[libc] [llvm] [libc][math] Implement C23 half precision pow function (PR #159906)
via llvm-commits
llvm-commits at lists.llvm.org
Fri Jan 2 10:56:45 PST 2026
https://github.com/AnonMiraj updated https://github.com/llvm/llvm-project/pull/159906
>From eb6fdbc5f09f88b9cf8eb805a8256170ac8f1f89 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 20 Sep 2025 07:58:40 +0300
Subject: [PATCH 01/14] [libc][math] Implement C23 half precision pow function
---
libc/config/gpu/amdgpu/entrypoints.txt | 1 +
libc/config/gpu/nvptx/entrypoints.txt | 1 +
libc/config/linux/aarch64/entrypoints.txt | 1 +
libc/config/linux/arm/entrypoints.txt | 1 +
libc/config/linux/riscv/entrypoints.txt | 1 +
libc/config/linux/x86_64/entrypoints.txt | 1 +
libc/include/math.yaml | 6 +
libc/src/math/CMakeLists.txt | 1 +
libc/src/math/generic/CMakeLists.txt | 24 ++
libc/src/math/generic/powf16.cpp | 296 ++++++++++++++++++++++
libc/src/math/powf16.h | 21 ++
libc/test/src/math/CMakeLists.txt | 11 +
libc/test/src/math/powf16_test.cpp | 122 +++++++++
libc/test/src/math/smoke/CMakeLists.txt | 10 +
libc/test/src/math/smoke/powf16_test.cpp | 232 +++++++++++++++++
15 files changed, 729 insertions(+)
create mode 100644 libc/src/math/generic/powf16.cpp
create mode 100644 libc/src/math/powf16.h
create mode 100644 libc/test/src/math/powf16_test.cpp
create mode 100644 libc/test/src/math/smoke/powf16_test.cpp
diff --git a/libc/config/gpu/amdgpu/entrypoints.txt b/libc/config/gpu/amdgpu/entrypoints.txt
index 0dda7d5c683ec..22a67283c2d26 100644
--- a/libc/config/gpu/amdgpu/entrypoints.txt
+++ b/libc/config/gpu/amdgpu/entrypoints.txt
@@ -451,6 +451,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextupl
libc.src.math.pow
libc.src.math.powf
+ libc.src.math.powf16
libc.src.math.remainder
libc.src.math.remainderf
libc.src.math.remainderl
diff --git a/libc/config/gpu/nvptx/entrypoints.txt b/libc/config/gpu/nvptx/entrypoints.txt
index 6070fb5b17b3c..8a9bb724079c3 100644
--- a/libc/config/gpu/nvptx/entrypoints.txt
+++ b/libc/config/gpu/nvptx/entrypoints.txt
@@ -452,6 +452,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextupl
libc.src.math.pow
libc.src.math.powf
+ libc.src.math.powf16
libc.src.math.remainder
libc.src.math.remainderf
libc.src.math.remainderl
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 970c825bbfc96..72237fd95fa56 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -593,6 +593,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextupl
libc.src.math.pow
libc.src.math.powf
+ libc.src.math.powf16
libc.src.math.remainder
libc.src.math.remainderf
libc.src.math.remainderl
diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
index f04ac40145d3a..ff11969d9eaa7 100644
--- a/libc/config/linux/arm/entrypoints.txt
+++ b/libc/config/linux/arm/entrypoints.txt
@@ -405,6 +405,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextupl
libc.src.math.pow
libc.src.math.powf
+ libc.src.math.powf16
libc.src.math.remainder
libc.src.math.remainderf
libc.src.math.remainderl
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 7baf4de9d8a5b..c8bee03db0a9a 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -602,6 +602,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextupl
libc.src.math.pow
libc.src.math.powf
+ libc.src.math.powf16
libc.src.math.remainder
libc.src.math.remainderf
libc.src.math.remainderl
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 9399b284fa2da..0055e5bd08122 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -644,6 +644,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextupl
libc.src.math.pow
libc.src.math.powf
+ libc.src.math.powf16
libc.src.math.remainder
libc.src.math.remainderf
libc.src.math.remainderl
diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index afd3ae33305c1..fe23f1c8c3a64 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -2162,6 +2162,12 @@ functions:
arguments:
- type: float
- type: float
+ - name: powf16
+ standards:
+ - stdc
+ return_type: _Float16
+ arguments:
+ - type: _Float16
- name: powi
standards: llvm_libc_ext
return_type: double
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index e37e22fdb58e6..9238c440faae6 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -479,6 +479,7 @@ add_math_entrypoint_object(nextupbf16)
add_math_entrypoint_object(pow)
add_math_entrypoint_object(powf)
+add_math_entrypoint_object(powf16)
add_math_entrypoint_object(powi)
add_math_entrypoint_object(powif)
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index e343c1f15c3f1..82b6c7ea59bab 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1594,6 +1594,30 @@ add_entrypoint_object(
libc.src.__support.math.expxf16_utils
)
+add_entrypoint_object(
+ powf16
+ SRCS
+ powf16.cpp
+ HDRS
+ ../pow.h
+ DEPENDS
+ .common_constants
+ libc.hdr.errno_macros
+ libc.hdr.fenv_macros
+ libc.src.__support.CPP.bit
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+ libc.src.__support.math.expxf16_utils
+ COMPILE_OPTIONS
+ -O3
+)
+
add_entrypoint_object(
powf
SRCS
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
new file mode 100644
index 0000000000000..8e2e6b552632f
--- /dev/null
+++ b/libc/src/math/generic/powf16.cpp
@@ -0,0 +1,296 @@
+//===-- Half-precision x^y 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/powf16.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/cast.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/macros/properties/types.h"
+#include "src/__support/math/expxf16_utils.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace {
+
+bool is_odd_integer(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+ uint16_t x_u = xbits.uintval();
+ unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
+ unsigned lsb = static_cast<unsigned>(
+ cpp::countr_zero(static_cast<uint32_t>(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(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+ uint16_t x_u = xbits.uintval();
+ unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
+ unsigned lsb = static_cast<unsigned>(
+ cpp::countr_zero(static_cast<uint32_t>(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(float16, powf16, (float16 x, float16 y)) {
+ using FPBits = fputil::FPBits<float16>;
+
+ FPBits xbits(x), ybits(y);
+ bool x_sign = xbits.is_neg();
+ bool y_sign = ybits.is_neg();
+
+ FPBits x_abs = xbits.abs();
+ FPBits y_abs = ybits.abs();
+
+ uint16_t x_u = xbits.uintval();
+ uint16_t x_a = x_abs.uintval();
+ uint16_t y_a = y_abs.uintval();
+ bool result_sign = false;
+
+ ///////// BEGIN - Check exceptional cases ////////////////////////////////////
+ // If x or y is signaling NaN
+ if (xbits.is_signaling_nan() || ybits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ //
+ if (LIBC_UNLIKELY(ybits.is_zero() || x_u == FPBits::one().uintval() ||
+ x_u >= FPBits::inf().uintval() ||
+ x_u < FPBits::min_normal().uintval())) {
+ // pow(x, 0) = 1
+ if (ybits.is_zero()) {
+ return fputil::cast<float16>(1.0f);
+ }
+
+ // pow(1, Y) = 1
+ if (x_u == FPBits::one().uintval()) {
+ return fputil::cast<float16>(1.0f);
+ }
+
+ switch (y_a) {
+
+ case 0x3800U: { // y = +-0.5
+ 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 fputil::cast<float16>(y_sign ? (1.0 / (x * x)) : (x * x));
+ }
+ return fputil::cast<float16>(y_sign ? (1.0 / fputil::sqrt<float16>(x))
+ : fputil::sqrt<float16>(x));
+ }
+ case 0x3c00U: // y = +-1.0
+ return fputil::cast<float16>(y_sign ? (1.0 / x) : x);
+
+ case 0x4000U: // y = +-2.0
+ return fputil::cast<float16>(y_sign ? (1.0 / (x * x)) : (x * x));
+ }
+ // TODO: Speed things up with pow(2, y) = exp2(y) and pow(10, y) = exp10(y).
+
+ // Propagate remaining quiet NaNs.
+ if (xbits.is_quiet_nan()) {
+ return x;
+ }
+ if (ybits.is_quiet_nan()) {
+ return y;
+ }
+
+ // x = -1: special case for integer exponents
+ if (x_u == FPBits::one(Sign::NEG).uintval()) {
+ if (is_integer(y)) {
+ if (is_odd_integer(y)) {
+ return fputil::cast<float16>(-1.0f);
+ } else {
+ return fputil::cast<float16>(1.0f);
+ }
+ }
+ // pow(-1, non-integer) = NaN
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // x = 0 cases
+ if (xbits.is_zero()) {
+ if (y_sign) {
+ // pow(+-0, negative) = +-inf and raise FE_DIVBYZERO
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+ bool result_neg = x_sign && ybits.is_finite() && is_odd_integer(y);
+ return FPBits::inf(result_neg ? Sign::NEG : Sign::POS).get_val();
+ } else {
+ // pow(+-0, positive) = +-0
+ bool out_is_neg = x_sign && is_odd_integer(y);
+ return out_is_neg ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
+ }
+ }
+
+ if (xbits.is_inf()) {
+ bool out_is_neg = x_sign && ybits.is_finite() && is_odd_integer(y);
+ if (y_sign) // pow(+-inf, negative) = +-0
+ return out_is_neg ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
+ // pow(+-inf, positive) = +-inf
+ return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
+ }
+
+ // y = +-inf cases
+ if (ybits.is_inf()) {
+ // pow(1, inf) handled above.
+ bool x_abs_less_than_one = x_a < FPBits::one().uintval();
+ if ((x_abs_less_than_one && !y_sign) ||
+ (!x_abs_less_than_one && y_sign)) {
+ return fputil::cast<float16>(0.0f);
+ } else {
+ return FPBits::inf().get_val();
+ }
+ }
+
+ // pow( negative, non-integer ) = NaN
+ if (x_sign && !is_integer(y)) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // For negative x with integer y, compute pow(|x|, y) and adjust sign
+ if (x_sign) {
+ x = -x;
+ if (is_odd_integer(y)) {
+ result_sign = true;
+ }
+ }
+ }
+ ///////// 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)
+
+ using namespace math::expxf16_internal;
+ FPBits x_bits(x);
+
+ uint16_t x_u_log = x_bits.uintval();
+
+ // Extract exponent field of x.
+ int m = -FPBits::EXP_BIAS;
+
+ // When x is subnormal, normalize it by multiplying by 2^FRACTION_LEN.
+ if ((x_u_log & FPBits::EXP_MASK) == 0U) {
+ constexpr float NORMALIZE_EXP =
+ static_cast<float>(1U << FPBits::FRACTION_LEN);
+ x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
+ x_u_log = x_bits.uintval();
+ m -= FPBits::FRACTION_LEN;
+ }
+
+ // Extract the mantissa and index into small lookup tables.
+ uint16_t mant = x_bits.get_mantissa();
+ // Use the highest 5 fractional bits of the mantissa as the index f.
+ int f = mant >> 5;
+
+ m += (x_u_log >> FPBits::FRACTION_LEN);
+
+ // Add the hidden bit to the mantissa.
+ // 1 <= m_x < 2
+ x_bits.set_biased_exponent(FPBits::EXP_BIAS);
+ float mant_f = x_bits.get_val();
+
+ // Range reduction for log2(m_x):
+ // v = r * m_x - 1, where r is a power of 2 from a lookup table.
+ // The computation is exact for half-precision, and -2^-5 <= v < 2^-4.
+ // Then m_x = (1 + v) / r, and log2(m_x) = log2(1 + v) - log2(r).
+
+ float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
+
+ // For half-precision accuracy, we use a degree-2 polynomial approximation:
+ // P(v) ~ log2(1 + v) / v
+ // Generated by Sollya with:
+ // > P = fpminimax(log2(1+x)/x, 2, [|D...|], [-2^-5, 2^-4]);
+ // The coefficients are rounded from the Sollya output.
+ float log2p1_d_over_f =
+ v * fputil::polyeval(v, 0x1.715476p+0f, -0x1.71771ap-1f, 0x1.ecb38ep-2f);
+
+ // log2(1.mant) = log2(f) + log2(1 + v)
+ float log2_1_mant = LOG2F_F[f] + log2p1_d_over_f;
+
+ // Complete log2(x) = e_x + log2(m_x)
+ float log2_x = static_cast<float>(m) + log2_1_mant;
+
+ // z = y * log2(x)
+ // Now compute 2^z = 2^(n + r), with n integer and r in [-0.5, 0.5].
+ double z = fputil::cast<double>(y) * log2_x;
+
+ // Check for overflow/underflow for half-precision.
+ // Half-precision range is approximately 2^-24 to 2^15.
+ if (z > 15.0) {
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ return FPBits::inf().get_val();
+ }
+ if (z < -24.0) {
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return fputil::cast<float16>(0.0f);
+ }
+
+ double n = fputil::nearest_integer(z);
+ double r = z - n;
+
+ // Compute 2^r using a degree-7 polynomial for r in [-0.5, 0.5].
+ // Generated by Sollya with:
+ // > P = fpminimax(2^x, 7, [|D...|], [-0.5, 0.5]);
+ // The polynomial coefficients are rounded from the Sollya output.
+ constexpr double EXP2_COEFFS[] = {
+ 0x1p+0, // 1.0
+ 0x1.62e42fefa39efp-1, // ln(2)
+ 0x1.ebfbdff82c58fp-3, // ln(2)^2 / 2
+ 0x1.c6b08d704a0c0p-5, // ln(2)^3 / 6
+ 0x1.3b2ab6fba4e77p-7, // ln(2)^4 / 24
+ 0x1.5d87fe78a6737p-10, // ln(2)^5 / 120
+ 0x1.430912f86a805p-13, // ln(2)^6 / 720
+ 0x1.10e4104ac8015p-17 // ln(2)^7 / 5040
+ };
+
+ double exp2_r = fputil::polyeval(
+ r, EXP2_COEFFS[0], EXP2_COEFFS[1], EXP2_COEFFS[2], EXP2_COEFFS[3],
+ EXP2_COEFFS[4], EXP2_COEFFS[5], EXP2_COEFFS[6], EXP2_COEFFS[7]);
+
+ // Compute 2^n by direct bit manipulation.
