[libc-commits] [libc] 3b487d5 - [libc] Add implementation of hypot.

Tue Ly via libc-commits libc-commits at lists.llvm.org
Thu Dec 3 08:09:15 PST 2020


Author: Tue Ly
Date: 2020-12-03T11:08:20-05:00
New Revision: 3b487d51e2ec699c27387fc30374f0d035b2a482

URL: https://github.com/llvm/llvm-project/commit/3b487d51e2ec699c27387fc30374f0d035b2a482
DIFF: https://github.com/llvm/llvm-project/commit/3b487d51e2ec699c27387fc30374f0d035b2a482.diff

LOG: [libc] Add implementation of hypot.

Refactor src/math/hypotf.cpp and test/src/math/hypotf_test.cpp and reuse them for hypot and hypot_test

Differential Revision: https://reviews.llvm.org/D91831

Added: 
    libc/src/math/hypot.cpp
    libc/src/math/hypot.h
    libc/test/src/math/HypotTest.h
    libc/test/src/math/hypot_test.cpp
    libc/utils/FPUtil/Hypot.h

Modified: 
    libc/config/linux/aarch64/entrypoints.txt
    libc/config/linux/x86_64/entrypoints.txt
    libc/spec/stdc.td
    libc/src/math/CMakeLists.txt
    libc/src/math/hypotf.cpp
    libc/test/src/math/CMakeLists.txt
    libc/test/src/math/hypotf_test.cpp

Removed: 
    


################################################################################
diff  --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 1d8e5dd83672..3a3b050a6e06 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -68,6 +68,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.frexp
     libc.src.math.frexpf
     libc.src.math.frexpl
+    libc.src.math.hypot
     libc.src.math.hypotf
     libc.src.math.ilogb
     libc.src.math.ilogbf

diff  --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index d6d56f2e33a5..7401715058ac 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -104,6 +104,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.frexp
     libc.src.math.frexpf
     libc.src.math.frexpl
+    libc.src.math.hypot
     libc.src.math.hypotf
     libc.src.math.ilogb
     libc.src.math.ilogbf

diff  --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index 7275f1e0aacf..d40fe8df3942 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -280,6 +280,7 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"frexpf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<IntPtr>]>,
           FunctionSpec<"frexpl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<IntPtr>]>,
 
+          FunctionSpec<"hypot", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
           FunctionSpec<"hypotf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
 
           FunctionSpec<"ilogb", RetValSpec<IntType>, [ArgSpec<DoubleType>]>,

diff  --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index fd75a3b48bcb..8201d737ddb1 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -713,3 +713,15 @@ add_entrypoint_object(
   COMPILE_OPTIONS
     -O2
 )
+
+add_entrypoint_object(
+  hypot
+  SRCS
+    hypot.cpp
+  HDRS
+    hypot.h
+  DEPENDS
+    libc.utils.FPUtil.fputil
+  COMPILE_OPTIONS
+    -O2
+)

diff  --git a/libc/src/math/hypot.cpp b/libc/src/math/hypot.cpp
new file mode 100644
index 000000000000..9d59365ce3f2
--- /dev/null
+++ b/libc/src/math/hypot.cpp
@@ -0,0 +1,18 @@
+//===-- Implementation of hypot 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 "utils/FPUtil/Hypot.h"
+#include "src/__support/common.h"
+
+namespace __llvm_libc {
+
+double LLVM_LIBC_ENTRYPOINT(hypot)(double x, double y) {
+  return __llvm_libc::fputil::hypot(x, y);
+}
+
+} // namespace __llvm_libc

diff  --git a/libc/src/math/hypot.h b/libc/src/math/hypot.h
new file mode 100644
index 000000000000..6c901ee8f4c0
--- /dev/null
+++ b/libc/src/math/hypot.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for hypot -------------------------*- 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_HYPOT_H
+#define LLVM_LIBC_SRC_MATH_HYPOT_H
+
+namespace __llvm_libc {
+
+double hypot(double x, double y);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_HYPOT_H

