[libc][math][c23] Add exp2m1f16 C23 math function

libc/config/linux/x86_64/entrypoints.txt

@@ -611,6 +611,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.copysignf16
     libc.src.math.exp10f16
     libc.src.math.exp2f16
+    libc.src.math.exp2m1f16
     libc.src.math.expf16
     libc.src.math.expm1f16
     libc.src.math.f16add

libc/docs/math/index.rst

@@ -296,7 +296,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | exp2      | |check|          | |check|         |                        | |check|              |                        | 7.12.6.4               | F.10.3.4                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| exp2m1    | |check|          |                 |                        |                      |                        | 7.12.6.5               | F.10.3.5                   |
+| exp2m1    | |check|          |                 |                        | |check|              |                        | 7.12.6.5               | F.10.3.5                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | expm1     | |check|          | |check|         |                        | |check|              |                        | 7.12.6.6               | F.10.3.6                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/newhdrgen/yaml/math.yaml

@@ -284,6 +284,13 @@ functions:
     return_type: float
     arguments:
       - type: float
+  - name: exp2m1f16
+    standards:
+      - stdc
+    return_type: _Float16
+    arguments:
+      - type: _Float16
+    guard: LIBC_TYPES_HAS_FLOAT16
   - name: expf
     standards:
       - stdc

libc/spec/stdc.td

@@ -682,6 +682,7 @@ def StdC : StandardSpec<"stdc"> {
           GuardedFunctionSpec<"exp2f16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
 
           FunctionSpec<"exp2m1f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+          GuardedFunctionSpec<"exp2m1f16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
 
           FunctionSpec<"expm1", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"expm1f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

libc/src/math/CMakeLists.txt

@@ -121,6 +121,7 @@ add_math_entrypoint_object(exp2f)
 add_math_entrypoint_object(exp2f16)
 
 add_math_entrypoint_object(exp2m1f)
+add_math_entrypoint_object(exp2m1f16)
 
 add_math_entrypoint_object(exp10)
 add_math_entrypoint_object(exp10f)

libc/src/math/exp2m1f16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for exp2m1f16 ---------------------*- 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_EXP2M1F16_H
+#define LLVM_LIBC_SRC_MATH_EXP2M1F16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 exp2m1f16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_EXP2M1F16_H

libc/src/math/generic/CMakeLists.txt

@@ -1500,14 +1500,10 @@ add_entrypoint_object(
     .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
   COMPILE_OPTIONS
@@ -1535,6 +1531,29 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  exp2m1f16
+  SRCS
+    exp2m1f16.cpp
+  HDRS
+    ../exp2m1f16.h
+  DEPENDS
+    .expxf16
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.common
+    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.polyeval
+    libc.src.__support.FPUtil.rounding_mode
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.cpu_features
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   exp10
   SRCS

libc/src/math/generic/exp2f16.cpp

@@ -10,14 +10,10 @@
 #include "expxf16.h"
 #include "hdr/errno_macros.h"
 #include "hdr/fenv_macros.h"
-#include "src/__support/CPP/array.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/multiply_add.h"
-#include "src/__support/FPUtil/nearest_integer.h"
 #include "src/__support/FPUtil/rounding_mode.h"
 #include "src/__support/common.h"
 #include "src/__support/macros/config.h"
@@ -89,39 +85,8 @@ LLVM_LIBC_FUNCTION(float16, exp2f16, (float16 x)) {
   if (auto r = EXP2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
     return r.value();
 
