[libc][stdfix] Implement fxdivi functions (rdivi) (#154914)

This PR includes only one of the fxdivi functions (rdivi). It uses a
polynomial function for initial approximation followed by 4
newton-raphson iterations to calculate the reciprocal and finally
multiplies the numerator with it to get the result.


---------

Signed-off-by: Shreeyash Pandey <[email protected]>

Author: bojle

libc/config/linux/riscv/entrypoints.txt

@@ -1022,6 +1022,7 @@ if(LIBC_COMPILER_HAS_FIXED_POINT)
     libc.src.stdfix.idivulr
     libc.src.stdfix.idivuk
     libc.src.stdfix.idivulk
+    libc.src.stdfix.rdivi
   )
 endif()
 

libc/config/linux/x86_64/entrypoints.txt

@@ -1058,6 +1058,7 @@ if(LIBC_COMPILER_HAS_FIXED_POINT)
     libc.src.stdfix.idivulr
     libc.src.stdfix.idivuk
     libc.src.stdfix.idivulk
+    libc.src.stdfix.rdivi
   )
 endif()
 

libc/docs/headers/stdfix.rst

@@ -81,7 +81,7 @@ The following functions are included in the ISO/IEC TR 18037:2008 standard.
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+
 | muli          |                |             |               |            |                |             |                |             |               |            |                |             |
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+
-| \*divi        |                |             |               |            |                |             |                |             |               |            |                |             |
+| \*divi        |                |             |               | |check|    |                |             |                |             |               |            |                |             |
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+
 | round         | |check|        | |check|     | |check|       | |check|    | |check|        | |check|     | |check|        | |check|     | |check|       | |check|    | |check|        | |check|     |
 +---------------+----------------+-------------+---------------+------------+----------------+-------------+----------------+-------------+---------------+------------+----------------+-------------+

libc/include/stdfix.yaml

@@ -544,3 +544,11 @@ functions:
     arguments:
       - type: unsigned long accum
     guard: LIBC_COMPILER_HAS_FIXED_POINT
+  - name: rdivi
+    standards:
+      - stdc_ext
+    return_type: fract
+    arguments:
+      - type: int
+      - type: int
+    guard: LIBC_COMPILER_HAS_FIXED_POINT

libc/src/__support/fixed_point/fx_bits.h

@@ -10,9 +10,11 @@
 #define LLVM_LIBC_SRC___SUPPORT_FIXED_POINT_FX_BITS_H
 
 #include "include/llvm-libc-macros/stdfix-macros.h"
+#include "src/__support/CPP/algorithm.h"
 #include "src/__support/CPP/bit.h"
 #include "src/__support/CPP/limits.h" // numeric_limits
 #include "src/__support/CPP/type_traits.h"
+#include "src/__support/libc_assert.h"
 #include "src/__support/macros/attributes.h"   // LIBC_INLINE
 #include "src/__support/macros/config.h"       // LIBC_NAMESPACE_DECL
 #include "src/__support/macros/null_check.h"   // LIBC_CRASH_ON_VALUE
@@ -21,6 +23,8 @@
 
 #include "fx_rep.h"
 
+#include <stdio.h>
+
 #ifdef LIBC_COMPILER_HAS_FIXED_POINT
 
 namespace LIBC_NAMESPACE_DECL {
@@ -224,6 +228,113 @@ idiv(T x, T y) {
   return static_cast<XType>(result);
 }
 