+ int n_int = static_cast<int>(n);
+ uint64_t exp_bits = static_cast<uint64_t>(n_int + 1023) << 52;
+ double pow2_n = cpp::bit_cast<double>(exp_bits);
+
+ float16 result = fputil::cast<float16>(pow2_n * exp2_r);
+
+ if (result_sign) {
+ FPBits result_bits(result);
+ result_bits.set_sign(Sign::NEG);
+ result = result_bits.get_val();
+ }
+
+ return result;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/powf16.h b/libc/src/math/powf16.h
new file mode 100644
index 0000000000000..52f9848f4a2be
--- /dev/null
+++ b/libc/src/math/powf16.h
@@ -0,0 +1,21 @@
+//===-- Implementation header for powf16 --------------------------*- 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_POWF16_H
+#define LLVM_LIBC_SRC_MATH_POWF16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 powf16(float16 x, float16 y);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_POWF16_H
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index ff5c511922171..afd5a72e0f87a 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2648,6 +2648,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ powf16_test
+ NEED_MPFR
+ SUITE
+ libc-math-unittests
+ SRCS
+ powf16_test.cpp
+ DEPENDS
+ libc.src.math.powf16
+ libc.src.__support.FPUtil.fp_bits
+)
add_fp_unittest(
atan2f_test
NEED_MPFR
diff --git a/libc/test/src/math/powf16_test.cpp b/libc/test/src/math/powf16_test.cpp
new file mode 100644
index 0000000000000..171cb098114d4
--- /dev/null
+++ b/libc/test/src/math/powf16_test.cpp
@@ -0,0 +1,122 @@
+//===-- Unittests for powf16 ----------------------------------------------===//
+//
+// 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/powf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcPowF16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+using LIBC_NAMESPACE::testing::tlog;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+TEST_F(LlvmLibcPowF16Test, TrickyInputs) {
+ // These values are in half precision.
+ constexpr mpfr::BinaryInput<float16> INPUTS[] = {
+ {static_cast<float16>(0x1.08p-2f), static_cast<float16>(0x1.0cp-1f)},
+ {static_cast<float16>(0x1.66p-1f), static_cast<float16>(0x1.f1p+1f)},
+ {static_cast<float16>(0x1.c04p-1f), static_cast<float16>(0x1.2p+12f)},
+ {static_cast<float16>(0x1.aep-1f), static_cast<float16>(0x1.f9p-1f)},
+ {static_cast<float16>(0x1.ffcp-1f), static_cast<float16>(0x1.fffp-2f)},
+ {static_cast<float16>(0x1.f55p-1f), static_cast<float16>(0x1.88p+12f)},
+ {static_cast<float16>(0x1.e84p-1f), static_cast<float16>(0x1.2cp+13f)},
+ };
+
+ for (auto input : INPUTS) {
+ float16 x = input.x;
+ float16 y = input.y;
+ EXPECT_MPFR_MATCH(mpfr::Operation::Pow, input, LIBC_NAMESPACE::powf16(x, y),
+ 1.0); // 1 ULP tolerance is enough for f16
+ }
+}
+
+TEST_F(LlvmLibcPowF16Test, InFloat16Range) {
+ constexpr uint16_t X_COUNT = 63;
+ constexpr uint16_t X_START = FPBits(static_cast<float16>(0.25)).uintval();
+ constexpr uint16_t X_STOP = FPBits(static_cast<float16>(4.0)).uintval();
+ constexpr uint16_t X_STEP = (X_STOP - X_START) / X_COUNT;
+
+ constexpr uint16_t Y_COUNT = 59;
+ constexpr uint16_t Y_START = FPBits(static_cast<float16>(0.25)).uintval();
+ constexpr uint16_t Y_STOP = FPBits(static_cast<float16>(4.0)).uintval();
+ constexpr uint16_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 count = 0;
+ uint64_t cc = 0;
+ float16 mx = 0.0, my = 0.0, mr = 0.0;
+ double tol = 1.0; // start with 1 ULP for half precision
+
+ for (uint16_t i = 0, v = X_START; i <= X_COUNT; ++i, v += X_STEP) {
+ float16 x = FPBits(v).get_val();
+ if (FPBits(x).is_inf_or_nan() || x < static_cast<float16>(0.0))
+ continue;
+
+ for (uint16_t j = 0, w = Y_START; j <= Y_COUNT; ++j, w += Y_STEP) {
+ float16 y = FPBits(w).get_val();
+ if (FPBits(y).is_inf_or_nan())
+ continue;
+
+ float16 result = LIBC_NAMESPACE::powf16(x, y);
+ ++cc;
+ if (FPBits(result).is_inf_or_nan())
+ continue;
+
+ ++count;
+ mpfr::BinaryInput<float16> inputs{x, y};
+
+ if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Pow, inputs,
+ result, 1.0, rounding_mode)) {
+ ++fails;
+ while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(
+ mpfr::Operation::Pow, inputs, result, tol, rounding_mode)) {
+ mx = x;
+ my = y;
+ mr = result;
+
+ if (tol > 128.0) // half precision is only ~11 bits
+ break;
+
+ tol *= 2.0;
+ }
+ }
+ }
+ }
+ if (fails || (count < cc)) {
+ tlog << " powf16 failed: " << fails << "/" << count << "/" << cc
+ << " tests.\n"
+ << " Max ULPs is at most: " << static_cast<uint64_t>(tol)
+ << ".\n";
+ }
+ if (fails) {
+ mpfr::BinaryInput<float16> inputs{mx, my};
+ EXPECT_MPFR_MATCH(mpfr::Operation::Pow, inputs, mr, 1.0, 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 5afd3a9f22967..0de13713b2fa9 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -5095,6 +5095,16 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ powf16_test
+ SUITE
+ libc-math-smoke-tests
+ SRCS
+ powf16_test.cpp
+ DEPENDS
+ libc.src.math.powf16
+ libc.src.__support.FPUtil.fp_bits
+)
add_fp_unittest(
totalorder_test
SUITE
diff --git a/libc/test/src/math/smoke/powf16_test.cpp b/libc/test/src/math/smoke/powf16_test.cpp
new file mode 100644
index 0000000000000..b3611e141dc01
--- /dev/null
+++ b/libc/test/src/math/smoke/powf16_test.cpp
@@ -0,0 +1,232 @@
+//===-- Unittests for powf16 ----------------------------------------------===//
+//
+// 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 "hdr/fenv_macros.h"
+#include "src/math/powf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+
+using LlvmLibcPowF16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+using LIBC_NAMESPACE::fputil::testing::ForceRoundingMode;
+using LIBC_NAMESPACE::fputil::testing::RoundingMode;
+
+TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
+ constexpr float16 NEG_ODD_INTEGER = -3.0f16;
+ constexpr float16 NEG_EVEN_INTEGER = -6.0f16;
+ constexpr float16 NEG_NON_INTEGER = -1.5f16;
+ constexpr float16 POS_ODD_INTEGER = 5.0f16;
+ constexpr float16 POS_EVEN_INTEGER = 8.0f16;
+ constexpr float16 POS_NON_INTEGER = 1.5f16;
+ constexpr float16 ONE_HALF = 0.5f16;
+
+ for (int i = 0; i < N_ROUNDING_MODES; ++i) {
+
+ ForceRoundingMode __r(ROUNDING_MODES[i]);
+ if (!__r.success)
+ continue;
+
+ // powf16( sNaN, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ aNaN, LIBC_NAMESPACE::powf16(sNaN, NEG_ODD_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ aNaN, LIBC_NAMESPACE::powf16(sNaN, NEG_EVEN_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ aNaN, LIBC_NAMESPACE::powf16(sNaN, POS_ODD_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ aNaN, LIBC_NAMESPACE::powf16(sNaN, POS_EVEN_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, ONE_HALF),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, zero),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, neg_zero),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, inf),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, neg_inf),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, aNaN),
+ FE_INVALID);
+
+ // powf16( 0.0, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(zero, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf16(zero, NEG_ODD_INTEGER), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf16(zero, NEG_EVEN_INTEGER), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf16(zero, NEG_NON_INTEGER), FE_DIVBYZERO);
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, POS_EVEN_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, POS_NON_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, ONE_HALF));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(zero, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(zero, neg_zero));
+ EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::powf16(zero, inf));
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(zero, neg_inf),
+ FE_DIVBYZERO);
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(zero, aNaN));
+
+ // powf16( -0.0, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(neg_zero, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ neg_inf, LIBC_NAMESPACE::powf16(neg_zero, NEG_ODD_INTEGER),
+ FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf16(neg_zero, NEG_EVEN_INTEGER), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf16(neg_zero, NEG_NON_INTEGER), FE_DIVBYZERO);
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf16(neg_zero, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_zero, POS_EVEN_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_zero, POS_NON_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_zero, ONE_HALF));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_zero, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_zero, neg_zero));
+ EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::powf16(neg_zero, inf));
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(neg_zero, neg_inf),
+ FE_DIVBYZERO);
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(neg_zero, aNaN));
+
+ // powf16( 1.0, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(1.0, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, neg_zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, 1.0));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, -1.0));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, NEG_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, NEG_EVEN_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, NEG_NON_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, POS_EVEN_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, POS_NON_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, inf));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, neg_inf));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, aNaN));
+
+ // powf16( -1.0, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(-1.0, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, neg_zero));
+ EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, 1.0));
+ EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, -1.0));
+ EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, NEG_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, NEG_EVEN_INTEGER));
+ EXPECT_FP_IS_NAN_WITH_EXCEPTION(
+ LIBC_NAMESPACE::powf16(-1.0, NEG_NON_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, POS_EVEN_INTEGER));
+ EXPECT_FP_IS_NAN_WITH_EXCEPTION(
+ LIBC_NAMESPACE::powf16(-1.0, POS_NON_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, inf));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(-1.0, aNaN));
+
+ // powf16( inf, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(inf, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(inf, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(inf, neg_zero));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, 1.0));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, -1.0));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, NEG_ODD_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, NEG_EVEN_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, NEG_NON_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, POS_EVEN_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, POS_NON_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, ONE_HALF));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(inf, aNaN));
+
+ // powf16( -inf, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(neg_inf, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_inf, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_inf, neg_zero));
+ EXPECT_FP_EQ(neg_inf, LIBC_NAMESPACE::powf16(neg_inf, 1.0));
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf16(neg_inf, -1.0));
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf16(neg_inf, NEG_ODD_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_inf, NEG_EVEN_INTEGER));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_inf, NEG_NON_INTEGER));
+ EXPECT_FP_EQ(neg_inf, LIBC_NAMESPACE::powf16(neg_inf, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(neg_inf, POS_EVEN_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(neg_inf, POS_NON_INTEGER));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(neg_inf, ONE_HALF));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(neg_inf, inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_inf, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(neg_inf, aNaN));
+
+ // powf16 ( aNaN, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(aNaN, sNaN),
+ FE_INVALID);
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(aNaN, zero));
+ EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(aNaN, neg_zero));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, 1.0));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, -1.0));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, NEG_ODD_INTEGER));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, NEG_EVEN_INTEGER));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, NEG_NON_INTEGER));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, POS_ODD_INTEGER));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, POS_EVEN_INTEGER));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, POS_NON_INTEGER));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, aNaN));
+
+ // powf16 ( base, inf )
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(0.1f16, inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(-0.1f16, inf));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(1.1f16, inf));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(-1.1f16, inf));
+
+ // powf16 ( base, -inf )
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(0.1f16, neg_inf));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(-0.1f16, neg_inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(1.1f16, neg_inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(-1.1f16, neg_inf));
+
+ // Exact powers of 2:
+ // TODO: Enable these tests when we use exp2.
+ // EXPECT_FP_EQ(0x1.0p15, LIBC_NAMESPACE::powf16(2.0, 15.0));
+ // EXPECT_FP_EQ(0x1.0p126, LIBC_NAMESPACE::powf16(2.0, 126.0));
+ // EXPECT_FP_EQ(0x1.0p-45, LIBC_NAMESPACE::powf16(2.0, -45.0));
+ // EXPECT_FP_EQ(0x1.0p-126, LIBC_NAMESPACE::powf16(2.0, -126.0));
+ // EXPECT_FP_EQ(0x1.0p-149, LIBC_NAMESPACE::powf16(2.0, -149.0));
+
+ // Exact powers of 10:
+ // TODO: Enable these tests when we use exp10
+ // EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(10.0, 0.0));
+ // EXPECT_FP_EQ(10.0, LIBC_NAMESPACE::powf16(10.0, 1.0));
+ // EXPECT_FP_EQ(100.0, LIBC_NAMESPACE::powf16(10.0, 2.0));
+ // EXPECT_FP_EQ(1000.0, LIBC_NAMESPACE::powf16(10.0, 3.0));
+ // EXPECT_FP_EQ(10000.0, LIBC_NAMESPACE::powf16(10.0, 4.0));
+ // EXPECT_FP_EQ(100000.0, LIBC_NAMESPACE::powf16(10.0, 5.0));
+ // EXPECT_FP_EQ(1000000.0, LIBC_NAMESPACE::powf16(10.0, 6.0));
+ // EXPECT_FP_EQ(10000000.0, LIBC_NAMESPACE::powf16(10.0, 7.0));
+ // EXPECT_FP_EQ(100000000.0, LIBC_NAMESPACE::powf16(10.0, 8.0));
+ // EXPECT_FP_EQ(1000000000.0, LIBC_NAMESPACE::powf16(10.0, 9.0));
+ // EXPECT_FP_EQ(10000000000.0, LIBC_NAMESPACE::powf16(10.0, 10.0));
+
+ // Overflow / Underflow:
+ if (ROUNDING_MODES[i] != RoundingMode::Downward &&
+ ROUNDING_MODES[i] != RoundingMode::TowardZero) {
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(3.1f16, 21.0),
+ FE_OVERFLOW);
+ }
+ if (ROUNDING_MODES[i] != RoundingMode::Upward) {
+ EXPECT_FP_EQ_WITH_EXCEPTION(0.0, LIBC_NAMESPACE::powf16(3.1f16, -21.0),
+ FE_UNDERFLOW);
+ }
+ }
+}
>From 63c0781b3931af76bf602713745b5bf0f119a4ef Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 20 Sep 2025 08:09:23 +0300
Subject: [PATCH 02/14] fix formatting
---
libc/src/math/powf16.h | 2 +-
libc/test/src/math/powf16_test.cpp | 6 +-----
2 files changed, 2 insertions(+), 6 deletions(-)
diff --git a/libc/src/math/powf16.h b/libc/src/math/powf16.h
index 52f9848f4a2be..bd50f16edeede 100644
--- a/libc/src/math/powf16.h
+++ b/libc/src/math/powf16.h
@@ -1,4 +1,4 @@
-//===-- Implementation header for powf16 --------------------------*- C++ -*-===//
+//===-- Implementation header for powf16 ------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
diff --git a/libc/test/src/math/powf16_test.cpp b/libc/test/src/math/powf16_test.cpp
index 171cb098114d4..030f0e9cf8be3 100644
--- a/libc/test/src/math/powf16_test.cpp
+++ b/libc/test/src/math/powf16_test.cpp
@@ -6,7 +6,6 @@
//
//===----------------------------------------------------------------------===//
-
#include "src/math/powf16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
@@ -97,8 +96,7 @@ TEST_F(LlvmLibcPowF16Test, InFloat16Range) {
if (fails || (count < cc)) {
tlog << " powf16 failed: " << fails << "/" << count << "/" << cc
<< " tests.\n"
- << " Max ULPs is at most: " << static_cast<uint64_t>(tol)
- << ".\n";
+ << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
}
if (fails) {
mpfr::BinaryInput<float16> inputs{mx, my};
@@ -118,5 +116,3 @@ TEST_F(LlvmLibcPowF16Test, InFloat16Range) {
tlog << " Test Rounding Toward Zero...\n";
test(mpfr::RoundingMode::TowardZero);
}
-
-
>From a569163295ccb947c96c250a343f1398f13eba99 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Tue, 23 Sep 2025 09:31:48 +0300
Subject: [PATCH 03/14] add missing argument in math.yml
---
libc/include/math.yaml | 1 +
1 file changed, 1 insertion(+)
diff --git a/libc/include/math.yaml b/libc/include/math.yaml
index fe23f1c8c3a64..6358157189acc 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -2168,6 +2168,7 @@ functions:
return_type: _Float16
arguments:
- type: _Float16
+ - type: _Float16
- name: powi
standards: llvm_libc_ext
return_type: double
>From 0021bf3ba9d02b23aaf206793986b2d03e475b99 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Tue, 23 Sep 2025 09:32:00 +0300
Subject: [PATCH 04/14] remove optimzation option
---
libc/src/math/generic/CMakeLists.txt | 2 --
1 file changed, 2 deletions(-)
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 82b6c7ea59bab..f4d696f3bc822 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1614,8 +1614,6 @@ add_entrypoint_object(
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
libc.src.__support.math.expxf16_utils
- COMPILE_OPTIONS
- -O3
)
add_entrypoint_object(
>From 170ff2210d589942924accb037e8e38aa950b91e Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Wed, 24 Sep 2025 22:58:01 +0300
Subject: [PATCH 05/14] make tests exaustive
---
libc/test/src/math/powf16_test.cpp | 145 ++++++++++-------------------
1 file changed, 51 insertions(+), 94 deletions(-)
diff --git a/libc/test/src/math/powf16_test.cpp b/libc/test/src/math/powf16_test.cpp
index 030f0e9cf8be3..4f70291041bfc 100644
--- a/libc/test/src/math/powf16_test.cpp
+++ b/libc/test/src/math/powf16_test.cpp
@@ -12,107 +12,64 @@
#include "utils/MPFRWrapper/MPFRUtils.h"
using LlvmLibcPowF16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
-using LIBC_NAMESPACE::testing::tlog;
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
-TEST_F(LlvmLibcPowF16Test, TrickyInputs) {
- // These values are in half precision.
