[libc][stdfix] Add sqrt for fixed point types. (#83042)

Author: lntue

libc/config/linux/x86_64/entrypoints.txt

@@ -473,6 +473,12 @@ if(LIBC_COMPILER_HAS_FIXED_POINT)
     libc.src.stdfix.roundur
     libc.src.stdfix.roundulk
     libc.src.stdfix.roundulr
+    libc.src.stdfix.sqrtuhk
+    libc.src.stdfix.sqrtuhr
+    libc.src.stdfix.sqrtuk
+    libc.src.stdfix.sqrtur
+    # libc.src.stdfix.sqrtulk
+    libc.src.stdfix.sqrtulr
   )
 endif()
 

libc/docs/math/stdfix.rst

@@ -78,7 +78,7 @@ Fixed-point Arithmetics
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+
 | round         | |check|        | |check|     | |check|       | |check|    | |check|        | |check|     | |check|        | |check|     | |check|       | |check|    | |check|        | |check|     |
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+
-| sqrt          |                |             |               |            |                |             |                |             |               |            |                |             |
+| sqrt          | |check|        |             | |check|       |            | |check|        |             | |check|        |             | |check|       |            |                |             |
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+
 
 ================== =========

libc/spec/stdc_ext.td

@@ -47,6 +47,14 @@ def StdcExt : StandardSpec<"stdc_ext"> {
           GuardedFunctionSpec<"rounduhk", RetValSpec<UnsignedShortAccumType>, [ArgSpec<UnsignedShortAccumType>, ArgSpec<IntType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
           GuardedFunctionSpec<"rounduk", RetValSpec<UnsignedAccumType>, [ArgSpec<UnsignedAccumType>, ArgSpec<IntType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
           GuardedFunctionSpec<"roundulk", RetValSpec<UnsignedLongAccumType>, [ArgSpec<UnsignedLongAccumType>, ArgSpec<IntType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
+
+          GuardedFunctionSpec<"sqrtuhr", RetValSpec<UnsignedShortFractType>, [ArgSpec<UnsignedShortFractType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
+          GuardedFunctionSpec<"sqrtur", RetValSpec<UnsignedFractType>, [ArgSpec<UnsignedFractType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
+          GuardedFunctionSpec<"sqrtulr", RetValSpec<UnsignedLongFractType>, [ArgSpec<UnsignedLongFractType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
+
+          GuardedFunctionSpec<"sqrtuhk", RetValSpec<UnsignedShortAccumType>, [ArgSpec<UnsignedShortAccumType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
+          GuardedFunctionSpec<"sqrtuk", RetValSpec<UnsignedAccumType>, [ArgSpec<UnsignedAccumType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
+          GuardedFunctionSpec<"sqrtulk", RetValSpec<UnsignedLongAccumType>, [ArgSpec<UnsignedLongAccumType>], "LIBC_COMPILER_HAS_FIXED_POINT">,
       ]
   >;
 

libc/src/__support/fixed_point/CMakeLists.txt

@@ -21,3 +21,16 @@ add_header_library(
     libc.src.__support.CPP.bit
     libc.src.__support.math_extras
 )
+
+add_header_library(
+  sqrt
+  HDRS
+    sqrt.h
+  DEPENDS
+    .fx_rep
+    libc.include.llvm-libc-macros.stdfix_macros
+    libc.src.__support.macros.attributes
+    libc.src.__support.macros.optimization
+    libc.src.__support.CPP.bit
+    libc.src.__support.CPP.type_traits
+)

