0x8000'0000'0000'0000;
- } else {
- // pow( negative, non-integer ) = NaN
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
- }
- }
-
- ///////// END - Check exceptional cases //////////////////////////////////////
-
- // x^y = 2^( y * log2(x) )
- // = 2^( y * ( e_x + log2(m_x) ) )
- // First we compute log2(x) = e_x + log2(m_x)
-
- // Extract exponent field of x.
-
- // Use the highest 7 fractional bits of m_x as the index for look up tables.
- unsigned idx_x = static_cast<unsigned>(x_mant >> (FPBits::FRACTION_LEN - 7));
- // Add the hidden bit to the mantissa.
- // 1 <= m_x < 2
- FPBits m_x = FPBits(x_mant | 0x3ff0'0000'0000'0000);
-
- // Reduced argument for log2(m_x):
- // dx = r * m_x - 1.
- // The computation is exact, and -2^-8 <= dx < 2^-7.
- // Then m_x = (1 + dx) / r, and
- // log2(m_x) = log2( (1 + dx) / r )
- // = log2(1 + dx) - log2(r).
-
- // In order for the overall computations x^y = 2^(y * log2(x)) to have the
- // relative errors < 2^-52 (1ULP), we will need to evaluate the exponent part
- // y * log2(x) with absolute errors < 2^-52 (or better, 2^-53). Since the
- // whole exponent range for double precision is bounded by
- // |y * log2(x)| < 1076 ~ 2^10, we need to evaluate log2(x) with absolute
- // errors < 2^-53 * 2^-10 = 2^-63.
-
- // With that requirement, we use the following degree-6 polynomial
- // approximation:
- // P(dx) ~ log2(1 + dx) / dx
- // Generated by Sollya with:
- // > P = fpminimax(log2(1 + x)/x, 6, [|D...|], [-2^-8, 2^-7]); P;
- // > dirtyinfnorm(log2(1 + x) - x*P, [-2^-8, 2^-7]);
- // 0x1.d03cc...p-66
- constexpr double COEFFS[] = {0x1.71547652b82fep0, -0x1.71547652b82e7p-1,
- 0x1.ec709dc3b1fd5p-2, -0x1.7154766124215p-2,
- 0x1.2776bd90259d8p-2, -0x1.ec586c6f3d311p-3,
- 0x1.9c4775eccf524p-3};
- // Error: ulp(dx^2) <= (2^-7)^2 * 2^-52 = 2^-66
- // Extra errors from various computations and rounding directions, the overall
- // errors we can be bounded by 2^-65.
-
- double dx;
- DoubleDouble dx_c0;
-
- // Perform exact range reduction and exact product dx * c0.
-#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- dx = fputil::multiply_add(RD[idx_x], m_x.get_val(), -1.0); // Exact
- dx_c0 = fputil::exact_mult(COEFFS[0], dx);
-#else
- double c = FPBits(m_x.uintval() & 0x3fff'e000'0000'0000).get_val();
- dx = fputil::multiply_add(RD[idx_x], m_x.get_val() - c, CD[idx_x]); // Exact
- dx_c0 = fputil::exact_mult<double, 28>(dx, COEFFS[0]); // Exact
-#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
-
- double dx2 = dx * dx;
- double c0 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);
- double c1 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);
- double c2 = fputil::multiply_add(dx, COEFFS[6], COEFFS[5]);
-
- double p = fputil::polyeval(dx2, c0, c1, c2);
-
- // s = e_x - log2(r) + dx * P(dx)
- // Absolute error bound:
- // |log2(x) - log2_x.hi - log2_x.lo| < 2^-65.
-
- // Notice that e_x - log2(r).hi is exact, so we perform an exact sum of
- // e_x - log2(r).hi and the high part of the product dx * c0:
- // log2_x_hi.hi + log2_x_hi.lo = e_x - log2(r).hi + (dx * c0).hi
- DoubleDouble log2_x_hi =
- fputil::exact_add(e_x + LOG2_R_DD[idx_x].hi, dx_c0.hi);
- // The low part is dx^2 * p + low part of (dx * c0) + low part of -log2(r).