- constexpr mpfr::BinaryInput<float16> INPUTS[] = {
- {static_cast<float16>(0x1.08p-2f), static_cast<float16>(0x1.0cp-1f)},
- {static_cast<float16>(0x1.66p-1f), static_cast<float16>(0x1.f1p+1f)},
- {static_cast<float16>(0x1.c04p-1f), static_cast<float16>(0x1.2p+12f)},
- {static_cast<float16>(0x1.aep-1f), static_cast<float16>(0x1.f9p-1f)},
- {static_cast<float16>(0x1.ffcp-1f), static_cast<float16>(0x1.fffp-2f)},
- {static_cast<float16>(0x1.f55p-1f), static_cast<float16>(0x1.88p+12f)},
- {static_cast<float16>(0x1.e84p-1f), static_cast<float16>(0x1.2cp+13f)},
- };
-
- for (auto input : INPUTS) {
- float16 x = input.x;
- float16 y = input.y;
- EXPECT_MPFR_MATCH(mpfr::Operation::Pow, input, LIBC_NAMESPACE::powf16(x, y),
- 1.0); // 1 ULP tolerance is enough for f16
+static constexpr float16 SELECTED_VALS[] = {
+ 0.5f16, 0.83984375f16, 1.0f16, 2.0f16, 3.0f16, 3.140625f16, 15.5f16,
+};
+
+// Test selected x values against all possible y values.
+TEST_F(LlvmLibcPowF16Test, SelectedX_AllY) {
+ for (size_t i = 0; i < sizeof(SELECTED_VALS) / sizeof(SELECTED_VALS[0]);
+ ++i) {
+ float16 x = SELECTED_VALS[i];
+ for (uint16_t y_u = 0; y_u <= 0x7c00U; ++y_u) {
+ float16 y = FPBits(y_u).get_val();
+
+ mpfr::BinaryInput<float16> input{x, y};
+ float16 result = LIBC_NAMESPACE::powf16(x, y);
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input, result, 1.0);
+
+ // If the result is infinity and we expect it to continue growing, we can
+ // terminate the loop early.
+ if (FPBits(result).is_inf() && FPBits(result).is_pos()) {
+ // For x > 1, as y increases in the positive range, pow remains inf.
+ if (x > static_cast<float16>(1.0f) && y > static_cast<float16>(0.0f)) {
+ // The y_u loop covers the positive range up to 0x7BFF.
+ break;
+ }
+ // For 0 < x < 1, as y becomes more negative, pow becomes inf.
+ if (x > static_cast<float16>(0.0f) && x < static_cast<float16>(1.0f) &&
+ y < static_cast<float16>(0.0f)) {
+ // The y_u loop covers the negative range from 0x8000.
+ break;
+ }
+ }
+ }
}
}
-TEST_F(LlvmLibcPowF16Test, InFloat16Range) {
- constexpr uint16_t X_COUNT = 63;
- constexpr uint16_t X_START = FPBits(static_cast<float16>(0.25)).uintval();
- constexpr uint16_t X_STOP = FPBits(static_cast<float16>(4.0)).uintval();
- constexpr uint16_t X_STEP = (X_STOP - X_START) / X_COUNT;
-
- constexpr uint16_t Y_COUNT = 59;
- constexpr uint16_t Y_START = FPBits(static_cast<float16>(0.25)).uintval();
- constexpr uint16_t Y_STOP = FPBits(static_cast<float16>(4.0)).uintval();
- constexpr uint16_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 count = 0;
- uint64_t cc = 0;
- float16 mx = 0.0, my = 0.0, mr = 0.0;
- double tol = 1.0; // start with 1 ULP for half precision
-
- for (uint16_t i = 0, v = X_START; i <= X_COUNT; ++i, v += X_STEP) {
- float16 x = FPBits(v).get_val();
- if (FPBits(x).is_inf_or_nan() || x < static_cast<float16>(0.0))
- continue;
-
- for (uint16_t j = 0, w = Y_START; j <= Y_COUNT; ++j, w += Y_STEP) {
- float16 y = FPBits(w).get_val();
- if (FPBits(y).is_inf_or_nan())
- continue;
-
- float16 result = LIBC_NAMESPACE::powf16(x, y);
- ++cc;
- if (FPBits(result).is_inf_or_nan())
- continue;
-
- ++count;
- mpfr::BinaryInput<float16> inputs{x, y};
-
- if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Pow, inputs,
- result, 1.0, rounding_mode)) {
- ++fails;
- while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(
- mpfr::Operation::Pow, inputs, result, tol, rounding_mode)) {
- mx = x;
- my = y;
- mr = result;
-
- if (tol > 128.0) // half precision is only ~11 bits
- break;
-
- tol *= 2.0;
- }
+// Test selected y values against all possible x values.
+TEST_F(LlvmLibcPowF16Test, SelectedY_AllX) {
+ for (size_t i = 0; i < sizeof(SELECTED_VALS) / sizeof(SELECTED_VALS[0]);
+ ++i) {
+ float16 y = SELECTED_VALS[i];
+ for (uint16_t x_u = 0; x_u <= 0x7c00U; ++x_u) {
+ float16 x = FPBits(x_u).get_val();
+ mpfr::BinaryInput<float16> input{x, y};
+ float16 result = LIBC_NAMESPACE::powf16(x, y);
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input, result, 1.0);
+
+ // If the result is infinity and we expect it to continue growing, we can
+ // terminate the loop early.
+ if (FPBits(result).is_inf() && FPBits(result).is_pos()) {
+ // For y > 0, as x increases in the positive range, pow remains inf.
+ if (y > 0.0f16 && x > 0.0f16) {
+ // The x_u loop covers the positive range up to 0x7BFF.
+ break;
}
}
}
- if (fails || (count < cc)) {
- tlog << " powf16 failed: " << fails << "/" << count << "/" << cc
- << " tests.\n"
- << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
- }
- if (fails) {
- mpfr::BinaryInput<float16> inputs{mx, my};
- EXPECT_MPFR_MATCH(mpfr::Operation::Pow, inputs, mr, 1.0, 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);
+ }
}
>From f92d360c1afad0a064d8106f3f25e415edf8645b Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Wed, 24 Sep 2025 22:58:15 +0300
Subject: [PATCH 06/14] update log poly to double
---
libc/src/math/generic/powf16.cpp | 35 ++++++++++++++++----------------
1 file changed, 18 insertions(+), 17 deletions(-)
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index 8e2e6b552632f..1c998ca02e7e8 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -199,14 +199,13 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
int m = -FPBits::EXP_BIAS;
// When x is subnormal, normalize it by multiplying by 2^FRACTION_LEN.
- if ((x_u_log & FPBits::EXP_MASK) == 0U) {
- constexpr float NORMALIZE_EXP =
- static_cast<float>(1U << FPBits::FRACTION_LEN);
- x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
+ if ((x_u_log & FPBits::EXP_MASK) == 0U) { // Subnormal x
+ constexpr double NORMALIZE_EXP = 1.0 * (1U << FPBits::FRACTION_LEN);
+ x_bits = FPBits(fputil::cast<float16>(
+ fputil::cast<double>(x_bits.get_val()) * NORMALIZE_EXP));
x_u_log = x_bits.uintval();
m -= FPBits::FRACTION_LEN;
}
-
// Extract the mantissa and index into small lookup tables.
uint16_t mant = x_bits.get_mantissa();
// Use the highest 5 fractional bits of the mantissa as the index f.
@@ -217,28 +216,29 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
// Add the hidden bit to the mantissa.
// 1 <= m_x < 2
x_bits.set_biased_exponent(FPBits::EXP_BIAS);
- float mant_f = x_bits.get_val();
+ double mant_d = x_bits.get_val();
// Range reduction for log2(m_x):
// v = r * m_x - 1, where r is a power of 2 from a lookup table.
// The computation is exact for half-precision, and -2^-5 <= v < 2^-4.
// Then m_x = (1 + v) / r, and log2(m_x) = log2(1 + v) - log2(r).
- float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
-
+ double v =
+ fputil::multiply_add(mant_d, fputil::cast<double>(ONE_OVER_F_F[f]), -1.0);
// For half-precision accuracy, we use a degree-2 polynomial approximation:
// P(v) ~ log2(1 + v) / v
// Generated by Sollya with:
// > P = fpminimax(log2(1+x)/x, 2, [|D...|], [-2^-5, 2^-4]);
// The coefficients are rounded from the Sollya output.
- float log2p1_d_over_f =
- v * fputil::polyeval(v, 0x1.715476p+0f, -0x1.71771ap-1f, 0x1.ecb38ep-2f);
+
+ double log2p1_d_over_f =
+ v * fputil::polyeval(v, 0x1.715476p+0, -0x1.71771ap-1, 0x1.ecb38ep-2);
// log2(1.mant) = log2(f) + log2(1 + v)
- float log2_1_mant = LOG2F_F[f] + log2p1_d_over_f;
+ double log2_1_mant = LOG2F_F[f] + log2p1_d_over_f;
// Complete log2(x) = e_x + log2(m_x)
- float log2_x = static_cast<float>(m) + log2_1_mant;
+ double log2_x = static_cast<double>(m) + log2_1_mant;
// z = y * log2(x)
// Now compute 2^z = 2^(n + r), with n integer and r in [-0.5, 0.5].
@@ -246,10 +246,7 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
// Check for overflow/underflow for half-precision.
// Half-precision range is approximately 2^-24 to 2^15.
- if (z > 15.0) {
- fputil::raise_except_if_required(FE_OVERFLOW);
- return FPBits::inf().get_val();
- }
+ //
if (z < -24.0) {
fputil::raise_except_if_required(FE_UNDERFLOW);
return fputil::cast<float16>(0.0f);
@@ -282,7 +279,11 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
uint64_t exp_bits = static_cast<uint64_t>(n_int + 1023) << 52;
double pow2_n = cpp::bit_cast<double>(exp_bits);
- float16 result = fputil::cast<float16>(pow2_n * exp2_r);
+
+ double result_d = (pow2_n * exp2_r);
+ float16 result = fputil::cast<float16>(result_d);
+ if(result_d==65504.0)
+ return (65504.f16);
if (result_sign) {
FPBits result_bits(result);
>From f990040db58cd32028f2473749f3aecd04059e4c Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 11 Oct 2025 13:05:30 +0300
Subject: [PATCH 07/14] fix powf16 tests
---
libc/test/src/math/powf16_test.cpp | 34 ++++--------------------------
1 file changed, 4 insertions(+), 30 deletions(-)
diff --git a/libc/test/src/math/powf16_test.cpp b/libc/test/src/math/powf16_test.cpp
index 4f70291041bfc..090289ba1983d 100644
--- a/libc/test/src/math/powf16_test.cpp
+++ b/libc/test/src/math/powf16_test.cpp
@@ -28,24 +28,8 @@ TEST_F(LlvmLibcPowF16Test, SelectedX_AllY) {
float16 y = FPBits(y_u).get_val();
mpfr::BinaryInput<float16> input{x, y};
- float16 result = LIBC_NAMESPACE::powf16(x, y);
- EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input, result, 1.0);
-
- // If the result is infinity and we expect it to continue growing, we can
- // terminate the loop early.
- if (FPBits(result).is_inf() && FPBits(result).is_pos()) {
- // For x > 1, as y increases in the positive range, pow remains inf.
- if (x > static_cast<float16>(1.0f) && y > static_cast<float16>(0.0f)) {
- // The y_u loop covers the positive range up to 0x7BFF.
- break;
- }
- // For 0 < x < 1, as y becomes more negative, pow becomes inf.
- if (x > static_cast<float16>(0.0f) && x < static_cast<float16>(1.0f) &&
- y < static_cast<float16>(0.0f)) {
- // The y_u loop covers the negative range from 0x8000.
- break;
- }
- }
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input,
+ LIBC_NAMESPACE::powf16(x, y), 0.5);
}
}
}
@@ -58,18 +42,8 @@ TEST_F(LlvmLibcPowF16Test, SelectedY_AllX) {
for (uint16_t x_u = 0; x_u <= 0x7c00U; ++x_u) {
float16 x = FPBits(x_u).get_val();
mpfr::BinaryInput<float16> input{x, y};
- float16 result = LIBC_NAMESPACE::powf16(x, y);
- EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input, result, 1.0);
-
- // If the result is infinity and we expect it to continue growing, we can
- // terminate the loop early.
- if (FPBits(result).is_inf() && FPBits(result).is_pos()) {
- // For y > 0, as x increases in the positive range, pow remains inf.
- if (y > 0.0f16 && x > 0.0f16) {
- // The x_u loop covers the positive range up to 0x7BFF.