diff  --git a/libc/src/math/hypotf.cpp b/libc/src/math/hypotf.cpp
index 10ebbb1b9ec9..ebe7e97ee184 100644
--- a/libc/src/math/hypotf.cpp
+++ b/libc/src/math/hypotf.cpp
@@ -6,217 +6,12 @@
 //
 //===----------------------------------------------------------------------===//
 #include "src/__support/common.h"
-#include "utils/FPUtil/BasicOperations.h"
-#include "utils/FPUtil/FPBits.h"
+#include "utils/FPUtil/Hypot.h"
 
 namespace __llvm_libc {
 
-using namespace fputil;
-
-uint32_t findLeadingOne(uint32_t mant, int &shift_length) {
-  shift_length = 0;
-  constexpr int nsteps = 5;
-  constexpr uint32_t bounds[nsteps] = {1 << 16, 1 << 8, 1 << 4, 1 << 2, 1 << 1};
-  constexpr int shifts[nsteps] = {16, 8, 4, 2, 1};
-  for (int i = 0; i < nsteps; ++i) {
-    if (mant >= bounds[i]) {
-      shift_length += shifts[i];
-      mant >>= shifts[i];
-    }
-  }
-  return 1U << shift_length;
-}
-
-// Correctly rounded IEEE 754 HYPOT(x, y) with round to nearest, ties to even.
-//
-// Algorithm:
-//   -  Let a = max(|x|, |y|), b = min(|x|, |y|), then we have that:
-//          a <= sqrt(a^2 + b^2) <= min(a + b, a*sqrt(2))
-//   1. So if b < eps(a)/2, then HYPOT(x, y) = a.
-//
-//   -  Moreover, the exponent part of HYPOT(x, y) is either the same or 1 more
-//      than the exponent part of a.
-//
-//   2. For the remaining cases, we will use the digit-by-digit (shift-and-add)
-//      algorithm to compute SQRT(Z):
-//
-//   -  For Y = y0.y1...yn... = SQRT(Z),
-//      let Y(n) = y0.y1...yn be the first n fractional digits of Y.
-//
-//   -  The nth scaled residual R(n) is defined to be:
-//          R(n) = 2^n * (Z - Y(n)^2)
-//
-//   -  Since Y(n) = Y(n - 1) + yn * 2^(-n), the scaled residual
-//      satisfies the following recurrence formula:
-//          R(n) = 2*R(n - 1) - yn*(2*Y(n - 1) + 2^(-n)),
-//      with the initial conditions:
-//          Y(0) = y0, and R(0) = Z - y0.
-//
-//   -  So the nth fractional digit of Y = SQRT(Z) can be decided by:
-//          yn = 1  if 2*R(n - 1) >= 2*Y(n - 1) + 2^(-n),
-//               0  otherwise.
-//
-//   3. Precision analysis:
-//
-//   -  Notice that in the decision function:
-//          2*R(n - 1) >= 2*Y(n - 1) + 2^(-n),
-//      the right hand side only uses up to the 2^(-n)-bit, and both sides are
-//      non-negative, so R(n - 1) can be truncated at the 2^(-(n + 1))-bit, so
-//      that 2*R(n - 1) is corrected up to the 2^(-n)-bit.
-//
-//   -  Thus, in order to round SQRT(a^2 + b^2) correctly up to n-fractional
-//      bits, we need to perform the summation (a^2 + b^2) correctly up to (2n +
-//      2)-fractional bits, and the remaining bits are sticky bits (i.e. we only
-//      care if they are 0 or > 0), and the comparisons, additions/subtractions
-//      can be done in n-fractional bits precision.
-//
-//   -  For single precision (float), we can use uint64_t to store the sum a^2 +
-//      b^2 exact up to (2n + 2)-fractional bits.
-//
-//   -  Then we can feed this sum into the digit-by-digit algorithm for SQRT(Z)
-//      described above.
-//
-//
-// Special cases:
-//   - HYPOT(x, y) is +Inf if x or y is +Inf or -Inf; else
-//   - HYPOT(x, y) is NaN if x or y is NaN.
-//
 float LLVM_LIBC_ENTRYPOINT(hypotf)(float x, float y) {
-  FPBits<float> x_bits(x), y_bits(y);
-
-  if (x_bits.isInf() || y_bits.isInf()) {
-    return FPBits<float>::inf();
-  }
-  if (x_bits.isNaN()) {
-    return x;
-  }
-  if (y_bits.isNaN()) {
-    return y;
-  }
-
-  uint16_t a_exp, b_exp, out_exp;