-  // For -25 < x < 16, to compute 2^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,
-  //   2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
-  // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
-  // by adding hi to the exponent field of 2^mid.  2^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);
-
-  uint32_t exp2_hi_mid_bits =
-      EXP2_MID_BITS[x_mid] +
-      static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
-  float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
-  // Degree-3 minimax polynomial generated by Sollya with the following
-  // commands:
-  //   > display = hexadecimal;
-  //   > P = fpminimax((2^x - 1)/x, 2, [|SG...|], [-2^-4, 2^-4]);
-  //   > 1 + x * P;
-  float exp2_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.62e43p-1f, 0x1.ec0aa6p-3f,
-                                   0x1.c6b4a6p-5f);
+  // exp2(x) = exp2(hi + mid) * exp2(lo)
+  auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x);
   return fputil::cast<float16>(exp2_hi_mid * exp2_lo);
 }
 

libc/src/math/generic/exp2m1f16.cpp

@@ -0,0 +1,163 @@
+//===-- Half-precision 2^x - 1 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/exp2m1f16.h"
+#include "expxf16.h"
+#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/multiply_add.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 "src/__support/macros/properties/cpu_features.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+static constexpr fputil::ExceptValues<float16, 6> EXP2M1F16_EXCEPTS_LO = {{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    // x = 0x1.cf4p-13, exp2m1f16(x) = 0x1.41p-13 (RZ)
+    {0x0b3dU, 0x0904U, 1U, 0U, 1U},
+    // x = 0x1.4fcp-12, exp2m1f16(x) = 0x1.d14p-13 (RZ)
+    {0x0d3fU, 0x0b45U, 1U, 0U, 1U},
+    // x = 0x1.63p-11, exp2m1f16(x) = 0x1.ec4p-12 (RZ)
+    {0x118cU, 0x0fb1U, 1U, 0U, 0U},
+    // x = 0x1.6fp-7, exp2m1f16(x) = 0x1.fe8p-8 (RZ)
+    {0x21bcU, 0x1ffaU, 1U, 0U, 1U},
+    // x = -0x1.c6p-10, exp2m1f16(x) = -0x1.3a8p-10 (RZ)
+    {0x9718U, 0x94eaU, 0U, 1U, 0U},
+    // x = -0x1.cfcp-10, exp2m1f16(x) = -0x1.414p-10 (RZ)
+    {0x973fU, 0x9505U, 0U, 1U, 0U},
+}};
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 6;
+#else
+static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 7;
+#endif
+
+static constexpr fputil::ExceptValues<float16, N_EXP2M1F16_EXCEPTS_HI>
+    EXP2M1F16_EXCEPTS_HI = {{
+        // (input, RZ output, RU offset, RD offset, RN offset)
+        // x = 0x1.e58p-3, exp2m1f16(x) = 0x1.6dcp-3 (RZ)
+        {0x3396U, 0x31b7U, 1U, 0U, 0U},
+#ifndef LIBC_TARGET_CPU_HAS_FMA
+        // x = 0x1.2e8p-2, exp2m1f16(x) = 0x1.d14p-3 (RZ)
+        {0x34baU, 0x3345U, 1U, 0U, 0U},
+#endif
+        // x = 0x1.ad8p-2, exp2m1f16(x) = 0x1.598p-2 (RZ)
+        {0x36b6U, 0x3566U, 1U, 0U, 0U},
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+        // x = 0x1.edcp-2, exp2m1f16(x) = 0x1.964p-2 (RZ)
+        {0x37b7U, 0x3659U, 1U, 0U, 1U},
+#endif
+        // x = -0x1.804p-3, exp2m1f16(x) = -0x1.f34p-4 (RZ)
+        {0xb201U, 0xafcdU, 0U, 1U, 1U},
+        // x = -0x1.f3p-3, exp2m1f16(x) = -0x1.3e4p-3 (RZ)
+        {0xb3ccU, 0xb0f9U, 0U, 1U, 0U},
+        // x = -0x1.294p-1, exp2m1f16(x) = -0x1.53p-2 (RZ)
+        {0xb8a5U, 0xb54cU, 0U, 1U, 1U},
+#ifndef LIBC_TARGET_CPU_HAS_FMA
+        // x = -0x1.a34p-1, exp2m1f16(x) = -0x1.bb4p-2 (RZ)
+        {0xba8dU, 0xb6edU, 0U, 1U, 1U},
+#endif
+    }};
+
+LLVM_LIBC_FUNCTION(float16, exp2m1f16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits x_bits(x);
+
+  uint16_t x_u = x_bits.uintval();
+  uint16_t x_abs = x_u & 0x7fffU;
+
+  // When |x| <= 2^(-3), or |x| >= 11, or x is NaN.
+  if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x4980U)) {
+    // exp2m1(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 >= 16.
+    if (x_u >= 0x4c00 && x_bits.is_pos()) {
+      // exp2m1(+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 | FE_INEXACT);
+        return FPBits::inf().get_val();
+      default:
+        return FPBits::max_normal().get_val();
+      }
+    }
+
+    // When x < -11.
+    if (x_u > 0xc980U) {
+      // exp2m1(-inf) = -1
+      if (x_bits.is_inf())
+        return FPBits::one(Sign::NEG).get_val();
+
+      // When -12 < x < -11, round(2^x - 1, HP, RN) = -0x1.ffcp-1.
+      if (x_u < 0xca00U) {
+        return fputil::round_result_slightly_down(
+            fputil::cast<float16>(-0x1.ffcp-1));
+      }
+
+      // When x <= -12, round(2^x - 1, HP, RN) = -1.
+      switch (fputil::quick_get_round()) {
+      case FE_TONEAREST:
+      case FE_DOWNWARD:
+        return FPBits::one(Sign::NEG).get_val();
+      default:
+        return -0x1.ffcp-1;
+      }
+    }
+
+    // When |x| <= 2^(-3).
+    if (x_abs <= 0x3000U) {
+      if (auto r = EXP2M1F16_EXCEPTS_LO.lookup(x_u);
+          LIBC_UNLIKELY(r.has_value()))
+        return r.value();
+
+      float xf = x;
+      // Degree-5 minimax polynomial generated by Sollya with the following
+      // commands:
+      //   > display = hexadecimal;
+      //   > P = fpminimax((2^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]);
+      //   > x * P;
+      return fputil::cast<float16>(
+          xf * fputil::polyeval(xf, 0x1.62e43p-1f, 0x1.ebfbdep-3f,
+                                0x1.c6af88p-5f, 0x1.3b45d6p-7f,
+                                0x1.641e7cp-10f));
+    }
+  }
+
+  if (auto r = EXP2M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  // exp2(x) = exp2(hi + mid) * exp2(lo)
+  auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x);
+  // exp2m1(x) = exp2(hi + mid) * exp2(lo) - 1
+  return fputil::cast<float16>(
+      fputil::multiply_add(exp2_hi_mid, exp2_lo, -1.0f));
+}
+
+} // namespace LIBC_NAMESPACE_DECL

