[libc][math][c23] Add expm1f16 C23 math function

libc/config/linux/x86_64/entrypoints.txt

@@ -584,6 +584,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.exp10f16
     libc.src.math.exp2f16
     libc.src.math.expf16
+    libc.src.math.expm1f16
     libc.src.math.f16add
     libc.src.math.f16addf
     libc.src.math.f16addl

libc/docs/math/index.rst

@@ -294,7 +294,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | exp2m1    | |check|          |                 |                        |                      |                        | 7.12.6.5               | F.10.3.5                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| expm1     | |check|          | |check|         |                        |                      |                        | 7.12.6.6               | F.10.3.6                   |
+| expm1     | |check|          | |check|         |                        | |check|              |                        | 7.12.6.6               | F.10.3.6                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | fma       | |check|          | |check|         |                        |                      |                        | 7.12.13.1              | F.10.10.1                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/spec/stdc.td

@@ -594,6 +594,7 @@ def StdC : StandardSpec<"stdc"> {
 
           FunctionSpec<"expm1", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"expm1f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+          GuardedFunctionSpec<"expm1f16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
 
           FunctionSpec<"exp10", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"exp10f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

libc/src/math/CMakeLists.txt

@@ -120,6 +120,7 @@ add_math_entrypoint_object(exp10f16)
 
 add_math_entrypoint_object(expm1)
 add_math_entrypoint_object(expm1f)
+add_math_entrypoint_object(expm1f16)
 
 add_math_entrypoint_object(f16add)
 add_math_entrypoint_object(f16addf)

libc/src/math/expm1f16.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for expm1f16 ----------------------*- 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_EXPM1F16_H
+#define LLVM_LIBC_SRC_MATH_EXPM1F16_H
+
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/properties/types.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float16 expm1f16(float16 x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_EXPM1F16_H

libc/src/math/generic/CMakeLists.txt

@@ -1322,14 +1322,12 @@ 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.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
@@ -1571,6 +1569,27 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  expm1f16
+  SRCS
+    expm1f16.cpp
+  HDRS
+    ../expm1f16.h
+  DEPENDS
+    .expxf16
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    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
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   powf
   SRCS
@@ -4878,4 +4897,7 @@ add_header_library(
     expxf16.h
   DEPENDS
     libc.src.__support.CPP.array
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.nearest_integer
+    libc.src.__support.FPUtil.polyeval
 )

libc/src/math/generic/expf16.cpp

@@ -7,15 +7,13 @@
 //===----------------------------------------------------------------------===//
 
 #include "src/math/expf16.h"
+#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/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"
@@ -41,28 +39,6 @@ static constexpr fputil::ExceptValues<float16, 3> EXPF16_EXCEPTS_HI = {{
     {0xa954U, 0x3bacU, 1U, 0U, 0U},
 }};
 
-// 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,
-};
-
 LLVM_LIBC_FUNCTION(float16, expf16, (float16 x)) {
   using FPBits = fputil::FPBits<float16>;
   FPBits x_bits(x);
@@ -135,38 +111,9 @@ LLVM_LIBC_FUNCTION(float16, expf16, (float16 x)) {
   if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
     return r.value();
 
-  // 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 static_cast<float16>(exp_hi * exp_mid * exp_lo);
+  // exp(x) = exp(hi + mid) * exp(lo)
+  auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);
+  return static_cast<float16>(exp_hi_mid * exp_lo);
 }
 
 } // namespace LIBC_NAMESPACE_DECL

libc/src/math/generic/expm1f16.cpp

@@ -0,0 +1,132 @@
+//===-- Half-precision e^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/expm1f16.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/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"
+
+namespace LIBC_NAMESPACE_DECL {
+
+static constexpr fputil::ExceptValues<float16, 1> EXPM1F16_EXCEPTS_LO = {{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    // x = 0x1.564p-5, expm1f16(x) = 0x1.5d4p-5 (RZ)
+    {0x2959U, 0x2975U, 1U, 0U, 1U},
+}};
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 2;
+#else
+static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 3;
+#endif
+
+static constexpr fputil::ExceptValues<float16, N_EXPM1F16_EXCEPTS_HI>
+    EXPM1F16_EXCEPTS_HI = {{
+        // (input, RZ output, RU offset, RD offset, RN offset)
+        // x = 0x1.c34p+0, expm1f16(x) = 0x1.34cp+2 (RZ)
+        {0x3f0dU, 0x44d3U, 1U, 0U, 1U},
+        // x = -0x1.e28p-3, expm1f16(x) = -0x1.adcp-3 (RZ)
+        {0xb38aU, 0xb2b7U, 0U, 1U, 1U},
+#ifndef LIBC_TARGET_CPU_HAS_FMA
+        // x = 0x1.a08p-3, exp10m1f(x) = 0x1.cdcp-3 (RZ)
+        {0x3282U, 0x3337U, 1U, 0U, 0U},
+#endif
+    }};
+
+LLVM_LIBC_FUNCTION(float16, expm1f16, (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 * log(2), or x is NaN.
+  if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x47a0U)) {
+    // expm1(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;
+    }
+
+    // expm1(+/-0) = +/-0
+    if (x_abs == 0)
+      return x;
+
+    // When x >= 16 * log(2).
+    if (x_bits.is_pos() && x_abs >= 0x498cU) {
+      // expm1(+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 * log(2).
+    if (x_u >= 0xc7a0U) {
+      // expm1(-inf) = -1
+      if (x_bits.is_inf())
+        return FPBits::one(Sign::NEG).get_val();
+
+      // When x > -0x1.0ap+3, round(expm1(x), HP, RN) = -1.
+      if (x_u > 0xc828U)
+        return fputil::round_result_slightly_up(
+            FPBits::one(Sign::NEG).get_val());
+      // When x <= -0x1.0ap+3, round(expm1(x), HP, RN) = -0x1.ffcp-1.
+      return fputil::round_result_slightly_down(
+          static_cast<float16>(-0x1.ffcp-1));
+    }
+
+    // When 0 < |x| <= 2^(-3).
+    if (x_abs <= 0x3000U && !x_bits.is_zero()) {
+      if (auto r = EXPM1F16_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(expm1(x)/x, 4, [|SG...|], [-2^-3, 2^-3]);
+      //   > x * P;
+      return static_cast<float16>(
+          xf * fputil::polyeval(xf, 0x1p+0f, 0x1.fffff8p-2f, 0x1.555556p-3f,
+                                0x1.55905ep-5f, 0x1.1124c2p-7f));
+    }
+  }
+
+  if (auto r = EXPM1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  // exp(x) = exp(hi + mid) * exp(lo)
+  auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);
+  // expm1(x) = exp(hi + mid) * exp(lo) - 1
+  return static_cast<float16>(fputil::multiply_add(exp_hi_mid, exp_lo, -1.0f));
+}
+
+} // namespace LIBC_NAMESPACE_DECL