+LIBC_INLINE long accum nrstep(long accum d, long accum x0) {
+  auto v = x0 * (2.lk - (d * x0));
+  return v;
+}
+
+// Divide the two integers and return a fixed_point value
+//
+// For reference, see:
+// https://en.wikipedia.org/wiki/Division_algorithm#Newton%E2%80%93Raphson_division
+// https://stackoverflow.com/a/9231996
+
+template <typename XType> LIBC_INLINE constexpr XType divi(int n, int d) {
+  // If the value of the second operand of the / operator is zero, the
+  // behavior is undefined. Ref: ISO/IEC TR 18037:2008(E) p.g. 16
+  LIBC_CRASH_ON_VALUE(d, 0);
+
+  if (LIBC_UNLIKELY(n == 0)) {
+    return FXRep<XType>::ZERO();
+  }
+  auto is_power_of_two = [](int n) { return (n > 0) && ((n & (n - 1)) == 0); };
+  long accum max_val = static_cast<long accum>(FXRep<XType>::MAX());
+  long accum min_val = static_cast<long accum>(FXRep<XType>::MIN());
+
+  if (is_power_of_two(cpp::abs(d))) {
+    int k = cpp::countr_zero<uint32_t>(static_cast<uint32_t>(cpp::abs(d)));
+    constexpr int F = FXRep<XType>::FRACTION_LEN;
+    int64_t scaled_n = static_cast<int64_t>(n) << F;
+    int64_t res64 = scaled_n >> k;
+    constexpr int TOTAL_BITS = sizeof(XType) * 8;
+    const int64_t max_limit = (1LL << (TOTAL_BITS - 1)) - 1;
+    const int64_t min_limit = -(1LL << (TOTAL_BITS - 1));
+    if (res64 > max_limit) {
+      return FXRep<XType>::MAX();
+    } else if (res64 < min_limit) {
+      return FXRep<XType>::MIN();
+    }
+    long accum res_accum =
+        static_cast<long accum>(res64) / static_cast<long accum>(1 << F);
+    res_accum = (d < 0) ? static_cast<long accum>(-1) * res_accum : res_accum;
+    if (res_accum > max_val) {
+      return FXRep<XType>::MAX();
+    } else if (res_accum < min_val) {
+      return FXRep<XType>::MIN();
+    }
+    return static_cast<XType>(res_accum);
+  }
+
+  bool result_is_negative = ((n < 0) != (d < 0));
+  int64_t n64 = static_cast<int64_t>(n);
+  int64_t d64 = static_cast<int64_t>(d);
+
+  uint64_t nv = static_cast<uint64_t>(n64 < 0 ? -n64 : n64);
+  uint64_t dv = static_cast<uint64_t>(d64 < 0 ? -d64 : d64);
+
+  if (d == INT_MIN) {
+    nv <<= 1;
+    dv >>= 1;
+  }
+
+  uint32_t clz = cpp::countl_zero<uint32_t>(static_cast<uint32_t>(dv)) - 1;
+  uint64_t scaled_val = dv << clz;
+  // Scale denominator to be in the range of [0.5,1]
+  FXBits<long accum> d_scaled{scaled_val};
+  uint64_t scaled_val_n = nv << clz;
+  // Scale the numerator as much as the denominator to maintain correctness of
+  // the original equation
+  FXBits<long accum> n_scaled{scaled_val_n};
+  long accum n_scaled_val = n_scaled.get_val();
+  long accum d_scaled_val = d_scaled.get_val();
+  // x0 = (48/17) - (32/17) * d_n
+  long accum a = 0x2.d89d89d8p0lk; // 48/17 = 2.8235294...
+  long accum b = 0x1.e1e1e1e1p0lk; // 32/17 = 1.8823529...
+  // Error of the initial approximation, as derived
+  // from the wikipedia article is
+  //  E0 = 1/17 = 0.059 (5.9%)
+  long accum initial_approx = a - (b * d_scaled_val);
+  // Since, 0.5 <= d_scaled_val <= 1.0, 0.9412 <= initial_approx <= 1.88235
+  LIBC_ASSERT((initial_approx >= 0x0.78793dd9p0lk) &&
+              (initial_approx <= 0x1.f0f0d845p0lk));
+  // Each newton-raphson iteration will square the error, due
+  // to quadratic convergence. So,
+  // E1 = (0.059)^2 = 0.0034
+  long accum val = nrstep(d_scaled_val, initial_approx);
+  if constexpr (FXRep<XType>::FRACTION_LEN > 8) {
+    // E2 = 0.0000121
+    val = nrstep(d_scaled_val, val);
+    if constexpr (FXRep<XType>::FRACTION_LEN > 16) {
+      // E3 = 1.468e−10
+      val = nrstep(d_scaled_val, val);
+    }
+  }
+  long accum res = n_scaled_val * val;
+
+  if (result_is_negative) {
+    res *= static_cast<long accum>(-1);
+  }
+
+  // Per clause 7.18a.6.1, saturate values on overflow
+  if (res > max_val) {
+    return FXRep<XType>::MAX();
+  } else if (res < min_val) {
+    return FXRep<XType>::MIN();
+  } else {
+    return static_cast<XType>(res);
+  }
+}
+
 } // namespace fixed_point
 } // namespace LIBC_NAMESPACE_DECL
 

libc/src/stdfix/CMakeLists.txt

@@ -89,6 +89,20 @@ foreach(suffix IN ITEMS r lr k lk ur ulr uk ulk)
   )
 endforeach()
 
+foreach(suffix IN ITEMS r)
+  add_entrypoint_object(
+    ${suffix}divi
+    HDRS
+      ${suffix}divi.h
+    SRCS
+      ${suffix}divi.cpp
+    COMPILE_OPTIONS
+      ${libc_opt_high_flag}
+    DEPENDS
+      libc.src.__support.fixed_point.fx_bits
+  )
+endforeach()
+
 add_entrypoint_object(
   uhksqrtus
   HDRS

libc/src/stdfix/rdivi.cpp

@@ -0,0 +1,21 @@
+//===-- Implementation of rdivi 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 "rdivi.h"
+#include "include/llvm-libc-macros/stdfix-macros.h" // fract
+#include "src/__support/common.h"                   // LLVM_LIBC_FUNCTION
+#include "src/__support/fixed_point/fx_bits.h"      // fixed_point
+#include "src/__support/macros/config.h"            // LIBC_NAMESPACE_DECL
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(fract, rdivi, (int a, int b)) {
+  return fixed_point::divi<fract>(a, b);
+}
+
+} // namespace LIBC_NAMESPACE_DECL

libc/src/stdfix/rdivi.h

@@ -0,0 +1,21 @@
+//===-- Implementation header for rdivi ------------------------*- 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_RDIVI_H
+#define LLVM_LIBC_SRC_STDFIX_RDIVI_H
+
+#include "include/llvm-libc-macros/stdfix-macros.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+fract rdivi(int a, int b);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_STDFIX_RDIVI_H

libc/test/src/stdfix/CMakeLists.txt

@@ -120,6 +120,22 @@ foreach(suffix IN ITEMS r lr k lk ur ulr uk ulk)
   )
 endforeach()
 