- break;
- }
- }
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input,
+ LIBC_NAMESPACE::powf16(x, y), 0.5);
}
}
}
>From 34f9d0a6284c170c6084ea15b056d84bea70763c Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sun, 2 Nov 2025 03:18:26 +0200
Subject: [PATCH 08/14] update powf16 approach
---
libc/src/math/generic/CMakeLists.txt | 2 +-
libc/src/math/generic/powf16.cpp | 333 +++++++++++++++++----------
2 files changed, 214 insertions(+), 121 deletions(-)
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index f4d696f3bc822..a0909e4b72c53 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1613,7 +1613,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
- libc.src.__support.math.expxf16_utils
+ libc.src.__support.math.exp10f_utils
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index 1c998ca02e7e8..22010e954183c 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -21,12 +21,53 @@
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
#include "src/__support/macros/properties/types.h"
-#include "src/__support/math/expxf16_utils.h"
+#include "src/__support/math/exp10f_utils.h"
+#include "src/math/generic/common_constants.h"
namespace LIBC_NAMESPACE_DECL {
namespace {
+static inline double exp2_range_reduced(double x) {
+ // k = round(x * 32) => (hi + mid) * 2^5
+ double kf = fputil::nearest_integer(x * 32.0);
+ int k = static_cast<int>(kf);
+ // dx = lo = x - (hi + mid) = x - k * 2^(-5)
+ double dx = fputil::multiply_add(-0x1.0p-5, kf, x); // -2^-5 * k + x
+
+ // hi = k >> MID_BITS
+ // exp_hi = hi shifted into double exponent field
+ int64_t hi = static_cast<int64_t>(k >> ExpBase::MID_BITS);
+ int64_t exp_hi = static_cast<int64_t>(
+ static_cast<uint64_t>(hi) << fputil::FPBits<double>::FRACTION_LEN);
+
+ // mh_bits = bits for 2^hi * 2^mid (lookup contains base bits for 2^mid)
+ int tab_index = k & ExpBase::MID_MASK; // mid index in [0, 31]
+ int64_t mh_bits = ExpBase::EXP_2_MID[tab_index] + exp_hi;
+
+ // mh = 2^(hi + mid)
+ double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
+
+ // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
+ // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
+ constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
+ 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
+ 0x1.5d88091198529p-10};
+
+ double dx_sq = dx * dx;
+ double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0); // 1 + ln2*dx
+ double c2 =
+ fputil::multiply_add(dx, COEFFS[2], COEFFS[1]); // COEFF1 + COEFF2*dx
+ double c3 =
+ fputil::multiply_add(dx, COEFFS[4], COEFFS[3]); // COEFF3 + COEFF4*dx
+ double p = fputil::multiply_add(dx_sq, c3, c2); // c2 + c3*dx^2
+
+ // 2^x = 2^(hi+mid) * 2^dx
+ // ≈ mh * (1 + dx * P(dx))
+ // = mh + (mh * dx) * P(dx)
+ double result = fputil::multiply_add(p, dx_sq * mh, c1 * mh);
+ return result;
+}
bool is_odd_integer(float16 x) {
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
@@ -66,6 +107,7 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
uint16_t x_u = xbits.uintval();
uint16_t x_a = x_abs.uintval();
uint16_t y_a = y_abs.uintval();
+ uint16_t y_u = ybits.uintval();
bool result_sign = false;
///////// BEGIN - Check exceptional cases ////////////////////////////////////
@@ -74,57 +116,106 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
-
- //
- if (LIBC_UNLIKELY(ybits.is_zero() || x_u == FPBits::one().uintval() ||
- x_u >= FPBits::inf().uintval() ||
- x_u < FPBits::min_normal().uintval())) {
+ if (LIBC_UNLIKELY(
+ ybits.is_zero() || x_u == FPBits::one().uintval() || xbits.is_nan() ||
+ ybits.is_nan() || x_u == FPBits::one().uintval() ||
+ x_u == FPBits::zero().uintval() || x_u >= FPBits::inf().uintval() ||
+ y_u >= FPBits::inf().uintval() ||
+ x_u < FPBits::min_normal().uintval() || y_a == 0x3400U ||
+ y_a == 0x3800U || y_a == 0x3A00U || y_a == 0x3800U ||
+ y_a == 0x3800U || y_a == 0x3D00U || y_a == 0x3E00U ||
+ y_a == 0x4100U || y_a == 0x4300U || y_a == 0x3c00U ||
+ y_a == 0x4000U || is_integer(y))) {
// pow(x, 0) = 1
if (ybits.is_zero()) {
- return fputil::cast<float16>(1.0f);
+ return 1.0f16;
}
// pow(1, Y) = 1
if (x_u == FPBits::one().uintval()) {
- return fputil::cast<float16>(1.0f);
+ return 1.0f16;
+ }
+ // 4. Handle remaining NaNs
+ // pow(NaN, y) = NaN (for y != 0)
+ if (xbits.is_nan()) {
+ return x;
+ }
+ // pow(x, NaN) = NaN (for x != 1)
+ if (ybits.is_nan()) {
+ return y;
}
-
switch (y_a) {
+ case 0x3400U: // y = ±0.25 (1/4)
+ case 0x3800U: // y = ±0.5 (1/2)
+ case 0x3A00U: // y = ±0.75 (3/4)
+ case 0x3D00U: // y = ±1.25 (5/4)
+ case 0x3E00U: // y = ±1.5 (3/2)
+ case 0x4100U: // y = ±2.5 (5/2)
+ case 0x4300U: // y = ±3.5 (7/2)
+ {
+ if (xbits.is_zero()) {
+ if (y_sign) {
+ // pow(±0, negative) handled below
+ break;
+ } else {
+ // pow(±0, positive_fractional) = +0
+ return FPBits::zero(Sign::POS).get_val();
+ }
+ }
- case 0x3800U: { // y = +-0.5
- 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 fputil::cast<float16>(y_sign ? (1.0 / (x * x)) : (x * x));
+ if (x_sign && !xbits.is_zero()) {
+ break; // pow(negative, non-integer) = NaN
}
- return fputil::cast<float16>(y_sign ? (1.0 / fputil::sqrt<float16>(x))
- : fputil::sqrt<float16>(x));
+
+ double x_d = static_cast<double>(x);
+ double sqrt_x = fputil::sqrt<double>(x_d);
+ double fourth_root = fputil::sqrt<double>(sqrt_x);
+ double result_d;
+
+ // Compute based on exponent value
+ switch (y_a) {
+ case 0x3400U: // 0.25 = x^(1/4)
+ result_d = fourth_root;
+ break;
+ case 0x3800U: // 0.5 = x^(1/2)
+ result_d = sqrt_x;
+ break;
+ case 0x3A00U: // 0.75 = x^(1/2) * x^(1/4)
+ result_d = sqrt_x * fourth_root;
+ break;
+ case 0x3D00U: // 1.25 = x * x^(1/4)
+ result_d = x_d * fourth_root;
+ break;
+ case 0x3E00U: // 1.5 = x * x^(1/2)
+ result_d = x_d * sqrt_x;
+ break;
+ case 0x4100U: // 2.5 = x^2 * x^(1/2)
+ result_d = x_d * x_d * sqrt_x;
+ break;
+ case 0x4300U: // 3.5 = x^3 * x^(1/2)
+ result_d = x_d * x_d * x_d * sqrt_x;
+ break;
+ }
+
+ result_d = y_sign ? (1.0 / result_d) : result_d;
+ return fputil::cast<float16>(result_d);
}
case 0x3c00U: // y = +-1.0
return fputil::cast<float16>(y_sign ? (1.0 / x) : x);
case 0x4000U: // y = +-2.0
- return fputil::cast<float16>(y_sign ? (1.0 / (x * x)) : (x * x));
+ double result_d = static_cast<double>(x) * static_cast<double>(x);
+ return fputil::cast<float16>(y_sign ? (1.0 / (result_d)) : (result_d));
}
// TODO: Speed things up with pow(2, y) = exp2(y) and pow(10, y) = exp10(y).
-
- // Propagate remaining quiet NaNs.
- if (xbits.is_quiet_nan()) {
- return x;
- }
- if (ybits.is_quiet_nan()) {
- return y;
- }
-
- // x = -1: special case for integer exponents
+ //
+ // pow(-1, y) for integer y
if (x_u == FPBits::one(Sign::NEG).uintval()) {
if (is_integer(y)) {
if (is_odd_integer(y)) {
- return fputil::cast<float16>(-1.0f);
+ return -1.0f16;
} else {
- return fputil::cast<float16>(1.0f);
+ return 1.0f16;
}
}
// pow(-1, non-integer) = NaN
@@ -133,7 +224,7 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
return FPBits::quiet_nan().get_val();
}
- // x = 0 cases
+ // pow(±0, y) cases
if (xbits.is_zero()) {
if (y_sign) {
// pow(+-0, negative) = +-inf and raise FE_DIVBYZERO
@@ -163,9 +254,13 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
bool x_abs_less_than_one = x_a < FPBits::one().uintval();
if ((x_abs_less_than_one && !y_sign) ||
(!x_abs_less_than_one && y_sign)) {
- return fputil::cast<float16>(0.0f);
+ // |x| < 1 and y = +inf => 0.0
+ // |x| > 1 and y = -inf => 0.0
+ return 0.0f;
} else {
- return FPBits::inf().get_val();
+ // |x| > 1 and y = +inf => +inf
+ // |x| < 1 and y = -inf => +inf
+ return FPBits::inf(Sign::POS).get_val();
}
}
@@ -176,121 +271,119 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
return FPBits::quiet_nan().get_val();
}
- // For negative x with integer y, compute pow(|x|, y) and adjust sign
- if (x_sign) {
- x = -x;
- if (is_odd_integer(y)) {
- result_sign = true;
+ bool result_sign = false;
+ if (x_sign && is_integer(y)) {
+ result_sign = is_odd_integer(y);
+ }
+
+ if (is_integer(y)) {
+ double base = x_abs.get_val();
+ double res = 1.0;
+ int yi = static_cast<int>(y_abs.get_val());
+
+ // Fast exponentiation by squaring
+ while (yi > 0) {
+ if (yi & 1)
+ res *= base;
+ base *= base;
+ yi = yi >> 1;
+ }
+
+ if (y_sign) {
+ res = 1.0 / res;
+ }
+
+ if (result_sign) {
+ res = -res;
+ }
+
+ if (FPBits(fputil::cast<float16>(res)).is_inf()) {
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ res = result_sign ? -0x1.0p20 : 0x1.0p20;
}
+
+ float16 final_res = fputil::cast<float16>(res);
+ return final_res;
}
}
+
///////// 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)
+ // Core computation: x^y = 2^( y * log2(x) )
+ // We compute log2(x) = log(x) / log(2) using a polynomial approximation.
- using namespace math::expxf16_internal;
+ // The exponent part (m) is added later to get the final log(x).
FPBits x_bits(x);
-
uint16_t x_u_log = x_bits.uintval();
// Extract exponent field of x.
- int m = -FPBits::EXP_BIAS;
-
- // When x is subnormal, normalize it by multiplying by 2^FRACTION_LEN.
- if ((x_u_log & FPBits::EXP_MASK) == 0U) { // Subnormal x
- constexpr double NORMALIZE_EXP = 1.0 * (1U << FPBits::FRACTION_LEN);
- x_bits = FPBits(fputil::cast<float16>(
- fputil::cast<double>(x_bits.get_val()) * NORMALIZE_EXP));
- x_u_log = x_bits.uintval();
- m -= FPBits::FRACTION_LEN;
+ int m = x_bits.get_exponent();
+
+ // When x is subnormal, normalize it by adjusting m.
+ if ((x_u_log & FPBits::EXP_MASK) == 0U) {
+ unsigned leading_zeros =
+ cpp::countl_zero(static_cast<uint32_t>(x_u_log)) - (32 - 16);
+
+ constexpr unsigned SUBNORMAL_SHIFT_CORRECTION = 5;
+ unsigned shift = leading_zeros - SUBNORMAL_SHIFT_CORRECTION;
+
+ x_bits.set_mantissa(static_cast<uint16_t>(x_u_log << shift));
+
+ m = 1 - FPBits::EXP_BIAS - static_cast<int>(shift);
}
+
// Extract the mantissa and index into small lookup tables.
uint16_t mant = x_bits.get_mantissa();
- // Use the highest 5 fractional bits of the mantissa as the index f.
- int f = mant >> 5;
-
- m += (x_u_log >> FPBits::FRACTION_LEN);
+ // Use the highest 7 fractional bits of the mantissa as the index f.
+ int f = mant >> (FPBits::FRACTION_LEN - 7);
- // Add the hidden bit to the mantissa.
- // 1 <= m_x < 2
+ // Reconstruct the mantissa value m_x so it's in the range [1.0, 2.0).
x_bits.set_biased_exponent(FPBits::EXP_BIAS);
double mant_d = x_bits.get_val();
- // Range reduction for log2(m_x):
- // v = r * m_x - 1, where r is a power of 2 from a lookup table.
- // The computation is exact for half-precision, and -2^-5 <= v < 2^-4.
- // Then m_x = (1 + v) / r, and log2(m_x) = log2(1 + v) - log2(r).
-
- double v =
- fputil::multiply_add(mant_d, fputil::cast<double>(ONE_OVER_F_F[f]), -1.0);
- // For half-precision accuracy, we use a degree-2 polynomial approximation:
- // P(v) ~ log2(1 + v) / v
- // Generated by Sollya with:
- // > P = fpminimax(log2(1+x)/x, 2, [|D...|], [-2^-5, 2^-4]);
- // The coefficients are rounded from the Sollya output.
+ double v = fputil::multiply_add<double>(mant_d, RD[f], -1.0);
+ double extra_factor = static_cast<double>(m) + LOG2_R[f];
- double log2p1_d_over_f =
- v * fputil::polyeval(v, 0x1.715476p+0, -0x1.71771ap-1, 0x1.ecb38ep-2);
+ // Degree-5 polynomial approximation of log2 generated by Sollya with:
+ // > P = fpminimax(log2(1 + x)/x, 4, [|1, D...|], [-2^-8, 2^-7]);
+ constexpr double COEFFS[5] = {0x1.71547652b8133p0, -0x1.71547652d1e33p-1,
+ 0x1.ec70a098473dep-2, -0x1.7154c5ccdf121p-2,
+ 0x1.2514fd90a130ap-2};
- // log2(1.mant) = log2(f) + log2(1 + v)
- double log2_1_mant = LOG2F_F[f] + log2p1_d_over_f;
+ double vsq = v * v;
+ double c0 = fputil::multiply_add(v, COEFFS[0], 0);
+ double c1 = fputil::multiply_add(v, COEFFS[2], COEFFS[1]);
+ double c2 = fputil::multiply_add(v, COEFFS[4], COEFFS[3]);
- // Complete log2(x) = e_x + log2(m_x)
- double log2_x = static_cast<double>(m) + log2_1_mant;
+ double log2_x = fputil::polyeval(vsq, c0, c1, c2);
- // z = y * log2(x)
- // Now compute 2^z = 2^(n + r), with n integer and r in [-0.5, 0.5].
- double z = fputil::cast<double>(y) * log2_x;
+ double y_d = fputil::cast<double>(y);
+ double z = fputil::multiply_add(y_d, log2_x, y_d * extra_factor);
- // Check for overflow/underflow for half-precision.
- // Half-precision range is approximately 2^-24 to 2^15.
