Math: Add functions to/from polar format for complex numbers

This patch adds functions sofm_icomplex32_to_polar() and
sofm_ipolar32_to_complex(). In polar format the Q1.31
(real, imag) numbers pair is converted to (magnitude, angle).
The magnitude is Q2.30 format and angle in -pi to +pi radians
in Q3.29 format.

The conversion to polar and back loses some quality so there
currently is no support for icomplex16.

Signed-off-by: Seppo Ingalsuo <seppo.ingalsuo@linux.intel.com>

Author: singalsu

src/include/sof/math/icomplex32.h

@@ -25,6 +25,16 @@ struct icomplex32 {
 	int32_t imag;
 };
 
+/**
+ * struct ipolar32 - Storage for complex number in polar format.
+ * @param magnitude The length of vector in Q2.30 format.
+ * @param angle The phase angle of the vector -pi to +pi in Q3.29 format.
+ */
+struct ipolar32 {
+	int32_t magnitude;
+	int32_t angle;
+};
+
 /*
  * These helpers are optimized for FFT calculation only.
  * e.g. _add/sub() assume the output won't be saturate so no check needed,
@@ -79,4 +89,25 @@ static inline void icomplex32_shift(const struct icomplex32 *input, int32_t n,
 	}
 }
 
+/**
+ * sofm_icomplex32_to_polar() - Convert (re, im) complex number to polar.
+ * @param complex Pointer to input complex number in Q1.31 format.
+ * @param polar Pointer to output complex number in Q2.30 format for
+ *		magnitude and Q3.29 for phase angle.
+ *
+ * The function can be used to convert data in-place with same address for
+ * input and output. It can be useful to save scratch memory.
+ */
+void sofm_icomplex32_to_polar(struct icomplex32 *complex, struct ipolar32 *polar);
+
+/**
+ * sofm_ipolar32_to_complex() - Convert complex number from polar to normal (re, im) format.
+ * @param polar Pointer to input complex number in polar format.
+ * @param complex Pointer to output complex number in normal format in Q1.31.
+ *
+ * This function can be used to convert data in-place with same address for input
+ * and output. It can be useful to save scratch memory.
+ */
+void sofm_ipolar32_to_complex(struct ipolar32 *polar, struct icomplex32 *complex);
+
 #endif /* __SOF_ICOMPLEX32_H__ */

src/math/CMakeLists.txt

@@ -91,6 +91,10 @@ if(CONFIG_MATH_MU_LAW_CODEC)
   list(APPEND base_files mu_law.c)
 endif()
 
+if(CONFIG_MATH_COMPLEX)
+  list(APPEND base_files complex.c)
+endif()
+
 is_zephyr(zephyr)
 if(zephyr) ###  Zephyr ###
 

src/math/Kconfig

@@ -95,9 +95,17 @@ config MATH_DECIBELS
 	  Select this to enable db2lin_fixed() and exp_fixed()
 	  functions.
 
+config MATH_COMPLEX
+	bool "Operations for complex numbers"
+	default n
+	help
+	  Select this to enable functions for complex numbers
+	  arithmetic such as conversions to/from polar format.
+
 config MATH_FFT
 	bool "FFT library"
 	default n
+	select MATH_COMPLEX
 	help
 	  Enable Fast Fourier Transform library, this should not be selected
 	  directly, please select it from other audio components where need it.

src/math/complex.c

@@ -0,0 +1,57 @@
+// SPDX-License-Identifier: BSD-3-Clause
+//
+// Copyright(c) 2026 Intel Corporation.
+//
+// Author: Seppo Ingalsuo <seppo.ingalsuo@linux.intel.com>
+//
+
+#include <rtos/symbol.h>
+#include <sof/audio/format.h>
+#include <sof/math/icomplex32.h>
+#include <sof/math/sqrt.h>
+#include <stdint.h>
+
+/* sofm_icomplex32_to_polar() - Convert (re, im) complex number to polar. */
+void sofm_icomplex32_to_polar(struct icomplex32 *complex, struct ipolar32 *polar)
+{
+	struct icomplex32 c = *complex;
+	int64_t squares_sum;
+	int32_t sqrt_arg;
+	int32_t acos_arg;
+	int32_t acos_val;
+
+	/* Calculate square of magnitudes Q1.31, result is Q2.62 */
+	squares_sum = (int64_t)c.real * c.real + (int64_t)c.imag * c.imag;
+
+	/* Square root */
+	sqrt_arg = Q_SHIFT_RND(squares_sum, 62, 30);
+	polar->magnitude = sofm_sqrt_int32(sqrt_arg); /* Q2.30 */
+
+	/* Avoid divide by zero and ambiguous angle for a zero vector. */
+	if (polar->magnitude == 0) {
+		polar->angle = 0;
+		return;
+	}
+
+	/* Calculate phase angle with acos( complex->real / polar->magnitude) */
+	acos_arg = sat_int32((((int64_t)c.real) << 29) / polar->magnitude); /* Q2.30 */
+	acos_val = acos_fixed_32b(acos_arg);				    /* Q3.29 */
+	polar->angle = (c.imag < 0) ? -acos_val : acos_val;
+}
+EXPORT_SYMBOL(sofm_icomplex32_to_polar);
+
+/* sofm_ipolar32_to_complex() - Convert complex number from polar to normal (re, im) format. */
+void sofm_ipolar32_to_complex(struct ipolar32 *polar, struct icomplex32 *complex)
+{
+	struct cordic_cmpx cexp;
+	int32_t phase;
+	int32_t magnitude;
+
+	/* The conversion can happen in-place, so load copies of the values first */
+	magnitude = polar->magnitude;
+	phase = Q_SHIFT_RND(polar->angle, 29, 28); /* Q3.29 to Q2.28 */
+	cmpx_exp_32b(phase, &cexp);		   /* Q2.30 */
+	complex->real = sat_int32(Q_MULTSR_32X32((int64_t)magnitude, cexp.re, 30, 30, 31));
+	complex->imag = sat_int32(Q_MULTSR_32X32((int64_t)magnitude, cexp.im, 30, 30, 31));
+}
+EXPORT_SYMBOL(sofm_ipolar32_to_complex);