[Derivatives] Implement forward-mode derivative for std::comp_ellint_1 by ayush4874 · Pull Request #1674 · vgvassilev/clad

ayush4874 · 2025-12-11T02:44:06Z

Summary

This PR implements the exact symbolic differentiation rule for std::comp_ellint_1 (Complete Elliptic Integral of the First Kind), resolving the fallback to numerical differentiation.

Fixes #1673

Mathematical Context

The derivative of the First Kind Elliptic Integral $K(k)$ is defined using the Second Kind Integral $E(k)$ as:

$$\frac{dK(k)}{dk} = \frac{E(k) - (1-k^2)K(k)}{k(1-k^2)}$$

where:

$K(k)$ maps to std::comp_ellint_1(k)
$E(k)$ maps to std::comp_ellint_2(k)

Implementation Details

File Modified: clad/Differentiator/BuiltinDerivatives.h
Changes:
- Implemented comp_ellint_1_pushforward in the clad::custom_derivatives namespace.
- Added the corresponding using declaration to register the function in the global lookup scope.
- The implementation handles the C++17 standard library calls for elliptic integrals.

Verification

I tested the implementation locally by differentiating a wrapper function for std::comp_ellint_1.

1. Compilation Check:
The compilation warning falling back to numerical differentiation is gone, confirming Clad is now using the symbolic rule.

2. Numerical Accuracy:
I verified the derivative output at $k = 0.5$:

Analytical Value: 0.541733...
Clad Output: 0.541732

This confirms the implementation produces the correct gradients for physics applications.

ayush4874 · 2025-12-11T04:59:24Z

Hi! I checked the README to find the community chat, but I couldn't find a Gitter or Discord link. Is there an active channel I should join for development discussions?

vgvassilev · 2025-12-11T06:36:59Z

include/clad/Differentiator/BuiltinDerivatives.h

 using std::pow_pullback;
 using std::pow_pushforward;
 using std::sqrt_pushforward;
+using std::comp_ellint_1_pushforward;


We will need a pullback for this and also tests.

Thanks for the review!

I replaced the manual pullback with comp_ellint_1_darg0 (derivative w.r.t arg 0). This allows Clad to automatically derive the reverse-mode pullback, resolving the signature ambiguity.

I also added a regression test (clad/test/Differentiator/EllipticTest.cpp) and verified the gradients against the analytical values locally.

Verification Output:

Forward Derivative: 0.541732 Reverse Derivative: 0.541732

vgvassilev · 2025-12-12T19:14:23Z

include/clad/Differentiator/BuiltinDerivatives.h

+// -------------------------------------------------------------------------
+// [Ayush GSoC 2026 Contribution]
+// Feature: Added support for Complete Elliptic Integral of the First Kind
+// Target: std::comp_ellint_1(k)
+// Formula: dK/dk = (E(k) - (1-k^2)*K(k)) / (k * (1-k^2))


Remove the redundant comments.

vgvassilev · 2025-12-12T19:16:20Z

test/Differentiator/EllipticTest.cpp

@@ -0,0 +1,33 @@
+// RUN: %clangxx -fplugin=%clad_plugin -std=c++17 %s -o %t


This test should be part of test/Features/stl-cmath.cpp

Done. I've moved the test case into test/Features/stl-cmath.cpp and removed the verbose comments from the header file.

vgvassilev · 2025-12-13T12:41:20Z

test/Features/stl-cmath.cpp

 //
 DEFINE_FUNCTIONS(erf)  // x in (-inf,+inf)

+double comp_ellint_1_wrapper(double k) {


You need to make this look the same as the other functions.

Done. Since comp_ellint_1 is a C++17 addition and does not have a legacy C equivalent (like comp_ellint_1f), I could not use the DEFINE_FUNCTIONS macro directly.

However, I have manually defined a templated wrapper f_comp_ellint_1 that follows the exact same naming convention and pattern as the macro, ensuring consistency with the rest of the file.

vgvassilev · 2025-12-13T17:44:40Z

test/Features/stl-cmath.cpp

-double comp_ellint_1_wrapper(double k) {
-  return std::comp_ellint_1(k);
-}
+// Manually defined to match DEFINE_FUNCTIONS pattern (comp_ellint_1f does not exist)


Still does not look as the surroundings. Please make sure you understand this file and its comments.

My apologies for the oversight. I realized upon closer inspection that DEFINE_FUNCTIONS generates suffix variants (f_...f, f_...l) that my previous template missed.

I have now added f_comp_ellint_1f and f_comp_ellint_1l manually to fully replicate the macro's behavior as requested.

vgvassilev · 2025-12-14T08:01:31Z

test/Features/stl-cmath.cpp

+inline float f_comp_ellint_1f(float x) { return std::comp_ellint_1(x); }
+inline long double f_comp_ellint_1l(long double x) { return std::comp_ellint_1(x); }


Why we cannot use DEFINE_FUNCTIONS here? Note this is missing the pullbacks and updating the section with the proper comment // ---- special fns. Also misses updating the table in the beginning of the file. Misses the range...