-  uint32_t a_mant, b_mant;
-  uint64_t a_mant_sq, b_mant_sq;
-  bool sticky_bits;
-
-  if ((x_bits.exponent >= y_bits.exponent + MantissaWidth<float>::value + 2) ||
-      (y == 0)) {
-    return abs(x);
-  } else if ((y_bits.exponent >=
-              x_bits.exponent + MantissaWidth<float>::value + 2) ||
-             (x == 0)) {
-    y_bits.sign = 0;
-    return abs(y);
-  }
-
-  if (x >= y) {
-    a_exp = x_bits.exponent;
-    a_mant = x_bits.mantissa;
-    b_exp = y_bits.exponent;
-    b_mant = y_bits.mantissa;
-  } else {
-    a_exp = y_bits.exponent;
-    a_mant = y_bits.mantissa;
-    b_exp = x_bits.exponent;
-    b_mant = x_bits.mantissa;
-  }
-
-  out_exp = a_exp;
-
-  // Add an extra bit to simplify the final rounding bit computation.
-  constexpr uint32_t one = 1U << (MantissaWidth<float>::value + 1);
-
-  a_mant <<= 1;
-  b_mant <<= 1;
-
-  uint32_t leading_one;
-  int y_mant_width;
-  if (a_exp != 0) {
-    leading_one = one;
-    a_mant |= one;
-    y_mant_width = MantissaWidth<float>::value + 1;
-  } else {
-    leading_one = findLeadingOne(a_mant, y_mant_width);
-  }
-
-  if (b_exp != 0) {
-    b_mant |= one;
-  }
-
-  a_mant_sq = static_cast<uint64_t>(a_mant) * a_mant;
-  b_mant_sq = static_cast<uint64_t>(b_mant) * b_mant;
-
-  // At this point, a_exp >= b_exp > a_exp - 25, so in order to line up aSqMant
-  // and bSqMant, we need to shift bSqMant to the right by (a_exp - b_exp) bits.
-  // But before that, remember to store the losing bits to sticky.
-  // The shift length is for a^2 and b^2, so it's double of the exponent
-  // 
diff erence between a and b.
-  uint16_t shift_length = 2 * (a_exp - b_exp);
-  sticky_bits = ((b_mant_sq & ((1ULL << shift_length) - 1)) != 0);
-  b_mant_sq >>= shift_length;
-
-  uint64_t sum = a_mant_sq + b_mant_sq;
-  if (sum >= (1ULL << (2 * y_mant_width + 2))) {
-    // a^2 + b^2 >= 4* leading_one^2, so we will need an extra bit to the left.
-    if (leading_one == one) {
-      // For normal result, we discard the last 2 bits of the sum and increase
-      // the exponent.
-      sticky_bits = sticky_bits || ((sum & 0x3U) != 0);
-      sum >>= 2;
-      ++out_exp;
-      if (out_exp >= FPBits<float>::maxExponent) {
-        return FPBits<float>::inf();
-      }
-    } else {
-      // For denormal result, we simply move the leading bit of the result to
-      // the left by 1.
-      leading_one <<= 1;
-      ++y_mant_width;
-    }
-  }
-
-  uint32_t Y = leading_one;
-  uint32_t R = static_cast<uint32_t>(sum >> y_mant_width) - leading_one;
-  uint32_t tailBits = static_cast<uint32_t>(sum) & (leading_one - 1);
-
-  for (uint32_t current_bit = leading_one >> 1; current_bit;
-       current_bit >>= 1) {
-    R = (R << 1) + ((tailBits & current_bit) ? 1 : 0);
-    uint32_t tmp = (Y << 1) + current_bit; // 2*y(n - 1) + 2^(-n)
-    if (R >= tmp) {
-      R -= tmp;
-      Y += current_bit;
-    }
-  }
-
-  bool round_bit = Y & 1U;
-  bool lsb = Y & 2U;
-
-  if (Y >= one) {
-    Y -= one;
-
-    if (out_exp == 0) {
-      out_exp = 1;
-    }
-  }
-
-  Y >>= 1;
-
-  // Round to the nearest, tie to even.
-  if (round_bit && (lsb || sticky_bits || (R != 0))) {
-    ++Y;
-  }
-
-  if (Y >= (one >> 1)) {
-    Y -= one >> 1;
-    ++out_exp;
-    if (out_exp >= FPBits<float>::maxExponent) {
-      return FPBits<float>::inf();
-    }
-  }
-
-  Y |= static_cast<uint32_t>(out_exp) << MantissaWidth<float>::value;
-  return *reinterpret_cast<float *>(&Y);
+  return __llvm_libc::fputil::hypot(x, y);
 }
 
