[libc-commits] [libc] f55963d - [libc] Add implementation for hypotf
Tue Ly via libc-commits
libc-commits at lists.llvm.org
Thu Sep 17 20:47:35 PDT 2020
Author: Tue Ly
Date: 2020-09-17T23:28:36-04:00
New Revision: f55963d501e46c9453d08a0c764ec40141230966
URL: https://github.com/llvm/llvm-project/commit/f55963d501e46c9453d08a0c764ec40141230966
DIFF: https://github.com/llvm/llvm-project/commit/f55963d501e46c9453d08a0c764ec40141230966.diff
LOG: [libc] Add implementation for hypotf
Truncating the sum of squares, and then use shift-and-add algorithm to compute its square root.
Required MPFR testing infra is updated in https://reviews.llvm.org/D87514
Differential Revision: https://reviews.llvm.org/D87516
Added:
libc/src/math/hypotf.cpp
libc/src/math/hypotf.h
libc/test/src/math/hypotf_test.cpp
Modified:
libc/config/linux/aarch64/entrypoints.txt
libc/config/linux/api.td
libc/config/linux/x86_64/entrypoints.txt
libc/spec/stdc.td
libc/src/math/CMakeLists.txt
libc/test/src/math/CMakeLists.txt
Removed:
################################################################################
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 34d07c24505d..e654d594bce0 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -64,6 +64,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.frexp
libc.src.math.frexpf
libc.src.math.frexpl
+ libc.src.math.hypotf
libc.src.math.logb
libc.src.math.logbf
libc.src.math.logbl
diff --git a/libc/config/linux/api.td b/libc/config/linux/api.td
index 33ae64c0a08c..40eec8f55c1c 100644
--- a/libc/config/linux/api.td
+++ b/libc/config/linux/api.td
@@ -191,6 +191,7 @@ def MathAPI : PublicAPI<"math.h"> {
"frexp",
"frexpf",
"frexpl",
+ "hypotf",
"logb",
"logbf",
"logbl",
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 6aca5e400d68..a67e4084dd5e 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -97,6 +97,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.frexp
libc.src.math.frexpf
libc.src.math.frexpl
+ libc.src.math.hypotf
libc.src.math.logb
libc.src.math.logbf
libc.src.math.logbl
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index 77fa971adc61..61b3dcb24ef0 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -296,6 +296,8 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"frexpf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<IntPtr>]>,
FunctionSpec<"frexpl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<IntPtr>]>,
+ FunctionSpec<"hypotf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
+
FunctionSpec<"logb", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
FunctionSpec<"logbf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"logbl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>]>,
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index 3b4f82172657..633a1cdddc54 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -593,3 +593,15 @@ add_entrypoint_object(
COMPILE_OPTIONS
-O2
)
+
+add_entrypoint_object(
+ hypotf
+ SRCS
+ hypotf.cpp
+ HDRS
+ hypotf.h
+ DEPENDS
+ libc.utils.FPUtil.fputil
+ COMPILE_OPTIONS
+ -O2
+)
diff --git a/libc/src/math/hypotf.cpp b/libc/src/math/hypotf.cpp
new file mode 100644
index 000000000000..10ebbb1b9ec9
--- /dev/null
+++ b/libc/src/math/hypotf.cpp
@@ -0,0 +1,222 @@
+//===-- 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
+//
+//===----------------------------------------------------------------------===//
+#include "src/__support/common.h"
+#include "utils/FPUtil/BasicOperations.h"
+#include "utils/FPUtil/FPBits.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);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/math/hypotf.h b/libc/src/math/hypotf.h
new file mode 100644
index 000000000000..084fd7f3ef81
--- /dev/null
+++ b/libc/src/math/hypotf.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for hypotf ------------------------*- 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_HYPOTF_H
+#define LLVM_LIBC_SRC_MATH_HYPOTF_H
+
+namespace __llvm_libc {
+
+float hypotf(float x, float y);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_HYPOTF_H
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index e1bac1a33906..a90736992f1f 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -591,3 +591,16 @@ add_fp_unittest(
libc.src.math.remquol
libc.utils.FPUtil.fputil
)
+
+add_fp_unittest(
+ hypotf_test
+ NEED_MPFR
+ SUITE
+ libc_math_unittests
+ SRCS
+ hypotf_test.cpp
+ DEPENDS
+ libc.include.math
+ libc.src.math.hypotf
+ libc.utils.FPUtil.fputil
+)
diff --git a/libc/test/src/math/hypotf_test.cpp b/libc/test/src/math/hypotf_test.cpp
new file mode 100644
index 000000000000..7b1ffd5241db
--- /dev/null
+++ b/libc/test/src/math/hypotf_test.cpp
@@ -0,0 +1,65 @@
+//===-- Unittests for hypotf ----------------------------------------------===//
+//
+// 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 "include/math.h"
+#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"
+
+using FPBits = __llvm_libc::fputil::FPBits<float>;
+using UIntType = FPBits::UIntType;
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+
+static const float zero = FPBits::zero();
+static const float negZero = FPBits::negZero();
+static const float nan = FPBits::buildNaN(1);
+static const float inf = FPBits::inf();
+static const float negInf = FPBits::negInf();
+
+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);
+
+ 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);
+
+ EXPECT_FP_EQ(__llvm_libc::hypotf(negZero, zero), zero);
+}
+
+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(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);
+ }
+}
More information about the libc-commits
mailing list