- //
- if (z < -24.0) {
+ // Check for underflow
+ // Float16 min normal is 2^-14, smallest subnormal is 2^-24
+ if (LIBC_UNLIKELY(z < -25.0)) {
fputil::raise_except_if_required(FE_UNDERFLOW);
- return fputil::cast<float16>(0.0f);
+ return result_sign ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
}
- double n = fputil::nearest_integer(z);
- double r = z - n;
-
- // Compute 2^r using a degree-7 polynomial for r in [-0.5, 0.5].
- // Generated by Sollya with:
- // > P = fpminimax(2^x, 7, [|D...|], [-0.5, 0.5]);
- // The polynomial coefficients are rounded from the Sollya output.
- constexpr double EXP2_COEFFS[] = {
- 0x1p+0, // 1.0
- 0x1.62e42fefa39efp-1, // ln(2)
- 0x1.ebfbdff82c58fp-3, // ln(2)^2 / 2
- 0x1.c6b08d704a0c0p-5, // ln(2)^3 / 6
- 0x1.3b2ab6fba4e77p-7, // ln(2)^4 / 24
- 0x1.5d87fe78a6737p-10, // ln(2)^5 / 120
- 0x1.430912f86a805p-13, // ln(2)^6 / 720
- 0x1.10e4104ac8015p-17 // ln(2)^7 / 5040
- };
-
- double exp2_r = fputil::polyeval(
- r, EXP2_COEFFS[0], EXP2_COEFFS[1], EXP2_COEFFS[2], EXP2_COEFFS[3],
- EXP2_COEFFS[4], EXP2_COEFFS[5], EXP2_COEFFS[6], EXP2_COEFFS[7]);
-
- // Compute 2^n by direct bit manipulation.
- int n_int = static_cast<int>(n);
- uint64_t exp_bits = static_cast<uint64_t>(n_int + 1023) << 52;
- double pow2_n = cpp::bit_cast<double>(exp_bits);
-
-
- double result_d = (pow2_n * exp2_r);
- float16 result = fputil::cast<float16>(result_d);
- if(result_d==65504.0)
- return (65504.f16);
+ // Check for overflow
+ // Float16 max is ~2^16
+ double result_d;
+ if (LIBC_UNLIKELY(z > 16.0)) {
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ result_d = result_sign ? -0x1.0p20 : 0x1.0p20;
+ } else {
+ result_d = exp2_range_reduced(z);
+ }
if (result_sign) {
- FPBits result_bits(result);
- result_bits.set_sign(Sign::NEG);
- result = result_bits.get_val();
+
+ result_d = -result_d;
}
+ float16 result = fputil::cast<float16>((result_d));
return result;
}
>From 6a5e424228811f8357ea89d16aa45901abb7c53c Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sun, 2 Nov 2025 03:18:55 +0200
Subject: [PATCH 09/14] update tests
---
libc/test/src/math/exhaustive/CMakeLists.txt | 15 +++
libc/test/src/math/exhaustive/powf16_test.cpp | 72 ++++++++++++
libc/test/src/math/powf16_test.cpp | 110 ++++++++++++++----
3 files changed, 174 insertions(+), 23 deletions(-)
create mode 100644 libc/test/src/math/exhaustive/powf16_test.cpp
diff --git a/libc/test/src/math/exhaustive/CMakeLists.txt b/libc/test/src/math/exhaustive/CMakeLists.txt
index 9ca4f93e6c411..4d3d9b557576a 100644
--- a/libc/test/src/math/exhaustive/CMakeLists.txt
+++ b/libc/test/src/math/exhaustive/CMakeLists.txt
@@ -357,6 +357,21 @@ add_fp_unittest(
-lpthread
)
+add_fp_unittest(
+ powf16_test
+ NO_RUN_POSTBUILD
+ NEED_MPFR
+ SUITE
+ libc_math_exhaustive_tests
+ SRCS
+ powf16_test.cpp
+ DEPENDS
+ .exhaustive_test
+ libc.src.math.powf16
+ libc.src.__support.FPUtil.fp_bits
+ LINK_LIBRARIES
+ -lpthread
+)
add_fp_unittest(
hypotf_test
NO_RUN_POSTBUILD
diff --git a/libc/test/src/math/exhaustive/powf16_test.cpp b/libc/test/src/math/exhaustive/powf16_test.cpp
new file mode 100644
index 0000000000000..61c99baa77508
--- /dev/null
+++ b/libc/test/src/math/exhaustive/powf16_test.cpp
@@ -0,0 +1,72 @@
+//===-- Exhaustive test for powf16 ----------------------------------------===//
+//
+// 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 "exhaustive_test.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/math/powf16.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+struct Powf16Checker : public virtual LIBC_NAMESPACE::testing::Test {
+ using FloatType = float16;
+ using FPBits = LIBC_NAMESPACE::fputil::FPBits<float16>;
+ using StorageType = typename FPBits::StorageType;
+
+ uint64_t check(uint16_t x_start, uint16_t x_stop, uint16_t y_start,
+ uint16_t y_stop, mpfr::RoundingMode rounding) {
+ mpfr::ForceRoundingMode r(rounding);
+ if (!r.success)
+ return true;
+ uint16_t xbits = x_start;
+ uint64_t failed = 0;
+ do {
+ float16 x = FPBits(xbits).get_val();
+ uint16_t ybits = y_start;
+ do {
+ float16 y = FPBits(ybits).get_val();
+ mpfr::BinaryInput<float16> input{x, y};
+ bool correct = TEST_MPFR_MATCH_ROUNDING_SILENTLY(
+ mpfr::Operation::Pow, input, LIBC_NAMESPACE::powf16(x, y), 0.5,
+ rounding);
+ failed += (!correct);
+ } while (ybits++ < y_stop);
+ } while (xbits++ < x_stop);
+ return failed;
+ }
+};
+
+using LlvmLibcPowf16ExhaustiveTest =
+ LlvmLibcExhaustiveMathTest<Powf16Checker, 1 << 8>;
+
+// Range: x in [0, inf], y in [0, inf]
+static constexpr uint16_t POS_START = 0x0000U;
+static constexpr uint16_t POS_STOP = 0x7C00U;
+
+TEST_F(LlvmLibcPowf16ExhaustiveTest, PositiveRange) {
+ test_full_range_all_roundings(POS_START, POS_STOP, POS_START, POS_STOP);
+}
+
+// Range: x in [-0, -inf], y in [0, inf]
+static constexpr uint16_t NEG_START = 0x8000U;
+static constexpr uint16_t NEG_STOP = 0xFC00U;
+
+TEST_F(LlvmLibcPowf16ExhaustiveTest, NegativeBasePositiveExponent) {
+ test_full_range_all_roundings(NEG_START, NEG_STOP, POS_START, POS_STOP);
+}
+
+// Range: x in [0, inf], y in [-0, -inf]
+TEST_F(LlvmLibcPowf16ExhaustiveTest, PositiveBaseNegativeExponent) {
+ test_full_range_all_roundings(POS_START, POS_STOP, NEG_START, NEG_STOP);
+}
+
+// Range: x in [-0, -inf], y in [-0, -inf]
+TEST_F(LlvmLibcPowf16ExhaustiveTest, NegativeRange) {
+ test_full_range_all_roundings(NEG_START, NEG_STOP, NEG_START, NEG_STOP);
+}
diff --git a/libc/test/src/math/powf16_test.cpp b/libc/test/src/math/powf16_test.cpp
index 090289ba1983d..1610e66184026 100644
--- a/libc/test/src/math/powf16_test.cpp
+++ b/libc/test/src/math/powf16_test.cpp
@@ -5,45 +5,109 @@
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
-
+#include "src/__support/CPP/bit.h"
#include "src/math/powf16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
using LlvmLibcPowF16Test = LIBC_NAMESPACE::testing::FPTest<float16>;
+using FPBits = LIBC_NAMESPACE::fputil::FPBits<float16>;
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
static constexpr float16 SELECTED_VALS[] = {
- 0.5f16, 0.83984375f16, 1.0f16, 2.0f16, 3.0f16, 3.140625f16, 15.5f16,
-};
-
-// Test selected x values against all possible y values.
-TEST_F(LlvmLibcPowF16Test, SelectedX_AllY) {
- for (size_t i = 0; i < sizeof(SELECTED_VALS) / sizeof(SELECTED_VALS[0]);
- ++i) {
- float16 x = SELECTED_VALS[i];
- for (uint16_t y_u = 0; y_u <= 0x7c00U; ++y_u) {
- float16 y = FPBits(y_u).get_val();
-
- mpfr::BinaryInput<float16> input{x, y};
+ 0.83984375f16, 1.414f16, 0.0625f16, 2.5f16,
+ 3.140625f16, 15.5f16, 2.f16, 3.25f16};
+
+// Test tricky inputs for selected x values against all possible y values.
+TEST_F(LlvmLibcPowF16Test, TrickyInput_SelectedX_AllY) {
+ for (float16 x_base : SELECTED_VALS) {
+ // Only test non-negative x_base
+ if (FPBits(x_base).is_neg())
+ continue;
+
+ // Loop through normal and subnormal values only (0x0001 to 0x7BFF)
+ for (uint16_t y_u = 1; y_u <= 0x7BFFU; ++y_u) {
+ float16 y_base = FPBits(y_u).get_val();
+
+ // Case 1: (+x, +y) - Standard positive case
+ mpfr::BinaryInput<float16> input1{x_base, y_base};
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input1,
+ LIBC_NAMESPACE::powf16(x_base, y_base),
+ 0.5);
+
+ // Case 2: (+x, -y) - Always valid for positive x
+ float16 y_neg = -y_base;
+ mpfr::BinaryInput<float16> input2{x_base, y_neg};
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input2,
+ LIBC_NAMESPACE::powf16(x_base, y_neg),
+ 0.5);
+ }
+
+ // Case 3: (-x, +y) - Only test with positive integer y values
+ for (int y_int = 1; y_int <= 2048; ++y_int) {
+ float16 y_val = static_cast<float16>(y_int);
+ float16 x_neg = -x_base;
+ mpfr::BinaryInput<float16> input{x_neg, y_val};
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input,
+ LIBC_NAMESPACE::powf16(x_neg, y_val), 0.5);
+ }
+
+ // Case 4: (-x, -y) - Only test with negative integer y values
+ for (int y_int = -2048; y_int < 0; ++y_int) {
+ float16 y_val = static_cast<float16>(y_int);
+ float16 x_neg = -x_base;
+ mpfr::BinaryInput<float16> input{x_neg, y_val};
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input,
- LIBC_NAMESPACE::powf16(x, y), 0.5);
+ LIBC_NAMESPACE::powf16(x_neg, y_val), 0.5);
}
}
}
-// Test selected y values against all possible x values.
-TEST_F(LlvmLibcPowF16Test, SelectedY_AllX) {
- for (size_t i = 0; i < sizeof(SELECTED_VALS) / sizeof(SELECTED_VALS[0]);
- ++i) {
- float16 y = SELECTED_VALS[i];
- for (uint16_t x_u = 0; x_u <= 0x7c00U; ++x_u) {
- float16 x = FPBits(x_u).get_val();
- mpfr::BinaryInput<float16> input{x, y};
+// Test tricky inputs for selected y values against all possible x values.
+TEST_F(LlvmLibcPowF16Test, TrickyInput_SelectedY_AllX) {
+ for (float16 y_base : SELECTED_VALS) {
+ // Only test non-negative y_base
+ if (FPBits(y_base).is_neg())
+ continue;
+
+ // Loop through normal and subnormal values only (0x0001 to 0x7BFF)
+ for (uint16_t x_u = 1; x_u <= 0x7BFFU; ++x_u) {
+ float16 x_base = FPBits(x_u).get_val();
+
+ // Case 1: (+x, +y) - Standard positive case
+ mpfr::BinaryInput<float16> input1{x_base, y_base};
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input1,
+ LIBC_NAMESPACE::powf16(x_base, y_base),
+ 0.5);
+
+ // Case 2: (+x, -y) - Always valid for positive x
+ float16 y_neg = -y_base;
+ mpfr::BinaryInput<float16> input2{x_base, y_neg};
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input2,
+ LIBC_NAMESPACE::powf16(x_base, y_neg),
+ 0.5);
+ }
+
+ // Case 3: (-x, +y) - Only test with positive integer x values
+ for (int x_int = 1; x_int <= 2048; ++x_int) {
+ float16 x_val = static_cast<float16>(x_int);
+ float16 x_neg = -x_val;
+ mpfr::BinaryInput<float16> input{x_neg, y_base};
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input,
+ LIBC_NAMESPACE::powf16(x_neg, y_base),
+ 0.5);
+ }
+
+ // Case 4: (-x, -y) - Only test with negative integer x values
+ for (int x_int = 1; x_int <= 2048; ++x_int) {
+ float16 x_val = static_cast<float16>(x_int);
+ float16 x_neg = -x_val;
+ float16 y_neg = -y_base;
+ mpfr::BinaryInput<float16> input{x_neg, y_neg};
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, input,
- LIBC_NAMESPACE::powf16(x, y), 0.5);
+ LIBC_NAMESPACE::powf16(x_neg, y_neg), 0.5);
}
}
}
>From 3081cea7bbbd70d0d4610a1682a2bcdb39b6082e Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Mon, 3 Nov 2025 02:46:45 +0200
Subject: [PATCH 10/14] fix build failure
---
libc/src/math/generic/CMakeLists.txt | 4 ++--
libc/src/math/generic/powf16.cpp | 7 ++++---
2 files changed, 6 insertions(+), 5 deletions(-)
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index a0909e4b72c53..b6f33a6f20c1c 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1599,9 +1599,8 @@ add_entrypoint_object(
SRCS
powf16.cpp
HDRS
- ../pow.h
+ ../powf16.h
DEPENDS
- .common_constants
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.CPP.bit
@@ -1614,6 +1613,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
libc.src.__support.math.exp10f_utils
+ libc.src.__support.math.common_constants
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index 22010e954183c..89d5f39a0131f 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -21,11 +21,12 @@
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
#include "src/__support/macros/properties/types.h"
+#include "src/__support/math/common_constants.h"
#include "src/__support/math/exp10f_utils.h"
-#include "src/math/generic/common_constants.h"
namespace LIBC_NAMESPACE_DECL {
+using namespace common_constants_internal;
namespace {
static inline double exp2_range_reduced(double x) {
// k = round(x * 32) => (hi + mid) * 2^5
@@ -256,7 +257,7 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
(!x_abs_less_than_one && y_sign)) {
// |x| < 1 and y = +inf => 0.0
// |x| > 1 and y = -inf => 0.0
- return 0.0f;
+ return 0.0f16;
} else {
// |x| > 1 and y = +inf => +inf
// |x| < 1 and y = -inf => +inf
@@ -351,7 +352,7 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
0x1.2514fd90a130ap-2};
double vsq = v * v;
- double c0 = fputil::multiply_add(v, COEFFS[0], 0);
+ double c0 = fputil::multiply_add(v, COEFFS[0], 0.0);
double c1 = fputil::multiply_add(v, COEFFS[2], COEFFS[1]);
double c2 = fputil::multiply_add(v, COEFFS[4], COEFFS[3]);
>From ccd510020c29a5fb2e8b7b153e611abf477eda74 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sun, 9 Nov 2025 11:22:29 +0200
Subject: [PATCH 11/14] handle LIBC_TARGET_CPU_HAS_FMA_DOUBLE
---
libc/src/math/generic/powf16.cpp | 16 +++++++++++-----
1 file changed, 11 insertions(+), 5 deletions(-)
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index 89d5f39a0131f..d5aa9773c07cb 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -341,16 +341,22 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
// Reconstruct the mantissa value m_x so it's in the range [1.0, 2.0).
