[libc][math] Implement cbrtf function correctly rounded to all rounding modes. (#97936)

lntue · web-flow · commit c9ee6b1977e7 · 2024-07-08T10:02:12.000-04:00
Fixes #92874 Algorithm: Let `x = (-1)^s * 2^e * (1 + m)`. - Step 1: Range reduction: reduce the exponent with: ``` y = cbrt(x) = (-1)^s * 2^(floor(e/3)) * 2^((e % 3)/3) * (1 + m)^(1/3) ``` - Step 2: Use the first 4 bit fractional bits of `m` to look up for a degree-7 polynomial approximation to: ``` (1 + m)^(1/3) ~ 1 + m * P(m). ``` - Step 3: Perform the multiplication: ``` 2^((e % 3)/3) * (1 + m)^(1/3). ``` - Step 4: Check for exact cases to prevent rounding and clear `FE_INEXACT` floating point exception. - Step 5: Combine with the exponent and sign before converting down to `float` and return.
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
@@ -123,6 +123,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
+    libc.src.math.cbrtf
     libc.src.math.copysign
     libc.src.math.copysignf
     libc.src.math.copysignl
diff --git a/libc/config/gpu/entrypoints.txt b/libc/config/gpu/entrypoints.txt
@@ -242,6 +242,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.atanf
     libc.src.math.atanh
     libc.src.math.atanhf
+    libc.src.math.cbrtf
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.copysign
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
@@ -345,6 +345,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
+    libc.src.math.cbrtf
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
@@ -216,6 +216,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
+    libc.src.math.cbrtf
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
@@ -347,6 +347,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
+    libc.src.math.cbrtf
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
@@ -370,6 +370,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.canonicalize
     libc.src.math.canonicalizef
     libc.src.math.canonicalizel
+    libc.src.math.cbrtf
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
@@ -121,6 +121,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.atan2f
     libc.src.math.atanf
     libc.src.math.atanhf
+    libc.src.math.cbrtf
     libc.src.math.copysign
     libc.src.math.copysignf
     libc.src.math.copysignl
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
@@ -266,7 +266,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | atanpi    |                  |                 |                        |                      |                        | 7.12.4.10              | F.10.1.10                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| cbrt      |                  |                 |                        |                      |                        | 7.12.7.1               | F.10.4.1                   |
+| cbrt      | |check|          |                 |                        |                      |                        | 7.12.7.1               | F.10.4.1                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | compoundn |                  |                 |                        |                      |                        | 7.12.7.2               | F.10.4.2                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
