[libc-commits] [libc] [libc][math] Implement C23 half precision pow function (PR #159906)
via libc-commits
libc-commits at lists.llvm.org
Sat Oct 11 03:14:32 PDT 2025
https://github.com/AnonMiraj updated https://github.com/llvm/llvm-project/pull/159906
>From f433dfd345fddec4bdadac0104d4edf5978b4238 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 20 Sep 2025 07:58:40 +0300
Subject: [PATCH 1/9] [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 4b6f3337036aa..7dd5118665456 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 d24cc740d4234..9aae829cd4004 100644
--- a/libc/config/gpu/nvptx/entrypoints.txt
+++ b/libc/config/gpu/nvptx/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/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 1bc5df9d45a93..584323d086079 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -589,6 +589,7 @@ 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 ec01030c77d4f..a5759d1901cb8 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 54ea983d64839..b19d1033f2b75 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -599,6 +599,7 @@ 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 1fc9a2b901c14..03785ce2f8779 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -629,6 +629,7 @@ 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 4e398676bf91e..ff1608e3ec3dd 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -2083,6 +2083,12 @@ 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 187bc92e5c2c6..3a1ab17341265 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -451,6 +451,7 @@ add_math_entrypoint_object(nextupf128)
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 419f562713b5f..fa5e0ed5b8451 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1581,6 +1581,30 @@ 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 e15df147c3c35..eec048e094bd8 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -2470,6 +2470,17 @@ 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 b800f7aba98d1..fa44c72e95618 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -4580,6 +4580,16 @@ 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 21275a3d2e754ae2e08779f70d3e35d0375530a0 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 20 Sep 2025 08:09:23 +0300
Subject: [PATCH 2/9] 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 7db870385ea3d2aec374b96749504eb8b01c73fb Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Tue, 23 Sep 2025 09:31:48 +0300
Subject: [PATCH 3/9] 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 ff1608e3ec3dd..09e9bfed6dad4 100644
--- a/libc/include/math.yaml
+++ b/libc/include/math.yaml
@@ -2089,6 +2089,7 @@ functions:
return_type: _Float16
arguments:
- type: _Float16
+ - type: _Float16
- name: powi
standards: llvm_libc_ext
return_type: double
>From 7a8db3f659e67bed70a8e301079d6f888b0d14c2 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Tue, 23 Sep 2025 09:32:00 +0300
Subject: [PATCH 4/9] 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 fa5e0ed5b8451..b1bc47d64fa82 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1601,8 +1601,6 @@ 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 7bb9c40553f60f5f24b5dbc65289fc8ae480c74b Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Wed, 24 Sep 2025 22:58:01 +0300
Subject: [PATCH 5/9] 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 28d52f6c1ca8b4094f3c7c5f12837a7e623f09ff Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Wed, 24 Sep 2025 22:58:15 +0300
Subject: [PATCH 6/9] 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 13dd3fff36f1bedb1764278655c0ea1bbaa89877 Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 11 Oct 2025 13:05:30 +0300
Subject: [PATCH 7/9] 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 6ac41238f056dbbb68e18798cdfe66b0c782e8ac Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 11 Oct 2025 13:13:25 +0300
Subject: [PATCH 8/9] update powf16 approach
---
libc/src/math/generic/CMakeLists.txt | 1 -
libc/src/math/generic/powf16.cpp | 180 ++++++++++++++++++---------
2 files changed, 124 insertions(+), 57 deletions(-)
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index b1bc47d64fa82..539b6d9286463 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1600,7 +1600,6 @@ 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
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/powf16.cpp b/libc/src/math/generic/powf16.cpp
index 1c998ca02e7e8..8d5333c82587c 100644
--- a/libc/src/math/generic/powf16.cpp
+++ b/libc/src/math/generic/powf16.cpp
@@ -21,7 +21,7 @@
#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/math/generic/common_constants.h"
namespace LIBC_NAMESPACE_DECL {
@@ -66,6 +66,7 @@ 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 ////////////////////////////////////
@@ -75,10 +76,12 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
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() ||
+ 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 == 0x3800U ||
+ y_a == 0x3c00U || y_a == 0x4000U || is_integer(y))) {
// pow(x, 0) = 1
if (ybits.is_zero()) {
return fputil::cast<float16>(1.0f);
@@ -96,8 +99,13 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
(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));
+ // For pow(x, 0.5), sqrt(x) is used. pow(0, -0.5) is handled below.
+ break;
+ }
+ // If x is not negative or special, use sqrt(x)
+ if (x_sign && !xbits.is_zero()) {
+ // pow(negative, non-integer) = NaN, handled below.
+ break;
}
return fputil::cast<float16>(y_sign ? (1.0 / fputil::sqrt<float16>(x))
: fputil::sqrt<float16>(x));
@@ -163,9 +171,13 @@ 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)) {
+ // |x| < 1 and y = +inf => 0.0
+ // |x| > 1 and y = -inf => 0.0
return fputil::cast<float16>(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();
}
}
@@ -175,7 +187,31 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
+ if (is_integer(y)) {
+ double base = x_abs.get_val();
+ double res = 1.0;
+ int yi = static_cast<int>(y_abs.get_val());
+
+ while (yi > 0) {
+ if (yi % 2 == 1)
+ res *= base;
+ base *= base;
+ yi /= 2;
+ }
+
+ if (y_sign) {
+ res = 1.0 / res;
+ }
+
+ float16 final_res = fputil::cast<float16>(res);
+ if (x_sign && is_odd_integer(y)) {
+ FPBits res_bits(final_res);
+ res_bits.set_sign(Sign::NEG);
+ return res_bits.get_val();
+ }
+ return final_res;
+ }
// For negative x with integer y, compute pow(|x|, y) and adjust sign
if (x_sign) {
x = -x;
@@ -184,72 +220,109 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
}
}
}
+
///////// 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).