libc/src/math/generic/expxf16.h

@@ -10,6 +10,7 @@
 #define LLVM_LIBC_SRC_MATH_GENERIC_EXPXF16_H
 
 #include "src/__support/CPP/array.h"
+#include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/FPUtil/PolyEval.h"
 #include "src/__support/FPUtil/multiply_add.h"
 #include "src/__support/FPUtil/nearest_integer.h"
@@ -89,6 +90,43 @@ constexpr cpp::array<uint32_t, 8> EXP2_MID_BITS = {
     0x3fb5'04f3U, 0x3fc5'672aU, 0x3fd7'44fdU, 0x3fea'c0c7U,
 };
 
+LIBC_INLINE ExpRangeReduction exp2_range_reduction(float16 x) {
+  // For -25 < x < 16, to compute 2^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,
+  //   2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
+  // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
+  // by adding hi to the exponent field of 2^mid.  2^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);
+
+  uint32_t exp2_hi_mid_bits =
+      EXP2_MID_BITS[x_mid] +
+      static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
+  float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
+  // Degree-3 minimax polynomial generated by Sollya with the following
+  // commands:
+  //   > display = hexadecimal;
+  //   > P = fpminimax((2^x - 1)/x, 2, [|SG...|], [-2^-4, 2^-4]);
+  //   > 1 + x * P;
+  float exp2_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.62e43p-1f, 0x1.ec0aa6p-3f,
+                                   0x1.c6b4a6p-5f);
+  return {exp2_hi_mid, exp2_lo};
+}
+
 } // namespace LIBC_NAMESPACE_DECL
 
 #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPXF16_H