@@ -382,6 +382,8 @@ def StdC : StandardSpec<"stdc"> {
       ],
       [], // Enumerations
       [
+          FunctionSpec<"cbrtf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+
           FunctionSpec<"copysign", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
           FunctionSpec<"copysignf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
           FunctionSpec<"copysignl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
diff --git a/libc/src/__support/FPUtil/CMakeLists.txt b/libc/src/__support/FPUtil/CMakeLists.txt
@@ -155,6 +155,8 @@ add_header_library(
     multiply_add.h
   DEPENDS
     libc.src.__support.common
+  FLAGS
+    FMA_OPT
 )
 
 add_header_library(
diff --git a/libc/src/__support/FPUtil/FEnvImpl.h b/libc/src/__support/FPUtil/FEnvImpl.h
@@ -67,6 +67,12 @@ LIBC_INLINE int set_env(const fenv_t *) { return 0; }
 
 namespace LIBC_NAMESPACE::fputil {
 
+LIBC_INLINE int clear_except_if_required(int excepts) {
+  if (math_errhandling & MATH_ERREXCEPT)
+    return clear_except(excepts);
+  return 0;
+}
+
 LIBC_INLINE int set_except_if_required(int excepts) {
   if (math_errhandling & MATH_ERREXCEPT)
     return set_except(excepts);
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
@@ -65,6 +65,8 @@ add_math_entrypoint_object(canonicalizel)
 add_math_entrypoint_object(canonicalizef16)
 add_math_entrypoint_object(canonicalizef128)
 
+add_math_entrypoint_object(cbrtf)
+
 add_math_entrypoint_object(ceil)
 add_math_entrypoint_object(ceilf)
 add_math_entrypoint_object(ceill)
diff --git a/libc/src/math/cbrtf.h b/libc/src/math/cbrtf.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for cbrtf -------------------------*- 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_CBRTF_H
+#define LLVM_LIBC_SRC_MATH_CBRTF_H
+
+namespace LIBC_NAMESPACE {
+
+float cbrtf(float x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_CBRTF_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
@@ -4092,3 +4092,19 @@ add_entrypoint_object(
   COMPILE_OPTIONS
     -O3
 )
+
+add_entrypoint_object(
+  cbrtf
+  SRCS
+    cbrtf.cpp
+  HDRS
+    ../cbrtf.h
+  COMPILE_OPTIONS
+    -O3
+  DEPENDS
+    libc.hdr.fenv_macros
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.macros.optimization
+)
diff --git a/libc/src/math/generic/cbrtf.cpp b/libc/src/math/generic/cbrtf.cpp
@@ -0,0 +1,157 @@
+//===-- Implementation of cbrtf 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/cbrtf.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE {
+
+namespace {
+
+// Look up table for 2^(i/3) for i = 0, 1, 2.
+constexpr double CBRT2[3] = {1.0, 0x1.428a2f98d728bp0, 0x1.965fea53d6e3dp0};
+
+// Degree-7 polynomials approximation of ((1 + x)^(1/3) - 1)/x for 0 <= x <= 1
+// generated by Sollya with:
+// > for i from 0 to 15 do {
+//     P = fpminimax((1 + x)^(1/3) - 1)/x, 6, [|D...|], [i/16, (i + 1)/16]);
+//     print("{", coeff(P, 0), ",", coeff(P, 1), ",", coeff(P, 2), ",",
+//           coeff(P, 3), ",", coeff(P, 4), ",", coeff(P, 5), ",",
+//           coeff(P, 6), "},");
+// };
+// Then (1 + x)^(1/3) ~ 1 + x * P(x).
+constexpr double COEFFS[16][7] = {
+    {0x1.55555555554ebp-2, -0x1.c71c71c678c0cp-4, 0x1.f9add2776de81p-5,
