From d6252a1620d192e753440588ea66156bf6198728 Mon Sep 17 00:00:00 2001
From: Karan Anand <anandkarancompsci@gmail.com>
Date: Thu, 27 Aug 2026 10:06:36 +0530
Subject: [PATCH 1/4] docs: add equations to combined and pi-scaled function
 READMEs

Add defining equations to the intro sections of sincos, sincosd,
sincospi, sinpi, cospi, atan2, cosm1 and their single-precision
variants. Includes range constraints for atan2.

Ref: https://github.com/stdlib-js/metr-issue-tracker/issues/1257
---
 .../@stdlib/math/base/special/atan2/README.md | 18 +++++++++++++++++
 .../math/base/special/atan2d/README.md        | 18 +++++++++++++++++
 .../math/base/special/atan2f/README.md        | 18 +++++++++++++++++
 .../@stdlib/math/base/special/cosm1/README.md | 16 +++++++++++++++
 .../math/base/special/cosm1f/README.md        | 16 +++++++++++++++
 .../@stdlib/math/base/special/cospi/README.md | 18 +++++++++++++++++
 .../math/base/special/cospif/README.md        | 18 +++++++++++++++++
 .../math/base/special/sincos/README.md        | 20 +++++++++++++++++++
 .../math/base/special/sincosd/README.md       | 18 +++++++++++++++++
 .../math/base/special/sincosdf/README.md      | 18 +++++++++++++++++
 .../math/base/special/sincosf/README.md       | 20 +++++++++++++++++++
 .../math/base/special/sincospi/README.md      | 20 +++++++++++++++++++
 .../math/base/special/sincospif/README.md     | 20 +++++++++++++++++++
 .../@stdlib/math/base/special/sinpi/README.md | 18 +++++++++++++++++
 .../math/base/special/sinpif/README.md        | 18 +++++++++++++++++
 15 files changed, 274 insertions(+)

diff --git a/lib/node_modules/@stdlib/math/base/special/atan2/README.md b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
index ae83ba4074a4..66802940b5cc 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
+<section class="intro">
+
+The two-argument [arctangent][arctangent] function is defined as
+
+<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\theta = \operatorname{atan2}(y, x), \quad \theta \in (-\pi, \pi]" alt="Two-argument arctangent function"> -->
+
+```math
+\theta = \mathop{\mathrm{atan2}}(y, x), \quad \theta \in (-\pi, \pi]
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -197,6 +213,8 @@ int main( void ) {
 
 <section class="links">
 
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
 <!-- <related-links> -->
 
 [@stdlib/math/base/special/atan]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/atan
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
index fec877abb79d..50c820b29791 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the angle in the plane (in degrees) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
+<section class="intro">
+
+The two-argument [arctangent][arctangent] function returning an angle in degrees is defined as
+
+<!-- <equation class="equation" label="eq:atan2d_function" align="center" raw="\theta = \frac{180}{\pi} \operatorname{atan2}(y, x), \quad \theta \in (-180, 180]" alt="Two-argument arctangent function in degrees"> -->
+
+```math
+\theta = \frac{180}{\pi} \mathop{\mathrm{atan2}}(y, x), \quad \theta \in (-180, 180]
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -192,6 +208,8 @@ int main( void ) {
 
 <section class="links">
 
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
 <!-- <related-links> -->
 
 <!-- </related-links> -->
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
index 7285ee42a6f8..581bd353acc3 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)` as a single-precision floating-point number.
 
+<section class="intro">
+
+The two-argument [arctangent][arctangent] function is defined as
+
+<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\theta = \operatorname{atan2}(y, x), \quad \theta \in (-\pi, \pi]" alt="Two-argument arctangent function"> -->
+
+```math
+\theta = \mathop{\mathrm{atan2}}(y, x), \quad \theta \in (-\pi, \pi]
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -191,6 +207,8 @@ int main( void ) {
 
 <section class="links">
 
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
 <!-- <related-links> -->
 
 <!-- </related-links> -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cosm1/README.md b/lib/node_modules/@stdlib/math/base/special/cosm1/README.md
index 200f79b7ad85..def42b411c91 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosm1/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosm1/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `cos(x) - 1`.
 