As I've said -- needs to look like the other functions tests in the same file.

I have updated the file to fully match the surrounding style and structure as requested:

Added comp_ellint_1 to the feature table at the top of the file.

Moved the implementation to the "Special Functions" section with the // k in (-1, 1) range comment.

Defined comp_ellint_1f and comp_ellint_1l wrappers so I can use DEFINE_FUNCTIONS(comp_ellint_1) directly.

Updated the test case in main() to use the standard CHECK_ALL_RANGE macro.

@vgvassilev it's ready for review, can you have a look?

Why adding only this special function and not the rest?

I initially isolated comp_ellint_1 to ensure the testing pattern for special functions was correct before expanding.

Since comp_ellint_2 (Complete Elliptic Integral of the Second Kind) is actually required for the derivative of comp_ellint_1, it is logical to group them. I will update this PR to include std::comp_ellint_2 and std::comp_ellint_3 so they can be reviewed together. I'll push those changes shortly.

Done, can you have a look?

github-actions

clang-tidy made some suggestions

github-actions · 2026-01-03T20:37:18Z

include/clad/Differentiator/BuiltinDerivatives.h

+}
+
+// This allows Clad to auto-generate both Forward and Reverse mode.
+CUDA_HOST_DEVICE double comp_ellint_1_darg0(double k) {


warning: function 'comp_ellint_1_darg0' defined in a header file; function definitions in header files can lead to ODR violations [misc-definitions-in-headers]

CUDA_HOST_DEVICE double comp_ellint_1_darg0(double k) { ^

Additional context

include/clad/Differentiator/BuiltinDerivatives.h:1079: make as 'inline'

CUDA_HOST_DEVICE double comp_ellint_1_darg0(double k) { ^

vgvassilev · 2026-01-10T08:24:02Z

include/clad/Differentiator/BuiltinDerivatives.h

  *d_y += (y / h) * d_z;
 }

+CUDA_HOST_DEVICE inline double comp_ellint_1_darg0(double k) {


Do we need the _darg versions here?

You're right, we don't need them. I've removed the _darg helpers and moved the derivative logic directly inside the pushforward templates.

vgvassilev · 2026-01-12T06:34:46Z

test/Features/stl-cmath.cpp

+inline float comp_ellint_1f(float x) { return std::comp_ellint_1(x); }
+inline long double comp_ellint_1l(long double x) { return std::comp_ellint_1(x); }
+
+DEFINE_FUNCTIONS(comp_ellint_1)


Can you add the domain of x?

Done. I've added comments specifying the domain is k in (-1, 1) for these integrals.

look how was done for the other functions.

vgvassilev · 2026-01-12T06:35:30Z

test/Features/stl-cmath.cpp

+  double k = 0.5, nu = 0.3;
+
+  // Test differentiation w.r.t 'k' (Arg 0)
+  auto d_ellint3_k = clad::differentiate(std::comp_ellint_3, 0);
+  double res_k = d_ellint3_k.execute(k, nu);
+
+  // Test differentiation w.r.t 'nu' (Arg 1)
+  auto d_ellint3_nu = clad::differentiate(std::comp_ellint_3, 1);
+  double res_nu = d_ellint3_nu.execute(k, nu);
+
+  // Simple check to ensure we got numbers back (prevents unused var warning)
+  (void)res_k; 
+  (void)res_nu;


Here we should compare against the numerical, right? See what the CHECK macro does.

You are right. I updated the test to compare the symbolic result against a Finite Difference numerical approximation. The test will now fail (return 1) if the derivative deviates from the numerical reference.

vgvassilev · 2026-01-12T09:36:32Z

test/Features/stl-cmath.cpp

+inline float comp_ellint_1f(float x) { return std::comp_ellint_1(x); }
+inline long double comp_ellint_1l(long double x) { return std::comp_ellint_1(x); }
+
+DEFINE_FUNCTIONS(comp_ellint_1)


look how was done for the other functions.

vgvassilev · 2026-01-12T09:36:51Z

test/Features/stl-cmath.cpp

-  double res_k = d_ellint3_k.execute(k, nu);
+  double sym_k = d_ellint3_k.execute(k, nu);
+  // Numerical approximation: (f(k+h) - f(k-h)) / 2h
+  double num_k = (std::comp_ellint_3(k + h, nu) - std::comp_ellint_3(k - h, nu)) / (2 * h);


There is an api in this file that gets you the numerical part.

I see the pattern now. I updated the tests to match atan2 and pow by using the f_ wrappers.

For comp_ellint_3, I fixed the second arg in the wrapper so I can just use CHECK_ALL_RANGE, which handles the numerical verification automatically.

vgvassilev

LGTM!

vgvassilev · 2026-02-03T09:53:07Z

(assuming the bots are green)

github-actions · 2026-02-03T09:54:23Z

clang-tidy review says "All clean, LGTM! 👍"

ayush4874 · 2026-02-03T14:40:33Z

CI failures were caused by comp_ellint_1 (C++17) breaking the C++11/14 builds.