+     -0x1.511e10aa964a7p-5, 0x1.ee44165937fa2p-6, -0x1.7c5c9e059345dp-6,
+     0x1.047f75e0aff14p-6},
+    {0x1.5555554d1149ap-2, -0x1.c71c676fcb5bp-4, 0x1.f9ab127dc57ebp-5,
+     -0x1.50ea8fd1d4c15p-5, 0x1.e9d68f28ced43p-6, -0x1.60e0e1e661311p-6,
+     0x1.716eca1d6e3bcp-7},
+    {0x1.5555546377d45p-2, -0x1.c71bc1c6d49d2p-4, 0x1.f9924cc0ed24dp-5,
+     -0x1.4fea3beb53b3bp-5, 0x1.de028a9a07b1bp-6, -0x1.3b090d2233524p-6,
+     0x1.0aeca34893785p-7},
+    {0x1.55554dce9f649p-2, -0x1.c7188b34b98f8p-4, 0x1.f93e1af34af49p-5,
+     -0x1.4d9a06be75c63p-5, 0x1.cb943f4f68992p-6, -0x1.139a685a5e3c4p-6,
+     0x1.88410674c6a5dp-8},
+    {0x1.5555347d211c3p-2, -0x1.c70f2a4b1a5fap-4, 0x1.f88420e8602c3p-5,
+     -0x1.49becfa4ed3ep-5, 0x1.b475cd9013162p-6, -0x1.dcfee1dd2f8efp-7,
+     0x1.249bb51a1c498p-8},
+    {0x1.5554f01b33dbap-2, -0x1.c6facb929dbf1p-4, 0x1.f73fb7861252ep-5,
+     -0x1.4459a4a0071fap-5, 0x1.9a8df2b504fc2p-6, -0x1.9a7ce3006d06ep-7,
+     0x1.ba9230918fa2ep-9},
+    {0x1.55545c695db5fp-2, -0x1.c6d6089f20275p-4, 0x1.f556e0ea80efp-5,
+     -0x1.3d91372d083f4p-5, 0x1.7f66cff331f4p-6, -0x1.606a562491737p-7,
+     0x1.52e3e17c71069p-9},
+    {0x1.55534a879232ap-2, -0x1.c69b836998b84p-4, 0x1.f2bb26dac0e4cp-5,
+     -0x1.359eed43716d7p-5, 0x1.64218cd824fbcp-6, -0x1.2e703e2e091e8p-7,
+     0x1.0677d9af6aad4p-9},
+    {0x1.5551836bb5494p-2, -0x1.c64658c15353bp-4, 0x1.ef68517451a6ep-5,
+     -0x1.2cc20a980dceep-5, 0x1.49843e0fad93ap-6, -0x1.03c59ccb68e54p-7,
+     0x1.9ad325dc7adcbp-10},
+    {0x1.554ecacb0d035p-2, -0x1.c5d2664026ffcp-4, 0x1.eb624796ba809p-5,
+     -0x1.233803d19a535p-5, 0x1.300decb1c3c28p-6, -0x1.befe18031ec3dp-8,
+     0x1.449f5ee175c69p-10},
+    {0x1.554ae1f5ae815p-2, -0x1.c53c6b14ff6b2p-4, 0x1.e6b2d5127bb5bp-5,
+     -0x1.19387336788a3p-5, 0x1.180955a6ab255p-6, -0x1.81696703ba369p-8,
+     0x1.02cb36389bd79p-10},
+    {0x1.55458a59f356ep-2, -0x1.c4820dd631ae9p-4, 0x1.e167af818bd15p-5,
+     -0x1.0ef35f6f72e52p-5, 0x1.019c33b65e4ebp-6, -0x1.4d25bdd52d3a5p-8,
+     0x1.a008ae91f5936p-11},
+    {0x1.553e878eafee1p-2, -0x1.c3a1d0b2a3db2p-4, 0x1.db90d8ed9f89bp-5,
+     -0x1.0490e20f1ae91p-5, 0x1.d9a5d1fc42fe3p-7, -0x1.20bf8227c2abfp-8,
+     0x1.50f8174cdb6e9p-11},
+    {0x1.5535a0dedf1b1p-2, -0x1.c29afb8bd01a1p-4, 0x1.d53f6371c1e27p-5,
+     -0x1.f463209b433e2p-6, 0x1.b35222a17e44p-7, -0x1.f5efbf505e133p-9,
+     0x1.12e0e94e8586dp-11},
+    {0x1.552aa25e57bfdp-2, -0x1.c16d811e4acadp-4, 0x1.ce8489b47aa51p-5,
+     -0x1.dfde7ff758ea8p-6, 0x1.901f43aac38c8p-7, -0x1.b581d07df5ad5p-9,
+     0x1.c3726535f1fc6p-12},
+    {0x1.551d5d9b204d3p-2, -0x1.c019e328f8db1p-4, 0x1.c7710f44fc3cep-5,
+     -0x1.cbbbe25ea8ba4p-6, 0x1.6fe270088623dp-7, -0x1.7e6fc79733761p-9,
+     0x1.75077abf18d84p-12},
+};
+
+} // anonymous namespace
+
+LLVM_LIBC_FUNCTION(float, cbrtf, (float x)) {
+  using FloatBits = typename fputil::FPBits<float>;
+  using DoubleBits = typename fputil::FPBits<double>;
+
+  FloatBits x_bits(x);
+
+  uint32_t x_abs = x_bits.uintval() & 0x7fff'ffff;
+  uint32_t sign_bit = (x_bits.uintval() >> 31) << DoubleBits::EXP_LEN;
+
+  if (LIBC_UNLIKELY(x_abs == 0 || x_abs >= 0x7f80'0000)) {
+    // x is 0, Inf, or NaN.