+<section class="intro">
+
+The function computes `cos(x) - 1` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:cosm1_function" align="center" raw="y = \cos(x) - 1" alt="Cosine minus one"> -->
+
+```math
+y = \cos(x) - 1
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md b/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md
index 3a4ed265f183..cd389f636c1c 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `cos(x) - 1`.
 
+<section class="intro">
+
+The function computes `cos(x) - 1` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:cosm1_function" align="center" raw="y = \cos(x) - 1" alt="Cosine minus one"> -->
+
+```math
+y = \cos(x) - 1
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cospi/README.md b/lib/node_modules/@stdlib/math/base/special/cospi/README.md
index 45e09dd1aa80..fc242db8d35a 100644
--- a/lib/node_modules/@stdlib/math/base/special/cospi/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cospi/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosine][@stdlib/math/base/special/cos] of a number times [π][@stdlib/constants/float64/pi].
 
+<section class="intro">
+
+The function computes the [cosine][cosine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:cospi_function" align="center" raw="y = \cos(\pi x)" alt="Cosine of pi times x"> -->
+
+```math
+y = \cos(\pi x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -178,6 +194,8 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
 [@stdlib/constants/float64/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float64/pi
 
 <!-- <related-links> -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cospif/README.md b/lib/node_modules/@stdlib/math/base/special/cospif/README.md
index fabd3e9d5434..60928ae8b6ab 100644
--- a/lib/node_modules/@stdlib/math/base/special/cospif/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cospif/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosine][@stdlib/math/base/special/cosf] of a number times [π][@stdlib/constants/float32/pi].
 
+<section class="intro">
+
+The function computes the [cosine][cosine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:cospi_function" align="center" raw="y = \cos(\pi x)" alt="Cosine of pi times x"> -->
+
+```math
+y = \cos(\pi x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -172,6 +188,8 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
 [@stdlib/constants/float32/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float32/pi
 
 [@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf
diff --git a/lib/node_modules/@stdlib/math/base/special/sincos/README.md b/lib/node_modules/@stdlib/math/base/special/sincos/README.md
index cea6faf3a09e..6a7b5a1b89f9 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincos/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincos/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sin] and [cosine][@stdlib/math/base/special/cos] of an angle measured in radians.
 
+<section class="intro">
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number
+
+<!-- <equation class="equation" label="eq:sincos_function" align="center" raw="(y_s, y_c) = (\sin(x),\; \cos(x))" alt="Simultaneous sine and cosine"> -->
+
+```math
+(y_s, y_c) = (\sin(x),\; \cos(x))
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -198,6 +214,10 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 <!-- <related-links> -->
 
 [@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos
diff --git a/lib/node_modules/@stdlib/math/base/special/sincosd/README.md b/lib/node_modules/@stdlib/math/base/special/sincosd/README.md
index 276fdf307c16..3d4364188981 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincosd/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincosd/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sind] and [cosine][@stdlib/math/base/special/cosd] of an angle measured in degrees.
 
+<section class="intro">
+
+The function simultaneously computes the [sine][trigonometric-functions] and [cosine][trigonometric-functions] of an angle measured in degrees
+
+<!-- <equation class="equation" label="eq:sincosd_function" align="center" raw="(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)" alt="Simultaneous sine and cosine of an angle in degrees"> -->
+
+```math
+(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -191,6 +207,8 @@ int main( void ) {
 
 <section class="links">
 
+[trigonometric-functions]: https://en.wikipedia.org/wiki/Trigonometric_functions
+
 [@stdlib/math/base/special/cosd]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosd
 
 [@stdlib/math/base/special/sind]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sind
diff --git a/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md b/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md
index d4b46c2a8ba7..c03db37c19be 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sindf] and [cosine][@stdlib/math/base/special/cosdf] of a single-precision floating-point number (in degrees).
 