 } // namespace __llvm_libc

diff  --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index cdffe737d8df..8635e7aba427 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -736,3 +736,16 @@ add_fp_unittest(
     libc.src.math.hypotf
     libc.utils.FPUtil.fputil
 )
+
+add_fp_unittest(
+  hypot_test
+  NEED_MPFR
+  SUITE
+    libc_math_unittests
+  SRCS
+    hypot_test.cpp
+  DEPENDS
+    libc.include.math
+    libc.src.math.hypot
+    libc.utils.FPUtil.fputil
+)

diff  --git a/libc/test/src/math/HypotTest.h b/libc/test/src/math/HypotTest.h
new file mode 100644
index 000000000000..f90807b62c5f
--- /dev/null
+++ b/libc/test/src/math/HypotTest.h
@@ -0,0 +1,75 @@
+//===-- Utility class to test 
diff erent flavors of hypot ------------------===//
+//
+// 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_TEST_SRC_MATH_HYPOTTEST_H
+#define LLVM_LIBC_TEST_SRC_MATH_HYPOTTEST_H
+
+#include "include/math.h"
+#include "utils/FPUtil/FPBits.h"
+#include "utils/FPUtil/Hypot.h"
+#include "utils/FPUtil/TestHelpers.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+#include "utils/UnitTest/Test.h"
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+
+template <typename T>
+class HypotTestTemplate : public __llvm_libc::testing::Test {
+private:
+  using Func = T (*)(T, T);
+  using FPBits = __llvm_libc::fputil::FPBits<T>;
+  using UIntType = typename FPBits::UIntType;
+  const T nan = __llvm_libc::fputil::FPBits<T>::buildNaN(1);
+  const T inf = __llvm_libc::fputil::FPBits<T>::inf();
+  const T negInf = __llvm_libc::fputil::FPBits<T>::negInf();
+  const T zero = __llvm_libc::fputil::FPBits<T>::zero();
+  const T negZero = __llvm_libc::fputil::FPBits<T>::negZero();
+
+public:
+  void testSpecialNumbers(Func func) {
+    EXPECT_FP_EQ(func(inf, nan), inf);
+    EXPECT_FP_EQ(func(nan, negInf), inf);
+    EXPECT_FP_EQ(func(zero, inf), inf);
+    EXPECT_FP_EQ(func(negInf, negZero), inf);
+
+    EXPECT_FP_EQ(func(nan, nan), nan);
+    EXPECT_FP_EQ(func(nan, zero), nan);
+    EXPECT_FP_EQ(func(negZero, nan), nan);
+
+    EXPECT_FP_EQ(func(negZero, zero), zero);
+  }
+
+  void testSubnormalRange(Func func) {
+    constexpr UIntType count = 1000001;
+    constexpr UIntType step =
+        (FPBits::maxSubnormal - FPBits::minSubnormal) / count;
+    for (UIntType v = FPBits::minSubnormal, w = FPBits::maxSubnormal;
+         v <= FPBits::maxSubnormal && w >= FPBits::minSubnormal;
+         v += step, w -= step) {
+      T x = FPBits(v), y = FPBits(w);
+      T result = func(x, y);
+      mpfr::BinaryInput<T> input{x, y};
+      ASSERT_MPFR_MATCH(mpfr::Operation::Hypot, input, result, 0.5);
+    }
+  }
+
+  void testNormalRange(Func func) {
+    constexpr UIntType count = 1000001;
+    constexpr UIntType step = (FPBits::maxNormal - FPBits::minNormal) / count;
+    for (UIntType v = FPBits::minNormal, w = FPBits::maxNormal;
+         v <= FPBits::maxNormal && w >= FPBits::minNormal;
+         v += step, w -= step) {
+      T x = FPBits(v), y = FPBits(w);
+      T result = func(x, y);
+      mpfr::BinaryInput<T> input{x, y};
+      ASSERT_MPFR_MATCH(mpfr::Operation::Hypot, input, result, 0.5);
+    }
+  }
+};
+
+#endif // LLVM_LIBC_TEST_SRC_MATH_HYPOTTEST_H