+    return x;
+  }
+
+  double xd = static_cast<double>(x);
+  DoubleBits xd_bits(xd);
+
+  // When using biased exponent of x in double precision,
+  //   x_e = real_exponent_of_x + 1023
+  // Then:
+  //   x_e / 3 = real_exponent_of_x / 3 + 1023/3
+  //           = real_exponent_of_x / 3 + 341
+  // So to make it the correct biased exponent of x^(1/3), we add
+  //   1023 - 341 = 682
+  // to the quotient x_e / 3.
+  unsigned x_e = static_cast<unsigned>(xd_bits.get_biased_exponent());
+  unsigned out_e = (x_e / 3 + 682) | sign_bit;
+  unsigned shift_e = x_e % 3;
+
+  // Set x_m = 2^(x_e % 3) * (1.mantissa)
+  uint64_t x_m = xd_bits.get_mantissa();
+  // Use the leading 4 bits for look up table
+  unsigned idx = static_cast<unsigned>(x_m >> (DoubleBits::FRACTION_LEN - 4));
+
+  x_m |= static_cast<uint64_t>(DoubleBits::EXP_BIAS)
+         << DoubleBits::FRACTION_LEN;
+
+  double x_reduced = DoubleBits(x_m).get_val();
+  double dx = x_reduced - 1.0;
+
+  double dx_sq = dx * dx;
+  double c0 = fputil::multiply_add(dx, COEFFS[idx][0], 1.0);
+  double c1 = fputil::multiply_add(dx, COEFFS[idx][2], COEFFS[idx][1]);
+  double c2 = fputil::multiply_add(dx, COEFFS[idx][4], COEFFS[idx][3]);
+  double c3 = fputil::multiply_add(dx, COEFFS[idx][6], COEFFS[idx][5]);
+
+  double dx_4 = dx_sq * dx_sq;
+  double p0 = fputil::multiply_add(dx_sq, c1, c0);
+  double p1 = fputil::multiply_add(dx_sq, c3, c2);
+
+  double r = fputil::multiply_add(dx_4, p1, p0) * CBRT2[shift_e];
+
+  uint64_t r_m = DoubleBits(r).get_mantissa();
+  // Check if the output is exact.  To be exact, the smallest 1-bit of the
+  // output has to be at least 2^-7 or higher.  So we check the lowest 44 bits
+  // to see if they are within 2^(-52 + 3) errors from all zeros, then the
+  // result cube root is exact.
+  if (LIBC_UNLIKELY(((r_m + 8) & 0xfffffffffff) <= 16)) {
+    if ((r_m & 0xfffffffffff) <= 8)
+      r_m &= 0xffff'ffff'ffff'ffe0;
+    else
+      r_m = (r_m & 0xffff'ffff'ffff'ffe0) + 0x20;
+    fputil::clear_except_if_required(FE_INEXACT);
+  }
+  // Adjust exponent and sign.
