[libc][math] Refactor expf16 implementation to header-only in src/__support/math folder.

libc/shared/math.h

@@ -12,5 +12,6 @@
 #include "libc_common.h"
 
 #include "math/expf.h"
+#include "math/expf16.h"
 
 #endif // LLVM_LIBC_SHARED_MATH_H

libc/shared/math/expf16.h

@@ -0,0 +1,29 @@
+//===-- Shared expf16 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_EXPF16_H
+#define LLVM_LIBC_SHARED_MATH_EXPF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+#include "shared/libc_common.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/math/expf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::expf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_EXPF16_H

libc/src/__support/math/CMakeLists.txt

@@ -22,3 +22,36 @@ add_header_library(
     libc.src.__support.macros.config
     libc.src.__support.macros.optimization
 )
+
+add_header_library(
+  expf16_utils
+  HDRS
+    expf16_utils.h
+  DEPENDS
+    libc.src.__support.CPP.array
+    libc.src.__support.FPUtil.nearest_integer
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.macros.attributes
+    libc.include.llvm-libc-macros.float16_macros
+)
+
+add_header_library(
+  expf16
+  HDRS
+    expf16.h
+  DEPENDS
+    .expf16_utils
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.CPP.array
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.except_value_utils
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.nearest_integer
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.rounding_mode
+    libc.src.__support.macros.optimization
+    libc.include.llvm-libc-macros.float16_macros
+)

libc/src/__support/math/expf16.h

@@ -0,0 +1,141 @@
+//===-- Implementation header for expf16 ------------------------*- 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_EXPF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_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/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/except_value_utils.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+
+#include "expf16_utils.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr float16 expf16(float16 x) {
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  constexpr fputil::ExceptValues<float16, 2> EXPF16_EXCEPTS_LO = {{
+      // (input, RZ output, RU offset, RD offset, RN offset)
+      // x = 0x1.de4p-8, expf16(x) = 0x1.01cp+0 (RZ)
+      {0x1f79U, 0x3c07U, 1U, 0U, 0U},
+      // x = 0x1.73cp-6, expf16(x) = 0x1.05cp+0 (RZ)
+      {0x25cfU, 0x3c17U, 1U, 0U, 0U},
+  }};
+
+  constexpr fputil::ExceptValues<float16, 3> EXPF16_EXCEPTS_HI = {{
+      // (input, RZ output, RU offset, RD offset, RN offset)
+      // x = 0x1.c34p+0, expf16(x) = 0x1.74cp+2 (RZ)
+      {0x3f0dU, 0x45d3U, 1U, 0U, 1U},
+      // x = -0x1.488p-5, expf16(x) = 0x1.ebcp-1 (RZ)
+      {0xa922U, 0x3bafU, 1U, 0U, 0U},
+      // x = -0x1.55p-5, expf16(x) = 0x1.ebp-1 (RZ)
+      {0xa954U, 0x3bacU, 1U, 0U, 0U},
+  }};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+  using FPBits = fputil::FPBits<float16>;
+  FPBits x_bits(x);
+
+  uint16_t x_u = x_bits.uintval();
+  uint16_t x_abs = x_u & 0x7fffU;
+
+  // When 0 < |x| <= 2^(-5), or |x| >= 12, or x is NaN.
+  if (LIBC_UNLIKELY(x_abs <= 0x2800U || x_abs >= 0x4a00U)) {
+    // exp(NaN) = NaN
+    if (x_bits.is_nan()) {
+      if (x_bits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+
+      return x;
+    }
+
+    // When x >= 12.
+    if (x_bits.is_pos() && x_abs >= 0x4a00U) {
+      // exp(+inf) = +inf
+      if (x_bits.is_inf())
+        return FPBits::inf().get_val();
+
+      switch (fputil::quick_get_round()) {
+      case FE_TONEAREST:
+      case FE_UPWARD:
+        fputil::set_errno_if_required(ERANGE);
+        fputil::raise_except_if_required(FE_OVERFLOW);
+        return FPBits::inf().get_val();
+      default:
+        return FPBits::max_normal().get_val();
+      }
+    }
+
+    // When x <= -18.
+    if (x_u >= 0xcc80U) {
+      // exp(-inf) = +0
+      if (x_bits.is_inf())
+        return FPBits::zero().get_val();
+
+      fputil::set_errno_if_required(ERANGE);
+      fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
+
+      switch (fputil::quick_get_round()) {
+      case FE_UPWARD:
+        return FPBits::min_subnormal().get_val();
+      default:
+        return FPBits::zero().get_val();
+      }
+    }
+
+    // When 0 < |x| <= 2^(-5).
+    if (x_abs <= 0x2800U && !x_bits.is_zero()) {
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+      if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+        return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+      float xf = x;
+      // Degree-3 minimax polynomial generated by Sollya with the following
+      // commands:
+      //   > display = hexadecimal;
+      //   > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
+      //   > 1 + x * P;
+      return fputil::cast<float16>(
+          fputil::polyeval(xf, 0x1p+0f, 0x1p+0f, 0x1.0004p-1f, 0x1.555778p-3f));
+    }
+  }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+  if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+  // exp(x) = exp(hi + mid) * exp(lo)
+  auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);
+  return fputil::cast<float16>(exp_hi_mid * exp_lo);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H