diff  --git a/libc/test/src/math/hypot_test.cpp b/libc/test/src/math/hypot_test.cpp
new file mode 100644
index 000000000000..d723f5264afc
--- /dev/null
+++ b/libc/test/src/math/hypot_test.cpp
@@ -0,0 +1,20 @@
+//===-- Unittests for hypot -----------------------------------------------===//
+//
+// 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 "HypotTest.h"
+
+#include "include/math.h"
+#include "src/math/hypot.h"
+
+using HypotTest = HypotTestTemplate<double>;
+
+TEST_F(HypotTest, SpecialNumbers) { testSpecialNumbers(&__llvm_libc::hypot); }
+
+TEST_F(HypotTest, SubnormalRange) { testSubnormalRange(&__llvm_libc::hypot); }
+
+TEST_F(HypotTest, NormalRange) { testNormalRange(&__llvm_libc::hypot); }

diff  --git a/libc/test/src/math/hypotf_test.cpp b/libc/test/src/math/hypotf_test.cpp
index 1769307099a9..21d1bea03291 100644
--- a/libc/test/src/math/hypotf_test.cpp
+++ b/libc/test/src/math/hypotf_test.cpp
@@ -6,56 +6,15 @@
 //
 //===----------------------------------------------------------------------===//
 
-#include "src/math/hypotf.h"
-#include "utils/FPUtil/FPBits.h"
-#include "utils/FPUtil/TestHelpers.h"
-#include "utils/MPFRWrapper/MPFRUtils.h"
-#include "utils/UnitTest/Test.h"
-#include <math.h>
-
-using FPBits = __llvm_libc::fputil::FPBits<float>;
-using UIntType = FPBits::UIntType;
-
-namespace mpfr = __llvm_libc::testing::mpfr;
+#include "HypotTest.h"
 
-DECLARE_SPECIAL_CONSTANTS(float)
-
-TEST(HypotfTest, SpecialNumbers) {
-  EXPECT_FP_EQ(__llvm_libc::hypotf(inf, nan), inf);
-  EXPECT_FP_EQ(__llvm_libc::hypotf(nan, negInf), inf);
-  EXPECT_FP_EQ(__llvm_libc::hypotf(zero, inf), inf);
-  EXPECT_FP_EQ(__llvm_libc::hypotf(negInf, negZero), inf);
+#include "include/math.h"
+#include "src/math/hypotf.h"
 
-  EXPECT_FP_EQ(__llvm_libc::hypotf(nan, nan), nan);
-  EXPECT_FP_EQ(__llvm_libc::hypotf(nan, zero), nan);
-  EXPECT_FP_EQ(__llvm_libc::hypotf(negZero, nan), nan);
+using HypotfTest = HypotTestTemplate<float>;
 
-  EXPECT_FP_EQ(__llvm_libc::hypotf(negZero, zero), zero);
-}
+TEST_F(HypotfTest, SpecialNumbers) { testSpecialNumbers(&__llvm_libc::hypotf); }
 
