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 _______________________________________________ llvm-branch-commits mailing list llvm-branch-commits@lists.llvm.org https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-branch-commits