+ // Range reduction for log(m_x):
+ // v = r * m_x - 1
- 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.
+ // log(1+v) = v + v^2 * P(v)
+
+ // log(m_x) = log(1+v) - log(r).
+
+ double log_m_x;
+
+ double v = fputil::multiply_add<double>(mant_d, R[f], -1.0);
- double log2p1_d_over_f =
- v * fputil::polyeval(v, 0x1.715476p+0, -0x1.71771ap-1, 0x1.ecb38ep-2);
+ double p_v = fputil::polyeval(v, LOG_COEFFS[0], LOG_COEFFS[1], LOG_COEFFS[2],
+ LOG_COEFFS[3], LOG_COEFFS[4], LOG_COEFFS[5]);
- // log2(1.mant) = log2(f) + log2(1 + v)
- double log2_1_mant = LOG2F_F[f] + log2p1_d_over_f;
+ // log(1+v) = v + v^2 * P(v)
+ double logp1_v = fputil::multiply_add<double>(v * v, p_v, v);
- // Complete log2(x) = e_x + log2(m_x)
- double log2_x = static_cast<double>(m) + log2_1_mant;
+ // log(m_x) = log(1+v) - log(r).
+ log_m_x = logp1_v + LOG_R[f];
+
+ // Complete log(x) = m * log(2) + log(m_x).
+ double log_x =
+ fputil::multiply_add<double>(static_cast<double>(m), LOG_2_HI, log_m_x);
+ // Convert to log2(x): log2(x) = log(x) / log(2)
+ double log2_x = log_x / LOG_2_HI;
// 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 < -24.0) {
+ // Check for underflow. Half-precision min normal exponent is -14 ,
+ // but the smallest subnormal is 2^-24.
+ if (LIBC_UNLIKELY(z < -25.0)) {
fputil::raise_except_if_required(FE_UNDERFLOW);
- return fputil::cast<float16>(0.0f);
+ // Determine sign of underflowed result
+ return result_sign ? FPBits::zero(Sign::NEG).get_val()
+ : FPBits::zero(Sign::POS).get_val();
+ }
+
+ // Check for overflow. The max value of float16 is ~2^16, so z > 16.0 will
+ // overflow.
+ if (LIBC_UNLIKELY(z > 16.0)) {
+ fputil::raise_except_if_required(FE_OVERFLOW);
+
+ float16 max_finite = FPBits::max_normal().get_val();
+ float16 neg_max_finite = FPBits::max_normal(Sign::NEG).get_val();
+
+ int round_mode = fputil::get_round();
+
+ if (result_sign) {
+ // Negative result overflows
+ // For TOWARDZERO or DOWNWARD rounding, the result is the most negative
+ // finite value.
+ if (round_mode == FE_TOWARDZERO || round_mode == FE_DOWNWARD) {
+ return neg_max_finite;
+ }
+ // For other rounding modes, the result is -Infinity.
+ return FPBits::inf(Sign::NEG).get_val();
+ } else {
+ // Positive result overflows
+ // For TOWARDZERO or DOWNWARD rounding, the result is the max finite
+ // value.
+ if (round_mode == FE_TOWARDZERO || round_mode == FE_DOWNWARD) {
+ return max_finite;
+ }
+ // For other rounding modes, the result is +Infinity.
+ return FPBits::inf(Sign::POS).get_val();
+ }
}
double n = fputil::nearest_integer(z);
@@ -278,12 +351,7 @@ LLVM_LIBC_FUNCTION(float16, powf16, (float16 x, float16 y)) {
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);
+ float16 result = fputil::cast<float16>((pow2_n * exp2_r));
if (result_sign) {
FPBits result_bits(result);
>From aed1d0e86bb8bbd60586edc1251974abb3332e9d Mon Sep 17 00:00:00 2001
From: anonmiraj <nabilmalek48 at gmail.com>
Date: Sat, 11 Oct 2025 13:13:53 +0300
Subject: [PATCH 9/9] fix for log_r table
---
libc/src/math/generic/common_constants.cpp | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index 2a15df243b5a4..d3be201e575f3 100644
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -133,7 +133,7 @@ const double LOG_R[128] = {
0x1.4b6fd6f970c1fp-1, 0x1.4f45a835a4e19p-1, 0x1.4f45a835a4e19p-1,
0x1.5322e26867857p-1, 0x1.5322e26867857p-1, 0x1.5707a26bb8c66p-1,
0x1.5707a26bb8c66p-1, 0x1.5af405c3649ep-1, 0x1.5af405c3649ep-1,
- 0x1.5ee82aa24192p-1, 0x0.000000000000p0};
+ 0x1.5ee82aa24192p-1, 0x1.62e42fefa38p-1};
const double LOG2_R[128] = {
0x0.0000000000000p+0, 0x1.72c7ba20f7327p-7, 0x1.743ee861f3556p-6,
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