+<section class="intro">
+
+The function simultaneously computes the [sine][trigonometric-functions] and [cosine][trigonometric-functions] of an angle measured in degrees
+
+<!-- <equation class="equation" label="eq:sincosd_function" align="center" raw="(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)" alt="Simultaneous sine and cosine of an angle in degrees"> -->
+
+```math
+(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -191,6 +207,8 @@ int main( void ) {
 
 <section class="links">
 
+[trigonometric-functions]: https://en.wikipedia.org/wiki/Trigonometric_functions
+
 [@stdlib/math/base/special/cosdf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosdf
 
 [@stdlib/math/base/special/sindf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sindf
diff --git a/lib/node_modules/@stdlib/math/base/special/sincosf/README.md b/lib/node_modules/@stdlib/math/base/special/sincosf/README.md
index 679924d9dec2..72c2f5394a73 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincosf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincosf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sinf] and [cosine][@stdlib/math/base/special/cosf] of a single-precision floating-point number (in radians).
 
+<section class="intro">
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number
+
+<!-- <equation class="equation" label="eq:sincos_function" align="center" raw="(y_s, y_c) = (\sin(x),\; \cos(x))" alt="Simultaneous sine and cosine"> -->
+
+```math
+(y_s, y_c) = (\sin(x),\; \cos(x))
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -195,6 +211,10 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 [@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf
 
 [@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
diff --git a/lib/node_modules/@stdlib/math/base/special/sincospi/README.md b/lib/node_modules/@stdlib/math/base/special/sincospi/README.md
index 06adafc353f9..8bc8676c31c2 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincospi/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincospi/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sin] and [cosine][@stdlib/math/base/special/cos] of a number times [π][@stdlib/constants/float64/pi].
 
+<section class="intro">
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:sincospi_function" align="center" raw="(y_s, y_c) = (\sin(\pi x),\; \cos(\pi x))" alt="Sine and cosine of pi times x"> -->
+
+```math
+(y_s, y_c) = (\sin(\pi x),\; \cos(\pi x))
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -200,6 +216,10 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 [@stdlib/math/base/special/sin]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sin
 
 [@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos
diff --git a/lib/node_modules/@stdlib/math/base/special/sincospif/README.md b/lib/node_modules/@stdlib/math/base/special/sincospif/README.md
index e67b2a4f836c..f859afd8c78c 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincospif/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincospif/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sinf] and [cosine][@stdlib/math/base/special/cosf] of a single-precision floating-point number times [π][@stdlib/constants/float32/pi].
 
+<section class="intro">
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:sincospi_function" align="center" raw="(y_s, y_c) = (\sin(\pi x),\; \cos(\pi x))" alt="Sine and cosine of pi times x"> -->
+
+```math
+(y_s, y_c) = (\sin(\pi x),\; \cos(\pi x))
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -202,6 +218,10 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 [@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
 
 [@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf
diff --git a/lib/node_modules/@stdlib/math/base/special/sinpi/README.md b/lib/node_modules/@stdlib/math/base/special/sinpi/README.md
index b94fa78f78ce..5344b75b52de 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinpi/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinpi/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [sine][@stdlib/math/base/special/sin] of a number times [π][@stdlib/constants/float64/pi].
 
+<section class="intro">
+
+The function computes the [sine][sine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:sinpi_function" align="center" raw="y = \sin(\pi x)" alt="Sine of pi times x"> -->
+
+```math
+y = \sin(\pi x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -178,6 +194,8 @@ int main( void ) {
 
 <section class="links">
 
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 [@stdlib/constants/float64/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float64/pi
 
 <!-- <related-links> -->
diff --git a/lib/node_modules/@stdlib/math/base/special/sinpif/README.md b/lib/node_modules/@stdlib/math/base/special/sinpif/README.md
index 2621ef1a6635..65f05bccb74c 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinpif/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinpif/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [sine][@stdlib/math/base/special/sinf] of a number times [π][@stdlib/constants/float32/pi].
 
