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

bojle · 2025-08-22T09:07:02Z

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.

@lntue @PiJoules

github-actions · 2025-08-22T09:07:19Z

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llvmbot · 2025-08-22T09:07:53Z

@llvm/pr-subscribers-libc

Author: Shreeyash Pandey (bojle)

Changes

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.

Full diff: https://github.com/llvm/llvm-project/pull/154914.diff

6 Files Affected:

(modified) libc/config/linux/riscv/entrypoints.txt (+1)
(modified) libc/config/linux/x86_64/entrypoints.txt (+1)
(modified) libc/include/stdfix.yaml (+8)
(modified) libc/src/__support/fixed_point/fx_bits.h (+41)
(modified) libc/src/stdfix/CMakeLists.txt (+14)
(modified) libc/test/src/stdfix/CMakeLists.txt (+16)

diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 1a03683d72e61..b783dd4b04c74 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/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()
 
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 5590f1a15ac57..f6beccc7229dd 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/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()
 
diff --git a/libc/include/stdfix.yaml b/libc/include/stdfix.yaml
index 5b385124eb63d..451330c3478d2 100644
--- a/libc/include/stdfix.yaml
+++ b/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
diff --git a/libc/src/__support/fixed_point/fx_bits.h b/libc/src/__support/fixed_point/fx_bits.h
index 00c6119b4f353..13eecba981664 100644
--- a/libc/src/__support/fixed_point/fx_bits.h
+++ b/libc/src/__support/fixed_point/fx_bits.h
@@ -224,6 +224,47 @@ idiv(T x, T y) {
   return static_cast<XType>(result);
 }
 
+inline long accum nrstep(long accum d, long accum x0) {
+  auto v = x0 * (2 - (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);
+
+  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 */
+  long accum initial_approx = a - (b * d_scaled_val);
+  long accum val = nrstep(d_scaled_val, initial_approx);
+  val = nrstep(d_scaled_val, val);
+  val = nrstep(d_scaled_val, val);
+  val = nrstep(d_scaled_val, val);
+  long accum res = n_scaled_val * val;
+  return static_cast<XType>(res);
+}
+
 } // namespace fixed_point
 } // namespace LIBC_NAMESPACE_DECL
 
diff --git a/libc/src/stdfix/CMakeLists.txt b/libc/src/stdfix/CMakeLists.txt
index 843111e3f80b1..3cbabd17ad34c 100644
--- a/libc/src/stdfix/CMakeLists.txt
+++ b/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
diff --git a/libc/test/src/stdfix/CMakeLists.txt b/libc/test/src/stdfix/CMakeLists.txt
index e2b4bc1805f7c..741522276feaa 100644
--- a/libc/test/src/stdfix/CMakeLists.txt
+++ b/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

llvmbot · 2025-08-22T09:07:53Z

@llvm/pr-subscribers-backend-risc-v

Author: Shreeyash Pandey (bojle)

Changes

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.

Full diff: https://github.com/llvm/llvm-project/pull/154914.diff

6 Files Affected:

(modified) libc/config/linux/riscv/entrypoints.txt (+1)
(modified) libc/config/linux/x86_64/entrypoints.txt (+1)
(modified) libc/include/stdfix.yaml (+8)
(modified) libc/src/__support/fixed_point/fx_bits.h (+41)
(modified) libc/src/stdfix/CMakeLists.txt (+14)
(modified) libc/test/src/stdfix/CMakeLists.txt (+16)

diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 1a03683d72e61..b783dd4b04c74 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/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()
 
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 5590f1a15ac57..f6beccc7229dd 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/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()
 
diff --git a/libc/include/stdfix.yaml b/libc/include/stdfix.yaml
index 5b385124eb63d..451330c3478d2 100644
--- a/libc/include/stdfix.yaml
+++ b/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
diff --git a/libc/src/__support/fixed_point/fx_bits.h b/libc/src/__support/fixed_point/fx_bits.h
index 00c6119b4f353..13eecba981664 100644
--- a/libc/src/__support/fixed_point/fx_bits.h
+++ b/libc/src/__support/fixed_point/fx_bits.h
@@ -224,6 +224,47 @@ idiv(T x, T y) {
   return static_cast<XType>(result);
 }
 
+inline long accum nrstep(long accum d, long accum x0) {
+  auto v = x0 * (2 - (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);
+
+  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 */
+  long accum initial_approx = a - (b * d_scaled_val);
+  long accum val = nrstep(d_scaled_val, initial_approx);
+  val = nrstep(d_scaled_val, val);
+  val = nrstep(d_scaled_val, val);
+  val = nrstep(d_scaled_val, val);
+  long accum res = n_scaled_val * val;
+  return static_cast<XType>(res);
+}
+
 } // namespace fixed_point
 } // namespace LIBC_NAMESPACE_DECL
 
diff --git a/libc/src/stdfix/CMakeLists.txt b/libc/src/stdfix/CMakeLists.txt
index 843111e3f80b1..3cbabd17ad34c 100644
--- a/libc/src/stdfix/CMakeLists.txt
+++ b/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
diff --git a/libc/test/src/stdfix/CMakeLists.txt b/libc/test/src/stdfix/CMakeLists.txt
index e2b4bc1805f7c..741522276feaa 100644
--- a/libc/test/src/stdfix/CMakeLists.txt
+++ b/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

PiJoules · 2025-08-22T18:08:04Z

Thanks. Could you add some tests for this?