x_bits.set_biased_exponent(FPBits::EXP_BIAS);
double mant_d = x_bits.get_val();
-
- double v = fputil::multiply_add<double>(mant_d, RD[f], -1.0);
- double extra_factor = static_cast<double>(m) + LOG2_R[f];
-
- // Degree-5 polynomial approximation of log2 generated by Sollya with:
+ // Degree-5 polynomial approximation
+ // of log2 generated by Sollya with:
// > P = fpminimax(log2(1 + x)/x, 4, [|1, D...|], [-2^-8, 2^-7]);
constexpr double COEFFS[5] = {0x1.71547652b8133p0, -0x1.71547652d1e33p-1,
0x1.ec70a098473dep-2, -0x1.7154c5ccdf121p-2,
0x1.2514fd90a130ap-2};
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double v = fputil::multiply_add<double>(mant_d, RD[f], -1.0);
+#else
+ double c = fputil::FPBits<double>(fputil::FPBits<double>(mant_d).uintval() &
+ 0x3fff'e000'0000'0000)
+ .get_val();
+ double v = fputil::multiply_add(RD[f], mant_d - c, CD[f]);
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double extra_factor = static_cast<double>(m) + LOG2_R[f];
double vsq = v * v;
double c0 = fputil::multiply_add(v, COEFFS[0], 0.0);
double c1 = fputil::multiply_add(v, COEFFS[2], COEFFS[1]);
>From 48f0dd7c06dc9b37ea3555b0669b78316f1073a5 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sun, 9 Nov 2025 11:25:10 +0200
Subject: [PATCH 12/14] ensure f16 literals are used in smoke test
---
libc/test/src/math/smoke/powf16_test.cpp | 130 ++++++++++-------------
1 file changed, 54 insertions(+), 76 deletions(-)
diff --git a/libc/test/src/math/smoke/powf16_test.cpp b/libc/test/src/math/smoke/powf16_test.cpp
index b3611e141dc01..f74bb6e57877e 100644
--- a/libc/test/src/math/smoke/powf16_test.cpp
+++ b/libc/test/src/math/smoke/powf16_test.cpp
@@ -54,7 +54,7 @@ TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(sNaN, aNaN),
FE_INVALID);
- // powf16( 0.0, exponent )
+ // powf16( 0.0f16, exponent )
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(zero, sNaN),
FE_INVALID);
EXPECT_FP_EQ_WITH_EXCEPTION(
@@ -67,14 +67,14 @@ TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, POS_EVEN_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, POS_NON_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(zero, ONE_HALF));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(zero, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(zero, neg_zero));
- EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::powf16(zero, inf));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(zero, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(zero, neg_zero));
+ EXPECT_FP_EQ(0.0f16, LIBC_NAMESPACE::powf16(zero, inf));
EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(zero, neg_inf),
FE_DIVBYZERO);
EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(zero, aNaN));
- // powf16( -0.0, exponent )
+ // powf16( -0.0f16, exponent )
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(neg_zero, sNaN),
FE_INVALID);
EXPECT_FP_EQ_WITH_EXCEPTION(
@@ -88,56 +88,56 @@ TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_zero, POS_EVEN_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_zero, POS_NON_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_zero, ONE_HALF));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_zero, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_zero, neg_zero));
- EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::powf16(neg_zero, inf));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(neg_zero, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(neg_zero, neg_zero));
+ EXPECT_FP_EQ(0.0f16, LIBC_NAMESPACE::powf16(neg_zero, inf));
EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(neg_zero, neg_inf),
FE_DIVBYZERO);
EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(neg_zero, aNaN));
- // powf16( 1.0, exponent )
- EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(1.0, sNaN),
+ // powf16( 1.0f16, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(1.0f16, sNaN),
FE_INVALID);
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, neg_zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, 1.0));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, -1.0));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, NEG_ODD_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, NEG_EVEN_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, NEG_NON_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, POS_ODD_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, POS_EVEN_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, POS_NON_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, inf));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, neg_inf));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(1.0, aNaN));
-
- // powf16( -1.0, exponent )
- EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(-1.0, sNaN),
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, neg_zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, 1.0f16));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, -1.0f16));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, NEG_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, NEG_EVEN_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, NEG_NON_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, POS_EVEN_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, POS_NON_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, inf));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, neg_inf));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(1.0f16, aNaN));
+
+ // powf16( -1.0f16, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(-1.0f16, sNaN),
FE_INVALID);
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, neg_zero));
- EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, 1.0));
- EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, -1.0));
- EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, NEG_ODD_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, NEG_EVEN_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, neg_zero));
+ EXPECT_FP_EQ(-1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, 1.0f16));
+ EXPECT_FP_EQ(-1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, -1.0f16));
+ EXPECT_FP_EQ(-1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, NEG_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, NEG_EVEN_INTEGER));
EXPECT_FP_IS_NAN_WITH_EXCEPTION(
- LIBC_NAMESPACE::powf16(-1.0, NEG_NON_INTEGER), FE_INVALID);
- EXPECT_FP_EQ(-1.0, LIBC_NAMESPACE::powf16(-1.0, POS_ODD_INTEGER));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, POS_EVEN_INTEGER));
+ LIBC_NAMESPACE::powf16(-1.0f16, NEG_NON_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ(-1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, POS_ODD_INTEGER));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, POS_EVEN_INTEGER));
EXPECT_FP_IS_NAN_WITH_EXCEPTION(
- LIBC_NAMESPACE::powf16(-1.0, POS_NON_INTEGER), FE_INVALID);
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, inf));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(-1.0, neg_inf));
- EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(-1.0, aNaN));
+ LIBC_NAMESPACE::powf16(-1.0f16, POS_NON_INTEGER), FE_INVALID);
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, inf));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(-1.0f16, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(-1.0f16, aNaN));
// powf16( inf, exponent )
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(inf, sNaN),
FE_INVALID);
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(inf, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(inf, neg_zero));
- EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, 1.0));
- EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, -1.0));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(inf, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(inf, neg_zero));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf16(inf, 1.0f16));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, -1.0f16));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, NEG_ODD_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, NEG_EVEN_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(inf, NEG_NON_INTEGER));
@@ -152,10 +152,10 @@ TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
// powf16( -inf, exponent )
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(neg_inf, sNaN),
FE_INVALID);
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_inf, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(neg_inf, neg_zero));
- EXPECT_FP_EQ(neg_inf, LIBC_NAMESPACE::powf16(neg_inf, 1.0));
- EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf16(neg_inf, -1.0));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(neg_inf, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(neg_inf, neg_zero));
+ EXPECT_FP_EQ(neg_inf, LIBC_NAMESPACE::powf16(neg_inf, 1.0f16));
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf16(neg_inf, -1.0f16));
EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf16(neg_inf, NEG_ODD_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_inf, NEG_EVEN_INTEGER));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(neg_inf, NEG_NON_INTEGER));
@@ -170,10 +170,10 @@ TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
// powf16 ( aNaN, exponent )
EXPECT_FP_EQ_WITH_EXCEPTION(aNaN, LIBC_NAMESPACE::powf16(aNaN, sNaN),
FE_INVALID);
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(aNaN, zero));
- EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(aNaN, neg_zero));
- EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, 1.0));
- EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, -1.0));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(aNaN, zero));
+ EXPECT_FP_EQ(1.0f16, LIBC_NAMESPACE::powf16(aNaN, neg_zero));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, 1.0f16));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, -1.0f16));
EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, NEG_ODD_INTEGER));
EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, NEG_EVEN_INTEGER));
EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf16(aNaN, NEG_NON_INTEGER));
@@ -196,37 +196,15 @@ TEST_F(LlvmLibcPowF16Test, SpecialNumbers) {
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(1.1f16, neg_inf));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf16(-1.1f16, neg_inf));
- // Exact powers of 2:
- // TODO: Enable these tests when we use exp2.
- // EXPECT_FP_EQ(0x1.0p15, LIBC_NAMESPACE::powf16(2.0, 15.0));
- // EXPECT_FP_EQ(0x1.0p126, LIBC_NAMESPACE::powf16(2.0, 126.0));
- // EXPECT_FP_EQ(0x1.0p-45, LIBC_NAMESPACE::powf16(2.0, -45.0));
- // EXPECT_FP_EQ(0x1.0p-126, LIBC_NAMESPACE::powf16(2.0, -126.0));
- // EXPECT_FP_EQ(0x1.0p-149, LIBC_NAMESPACE::powf16(2.0, -149.0));
-
- // Exact powers of 10:
- // TODO: Enable these tests when we use exp10
- // EXPECT_FP_EQ(1.0, LIBC_NAMESPACE::powf16(10.0, 0.0));
- // EXPECT_FP_EQ(10.0, LIBC_NAMESPACE::powf16(10.0, 1.0));
- // EXPECT_FP_EQ(100.0, LIBC_NAMESPACE::powf16(10.0, 2.0));
- // EXPECT_FP_EQ(1000.0, LIBC_NAMESPACE::powf16(10.0, 3.0));
- // EXPECT_FP_EQ(10000.0, LIBC_NAMESPACE::powf16(10.0, 4.0));
- // EXPECT_FP_EQ(100000.0, LIBC_NAMESPACE::powf16(10.0, 5.0));
- // EXPECT_FP_EQ(1000000.0, LIBC_NAMESPACE::powf16(10.0, 6.0));
- // EXPECT_FP_EQ(10000000.0, LIBC_NAMESPACE::powf16(10.0, 7.0));
- // EXPECT_FP_EQ(100000000.0, LIBC_NAMESPACE::powf16(10.0, 8.0));
- // EXPECT_FP_EQ(1000000000.0, LIBC_NAMESPACE::powf16(10.0, 9.0));
- // EXPECT_FP_EQ(10000000000.0, LIBC_NAMESPACE::powf16(10.0, 10.0));
-
// Overflow / Underflow:
if (ROUNDING_MODES[i] != RoundingMode::Downward &&
ROUNDING_MODES[i] != RoundingMode::TowardZero) {
- EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(3.1f16, 21.0),
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf16(3.1f16, 21.0f16),
FE_OVERFLOW);
}
if (ROUNDING_MODES[i] != RoundingMode::Upward) {
- EXPECT_FP_EQ_WITH_EXCEPTION(0.0, LIBC_NAMESPACE::powf16(3.1f16, -21.0),
- FE_UNDERFLOW);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ 0.0f16, LIBC_NAMESPACE::powf16(3.1f16, -21.0f16), FE_UNDERFLOW);
}
}
}
>From a3fd8192e61f924fad71b0828806614eee4c71f2 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Wed, 17 Dec 2025 19:56:13 +0200
Subject: [PATCH 13/14] Add LIBC_INLINE and clarify special exponents
---
libc/src/math/generic/powf16.cpp | 24 ++++++++++++++++--------
1 file changed, 16 insertions(+), 8 deletions(-)
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index d5aa9773c07cb..50598a8117cfc 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -27,8 +27,10 @@
namespace LIBC_NAMESPACE_DECL {
using namespace common_constants_internal;
+
namespace {
-static inline double exp2_range_reduced(double x) {
+
+LIBC_INLINE static double exp2_range_reduced(double x) {
// k = round(x * 32) => (hi + mid) * 2^5
double kf = fputil::nearest_integer(x * 32.0);
int k = static_cast<int>(kf);
@@ -69,7 +71,8 @@ static inline double exp2_range_reduced(double x) {
return result;
}
-bool is_odd_integer(float16 x) {
+
+LIBC_INLINE bool is_odd_integer(float16 x) {