+<section class="intro">
+
+The function computes the [sine][sine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:sinpi_function" align="center" raw="y = \sin(\pi x)" alt="Sine of pi times x"> -->
+
+```math
+y = \sin(\pi x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -172,6 +188,8 @@ int main( void ) {
 
 <section class="links">
 
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 [@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
 
 [@stdlib/constants/float32/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float32/pi

From 1dfd07d8a00de754f47d405bb8536887f6fae1b7 Mon Sep 17 00:00:00 2001
From: Karan Anand <anandkarancompsci@gmail.com>
Date: Fri, 4 Sep 2026 00:54:22 +0530
Subject: [PATCH 2/4] chore: code review

---
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description: Results of running static analysis checks when committing changes.
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  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 .../@stdlib/math/base/special/atan2/README.md          | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/lib/node_modules/@stdlib/math/base/special/atan2/README.md b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
index 66802940b5cc..11309963f883 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
@@ -51,19 +51,19 @@ var atan2 = require( '@stdlib/math/base/special/atan2' );
 Computes the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
 ```javascript
-var v = atan2( 2.0, 2.0 ); // => atan(1.0)
+var v = atan2( 2.0, 2.0 );
 // returns ~0.785
 
-v = atan2( 6.0, 2.0 ); // => atan(3.0)
+v = atan2( 6.0, 2.0 );
 // returns ~1.249
 
-v = atan2( -1.0, -1.0 ); // => atan(1.0) - π
+v = atan2( -1.0, -1.0 );
 // returns ~-2.356
 
-v = atan2( 3.0, 0.0 ); // => π/2
+v = atan2( 3.0, 0.0 );
 // returns ~1.571
 
-v = atan2( -2.0, 0.0 ); // => -π/2
+v = atan2( -2.0, 0.0 );
 // returns ~-1.571
 
 v = atan2( 0.0, 0.0 );

From 0bd6163f8efd0db55b6d2aa270cd1b7ab13136e0 Mon Sep 17 00:00:00 2001
From: Karan Anand <anandkarancompsci@gmail.com>
Date: Fri, 4 Sep 2026 01:01:03 +0530
Subject: [PATCH 3/4] chore: code review

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown_pkg_readmes
    status: passed
  - task: lint_markdown_docs
    status: na
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: na
  - task: lint_javascript_src
    status: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: na
  - task: lint_javascript_benchmarks
    status: na
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 .../@stdlib/math/base/special/atan2d/README.md         |  6 +++---
 .../@stdlib/math/base/special/atan2f/README.md         | 10 +++++-----
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
index 50c820b29791..e9b5070e23a3 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
@@ -51,13 +51,13 @@ var atan2d = require( '@stdlib/math/base/special/atan2d' );
 Computes the angle in the plane (in degrees) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
 ```javascript
-var v = atan2d( 2.0, 2.0 ); // => atand(1.0)
+var v = atan2d( 2.0, 2.0 );
 // returns ~45.0
 
-v = atan2d( 6.0, 2.0 ); // => atand(3.0)
+v = atan2d( 6.0, 2.0 );
 // returns ~71.565
 
-v = atan2d( -1.0, -1.0 ); // => atand(1.0) - 180.0
+v = atan2d( -1.0, -1.0 );
 // returns ~-135.0
 