libc/src/__support/math/expf16_utils.h

@@ -0,0 +1,89 @@
+//===-- Common utils for expf16 functions -----------------------*- 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_EXPF16_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_UTILS_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/CPP/array.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Generated by Sollya with the following commands:
+//   > display = hexadecimal;
+//   > for i from -18 to 12 do print(round(exp(i), SG, RN));
+static constexpr cpp::array<float, 31> EXP_HI = {
+    0x1.05a628p-26f, 0x1.639e32p-25f, 0x1.e355bcp-24f, 0x1.4875cap-22f,
+    0x1.be6c7p-21f,  0x1.2f6054p-19f, 0x1.9c54c4p-18f, 0x1.183542p-16f,
+    0x1.7cd79cp-15f, 0x1.02cf22p-13f, 0x1.5fc21p-12f,  0x1.de16bap-11f,
+    0x1.44e52p-9f,   0x1.b993fep-8f,  0x1.2c155cp-6f,  0x1.97db0cp-5f,
+    0x1.152aaap-3f,  0x1.78b564p-2f,  0x1p+0f,         0x1.5bf0a8p+1f,
+    0x1.d8e64cp+2f,  0x1.415e5cp+4f,  0x1.b4c902p+5f,  0x1.28d38ap+7f,
+    0x1.936dc6p+8f,  0x1.122886p+10f, 0x1.749ea8p+11f, 0x1.fa7158p+12f,
+    0x1.5829dcp+14f, 0x1.d3c448p+15f, 0x1.3de166p+17f,
+};
+
+// Generated by Sollya with the following commands:
+//   > display = hexadecimal;
+//   > for i from 0 to 7 do print(round(exp(i * 2^-3), SG, RN));
+static constexpr cpp::array<float, 8> EXP_MID = {
+    0x1p+0f,        0x1.221604p+0f, 0x1.48b5e4p+0f, 0x1.747a52p+0f,
+    0x1.a61298p+0f, 0x1.de455ep+0f, 0x1.0ef9dcp+1f, 0x1.330e58p+1f,
+};
+
+struct ExpRangeReduction {
+  float exp_hi_mid;
+  float exp_lo;
+};
+
+static constexpr ExpRangeReduction exp_range_reduction(float16 x) {
+  // For -18 < x < 12, to compute exp(x), we perform the following range
+  // reduction: find hi, mid, lo, such that:
+  //   x = hi + mid + lo, in which
+  //     hi is an integer,
+  //     mid * 2^3 is an integer,
+  //     -2^(-4) <= lo < 2^(-4).
+  // In particular,
+  //   hi + mid = round(x * 2^3) * 2^(-3).
+  // Then,
+  //   exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
+  // We store exp(hi) and exp(mid) in the lookup tables EXP_HI and EXP_MID
+  // respectively.  exp(lo) is computed using a degree-3 minimax polynomial
+  // generated by Sollya.
+
+  float xf = x;
+  float kf = fputil::nearest_integer(xf * 0x1.0p+3f);
+  int x_hi_mid = static_cast<int>(kf);
+  int x_hi = x_hi_mid >> 3;
+  int x_mid = x_hi_mid & 0x7;
+  // lo = x - (hi + mid) = round(x * 2^3) * (-2^(-3)) + x
+  float lo = fputil::multiply_add(kf, -0x1.0p-3f, xf);
+
+  float exp_hi = EXP_HI[x_hi + 18];
+  float exp_mid = EXP_MID[x_mid];
+  // Degree-3 minimax polynomial generated by Sollya with the following
+  // commands:
+  //   > display = hexadecimal;
+  //   > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-4, 2^-4]);
+  //   > 1 + x * P;
+  float exp_lo =
+      fputil::polyeval(lo, 0x1p+0f, 0x1p+0f, 0x1.001p-1f, 0x1.555ddep-3f);
+  return {exp_hi * exp_mid, exp_lo};
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_UTILS_H

libc/src/math/generic/CMakeLists.txt

@@ -1332,19 +1332,8 @@ add_entrypoint_object(
   HDRS
     ../expf16.h
   DEPENDS
-    .expxf16
-    libc.hdr.errno_macros
-    libc.hdr.fenv_macros
-    libc.src.__support.CPP.array
-    libc.src.__support.FPUtil.cast
-    libc.src.__support.FPUtil.except_value_utils
-    libc.src.__support.FPUtil.fenv_impl
-    libc.src.__support.FPUtil.fp_bits
-    libc.src.__support.FPUtil.multiply_add
-    libc.src.__support.FPUtil.nearest_integer
-    libc.src.__support.FPUtil.polyeval
-    libc.src.__support.FPUtil.rounding_mode
-    libc.src.__support.macros.optimization
+    libc.src.__support.math.expf16
+    libc.src.errno.errno
 )
 
 add_entrypoint_object(
@@ -5075,11 +5064,10 @@ add_header_library(
   HDRS
     expxf16.h
   DEPENDS
-    libc.src.__support.CPP.array
     libc.src.__support.FPUtil.cast
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.multiply_add
     libc.src.__support.FPUtil.nearest_integer
-    libc.src.__support.FPUtil.polyeval
     libc.src.__support.macros.attributes
+    libc.src.__support.math.expf16_utils
 )