-TEST(HypotfTest, SubnormalRange) {
-  constexpr UIntType count = 1000001;
-  constexpr UIntType step =
-      (FPBits::maxSubnormal - FPBits::minSubnormal) / count;
-  for (UIntType v = FPBits::minSubnormal, w = FPBits::maxSubnormal;
-       v <= FPBits::maxSubnormal && w >= FPBits::minSubnormal;
-       v += step, w -= step) {
-    float x = FPBits(v), y = FPBits(w);
-    float result = __llvm_libc::hypotf(x, y);
-    mpfr::BinaryInput<float> input{x, y};
-    ASSERT_MPFR_MATCH(mpfr::Operation::Hypot, input, result, 0.5);
-  }
-}
+TEST_F(HypotfTest, SubnormalRange) { testSubnormalRange(&__llvm_libc::hypotf); }
 
-TEST(HypotfTest, NormalRange) {
-  constexpr UIntType count = 1000001;
-  constexpr UIntType step = (FPBits::maxNormal - FPBits::minNormal) / count;
-  for (UIntType v = FPBits::minNormal, w = FPBits::maxNormal;
-       v <= FPBits::maxNormal && w >= FPBits::minNormal; v += step, w -= step) {
-    float x = FPBits(v), y = FPBits(w);
-    float result = __llvm_libc::hypotf(x, y);
-    ;
-    mpfr::BinaryInput<float> input{x, y};
-    ASSERT_MPFR_MATCH(mpfr::Operation::Hypot, input, result, 0.5);
-  }
-}
+TEST_F(HypotfTest, NormalRange) { testNormalRange(&__llvm_libc::hypotf); }