 v = atan2d( 3.0, 0.0 );
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
index 581bd353acc3..3329899418cc 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
@@ -51,19 +51,19 @@ var atan2f = require( '@stdlib/math/base/special/atan2f' );
 Computes the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)` as a single-precision floating-point number.
 
 ```javascript
-var v = atan2f( 2.0, 2.0 ); // => atanf( 1.0 )
+var v = atan2f( 2.0, 2.0 );
 // returns ~0.785
 
-v = atan2f( 6.0, 2.0 ); // => atanf( 3.0 )
+v = atan2f( 6.0, 2.0 );
 // returns ~1.249
 
-v = atan2f( -1.0, -1.0 ); // => atanf( 1.0 ) - π
+v = atan2f( -1.0, -1.0 );
 // returns ~-2.356
 
-v = atan2f( 3.0, 0.0 ); // => π/2
+v = atan2f( 3.0, 0.0 );
 // returns ~1.571
 
-v = atan2f( -2.0, 0.0 ); // => -π/2
+v = atan2f( -2.0, 0.0 );
 // returns ~-1.571
 
 v = atan2f( 0.0, 0.0 );

From 4b7f1a33a291a7c748ac12a94e2e251ad70fae85 Mon Sep 17 00:00:00 2001
From: Karan Anand <anandkarancompsci@gmail.com>
Date: Fri, 4 Sep 2026 11:31:02 +0530
Subject: [PATCH 4/4] chore: code review

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown_pkg_readmes
    status: passed
  - task: lint_markdown_docs
    status: na
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: na
  - task: lint_javascript_src
    status: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: na
  - task: lint_javascript_benchmarks
    status: na
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 lib/node_modules/@stdlib/math/base/special/atan2/README.md  | 4 ++--
 lib/node_modules/@stdlib/math/base/special/atan2d/README.md | 4 ++--
 lib/node_modules/@stdlib/math/base/special/atan2f/README.md | 4 ++--
 3 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/node_modules/@stdlib/math/base/special/atan2/README.md b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
index 11309963f883..272391c18784 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
@@ -26,10 +26,10 @@ limitations under the License.
 
 The two-argument [arctangent][arctangent] function is defined as
 
-<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\theta = \operatorname{atan2}(y, x), \quad \theta \in (-\pi, \pi]" alt="Two-argument arctangent function"> -->
+<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\operatorname{atan2}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}" alt="Two-argument arctangent function"> -->
 
 ```math
-\theta = \mathop{\mathrm{atan2}}(y, x), \quad \theta \in (-\pi, \pi]
+\mathop{\mathrm{atan2}}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}
 ```
 
 <!-- </equation> -->
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
index e9b5070e23a3..3aae8b5b5cd4 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
@@ -26,10 +26,10 @@ limitations under the License.
 
 The two-argument [arctangent][arctangent] function returning an angle in degrees is defined as
 
-<!-- <equation class="equation" label="eq:atan2d_function" align="center" raw="\theta = \frac{180}{\pi} \operatorname{atan2}(y, x), \quad \theta \in (-180, 180]" alt="Two-argument arctangent function in degrees"> -->
+<!-- <equation class="equation" label="eq:atan2d_function" align="center" raw="\operatorname{atan2d}(y, x) = \frac{180}{\pi} \operatorname{atan2}(y, x) = \begin{cases} \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) + 180 & \textrm{if}\ x < 0,\ y \geq 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) - 180 & \textrm{if}\ x < 0,\ y < 0 \\ +90 & \textrm{if}\ x = 0,\ y > 0 \\ -90 & \textrm{if}\ x = 0,\ y < 0 \end{cases}" alt="Two-argument arctangent function in degrees"> -->
 
 ```math
-\theta = \frac{180}{\pi} \mathop{\mathrm{atan2}}(y, x), \quad \theta \in (-180, 180]
+\mathop{\mathrm{atan2d}}(y, x) = \frac{180}{\pi}\mathop{\mathrm{atan2}}(y, x) = \begin{cases} \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) + 180 & \textrm{if}\ x < 0,\ y \geq 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) - 180 & \textrm{if}\ x < 0,\ y < 0 \\ +90 & \textrm{if}\ x = 0,\ y > 0 \\ -90 & \textrm{if}\ x = 0,\ y < 0 \end{cases}
 ```
 
 <!-- </equation> -->
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
index 3329899418cc..8593ee3545b7 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
@@ -26,10 +26,10 @@ limitations under the License.
 
 The two-argument [arctangent][arctangent] function is defined as
 
-<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\theta = \operatorname{atan2}(y, x), \quad \theta \in (-\pi, \pi]" alt="Two-argument arctangent function"> -->
+<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\operatorname{atan2}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}" alt="Two-argument arctangent function"> -->
 
 ```math
-\theta = \mathop{\mathrm{atan2}}(y, x), \quad \theta \in (-\pi, \pi]
+\mathop{\mathrm{atan2}}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}
 ```
 
 <!-- </equation> -->