+foreach(suffix IN ITEMS r)
+  add_libc_test(
+    ${suffix}divi_test
+    SUITE
+      libc-stdfix-tests
+    HDRS
+      DivITest.h
+    SRCS
+      ${suffix}divi_test.cpp
+    DEPENDS
+      libc.src.stdfix.${suffix}divi
+      libc.src.__support.fixed_point.fx_bits
+      libc.hdr.signal_macros
+  )
+endforeach()
+
 add_libc_test(
   uhksqrtus_test
   SUITE

libc/test/src/stdfix/DivITest.h

@@ -0,0 +1,74 @@
+//===-- Utility class to test fxdivi functions ------------------*- 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
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/CPP/type_traits.h"
+#include "src/__support/fixed_point/fx_bits.h"
+#include "src/__support/fixed_point/fx_rep.h"
+#include "test/UnitTest/Test.h"
+
+template <typename XType> XType get_epsilon() = delete;
+template <> fract get_epsilon() { return FRACT_EPSILON; }
+template <> unsigned fract get_epsilon() { return UFRACT_EPSILON; }
+template <> long fract get_epsilon() { return LFRACT_EPSILON; }
+
+template <typename XType>
+class DivITest : public LIBC_NAMESPACE::testing::Test {
+  using FXRep = LIBC_NAMESPACE::fixed_point::FXRep<XType>;
+  using FXBits = LIBC_NAMESPACE::fixed_point::FXBits<XType>;
+
+public:
+  typedef XType (*DivIFunc)(int, int);
+
+  void testBasic(DivIFunc func) {
+    XType epsilon = get_epsilon<XType>();
+    EXPECT_LT((func(2, 3) - 0.666656494140625r), epsilon);
+    EXPECT_LT((func(3, 4) - 0.75r), epsilon);
+    EXPECT_LT((func(1043, 2764) - 0.3773516643r), epsilon);
+    EXPECT_LT((func(60000, 720293) - 0.08329943509r), epsilon);
+
+    EXPECT_EQ(func(128, 256), 0.5r);
+    EXPECT_EQ(func(1, 2), 0.5r);
+    EXPECT_EQ(func(1, 4), 0.25r);
+    EXPECT_EQ(func(1, 8), 0.125r);
+    EXPECT_EQ(func(1, 16), 0.0625r);
+
+    EXPECT_EQ(func(-1, 2), -0.5r);
+    EXPECT_EQ(func(1, -4), -0.25r);
+    EXPECT_EQ(func(-1, 8), -0.125r);
+    EXPECT_EQ(func(1, -16), -0.0625r);
+  }
+
+  void testSpecial(DivIFunc func) {
+    XType epsilon = get_epsilon<XType>();
+    EXPECT_EQ(func(0, 10), 0.r);
+    EXPECT_EQ(func(0, -10), 0.r);
+    EXPECT_EQ(func(-(1 << FRACT_FBIT), 1 << FRACT_FBIT), FRACT_MIN);
+    EXPECT_EQ(func((1 << FRACT_FBIT) - 1, 1 << FRACT_FBIT), FRACT_MAX);
+    // From Section 7.18a.6.1, functions returning a fixed-point value, the
+    // return value is saturated on overflow.
+    EXPECT_EQ(func(INT_MAX, INT_MAX), FRACT_MAX);
+    EXPECT_LT(func(INT_MAX - 1, INT_MAX) - 0.99999999r, epsilon);
+    EXPECT_EQ(func(INT_MIN, INT_MAX), FRACT_MIN);
+    // Expecting 0 here as fract is not precise enough to
+    // handle 1/INT_MAX
+    EXPECT_LT(func(1, INT_MAX) - 0.r, epsilon);
+    // This results in 1.1739, which should be saturated to FRACT_MAX
+    EXPECT_EQ(func(27, 23), FRACT_MAX);
+
+    EXPECT_EQ(func(INT_MIN, 1), FRACT_MIN);
+    EXPECT_LT(func(1, INT_MIN) - 0.r, epsilon);
+
+    EXPECT_EQ(func(INT_MIN, INT_MIN), 1.r);
+  }
+};
+
+#define LIST_DIVI_TESTS(Name, XType, func)                                     \
+  using LlvmLibc##Name##diviTest = DivITest<XType>;                            \
+  TEST_F(LlvmLibc##Name##diviTest, Basic) { testBasic(&func); }                \
+  TEST_F(LlvmLibc##Name##diviTest, Special) { testSpecial(&func); }            \
+  static_assert(true, "Require semicolon.")