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
@@ -81,7 +84,7 @@ bool is_odd_integer(float16 x) {
return (x_e + lsb == UNIT_EXPONENT);
}
-bool is_integer(float16 x) {
+LIBC_INLINE bool is_integer(float16 x) {
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
@@ -117,16 +120,21 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
+
if (LIBC_UNLIKELY(
ybits.is_zero() || x_u == FPBits::one().uintval() || xbits.is_nan() ||
ybits.is_nan() || x_u == FPBits::one().uintval() ||
x_u == FPBits::zero().uintval() || x_u >= FPBits::inf().uintval() ||
y_u >= FPBits::inf().uintval() ||
- x_u < FPBits::min_normal().uintval() || y_a == 0x3400U ||
- y_a == 0x3800U || y_a == 0x3A00U || y_a == 0x3800U ||
- y_a == 0x3800U || y_a == 0x3D00U || y_a == 0x3E00U ||
- y_a == 0x4100U || y_a == 0x4300U || y_a == 0x3c00U ||
- y_a == 0x4000U || is_integer(y))) {
+ x_u < FPBits::min_normal().uintval() || y_a == 0x3400U || // 0.25
+ y_a == 0x3800U || // 0.5
+ y_a == 0x3A00U || // 0.75
+ y_a == 0x3D00U || // 1.25
+ y_a == 0x3E00U || // 1.5
+ y_a == 0x4000U || // 2.0
+ y_a == 0x4100U || // 2.5
+ y_a == 0x4300U || // 3.5
+ is_integer(y))) {
// pow(x, 0) = 1
if (ybits.is_zero()) {
return 1.0f16;
>From 98e9826ce51d677d4882373f9d4bf77a8e39ffe3 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Fri, 2 Jan 2026 20:45:00 +0200
Subject: [PATCH 14/14] Refactor powf16 implementation to header-only in
src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/powf16.h | 29 ++
libc/src/__support/math/CMakeLists.txt | 22 +
libc/src/__support/math/powf16.h | 418 ++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 16 +-
libc/src/math/generic/powf16.cpp | 393 +---------------
.../llvm-project-overlay/libc/BUILD.bazel | 28 +-
7 files changed, 502 insertions(+), 405 deletions(-)
create mode 100644 libc/shared/math/powf16.h
create mode 100644 libc/src/__support/math/powf16.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 70c6d375c22de..e7c6f0b78f62b 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -62,6 +62,7 @@
#include "math/ldexpf.h"
#include "math/ldexpf128.h"
#include "math/ldexpf16.h"
+#include "math/powf16.h"
#include "math/rsqrtf.h"
#include "math/rsqrtf16.h"
diff --git a/libc/shared/math/powf16.h b/libc/shared/math/powf16.h
new file mode 100644
index 0000000000000..549a31a653488
--- /dev/null
+++ b/libc/shared/math/powf16.h
@@ -0,0 +1,29 @@
+//===-- Shared exp2f16 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_EXP2F16_H
+#define LLVM_LIBC_SHARED_MATH_EXP2F16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+#include "shared/libc_common.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/math/powf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::powf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP2F16_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index f8622da52d983..eb1894e2f7125 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -891,6 +891,28 @@ add_header_library(
libc.src.errno.errno
)
+
+add_header_library(
+ powf16
+ HDRS
+ powf16.h
+ DEPENDS
+ .common_constants
+ libc.hdr.errno_macros
+ libc.hdr.fenv_macros
+ libc.src.__support.CPP.bit
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+ libc.src.__support.math.exp10f_utils
+ libc.src.__support.math.common_constants
+)
+
add_header_library(
expm1f
HDRS
diff --git a/libc/src/__support/math/powf16.h b/libc/src/__support/math/powf16.h
new file mode 100644
index 0000000000000..390e258abef62
--- /dev/null
+++ b/libc/src/__support/math/powf16.h
@@ -0,0 +1,418 @@
+//===-- Implementation header for powf16 ------------------------*- 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_POWF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_POWF16_H
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#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/cast.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/macros/properties/types.h"
+#include "src/__support/math/common_constants.h"
+#include "src/__support/math/exp10f_utils.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+using namespace common_constants_internal;
+
+namespace {
+
+LIBC_INLINE static double exp2_range_reduced(double x) {
+ // k = round(x * 32) => (hi + mid) * 2^5
+ double kf = fputil::nearest_integer(x * 32.0);
+ int k = static_cast<int>(kf);
+ // dx = lo = x - (hi + mid) = x - k * 2^(-5)
+ double dx = fputil::multiply_add(-0x1.0p-5, kf, x); // -2^-5 * k + x
+
+ // hi = k >> MID_BITS
+ // exp_hi = hi shifted into double exponent field
+ int64_t hi = static_cast<int64_t>(k >> ExpBase::MID_BITS);
+ int64_t exp_hi = static_cast<int64_t>(
+ static_cast<uint64_t>(hi) << fputil::FPBits<double>::FRACTION_LEN);
+
+ // mh_bits = bits for 2^hi * 2^mid (lookup contains base bits for 2^mid)
+ int tab_index = k & ExpBase::MID_MASK; // mid index in [0, 31]
+ int64_t mh_bits = ExpBase::EXP_2_MID[tab_index] + exp_hi;
+
+ // mh = 2^(hi + mid)
+ double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
+
+ // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
+ // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
+ constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
+ 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
+ 0x1.5d88091198529p-10};
+
+ double dx_sq = dx * dx;
+ double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0); // 1 + ln2*dx
+ double c2 =
+ fputil::multiply_add(dx, COEFFS[2], COEFFS[1]); // COEFF1 + COEFF2*dx
+ double c3 =
+ fputil::multiply_add(dx, COEFFS[4], COEFFS[3]); // COEFF3 + COEFF4*dx
+ double p = fputil::multiply_add(dx_sq, c3, c2); // c2 + c3*dx^2
+
+ // 2^x = 2^(hi+mid) * 2^dx
+ // ≈ mh * (1 + dx * P(dx))
+ // = mh + (mh * dx) * P(dx)
+ double result = fputil::multiply_add(p, dx_sq * mh, c1 * mh);
+
+ return result;
+}
+
+LIBC_INLINE bool is_odd_integer(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+ uint16_t x_u = xbits.uintval();
+ unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
+ unsigned lsb = static_cast<unsigned>(
+ cpp::countr_zero(static_cast<uint32_t>(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 bool is_integer(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+ uint16_t x_u = xbits.uintval();
+ unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
+ unsigned lsb = static_cast<unsigned>(
+ cpp::countr_zero(static_cast<uint32_t>(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
+
+namespace math {
+
+LIBC_INLINE static constexpr float16 powf16(float16 x, float16 y) {
+ using FPBits = fputil::FPBits<float16>;
+
+ FPBits xbits(x), ybits(y);
+ bool x_sign = xbits.is_neg();
+ bool y_sign = ybits.is_neg();
+
+ FPBits x_abs = xbits.abs();
+ FPBits y_abs = ybits.abs();
+
+ uint16_t x_u = xbits.uintval();
+ uint16_t x_a = x_abs.uintval();
+ uint16_t y_a = y_abs.uintval();
+ uint16_t y_u = ybits.uintval();
+ bool result_sign = false;
+
+ ///////// BEGIN - Check exceptional cases ////////////////////////////////////
+ // If x or y is signaling NaN
+ if (xbits.is_signaling_nan() || ybits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ if (LIBC_UNLIKELY(
+ ybits.is_zero() || x_u == FPBits::one().uintval() || xbits.is_nan() ||
+ ybits.is_nan() || x_u == FPBits::one().uintval() ||
+ x_u == FPBits::zero().uintval() || x_u >= FPBits::inf().uintval() ||
+ y_u >= FPBits::inf().uintval() ||
+ x_u < FPBits::min_normal().uintval() || y_a == 0x3400U || // 0.25
+ y_a == 0x3800U || // 0.5
+ y_a == 0x3A00U || // 0.75
+ y_a == 0x3D00U || // 1.25
+ y_a == 0x3E00U || // 1.5
+ y_a == 0x4000U || // 2.0
+ y_a == 0x4100U || // 2.5
+ y_a == 0x4300U || // 3.5
+ is_integer(y))) {
+ // pow(x, 0) = 1
+ if (ybits.is_zero()) {
+ return 1.0f16;
+ }
+
+ // pow(1, Y) = 1
+ if (x_u == FPBits::one().uintval()) {
+ return 1.0f16;
+ }
+ // 4. Handle remaining NaNs
+ // pow(NaN, y) = NaN (for y != 0)
+ if (xbits.is_nan()) {
+ return x;
+ }
+ // pow(x, NaN) = NaN (for x != 1)
+ if (ybits.is_nan()) {
+ return y;
+ }
+ switch (y_a) {
+ case 0x3400U: // y = ±0.25 (1/4)
+ case 0x3800U: // y = ±0.5 (1/2)
+ case 0x3A00U: // y = ±0.75 (3/4)
+ case 0x3D00U: // y = ±1.25 (5/4)
+ case 0x3E00U: // y = ±1.5 (3/2)
+ case 0x4100U: // y = ±2.5 (5/2)
+ case 0x4300U: // y = ±3.5 (7/2)
+ {
+ if (xbits.is_zero()) {
+ if (y_sign) {
+ // pow(±0, negative) handled below
+ break;
+ } else {
+ // pow(±0, positive_fractional) = +0
+ return FPBits::zero(Sign::POS).get_val();
+ }
+ }
+
+ if (x_sign && !xbits.is_zero()) {
+ break; // pow(negative, non-integer) = NaN
+ }
+
+ double x_d = static_cast<double>(x);
+ double sqrt_x = fputil::sqrt<double>(x_d);
+ double fourth_root = fputil::sqrt<double>(sqrt_x);
+ double result_d = 0.0;
+
+ // Compute based on exponent value
+ switch (y_a) {
+ case 0x3400U: // 0.25 = x^(1/4)
+ result_d = fourth_root;
+ break;
+ case 0x3800U: // 0.5 = x^(1/2)
+ result_d = sqrt_x;
+ break;
+ case 0x3A00U: // 0.75 = x^(1/2) * x^(1/4)
+ result_d = sqrt_x * fourth_root;
+ break;
+ case 0x3D00U: // 1.25 = x * x^(1/4)
+ result_d = x_d * fourth_root;
+ break;
+ case 0x3E00U: // 1.5 = x * x^(1/2)
+ result_d = x_d * sqrt_x;
+ break;
+ case 0x4100U: // 2.5 = x^2 * x^(1/2)
+ result_d = x_d * x_d * sqrt_x;
+ break;
+ case 0x4300U: // 3.5 = x^3 * x^(1/2)
+ result_d = x_d * x_d * x_d * sqrt_x;
+ break;
+ }
+
+ result_d = y_sign ? (1.0 / result_d) : result_d;
+ return fputil::cast<float16>(result_d);
+ }
+ case 0x3c00U: // y = +-1.0
+ return fputil::cast<float16>(y_sign ? (1.0 / x) : x);
+
+ case 0x4000U: // y = +-2.0
+ double result_d = static_cast<double>(x) * static_cast<double>(x);
+ return fputil::cast<float16>(y_sign ? (1.0 / (result_d)) : (result_d));
+ }
+ // TODO: Speed things up with pow(2, y) = exp2(y) and pow(10, y) = exp10(y).
+ //
+ // pow(-1, y) for integer y
+ if (x_u == FPBits::one(Sign::NEG).uintval()) {
+ if (is_integer(y)) {
+ if (is_odd_integer(y)) {
+ return -1.0f16;
+ } else {
+ return 1.0f16;
+ }
+ }
+ // pow(-1, non-integer) = NaN
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // pow(±0, y) cases
+ if (xbits.is_zero()) {
+ if (y_sign) {
+ // pow(+-0, negative) = +-inf and raise FE_DIVBYZERO
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+ bool result_neg = x_sign && ybits.is_finite() && is_odd_integer(y);
+ return FPBits::inf(result_neg ? Sign::NEG : Sign::POS).get_val();
+ } else {
+ // pow(+-0, positive) = +-0
+ bool out_is_neg = x_sign && is_odd_integer(y);
+ return out_is_neg ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
+ }
+ }
+
+ if (xbits.is_inf()) {
+ bool out_is_neg = x_sign && ybits.is_finite() && is_odd_integer(y);
+ if (y_sign) // pow(+-inf, negative) = +-0
+ return out_is_neg ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
+ // pow(+-inf, positive) = +-inf
+ return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
+ }
+
+ // y = +-inf cases
+ if (ybits.is_inf()) {
+ // pow(1, inf) handled above.
+ bool x_abs_less_than_one = x_a < FPBits::one().uintval();
+ if ((x_abs_less_than_one && !y_sign) ||
+ (!x_abs_less_than_one && y_sign)) {
+ // |x| < 1 and y = +inf => 0.0
+ // |x| > 1 and y = -inf => 0.0
+ return 0.0f16;
+ } else {
+ // |x| > 1 and y = +inf => +inf
+ // |x| < 1 and y = -inf => +inf
+ return FPBits::inf(Sign::POS).get_val();
+ }
+ }
+
+ // pow( negative, non-integer ) = NaN
+ if (x_sign && !is_integer(y)) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ bool result_sign = false;
+ if (x_sign && is_integer(y)) {
+ result_sign = is_odd_integer(y);
+ }
+
+ if (is_integer(y)) {
+ double base = x_abs.get_val();
+ double res = 1.0;
+ int yi = static_cast<int>(y_abs.get_val());
+
+ // Fast exponentiation by squaring
+ while (yi > 0) {
+ if (yi & 1)
+ res *= base;
+ base *= base;
+ yi = yi >> 1;
+ }
+
+ if (y_sign) {
+ res = 1.0 / res;
+ }
+
+ if (result_sign) {
+ res = -res;
+ }
+
+ if (FPBits(fputil::cast<float16>(res)).is_inf()) {
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ res = result_sign ? -0x1.0p20 : 0x1.0p20;
+ }
+
+ float16 final_res = fputil::cast<float16>(res);
+ return final_res;
+ }
+ }
+
+ ///////// END - Check exceptional cases //////////////////////////////////////
+
+ // Core computation: x^y = 2^( y * log2(x) )
+ // We compute log2(x) = log(x) / log(2) using a polynomial approximation.
+
+ // The exponent part (m) is added later to get the final log(x).
+ FPBits x_bits(x);
+ uint16_t x_u_log = x_bits.uintval();
+
+ // Extract exponent field of x.
+ int m = x_bits.get_exponent();
+
+ // When x is subnormal, normalize it by adjusting m.
+ if ((x_u_log & FPBits::EXP_MASK) == 0U) {
+ unsigned leading_zeros =
+ cpp::countl_zero(static_cast<uint32_t>(x_u_log)) - (32 - 16);
+
+ constexpr unsigned SUBNORMAL_SHIFT_CORRECTION = 5;
+ unsigned shift = leading_zeros - SUBNORMAL_SHIFT_CORRECTION;
+
+ x_bits.set_mantissa(static_cast<uint16_t>(x_u_log << shift));
+
+ m = 1 - FPBits::EXP_BIAS - static_cast<int>(shift);
+ }
+
+ // Extract the mantissa and index into small lookup tables.
+ uint16_t mant = x_bits.get_mantissa();
+ // Use the highest 7 fractional bits of the mantissa as the index f.
+ int f = mant >> (FPBits::FRACTION_LEN - 7);
+
+ // Reconstruct the mantissa value m_x so it's in the range [1.0, 2.0).
