feat: add C implementation for lapack/base/dlassq

lib/node_modules/@stdlib/lapack/base/dlassq/README.md

@@ -185,23 +185,54 @@ console.log( out );
 ### Usage
 
 ```c
-TODO
+#include "stdlib/lapack/base/dlassq.h"
 ```
 
-#### TODO
+#### c\_dlassq( N, \*X, incX, \*scale, \*sumsq )
 
-TODO.
+Returns an updated sum of squares represented in scaled form.
 
 ```c
-TODO
+double X[] = { 1.0, 2.0, 3.0, 4.0 };
+double scale = 1.0;
+double sumsq = 0.0;
+
+c_dlassq( 4, X, 1, &scale, &sumsq );
+// scale => 1.0
+// sumsq => 30.0
 ```
 
-TODO
+The function has the following parameters:
+
+-   **N**: `[in] LAPACK_INT` number of indexed elements.
+-   **X**: `[in] double*` input array.
+-   **incX**: `[in] LAPACK_INT` stride length for `X`.
+-   **scale**: `[in,out] double*` pointer to scaling factor.
+-   **sumsq**: `[in,out] double*` pointer to sum of squares.
+
+#### c\_dlassq\_ndarray( N, \*X, strideX, offsetX, \*scale, \*sumsq )
+
+Returns an updated sum of squares represented in scaled form using alternative indexing semantics.
 
 ```c
-TODO
+double X[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
+double scale = 1.0;
+double sumsq = 0.0;
+
+c_dlassq_ndarray( 4, X, 1, 1, &scale, &sumsq );
+// scale => 1.0
+// sumsq => 30.0
 ```
 
+The function has the following parameters:
+
+-   **N**: `[in] LAPACK_INT` number of indexed elements.
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] LAPACK_INT` stride length for `X`.
+-   **offsetX**: `[in] LAPACK_INT` starting index for `X`.
+-   **scale**: `[in,out] double*` pointer to scaling factor.
+-   **sumsq**: `[in,out] double*` pointer to sum of squares.
+
 </section>
 
 <!-- /.usage -->
@@ -221,7 +252,32 @@ TODO
 ### Examples
 
 ```c
-TODO
+#include "stdlib/lapack/base/dlassq.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create a strided array:
+    double X[] = { 1.0, 2.0, 3.0, 4.0 };
+
+    // Specify the number of elements:
+    const int N = 4;
+
+    // Specify the stride length:
+    const int strideX = 1;
+
+    // Initialize scaling factor and sum of squares:
+    double scale = 1.0;
+    double sumsq = 0.0;
+
+    // Compute the updated sum of squares in scaled form:
+    c_dlassq( N, X, strideX, &scale, &sumsq );
+
+    // Print the results:
+    printf( "scale: %f\n", scale );
+    printf( "sumsq: %f\n", sumsq );
+
+    return 0;
+}
 ```
 
 </section>

lib/node_modules/@stdlib/lapack/base/dlassq/benchmark/c/Makefile

@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+	QUIET := @
+else
+	QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+	OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+	CC := $(C_COMPILER)
+else
+	CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+	-std=c99 \
+	-O3 \
+	-Wall \
+	-pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+	fPIC ?=
+else
+	fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := benchmark.size.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+	$(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled benchmarks.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+	$(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+	$(QUIET) -rm -f *.o *.out
+
+.PHONY: clean