+  uint64_t r_bits =
+      r_m | (static_cast<uint64_t>(out_e) << DoubleBits::FRACTION_LEN);
+
+  return static_cast<float>(DoubleBits(r_bits).get_val());
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
@@ -2213,6 +2213,18 @@ add_fp_unittest(
     libc.src.math.f16sqrtl
 )
 
+add_fp_unittest(
+  cbrtf_test
+  NEED_MPFR
+  SUITE
+    libc-math-unittests
+  SRCS
+    cbrtf_test.cpp
+  DEPENDS
+    libc.src.math.cbrtf
+    libc.src.__support.FPUtil.fp_bits
+)
+
 add_subdirectory(generic)
 add_subdirectory(smoke)
 
diff --git a/libc/test/src/math/cbrtf_test.cpp b/libc/test/src/math/cbrtf_test.cpp
@@ -0,0 +1,42 @@
+//===-- Unittests for cbrtf -----------------------------------------------===//
+//
+// 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/math_macros.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/math/cbrtf.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+using LlvmLibcCbrtfTest = LIBC_NAMESPACE::testing::FPTest<float>;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+TEST_F(LlvmLibcCbrtfTest, InFloatRange) {
+  constexpr uint32_t COUNT = 100'000;
+  const uint32_t STEP = FPBits(inf).uintval() / COUNT;
+  for (uint32_t i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
+    float x = FPBits(v).get_val();
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cbrt, x,
+                                   LIBC_NAMESPACE::cbrtf(x), 0.5);
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cbrt, -x,
+                                   LIBC_NAMESPACE::cbrtf(-x), 0.5);
+  }
+}
+
+TEST_F(LlvmLibcCbrtfTest, SpecialValues) {
+  constexpr float INPUTS[] = {
+      0x1.60451p2f, 0x1.31304cp1f, 0x1.d17cp2f, 0x1.bp-143f, 0x1.338cp2f,
+  };
+  for (float v : INPUTS) {
+    float x = FPBits(v).get_val();
+    mpfr::ForceRoundingMode r(mpfr::RoundingMode::Upward);
+    EXPECT_MPFR_MATCH(mpfr::Operation::Cbrt, x, LIBC_NAMESPACE::cbrtf(x), 0.5,
+                      mpfr::RoundingMode::Upward);
+  }
+}
diff --git a/libc/test/src/math/exhaustive/CMakeLists.txt b/libc/test/src/math/exhaustive/CMakeLists.txt
@@ -486,3 +486,19 @@ add_fp_unittest(
   LINK_LIBRARIES
     -lpthread
 )
+
+add_fp_unittest(
+  cbrtf_test
+  NO_RUN_POSTBUILD
+  NEED_MPFR
+  SUITE
+    libc_math_exhaustive_tests
+  SRCS
+    cbrtf_test.cpp
+  DEPENDS
+    .exhaustive_test
+    libc.src.math.cbrtf
+    libc.src.__support.FPUtil.fp_bits
+  LINK_LIBRARIES
+    -lpthread
+)
diff --git a/libc/test/src/math/exhaustive/cbrtf_test.cpp b/libc/test/src/math/exhaustive/cbrtf_test.cpp
diff --git a/libc/test/src/math/exhaustive/exhaustive_test.h b/libc/test/src/math/exhaustive/exhaustive_test.h
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
diff --git a/libc/test/src/math/smoke/cbrtf_test.cpp b/libc/test/src/math/smoke/cbrtf_test.cpp
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.h b/libc/utils/MPFRWrapper/MPFRUtils.h

Original file line number	Diff line number	Diff line change
`@@ -382,6 +382,8 @@ def StdC : StandardSpec<"stdc"> {`
`382`	`382`	`],`
`383`	`383`	`[], // Enumerations`
`384`	`384`	`[`
	`385`	`+ FunctionSpec<"cbrtf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,`
	`386`	`+`
`385`	`387`	`FunctionSpec<"copysign", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,`
`386`	`388`	`FunctionSpec<"copysignf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,`
`387`	`389`	`FunctionSpec<"copysignl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,`
Original file line number	Diff line number	Diff line change
`@@ -155,6 +155,8 @@ add_header_library(`
`155`	`155`	`multiply_add.h`
`156`	`156`	`DEPENDS`
`157`	`157`	`libc.src.__support.common`
	`158`	`+ FLAGS`
	`159`	`+ FMA_OPT`
`158`	`160`	`)`
`159`	`161`
`160`	`162`	`add_header_library(`