I’ve added #if __cplusplus >= 201703L guards around the implementation and using declarations in BuiltinDerivatives.h. The build should pass now.

Implemented the derivative of the Complete Elliptic Integral of the First Kind (std::comp_ellint_1) using the standard formula involving std::comp_ellint_2. Verified against numerical differentiation.

…cro, sections)

…erical API

github-actions · 2026-02-03T18:13:29Z

clang-tidy review says "All clean, LGTM! 👍"

github-actions · 2026-02-04T06:52:09Z

clang-tidy review says "All clean, LGTM! 👍"

… errors

github-actions · 2026-02-06T11:38:08Z

clang-tidy review says "All clean, LGTM! 👍"

vgvassilev · 2026-02-18T07:16:01Z

Hi @ayush4874, what is the state of this PR -- it seems to be failing on a lot of platforms.

…lint derivatives

ayush4874 · 2026-02-19T16:53:48Z

Hi @vgvassilev, apologies, I was busy with semester exams. I just pushed the fix for the CI failures.

The root cause was a type promotion mismatch. libstdc++ silently promotes float to double for these elliptic integrals. Since my _pushforward templates were strictly returning T, Clad rejected the signature, fell back to parsing the raw STL headers, and tripped over __builtin_isnan (which triggered the -Werror failures).

I fixed it by updating the templates with decltype and AdjOutType to catch the exact promoted return type. I also dropped the manual pullbacks for the 1-arg functions (comp_ellint_1 and 2) since Clad auto-derives them anyway, but I kept the explicit pullback for the multi-variable comp_ellint_3.

Tests are passing cleanly locally now.

github-actions · 2026-02-19T17:30:33Z

clang-tidy review says "All clean, LGTM! 👍"

codecov · 2026-02-19T17:35:11Z

Codecov Report

✅ All modified and coverable lines are covered by tests.

📢 Thoughts on this report? Let us know!

…ibility and fix clang-format

ayush4874 · 2026-02-19T17:49:06Z

Pushed a fix for the Mac CI failures. Older versions of libc++ don't support these math functions, so I added the proper macro guards. Formatting is fixed too.

vgvassilev reviewed Dec 11, 2025

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vgvassilev approved these changes Feb 3, 2026

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vgvassilev force-pushed the feature/ellint-derivatives branch from 3944d20 to 2190f7b Compare February 3, 2026 09:46

ayush4874 added 11 commits February 3, 2026 20:08

[Derivatives] Add support for std::comp_ellint_1

1f55b2f

Implemented the derivative of the Complete Elliptic Integral of the First Kind (std::comp_ellint_1) using the standard formula involving std::comp_ellint_2. Verified against numerical differentiation.

Implement derivative (darg0) and tests for std::comp_ellint_1

a4df60d

Refactor: Move ellint_1 test to stl-cmath.cpp and clean comments

5f82a9d

Refactor: Use templated wrapper for ellint_1 to match test style

98de955

Refactor: Add full set of manual wrappers (f/l suffixes) for ellint_1

7e4deb8

Refactor: Integrate comp_ellint_1 fully into stl-cmath.cpp (table, ma…

32e0513

…cro, sections)

Fix: Resolve ODR violation and implement comp_ellint_2/3

984e443

Refactor: Inline derivative logic into pushforward templates

e7cf40f

Test: Add domain comments and verify comp_ellint_3 numerically

4693ac0

Test: Refactor comp_ellint tests to match atan2/pow style and use num…

1e46a93

…erical API

Fix: Guard C++17 ellint derivatives to fix CI build on older standards

c686d61

vgvassilev force-pushed the feature/ellint-derivatives branch from 523878c to c686d61 Compare February 3, 2026 18:08

Fix: Guard C++17 test code for older compilers

b6b2156

ayush4874 added 2 commits February 4, 2026 09:56

Fix: Remove redundant DEFINE_FUNCTIONS macros to resolve redefinition…

e8be707

… errors

Fix: Use correct initializer list syntax for elliptic integral tests

bece3fe

Fix: Resolve CI failures by fixing type promotion mismatch in comp_el…

6b6d0c7

…lint derivatives

Fix: Guard ellint functions with feature test macros for macOS compat…

71439f3

…ibility and fix clang-format

		@@ -0,0 +1,33 @@
		// RUN: %clangxx -fplugin=%clad_plugin -std=c++17 %s -o %t

		inline float f_comp_ellint_1f(float x) { return std::comp_ellint_1(x); }
		inline long double f_comp_ellint_1l(long double x) { return std::comp_ellint_1(x); }

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ayush4874 commented Dec 11, 2025

Summary

Mathematical Context

Implementation Details

Verification

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