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

libc/config/linux/riscv/entrypoints.txt

@@ -986,6 +986,7 @@ 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

@@ -1019,6 +1019,7 @@ if(LIBC_COMPILER_HAS_FIXED_POINT)
     libc.src.stdfix.idivulr
     libc.src.stdfix.idivuk
     libc.src.stdfix.idivulk
+    libc.src.stdfix.rdivi
   )
 endif()
 

libc/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

@@ -224,6 +224,70 @@ 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();
+  }
+  bool d_is_signed = false;
+  if (d < 0) {
+    d = (d * -1);
+    d_is_signed = true;
+  }
+
+  unsigned int nv = static_cast<unsigned int>(n);
+  unsigned int dv = static_cast<unsigned int>(d);
+  unsigned int clz = cpp::countl_zero<unsigned int>(dv) - 1;
+  unsigned long int scaled_val = dv << clz;
+  /* Scale denominator to be in the range of [0.5,1] */
+  FXBits<long accum> d_scaled{scaled_val};
+  unsigned long int 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 = 2.8235lk; /* 48/17 */
+  long accum b = 1.8823lk; /* 32/17 */
+  /* 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);
+  /* 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);
+  /* E2 = 0.0000121 */
+  val = nrstep(d_scaled_val, val);
+  /* E3 = 1.468e−10 */
+  val = nrstep(d_scaled_val, val);
+  /* E4 = 2.155e−20 */
+  val = nrstep(d_scaled_val, val);
+  long accum res = n_scaled_val * val;
+  if (d_is_signed) {
+    res *= static_cast<XType>(-1);
+  }
+  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 +1,65 @@
+//===-- 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) {
+    EXPECT_EQ(func(0,10), 0.r);
+    EXPECT_EQ(func(0,-10), 0.r);
+    EXPECT_EQ(func(-32768,32768), FRACT_MIN);
+    EXPECT_EQ(func(32767,32768), FRACT_MAX);  
+    EXPECT_EQ(func(INT_MAX,INT_MAX), 1.0r);
+    EXPECT_EQ(func(INT_MAX-1,INT_MAX), 0.99999999r);
+    EXPECT_EQ(func(INT_MIN,INT_MAX), FRACT_MIN);
+    /* Expecting 0 here as fract is not precise enough to 
+     * handle 1/INT_MAX
+     */
+    EXPECT_EQ(func(1, INT_MAX), 0.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.")

libc/test/src/stdfix/rdivi_test.cpp

@@ -0,0 +1,14 @@
+//===-- Unittests for rdivi -----------------------------------------------===//
+//
+// 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 "DivITest.h"
+
+#include "llvm-libc-macros/stdfix-macros.h" // fract
+#include "src/stdfix/rdivi.h"
+
+LIST_DIVI_TESTS(r, fract, LIBC_NAMESPACE::rdivi);