bojle · 2025-08-22T18:18:01Z

Oops, forgot to add them. I've pushed the tests too. Please check now. @PiJoules

libc/test/src/stdfix/DivITest.h

libc/src/__support/fixed_point/fx_bits.h

github-actions · 2025-08-26T15:43:52Z

✅ With the latest revision this PR passed the C/C++ code formatter.

libc/src/__support/fixed_point/fx_bits.h

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

libc/test/src/stdfix/DivITest.h

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

PiJoules

I think we're almost there. Just a couple more changes to test I'd like to see for more confidence.

libc/test/src/stdfix/DivITest.h

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

PiJoules

LGTM. Lets wait for @lntue to take another look before submitting.

bojle · 2025-09-12T14:28:15Z

Hi @PiJoules,
If @lntue isn't available, can we have someone else from libc take a look at this?
Once this is merged, I plan to start and finish other fxdivi implementations.

libc/src/__support/fixed_point/fx_bits.h

lntue · 2025-09-12T15:05:32Z

libc/src/__support/fixed_point/fx_bits.h

+  long accum a = 2.8235lk; /* 48/17 */
+  long accum b = 1.8823lk; /* 32/17 */


Use hexadecimal to be precise. 5-decimal-digit precision is not enough to specified 32-bit fractional part of long accum

libc/src/__support/fixed_point/fx_bits.h

lntue · 2025-09-12T15:13:16Z

From clang-format CI:

error: clang-format exited with code 1
diff --git a/libc/src/stdfix/rdivi.cpp b/libc/src/stdfix/rdivi.cpp
index 56de3eb3a..7021a8b1c 100644
--- a/libc/src/stdfix/rdivi.cpp
+++ b/libc/src/stdfix/rdivi.cpp
@@ -6,11 +6,11 @@
 //
 //===----------------------------------------------------------------------===//
 
-#include "include/llvm-libc-macros/stdfix-macros.h" // fract
 #include "rdivi.h"
-#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
+#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 {

libc/src/__support/fixed_point/fx_bits.h

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

libc/src/__support/fixed_point/fx_bits.h

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

lntue · 2025-09-26T15:26:32Z

libc/src/__support/fixed_point/fx_bits.h

+  // E2 = 0.0000121
+  val = nrstep(d_scaled_val, val);
+  // E3 = 1.468e−10
+  val = nrstep(d_scaled_val, val);
+


We can skip further Newton-Raphson steps for smaller types:

if constexpr (FXRep<XType>::FRACTION_LENGTH > 8) { val = nrstep(...); if constexpr(FXRep<XType>::FRACTION_LENGTH > 16) val = nrstep(...); }

Doing this, I end up losing precision for finite result tests. For example, 128/256 results in 0.499969. With 3 iterations, the result is precisely 0.5. If the results, even for finite tests is acceptable to be +- epsilon, I can re-write the tests to do EXPECT_LT instead of EXPECT_EQ

Theoretically, to get correct rounding for division, we will need twice the precision. So with 32-bit inputs, we will need 64-bit precision before rounding to the targeted format. In here, we are actually operating on a bit more than 32-bit precision, so there will be results that are not correctly rounded.

Nonetheless, dividing a power of 2 not correctly might be a surprise to people, so maybe we can add a special branch for the case d is a power of 2. WDYT?

Since this is a performance tradeoff, having performance numbers would be a
good idea. The difference is 3 inline function calls back to back vs a for
loop with a bound only known at runtime. The former has a clear dataflow with
no branches (pipeline friendly?), and latter has a cmp and branch with unknown
loop count. We could measure both, then make this decision?

I made these mods to the code:

long accum val = nrstep(d_scaled_val, initial_approx); if (isPowerOfTwo(d)) { // E2 = 0.0000121 val = nrstep(d_scaled_val, val); // E3 = 1.468e−10 val = nrstep(d_scaled_val, val); }

and set up a naive time measurement script.

The results:

With contiguos 3 iterations (dividing 76/128 for 10k iterations): 650us With if statements for po2 (76/128 for 10k iterations): 526us

So, I think I should add checks for po2.

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

lntue · 2025-10-06T02:23:41Z

libc/src/__support/fixed_point/fx_bits.h

+  // Division with a power of 2 would generally be expected to be
+  // exact, we handle this by specially treating po2 cases and having
+  // extra iterations for them.
+  if (FXRep<XType>::FRACTION_LEN > 8 || isPowerOfTwo(cpp::abs(d))) {


when the denominator is a power of two, it's better to just perform right shifts (be careful with signed-ness and overflow). Then the other conditions on the fraction lengths can be constexpr, i.e. no runtime cost.

llvmbot added backend:RISC-V libc labels Aug 22, 2025

bojle mentioned this pull request Aug 22, 2025

Implement fixed point fxdivi functions in llvm-libc #129126

Open

PiJoules requested review from PiJoules and lntue August 22, 2025 18:01

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[libc][stdfix] Implement fxdivi functions

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[libc] add a few tests to handles edge cases with FRACT_{MIN/MAX}

71d283b

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[libc] fix formatting for rdivi.cpp

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[libc] comments, remove extra iterations, and misc changes

c614888

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lntue reviewed Oct 6, 2025

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		long accum a = 2.8235lk; /* 48/17 */
		long accum b = 1.8823lk; /* 32/17 */

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

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

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