- double log2_x_lo =
- fputil::multiply_add(dx2, p, dx_c0.lo + LOG2_R_DD[idx_x].lo);
- // Perform accurate sums.
- DoubleDouble log2_x = fputil::exact_add(log2_x_hi.hi, log2_x_lo);
- log2_x.lo += log2_x_hi.lo;
-
- // To compute 2^(y * log2(x)), we break the exponent into 3 parts:
- // y * log(2) = hi + mid + lo, where
- // hi is an integer
- // mid * 2^6 is an integer
- // |lo| <= 2^-7
- // Then:
- // x^y = 2^(y * log2(x)) = 2^hi * 2^mid * 2^lo,
- // In which 2^mid is obtained from a look-up table of size 2^6 = 64 elements,
- // and 2^lo ~ 1 + lo * P(lo).
- // Thus, we have:
- // hi + mid = 2^-6 * round( 2^6 * y * log2(x) )
- // If we restrict the output such that |hi| < 150, (hi + mid) uses (8 + 6)
- // bits, hence, if we use double precision to perform
- // round( 2^6 * y * log2(x))
- // the lo part is bounded by 2^-7 + 2^(-(52 - 14)) = 2^-7 + 2^-38
-
- // In the following computations:
- // y6 = 2^6 * y
- // hm = 2^6 * (hi + mid) = round(2^6 * y * log2(x)) ~ round(y6 * s)
- // lo6 = 2^6 * lo = 2^6 * (y - (hi + mid)) = y6 * log2(x) - hm.
- double y6 = y * 0x1.0p6; // Exact.
-
- DoubleDouble y6_log2_x = fputil::exact_mult(y6, log2_x.hi);
- y6_log2_x.lo = fputil::multiply_add(y6, log2_x.lo, y6_log2_x.lo);
-
- // Check overflow/underflow.
- double scale = 1.0;
-
- // |2^(hi + mid) - exp2_hi_mid| <= ulp(exp2_hi_mid) / 2
- // Clamp the exponent part into smaller range that fits double precision.
- // For those exponents that are out of range, the final conversion will round
- // them correctly to inf/max float or 0/min float accordingly.
- constexpr double UPPER_EXP_BOUND = 512.0 * 0x1.0p6;
- if (LIBC_UNLIKELY(FPBits(y6_log2_x.hi).abs().get_val() >= UPPER_EXP_BOUND)) {
- if (FPBits(y6_log2_x.hi).sign() == Sign::POS) {
- scale = 0x1.0p512;
- y6_log2_x.hi -= 512.0 * 64.0;
- if (y6_log2_x.hi > 513.0 * 64.0)
- y6_log2_x.hi = 513.0 * 64.0;
- } else {
- scale = 0x1.0p-512;
- y6_log2_x.hi += 512.0 * 64.0;
- if (y6_log2_x.hi < (-1076.0 + 512.0) * 64.0)
- y6_log2_x.hi = -564.0 * 64.0;
- }
- }
-
- double hm = fputil::nearest_integer(y6_log2_x.hi);
-
- // lo6 = 2^6 * lo.
- double lo6_hi = y6_log2_x.hi - hm;
- double lo6 = lo6_hi + y6_log2_x.lo;
-
- int hm_i = static_cast<int>(hm);
- unsigned idx_y = static_cast<unsigned>(hm_i) & 0x3f;
-
- // 2^hi
- int64_t exp2_hi_i = static_cast<int64_t>(
- static_cast<uint64_t>(static_cast<int64_t>(hm_i >> 6))
- << FPBits::FRACTION_LEN);
- // 2^mid
- int64_t exp2_mid_hi_i =
- static_cast<int64_t>(FPBits(EXP2_MID1[idx_y].hi).uintval());
- int64_t exp2_mid_lo_i =
- static_cast<int64_t>(FPBits(EXP2_MID1[idx_y].mid).uintval());
- // (-1)^sign * 2^hi * 2^mid
- // Error <= 2^hi * 2^-53
- uint64_t exp2_hm_hi_i =
- static_cast<uint64_t>(exp2_hi_i + exp2_mid_hi_i) + sign;
- // The low part could be 0.