diff  --git a/libc/utils/FPUtil/Hypot.h b/libc/utils/FPUtil/Hypot.h
new file mode 100644
index 000000000000..6795f9dcb3ae
--- /dev/null
+++ b/libc/utils/FPUtil/Hypot.h
@@ -0,0 +1,267 @@
+//===-- Implementation of hypotf 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_UTILS_FPUTIL_HYPOT_H
+#define LLVM_LIBC_UTILS_FPUTIL_HYPOT_H
+
+#include "BasicOperations.h"
+#include "FPBits.h"
+#include "utils/CPP/TypeTraits.h"
+
+namespace __llvm_libc {
+namespace fputil {
+
+namespace internal {
+
+template <typename T> static inline T findLeadingOne(T mant, int &shift_length);
+
+template <>
+inline uint32_t findLeadingOne<uint32_t>(uint32_t mant, int &shift_length) {
+  shift_length = 0;
+  constexpr int nsteps = 5;
+  constexpr uint32_t bounds[nsteps] = {1 << 16, 1 << 8, 1 << 4, 1 << 2, 1 << 1};
+  constexpr int shifts[nsteps] = {16, 8, 4, 2, 1};
+  for (int i = 0; i < nsteps; ++i) {
+    if (mant >= bounds[i]) {
+      shift_length += shifts[i];
+      mant >>= shifts[i];
+    }
+  }
+  return 1U << shift_length;
+}
+
+template <>
+inline uint64_t findLeadingOne<uint64_t>(uint64_t mant, int &shift_length) {
+  shift_length = 0;
+  constexpr int nsteps = 6;
+  constexpr uint64_t bounds[nsteps] = {1ULL << 32, 1ULL << 16, 1ULL << 8,
+                                       1ULL << 4,  1ULL << 2,  1ULL << 1};
+  constexpr int shifts[nsteps] = {32, 16, 8, 4, 2, 1};
+  for (int i = 0; i < nsteps; ++i) {
+    if (mant >= bounds[i]) {
+      shift_length += shifts[i];
+      mant >>= shifts[i];
+    }
+  }
+  return 1ULL << shift_length;
+}
+
+} // namespace internal
+
+template <typename T> struct DoubleLength;
+
+template <> struct DoubleLength<uint16_t> { using Type = uint32_t; };
+
+template <> struct DoubleLength<uint32_t> { using Type = uint64_t; };
+
+template <> struct DoubleLength<uint64_t> { using Type = __uint128_t; };
+
+// Correctly rounded IEEE 754 HYPOT(x, y) with round to nearest, ties to even.
+//
+// Algorithm:
+//   -  Let a = max(|x|, |y|), b = min(|x|, |y|), then we have that:
+//          a <= sqrt(a^2 + b^2) <= min(a + b, a*sqrt(2))
+//   1. So if b < eps(a)/2, then HYPOT(x, y) = a.
+//
+//   -  Moreover, the exponent part of HYPOT(x, y) is either the same or 1 more
+//      than the exponent part of a.
+//
+//   2. For the remaining cases, we will use the digit-by-digit (shift-and-add)
+//      algorithm to compute SQRT(Z):
+//
+//   -  For Y = y0.y1...yn... = SQRT(Z),
+//      let Y(n) = y0.y1...yn be the first n fractional digits of Y.
+//
+//   -  The nth scaled residual R(n) is defined to be:
+//          R(n) = 2^n * (Z - Y(n)^2)
+//
+//   -  Since Y(n) = Y(n - 1) + yn * 2^(-n), the scaled residual
+//      satisfies the following recurrence formula:
+//          R(n) = 2*R(n - 1) - yn*(2*Y(n - 1) + 2^(-n)),
+//      with the initial conditions:
+//          Y(0) = y0, and R(0) = Z - y0.
+//
+//   -  So the nth fractional digit of Y = SQRT(Z) can be decided by:
+//          yn = 1  if 2*R(n - 1) >= 2*Y(n - 1) + 2^(-n),
+//               0  otherwise.
+//
+//   3. Precision analysis:
+//
+//   -  Notice that in the decision function:
+//          2*R(n - 1) >= 2*Y(n - 1) + 2^(-n),
+//      the right hand side only uses up to the 2^(-n)-bit, and both sides are
+//      non-negative, so R(n - 1) can be truncated at the 2^(-(n + 1))-bit, so
+//      that 2*R(n - 1) is corrected up to the 2^(-n)-bit.
+//
+//   -  Thus, in order to round SQRT(a^2 + b^2) correctly up to n-fractional
+//      bits, we need to perform the summation (a^2 + b^2) correctly up to (2n +
+//      2)-fractional bits, and the remaining bits are sticky bits (i.e. we only
+//      care if they are 0 or > 0), and the comparisons, additions/subtractions
+//      can be done in n-fractional bits precision.
+//
+//   -  For single precision (float), we can use uint64_t to store the sum a^2 +
+//      b^2 exact up to (2n + 2)-fractional bits.
+//
+//   -  Then we can feed this sum into the digit-by-digit algorithm for SQRT(Z)
+//      described above.
+//
+//
+// Special cases:
+//   - HYPOT(x, y) is +Inf if x or y is +Inf or -Inf; else
+//   - HYPOT(x, y) is NaN if x or y is NaN.
+//
+template <typename T,