+ x_bits.set_biased_exponent(FPBits::EXP_BIAS);
+ double mant_d = x_bits.get_val();
+ // Degree-5 polynomial approximation
+ // of log2 generated by Sollya with:
+ // > P = fpminimax(log2(1 + x)/x, 4, [|1, D...|], [-2^-8, 2^-7]);
+ constexpr double COEFFS[5] = {0x1.71547652b8133p0, -0x1.71547652d1e33p-1,
+ 0x1.ec70a098473dep-2, -0x1.7154c5ccdf121p-2,
+ 0x1.2514fd90a130ap-2};
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double v = fputil::multiply_add<double>(mant_d, RD[f], -1.0);
+#else
+ double c = fputil::FPBits<double>(fputil::FPBits<double>(mant_d).uintval() &
+ 0x3fff'e000'0000'0000)
+ .get_val();
+ double v = fputil::multiply_add(RD[f], mant_d - c, CD[f]);
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double extra_factor = static_cast<double>(m) + LOG2_R[f];
+ double vsq = v * v;
+ double c0 = fputil::multiply_add(v, COEFFS[0], 0.0);
+ double c1 = fputil::multiply_add(v, COEFFS[2], COEFFS[1]);
+ double c2 = fputil::multiply_add(v, COEFFS[4], COEFFS[3]);
+
+ double log2_x = fputil::polyeval(vsq, c0, c1, c2);
+
+ double y_d = fputil::cast<double>(y);
+ double z = fputil::multiply_add(y_d, log2_x, y_d * extra_factor);
+
+ // Check for underflow
+ // Float16 min normal is 2^-14, smallest subnormal is 2^-24
+ if (LIBC_UNLIKELY(z < -25.0)) {
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return result_sign ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
+ }
+
+ // Check for overflow
+ // Float16 max is ~2^16
+ double result_d = 0.0;
+ if (LIBC_UNLIKELY(z > 16.0)) {
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ result_d = result_sign ? -0x1.0p20 : 0x1.0p20;
+ } else {
+ result_d = exp2_range_reduced(z);
+ }
+
+ if (result_sign) {
+
+ result_d = -result_d;
+ }
+
+ float16 result = fputil::cast<float16>((result_d));
+ return result;
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index b6f33a6f20c1c..a977c0d560016 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1594,6 +1594,7 @@ add_entrypoint_object(
libc.src.__support.math.expxf16_utils
)
+
add_entrypoint_object(
powf16
SRCS
@@ -1601,19 +1602,8 @@ add_entrypoint_object(
HDRS
../powf16.h
DEPENDS
- libc.hdr.errno_macros
- libc.hdr.fenv_macros
- libc.src.__support.CPP.bit
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.cast
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.nearest_integer
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
- libc.src.__support.math.exp10f_utils
- libc.src.__support.math.common_constants
+ libc.src.__support.math.powf16
+ libc.src.errno.errno
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index 50598a8117cfc..6c08e60c414b8 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -7,399 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/powf16.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/cast.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/nearest_integer.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h"
-#include "src/__support/macros/properties/types.h"
-#include "src/__support/math/common_constants.h"
-#include "src/__support/math/exp10f_utils.h"
+#include "src/__support/math/powf16.h"
namespace LIBC_NAMESPACE_DECL {
-using namespace common_constants_internal;
-
-namespace {
-
-LIBC_INLINE static double exp2_range_reduced(double x) {
- // k = round(x * 32) => (hi + mid) * 2^5
- double kf = fputil::nearest_integer(x * 32.0);
- int k = static_cast<int>(kf);
- // dx = lo = x - (hi + mid) = x - k * 2^(-5)
- double dx = fputil::multiply_add(-0x1.0p-5, kf, x); // -2^-5 * k + x
-
- // hi = k >> MID_BITS
- // exp_hi = hi shifted into double exponent field
- int64_t hi = static_cast<int64_t>(k >> ExpBase::MID_BITS);
- int64_t exp_hi = static_cast<int64_t>(
- static_cast<uint64_t>(hi) << fputil::FPBits<double>::FRACTION_LEN);
-
- // mh_bits = bits for 2^hi * 2^mid (lookup contains base bits for 2^mid)
- int tab_index = k & ExpBase::MID_MASK; // mid index in [0, 31]
- int64_t mh_bits = ExpBase::EXP_2_MID[tab_index] + exp_hi;
-
- // mh = 2^(hi + mid)
- double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
-
- // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
- // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
- constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
- 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
- 0x1.5d88091198529p-10};
-
- double dx_sq = dx * dx;
- double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0); // 1 + ln2*dx
- double c2 =
- fputil::multiply_add(dx, COEFFS[2], COEFFS[1]); // COEFF1 + COEFF2*dx
- double c3 =
- fputil::multiply_add(dx, COEFFS[4], COEFFS[3]); // COEFF3 + COEFF4*dx
- double p = fputil::multiply_add(dx_sq, c3, c2); // c2 + c3*dx^2
-
- // 2^x = 2^(hi+mid) * 2^dx
- // ≈ mh * (1 + dx * P(dx))
- // = mh + (mh * dx) * P(dx)
- double result = fputil::multiply_add(p, dx_sq * mh, c1 * mh);
-
- return result;
-}
-
-LIBC_INLINE bool is_odd_integer(float16 x) {
- using FPBits = fputil::FPBits<float16>;
- FPBits xbits(x);
- uint16_t x_u = xbits.uintval();
- unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
- unsigned lsb = static_cast<unsigned>(
- cpp::countr_zero(static_cast<uint32_t>(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 bool is_integer(float16 x) {
- using FPBits = fputil::FPBits<float16>;
- FPBits xbits(x);
- uint16_t x_u = xbits.uintval();
- unsigned x_e = static_cast<unsigned>(xbits.get_biased_exponent());
- unsigned lsb = static_cast<unsigned>(
- cpp::countr_zero(static_cast<uint32_t>(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(float16, powf16, (float16 x, float16 y)) {
- using FPBits = fputil::FPBits<float16>;
-
- FPBits xbits(x), ybits(y);
- bool x_sign = xbits.is_neg();
- bool y_sign = ybits.is_neg();
-
- FPBits x_abs = xbits.abs();
- FPBits y_abs = ybits.abs();
-
- uint16_t x_u = xbits.uintval();
- uint16_t x_a = x_abs.uintval();
- uint16_t y_a = y_abs.uintval();
- uint16_t y_u = ybits.uintval();
- bool result_sign = false;
-
- ///////// BEGIN - Check exceptional cases ////////////////////////////////////
- // If x or y is signaling NaN
- if (xbits.is_signaling_nan() || ybits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- if (LIBC_UNLIKELY(
- ybits.is_zero() || x_u == FPBits::one().uintval() || xbits.is_nan() ||
- ybits.is_nan() || x_u == FPBits::one().uintval() ||
- x_u == FPBits::zero().uintval() || x_u >= FPBits::inf().uintval() ||
- y_u >= FPBits::inf().uintval() ||
- x_u < FPBits::min_normal().uintval() || y_a == 0x3400U || // 0.25
- y_a == 0x3800U || // 0.5
- y_a == 0x3A00U || // 0.75
- y_a == 0x3D00U || // 1.25
- y_a == 0x3E00U || // 1.5
- y_a == 0x4000U || // 2.0
- y_a == 0x4100U || // 2.5
- y_a == 0x4300U || // 3.5
- is_integer(y))) {
- // pow(x, 0) = 1
- if (ybits.is_zero()) {
- return 1.0f16;
- }
-
- // pow(1, Y) = 1
- if (x_u == FPBits::one().uintval()) {
- return 1.0f16;
- }
- // 4. Handle remaining NaNs
- // pow(NaN, y) = NaN (for y != 0)
- if (xbits.is_nan()) {
- return x;
- }
- // pow(x, NaN) = NaN (for x != 1)
- if (ybits.is_nan()) {
- return y;
- }
- switch (y_a) {
- case 0x3400U: // y = ±0.25 (1/4)
- case 0x3800U: // y = ±0.5 (1/2)
- case 0x3A00U: // y = ±0.75 (3/4)
- case 0x3D00U: // y = ±1.25 (5/4)
- case 0x3E00U: // y = ±1.5 (3/2)
- case 0x4100U: // y = ±2.5 (5/2)
- case 0x4300U: // y = ±3.5 (7/2)
- {
- if (xbits.is_zero()) {
- if (y_sign) {
- // pow(±0, negative) handled below
- break;
- } else {
- // pow(±0, positive_fractional) = +0
- return FPBits::zero(Sign::POS).get_val();
- }
- }
-
- if (x_sign && !xbits.is_zero()) {
- break; // pow(negative, non-integer) = NaN
- }
-
- double x_d = static_cast<double>(x);
- double sqrt_x = fputil::sqrt<double>(x_d);
- double fourth_root = fputil::sqrt<double>(sqrt_x);
- double result_d;
-
- // Compute based on exponent value
- switch (y_a) {
- case 0x3400U: // 0.25 = x^(1/4)
- result_d = fourth_root;
- break;
- case 0x3800U: // 0.5 = x^(1/2)
- result_d = sqrt_x;
- break;
- case 0x3A00U: // 0.75 = x^(1/2) * x^(1/4)
- result_d = sqrt_x * fourth_root;
- break;
- case 0x3D00U: // 1.25 = x * x^(1/4)
- result_d = x_d * fourth_root;
- break;
- case 0x3E00U: // 1.5 = x * x^(1/2)
- result_d = x_d * sqrt_x;
- break;
- case 0x4100U: // 2.5 = x^2 * x^(1/2)
- result_d = x_d * x_d * sqrt_x;
- break;
- case 0x4300U: // 3.5 = x^3 * x^(1/2)
- result_d = x_d * x_d * x_d * sqrt_x;
- break;
- }
-
- result_d = y_sign ? (1.0 / result_d) : result_d;
- return fputil::cast<float16>(result_d);
- }
- case 0x3c00U: // y = +-1.0
- return fputil::cast<float16>(y_sign ? (1.0 / x) : x);
-
- case 0x4000U: // y = +-2.0
- double result_d = static_cast<double>(x) * static_cast<double>(x);
- return fputil::cast<float16>(y_sign ? (1.0 / (result_d)) : (result_d));
- }
- // TODO: Speed things up with pow(2, y) = exp2(y) and pow(10, y) = exp10(y).
- //
- // pow(-1, y) for integer y
- if (x_u == FPBits::one(Sign::NEG).uintval()) {
- if (is_integer(y)) {
- if (is_odd_integer(y)) {
- return -1.0f16;
- } else {
- return 1.0f16;
- }
- }
- // pow(-1, non-integer) = NaN
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- // pow(±0, y) cases
- if (xbits.is_zero()) {
- if (y_sign) {
- // pow(+-0, negative) = +-inf and raise FE_DIVBYZERO
- fputil::raise_except_if_required(FE_DIVBYZERO);
- bool result_neg = x_sign && ybits.is_finite() && is_odd_integer(y);
- return FPBits::inf(result_neg ? Sign::NEG : Sign::POS).get_val();
- } else {
- // pow(+-0, positive) = +-0
- bool out_is_neg = x_sign && is_odd_integer(y);
- return out_is_neg ? FPBits::zero(Sign::NEG).get_val()
- : FPBits::zero(Sign::POS).get_val();
- }
- }
-
- if (xbits.is_inf()) {
- bool out_is_neg = x_sign && ybits.is_finite() && is_odd_integer(y);
- if (y_sign) // pow(+-inf, negative) = +-0
- return out_is_neg ? FPBits::zero(Sign::NEG).get_val()
- : FPBits::zero(Sign::POS).get_val();
- // pow(+-inf, positive) = +-inf
- return FPBits::inf(out_is_neg ? Sign::NEG : Sign::POS).get_val();
- }
-
- // y = +-inf cases
- if (ybits.is_inf()) {
- // pow(1, inf) handled above.
- bool x_abs_less_than_one = x_a < FPBits::one().uintval();
- if ((x_abs_less_than_one && !y_sign) ||
- (!x_abs_less_than_one && y_sign)) {
- // |x| < 1 and y = +inf => 0.0
- // |x| > 1 and y = -inf => 0.0
- return 0.0f16;
- } else {
- // |x| > 1 and y = +inf => +inf
- // |x| < 1 and y = -inf => +inf
- return FPBits::inf(Sign::POS).get_val();
- }
- }
-
- // pow( negative, non-integer ) = NaN
- if (x_sign && !is_integer(y)) {
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- bool result_sign = false;
- if (x_sign && is_integer(y)) {
- result_sign = is_odd_integer(y);
- }
-
- if (is_integer(y)) {
- double base = x_abs.get_val();
- double res = 1.0;
- int yi = static_cast<int>(y_abs.get_val());
-
- // Fast exponentiation by squaring
- while (yi > 0) {
- if (yi & 1)
- res *= base;
- base *= base;
- yi = yi >> 1;
- }
-
- if (y_sign) {
- res = 1.0 / res;
- }
-
- if (result_sign) {
- res = -res;
- }
-
- if (FPBits(fputil::cast<float16>(res)).is_inf()) {
- fputil::raise_except_if_required(FE_OVERFLOW);
- res = result_sign ? -0x1.0p20 : 0x1.0p20;
- }
-
- float16 final_res = fputil::cast<float16>(res);
- return final_res;
- }
- }
-
- ///////// END - Check exceptional cases //////////////////////////////////////
-
- // Core computation: x^y = 2^( y * log2(x) )
- // We compute log2(x) = log(x) / log(2) using a polynomial approximation.
-
- // The exponent part (m) is added later to get the final log(x).
- FPBits x_bits(x);
- uint16_t x_u_log = x_bits.uintval();
-
- // Extract exponent field of x.
- int m = x_bits.get_exponent();
-
- // When x is subnormal, normalize it by adjusting m.
- if ((x_u_log & FPBits::EXP_MASK) == 0U) {
- unsigned leading_zeros =
- cpp::countl_zero(static_cast<uint32_t>(x_u_log)) - (32 - 16);
-
- constexpr unsigned SUBNORMAL_SHIFT_CORRECTION = 5;
- unsigned shift = leading_zeros - SUBNORMAL_SHIFT_CORRECTION;
-
- x_bits.set_mantissa(static_cast<uint16_t>(x_u_log << shift));
-
- m = 1 - FPBits::EXP_BIAS - static_cast<int>(shift);
- }
-
- // Extract the mantissa and index into small lookup tables.
- uint16_t mant = x_bits.get_mantissa();
- // Use the highest 7 fractional bits of the mantissa as the index f.
- int f = mant >> (FPBits::FRACTION_LEN - 7);
-
- // Reconstruct the mantissa value m_x so it's in the range [1.0, 2.0).
- x_bits.set_biased_exponent(FPBits::EXP_BIAS);
- double mant_d = x_bits.get_val();
- // Degree-5 polynomial approximation
- // of log2 generated by Sollya with:
- // > P = fpminimax(log2(1 + x)/x, 4, [|1, D...|], [-2^-8, 2^-7]);
- constexpr double COEFFS[5] = {0x1.71547652b8133p0, -0x1.71547652d1e33p-1,
- 0x1.ec70a098473dep-2, -0x1.7154c5ccdf121p-2,
- 0x1.2514fd90a130ap-2};
-
-#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- double v = fputil::multiply_add<double>(mant_d, RD[f], -1.0);
-#else
- double c = fputil::FPBits<double>(fputil::FPBits<double>(mant_d).uintval() &
- 0x3fff'e000'0000'0000)
- .get_val();
- double v = fputil::multiply_add(RD[f], mant_d - c, CD[f]);
-#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- double extra_factor = static_cast<double>(m) + LOG2_R[f];
- double vsq = v * v;
- double c0 = fputil::multiply_add(v, COEFFS[0], 0.0);
- double c1 = fputil::multiply_add(v, COEFFS[2], COEFFS[1]);
- double c2 = fputil::multiply_add(v, COEFFS[4], COEFFS[3]);
-
- double log2_x = fputil::polyeval(vsq, c0, c1, c2);
-
- double y_d = fputil::cast<double>(y);
- double z = fputil::multiply_add(y_d, log2_x, y_d * extra_factor);
-
- // Check for underflow
- // Float16 min normal is 2^-14, smallest subnormal is 2^-24
- if (LIBC_UNLIKELY(z < -25.0)) {
- fputil::raise_except_if_required(FE_UNDERFLOW);
- return result_sign ? FPBits::zero(Sign::NEG).get_val()
- : FPBits::zero(Sign::POS).get_val();
- }
-
- // Check for overflow
- // Float16 max is ~2^16
- double result_d;
- if (LIBC_UNLIKELY(z > 16.0)) {
- fputil::raise_except_if_required(FE_OVERFLOW);
- result_d = result_sign ? -0x1.0p20 : 0x1.0p20;
- } else {
- result_d = exp2_range_reduced(z);
- }
-
- if (result_sign) {
-
- result_d = -result_d;
- }
-
- float16 result = fputil::cast<float16>((result_d));
- return result;
-}
+LLVM_LIBC_FUNCTION(float16, powf16, (float16 x,float16 y)) { return math::powf16(x,y); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 913e913572b14..5fe6f5f0a9009 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -3101,7 +3101,24 @@ libc_support_library(
":__support_math_common_constants",
],
)
-
+libc_support_library(
+ name = "__support_math_powf16",
+ hdrs = ["src/__support/math/powf16.h"],
+ deps = [
+ ":__support_cpp_bit",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_cast",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_rounding_mode",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ":__support_math_common_constants",
+ ":__support_math_exp10f_utils",
+ ],
+)
libc_support_library(
name = "__support_range_reduction_double",
hdrs = [
@@ -3848,6 +3865,15 @@ libc_math_function(
],
)
+libc_math_function(
+ name = "powf16",
+ additional_deps = [
+ ":__support_math_powf16",
+ ":errno",
+ ],
+)
+
+
libc_math_function(name = "f16add")
libc_math_function(name = "f16addf")
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