- uint64_t exp2_hm_lo_i =
- idx_y != 0 ? static_cast<uint64_t>(exp2_hi_i + exp2_mid_lo_i) + sign
- : sign;
- double exp2_hm_hi = FPBits(exp2_hm_hi_i).get_val();
- double exp2_hm_lo = FPBits(exp2_hm_lo_i).get_val();
-
- // Degree-5 polynomial approximation P(lo6) ~ 2^(lo6 / 2^6) = 2^(lo).
- // Generated by Sollya with:
- // > P = fpminimax(2^(x/64), 5, [|1, D...|], [-2^-1, 2^-1]);
- // > dirtyinfnorm(2^(x/64) - P, [-0.5, 0.5]);
- // 0x1.a2b77e618f5c4c176fd11b7659016cde5de83cb72p-60
- constexpr double EXP2_COEFFS[] = {0x1p0,
- 0x1.62e42fefa39efp-7,
- 0x1.ebfbdff82a23ap-15,
- 0x1.c6b08d7076268p-23,
- 0x1.3b2ad33f8b48bp-31,
- 0x1.5d870c4d84445p-40};
-
- double lo6_sqr = lo6 * lo6;
-
- double d0 = fputil::multiply_add(lo6, EXP2_COEFFS[2], EXP2_COEFFS[1]);
- double d1 = fputil::multiply_add(lo6, EXP2_COEFFS[4], EXP2_COEFFS[3]);
- double pp = fputil::polyeval(lo6_sqr, d0, d1, EXP2_COEFFS[5]);
-
- double r = fputil::multiply_add(exp2_hm_hi * lo6, pp, exp2_hm_lo);
- r += exp2_hm_hi;
-
- return r * scale;
+ return math::pow(x, y);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/shared/CMakeLists.txt b/libc/test/shared/CMakeLists.txt
index 61625c0bc0444..1173b32e11e6a 100644
--- a/libc/test/shared/CMakeLists.txt
+++ b/libc/test/shared/CMakeLists.txt
@@ -70,6 +70,7 @@ add_fp_unittest(
libc.src.__support.math.ldexpf128
libc.src.__support.math.ldexpf16
libc.src.__support.math.llogbf
+ libc.src.__support.math.pow
libc.src.__support.math.rsqrtf
libc.src.__support.math.rsqrtf16
libc.src.__support.math.sin
diff --git a/libc/test/shared/shared_math_test.cpp b/libc/test/shared/shared_math_test.cpp
index 49047631fb227..428b17c7fbe89 100644
--- a/libc/test/shared/shared_math_test.cpp
+++ b/libc/test/shared/shared_math_test.cpp
@@ -98,6 +98,7 @@ TEST(LlvmLibcSharedMathTest, AllDouble) {
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::expm1(0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::fsqrt(0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::log(1.0));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::shared::pow(0.0, 0.0));
EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::shared::sin(0.0));
}
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 3d9491e8baa0c..91c1914ceeaed 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2957,6 +2957,25 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_pow",
+ hdrs = ["src/__support/math/pow.h"],
+ deps = [
+ ":__support_cpp_bit",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_sqrt",
+ ":__support_fputil_triple_double",
+ ":__support_macros_optimization",
+ ":__support_math_common_constants",
+ ":__support_math_exp10f",
+ ":__support_math_exp2f",
+ ],
+)
+
libc_support_library(
name = "__support_math_exp_constants",
hdrs = ["src/__support/math/exp_constants.h"],
@@ -4757,11 +4776,8 @@ libc_math_function(name = "nextupf16")
libc_math_function(
name = "pow",
additional_deps = [
- ":__support_fputil_double_double",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_sqrt",
- ":__support_math_common_constants",
+ ":__support_math_pow",
+ ":errno",
],
)
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