+          cpp::EnableIfType<cpp::IsFloatingPointType<T>::Value, int> = 0>
+static inline T hypot(T x, T y) {
+  using FPBits_t = FPBits<T>;
+  using UIntType = typename FPBits<T>::UIntType;
+  using DUIntType = typename DoubleLength<UIntType>::Type;
+
+  FPBits_t x_bits(x), y_bits(y);
+
+  if (x_bits.isInf() || y_bits.isInf()) {
+    return FPBits_t::inf();
+  }
+  if (x_bits.isNaN()) {
+    return x;
+  }
+  if (y_bits.isNaN()) {
+    return y;
+  }
+
+  uint16_t a_exp, b_exp, out_exp;
+  UIntType a_mant, b_mant;
+  DUIntType a_mant_sq, b_mant_sq;
+  bool sticky_bits;
+
+  if ((x_bits.exponent >= y_bits.exponent + MantissaWidth<T>::value + 2) ||
+      (y == 0)) {
+    return abs(x);
+  } else if ((y_bits.exponent >=
+              x_bits.exponent + MantissaWidth<T>::value + 2) ||
+             (x == 0)) {
+    y_bits.sign = 0;
+    return abs(y);
+  }
+
+  if (x >= y) {
+    a_exp = x_bits.exponent;
+    a_mant = x_bits.mantissa;
+    b_exp = y_bits.exponent;
+    b_mant = y_bits.mantissa;
+  } else {
+    a_exp = y_bits.exponent;
+    a_mant = y_bits.mantissa;
+    b_exp = x_bits.exponent;
+    b_mant = x_bits.mantissa;
+  }
+
+  out_exp = a_exp;
+
+  // Add an extra bit to simplify the final rounding bit computation.
+  constexpr UIntType one = UIntType(1) << (MantissaWidth<T>::value + 1);
+
+  a_mant <<= 1;
+  b_mant <<= 1;
+
+  UIntType leading_one;
+  int y_mant_width;
+  if (a_exp != 0) {
+    leading_one = one;
+    a_mant |= one;
+    y_mant_width = MantissaWidth<T>::value + 1;
+  } else {
+    leading_one = internal::findLeadingOne(a_mant, y_mant_width);
+  }
+
+  if (b_exp != 0) {
+    b_mant |= one;
+  }
+
+  a_mant_sq = static_cast<DUIntType>(a_mant) * a_mant;
+  b_mant_sq = static_cast<DUIntType>(b_mant) * b_mant;
+
+  // At this point, a_exp >= b_exp > a_exp - 25, so in order to line up aSqMant
+  // and bSqMant, we need to shift bSqMant to the right by (a_exp - b_exp) bits.
+  // But before that, remember to store the losing bits to sticky.
+  // The shift length is for a^2 and b^2, so it's double of the exponent
+  // 
diff erence between a and b.
+  uint16_t shift_length = 2 * (a_exp - b_exp);
+  sticky_bits =
+      ((b_mant_sq & ((DUIntType(1) << shift_length) - DUIntType(1))) !=
+       DUIntType(0));
+  b_mant_sq >>= shift_length;
+
+  DUIntType sum = a_mant_sq + b_mant_sq;
+  if (sum >= (DUIntType(1) << (2 * y_mant_width + 2))) {
+    // a^2 + b^2 >= 4* leading_one^2, so we will need an extra bit to the left.
+    if (leading_one == one) {
+      // For normal result, we discard the last 2 bits of the sum and increase
+      // the exponent.
+      sticky_bits = sticky_bits || ((sum & 0x3U) != 0);
+      sum >>= 2;
+      ++out_exp;
+      if (out_exp >= FPBits_t::maxExponent) {
+        return FPBits_t::inf();
+      }
+    } else {
+      // For denormal result, we simply move the leading bit of the result to
+      // the left by 1.
+      leading_one <<= 1;
+      ++y_mant_width;
+    }
+  }
+
+  UIntType Y = leading_one;
+  UIntType R = static_cast<UIntType>(sum >> y_mant_width) - leading_one;
+  UIntType tailBits = static_cast<UIntType>(sum) & (leading_one - 1);
+
+  for (UIntType current_bit = leading_one >> 1; current_bit;
+       current_bit >>= 1) {
+    R = (R << 1) + ((tailBits & current_bit) ? 1 : 0);
+    UIntType tmp = (Y << 1) + current_bit; // 2*y(n - 1) + 2^(-n)
+    if (R >= tmp) {
+      R -= tmp;
+      Y += current_bit;
+    }
+  }
+
+  bool round_bit = Y & UIntType(1);
+  bool lsb = Y & UIntType(2);
+
+  if (Y >= one) {
+    Y -= one;
+
+    if (out_exp == 0) {
+      out_exp = 1;
+    }
+  }
+
+  Y >>= 1;
+
+  // Round to the nearest, tie to even.
+  if (round_bit && (lsb || sticky_bits || (R != 0))) {
+    ++Y;
+  }
+
+  if (Y >= (one >> 1)) {
+    Y -= one >> 1;
+    ++out_exp;
+    if (out_exp >= FPBits_t::maxExponent) {
+      return FPBits_t::inf();
+    }
+  }
+
+  Y |= static_cast<UIntType>(out_exp) << MantissaWidth<T>::value;
+  return *reinterpret_cast<T *>(&Y);
+}
+
+} // namespace fputil
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_UTILS_FPUTIL_HYPOT_H


        


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