libc/src/__support/fixed_point/sqrt.h

@@ -0,0 +1,129 @@
+//===-- Calculate square root of fixed point numbers. -----*- 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___SUPPORT_FIXEDPOINT_SQRT_H
+#define LLVM_LIBC_SRC___SUPPORT_FIXEDPOINT_SQRT_H
+
+#include "include/llvm-libc-macros/stdfix-macros.h"
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/type_traits.h"
+#include "src/__support/macros/attributes.h"   // LIBC_INLINE
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+#include "fx_rep.h"
+
+#ifdef LIBC_COMPILER_HAS_FIXED_POINT
+
+namespace LIBC_NAMESPACE::fixed_point {
+
+namespace internal {
+
+template <typename T> struct SqrtConfig;
+
+template <> struct SqrtConfig<unsigned short fract> {
+  using Type = unsigned short fract;
+  static constexpr int EXTRA_STEPS = 0;
+};
+
+template <> struct SqrtConfig<unsigned fract> {
+  using Type = unsigned fract;
+  static constexpr int EXTRA_STEPS = 1;
+};
+
+template <> struct SqrtConfig<unsigned long fract> {
+  using Type = unsigned long fract;
+  static constexpr int EXTRA_STEPS = 2;
+};
+
+template <>
+struct SqrtConfig<unsigned short accum> : SqrtConfig<unsigned fract> {};
+
+template <>
+struct SqrtConfig<unsigned accum> : SqrtConfig<unsigned long fract> {};
+
+// TODO: unsigned long accum type is 64-bit, and will need 64-bit fract type.
+// Probably we will use DyadicFloat<64> for intermediate computations instead.
+
+// Linear approximation for the initial values, with errors bounded by:
+//   max(1.5 * 2^-11, eps)
+// Generated with Sollya:
+// > for i from 4 to 15 do {
+//     P = fpminimax(sqrt(x), 1, [|8, 8|], [i * 2^-4, (i + 1)*2^-4],
+//                   fixed, absolute);
+//     print("{", coeff(P, 1), "uhr,", coeff(P, 0), "uhr},");
+//   };
+static constexpr unsigned short fract SQRT_FIRST_APPROX[12][2] = {
+    {0x1.e8p-1uhr, 0x1.0cp-2uhr}, {0x1.bap-1uhr, 0x1.28p-2uhr},
+    {0x1.94p-1uhr, 0x1.44p-2uhr}, {0x1.74p-1uhr, 0x1.6p-2uhr},
+    {0x1.6p-1uhr, 0x1.74p-2uhr},  {0x1.4ep-1uhr, 0x1.88p-2uhr},
+    {0x1.3ep-1uhr, 0x1.9cp-2uhr}, {0x1.32p-1uhr, 0x1.acp-2uhr},
+    {0x1.22p-1uhr, 0x1.c4p-2uhr}, {0x1.18p-1uhr, 0x1.d4p-2uhr},
+    {0x1.08p-1uhr, 0x1.fp-2uhr},  {0x1.04p-1uhr, 0x1.f8p-2uhr},
+};
+
+} // namespace internal
+
+template <typename T>
+LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_fixed_point_v<T>, T> sqrt(T x) {
+  using BitType = typename FXRep<T>::StorageType;
+  BitType x_bit = cpp::bit_cast<BitType>(x);
+
+  if (LIBC_UNLIKELY(x_bit == 0))
+    return FXRep<T>::ZERO();
+
+  int leading_zeros = cpp::countl_zero(x_bit);
+  constexpr int STORAGE_LENGTH = sizeof(BitType) * CHAR_BIT;
+  constexpr int EXP_ADJUSTMENT = STORAGE_LENGTH - FXRep<T>::FRACTION_LEN - 1;
+  // x_exp is the real exponent of the leading bit of x.
+  int x_exp = EXP_ADJUSTMENT - leading_zeros;
+  int shift = EXP_ADJUSTMENT - 1 - (x_exp & (~1));
+  // Normalize.
+  x_bit <<= shift;
+  using FracType = typename internal::SqrtConfig<T>::Type;
+  FracType x_frac = cpp::bit_cast<FracType>(x_bit);
+
+  // Use use Newton method to approximate sqrt(a):
+  //   x_{n + 1} = 1/2 (x_n + a / x_n)
+  // For the initial values, we choose x_0
+
+  // Use the leading 4 bits to do look up for sqrt(x).
+  // After normalization, 0.25 <= x_frac < 1, so the leading 4 bits of x_frac
+  // are between 0b0100 and 0b1111.  Hence the lookup table only needs 12
+  // entries, and we can get the index by subtracting the leading 4 bits of
+  // x_frac by 4 = 0b0100.
+  int index = (x_bit >> (STORAGE_LENGTH - 4)) - 4;
+  FracType a = static_cast<FracType>(internal::SQRT_FIRST_APPROX[index][0]);
+  FracType b = static_cast<FracType>(internal::SQRT_FIRST_APPROX[index][1]);
+
+  // Initial approximation step.
+  // Estimated error bounds: | r - sqrt(x_frac) | < max(1.5 * 2^-11, eps).
+  FracType r = a * x_frac + b;
+
+  // Further Newton-method iterations for square-root:
+  //   x_{n + 1} = 0.5 * (x_n + a / x_n)
+  // We distribute and do the multiplication by 0.5 first to avoid overflow.
+  // TODO: Investigate the performance and accuracy of using division-free
+  // iterations from:
+  //   Blanchard, J. D. and Chamberland, M., "Newton's Method Without Division",
+  //   The American Mathematical Monthly (2023).
+  //   https://chamberland.math.grinnell.edu/papers/newton.pdf
+  for (int i = 0; i < internal::SqrtConfig<T>::EXTRA_STEPS; ++i)
+    r = (r >> 1) + (x_frac >> 1) / r;
+
+  // Re-scaling
+  r >>= EXP_ADJUSTMENT - (x_exp >> 1);
+
+  // Return result.
+  return cpp::bit_cast<T>(r);
+}
+
+} // namespace LIBC_NAMESPACE::fixed_point
+
+#endif // LIBC_COMPILER_HAS_FIXED_POINT
+
+#endif // LLVM_LIBC_SRC___SUPPORT_FIXEDPOINT_SQRT_H

libc/src/stdfix/CMakeLists.txt

@@ -17,6 +17,21 @@ foreach(suffix IN ITEMS hr r lr hk k lk)
   )
 endforeach()
 
+foreach(suffix IN ITEMS uhr ur ulr uhk uk)
+  add_entrypoint_object(
+    sqrt${suffix}
+    HDRS
+      sqrt${suffix}.h
+    SRCS
+      sqrt${suffix}.cpp
+    COMPILE_OPTIONS
+      -O3
+      -ffixed-point
+    DEPENDS
+      libc.src.__support.fixed_point.sqrt
+  )
+endforeach()
+
 foreach(suffix IN ITEMS hr r lr hk k lk uhr ur ulr uhk uk ulk)
   add_entrypoint_object(
     round${suffix}

libc/src/stdfix/sqrtuhk.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of sqrtuhk 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 "sqrtuhk.h"
+#include "src/__support/common.h"
+#include "src/__support/fixed_point/sqrt.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(unsigned short accum, sqrtuhk, (unsigned short accum x)) {
+  return fixed_point::sqrt(x);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/stdfix/sqrtuhk.h

@@ -0,0 +1,20 @@
+//===-- Implementation header for sqrtuhk -----------------------*- 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_STDFIX_SQRTUHK_H
+#define LLVM_LIBC_SRC_STDFIX_SQRTUHK_H
+
+#include "include/llvm-libc-macros/stdfix-macros.h"
+
+namespace LIBC_NAMESPACE {
+
+unsigned short accum sqrtuhk(unsigned short accum x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_STDFIX_SQRTUHK_H

libc/src/stdfix/sqrtuhr.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of sqrtuhr 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 "sqrtuhr.h"
+#include "src/__support/common.h"
+#include "src/__support/fixed_point/sqrt.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(unsigned short fract, sqrtuhr, (unsigned short fract x)) {
+  return fixed_point::sqrt(x);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/stdfix/sqrtuhr.h

@@ -0,0 +1,20 @@
+//===-- Implementation header for sqrtuhr -----------------------*- 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_STDFIX_SQRTUHR_H
+#define LLVM_LIBC_SRC_STDFIX_SQRTUHR_H
+
+#include "include/llvm-libc-macros/stdfix-macros.h"
+
+namespace LIBC_NAMESPACE {
+
+unsigned short fract sqrtuhr(unsigned short fract x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_STDFIX_SQRTUHR_H

libc/src/stdfix/sqrtuk.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of sqrtuk 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 "sqrtuk.h"
+#include "src/__support/common.h"
+#include "src/__support/fixed_point/sqrt.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(unsigned accum, sqrtuk, (unsigned accum x)) {
+  return fixed_point::sqrt(x);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/stdfix/sqrtuk.h

@@ -0,0 +1,20 @@
+//===-- Implementation header for sqrtuk ------------------------*- 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_STDFIX_SQRTUK_H
+#define LLVM_LIBC_SRC_STDFIX_SQRTUK_H
+
+#include "include/llvm-libc-macros/stdfix-macros.h"
+
+namespace LIBC_NAMESPACE {
+
+unsigned accum sqrtuk(unsigned accum x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_STDFIX_SQRTUK_H

libc/src/stdfix/sqrtulr.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of sqrtulr 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 "sqrtulr.h"
+#include "src/__support/common.h"
+#include "src/__support/fixed_point/sqrt.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(unsigned long fract, sqrtulr, (unsigned long fract x)) {
+  return fixed_point::sqrt(x);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/stdfix/sqrtulr.h

@@ -0,0 +1,20 @@
+//===-- Implementation header for sqrtulr -----------------------*- 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_STDFIX_SQRTULR_H
+#define LLVM_LIBC_SRC_STDFIX_SQRTULR_H
+
+#include "include/llvm-libc-macros/stdfix-macros.h"
+
+namespace LIBC_NAMESPACE {
+
+unsigned long fract sqrtulr(unsigned long fract x);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_STDFIX_SQRTULR_H

libc/src/stdfix/sqrtur.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of sqrtur 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 "sqrtur.h"
+#include "src/__support/common.h"
+#include "src/__support/fixed_point/sqrt.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(unsigned fract, sqrtur, (unsigned fract x)) {
+  return fixed_point::sqrt(x);
+}
+
+} // namespace LIBC_NAMESPACE