Math: Replace exp() function with more accurate and fast version

The function sofm_exp_int32() if replaced with new sofm_exp_approx()
function. It's not a direct replacement so the name is
changed. The input range changes from +/- 5 to +/- 8.

The wrapper function sofm_exp_fixed() with input range -16 .. +7.6
is updated to use the new function with a simpler range reduction
for large negative input values. All current exponent function
usage in SOF components is for the wrapper function that remains
compatible.

The function sofm_db2lin_fixed() is updated to handle larger
negative input decibels values made possible by the new more
accurate exponent function.

The accuracy in exponent function for input ranges from -8 to +8 or
-16 to 7.6 depending on used exponent function improves from
absolute error of 1 to 1000 ppm to constant less than 1 ppm.

The cycles count for exponent function calculate decreases from
about 369 max to 78 max on MTL platform for HiFi code version with
-O2 or -O3 optimization. The generic C version on MTL platform is
max 88 cycles.

The DRC component is a heavy user of the exponent function. The
saving in MTL build of DRC is 10.5 MCPS, it drops from 22.17 to
11.70 with profiler run:

"scripts/sof-testbench-helper.sh -x -m drc -p profile.txt"

The saving in MTL build of multiband DRC is 30.2 MCPS, it drops from
127.95 to 97.78 with profiler run:

"scripts/sof-testbench-helper.sh -x -m drc_multiband -p profile.txt"

This patch also updates the cmocka test. The test functions are
changed due to changed function name, changed achievable accuracy.
Also the random values test points vector is replaced fixed a
fixed linearly spaced vector for repeatable test and risk for
random failures.

Signed-off-by: Seppo Ingalsuo <[email protected]>

src/include/sof/math/exp_fcn.h

@@ -26,40 +26,40 @@
 
 #endif
 
-/* TODO: Is there a MCPS difference */
-#define USING_QCONVERT	1
+/* Q5.27 int32(round(log((2^31 - 1)/2^20) * 2^27)) */
+#define SOFM_EXP_FIXED_INPUT_MAX	1023359037
 
-#if USING_QCONVERT
+/* Q8.24 int32(round((log((2^31 - 1)/2^20) * 20 / log(10)) * 2^24)) */
+#define SOFM_DB2LIN_INPUT_MAX		1111097957
 
-#include <sof/audio/format.h>
-#define SOFM_EXP_FIXED_INPUT_MIN	Q_CONVERT_FLOAT(-11.5, 27)		/* Q5.27 */
-#define SOFM_EXP_FIXED_INPUT_MAX	Q_CONVERT_FLOAT(7.6245, 27)		/* Q5.27 */
-#define SOFM_EXP_TWO_Q27		Q_CONVERT_FLOAT(2.0, 27)		/* Q5.27 */
-#define SOFM_EXP_MINUS_TWO_Q27		Q_CONVERT_FLOAT(-2.0, 27)		/* Q5.27 */
-#define SOFM_EXP_ONE_Q20		Q_CONVERT_FLOAT(1.0, 20)		/* Q12.20 */
-#define SOFM_EXP_MINUS_100_Q24		Q_CONVERT_FLOAT(-100.0, 24)		/* Q8.24 */
-#define SOFM_EXP_LOG10_DIV20_Q27	Q_CONVERT_FLOAT(0.1151292546, 27)	/* Q5.27 */
-
-#else
-
-#define SOFM_EXP_FIXED_INPUT_MIN	-1543503872	/* Q_CONVERT_FLOAT(-11.5, 27) */
-#define SOFM_EXP_FIXED_INPUT_MAX	 1023343067	/* Q_CONVERT_FLOAT(7.6245, 27) */
-#define SOFM_EXP_TWO_Q27		 268435456	/* Q_CONVERT_FLOAT(2.0, 27) */
-#define SOFM_EXP_MINUS_TWO_Q27		-268435456	/* Q_CONVERT_FLOAT(-2.0, 27) */
-#define SOFM_EXP_ONE_Q20		 1048576	/* Q_CONVERT_FLOAT(1.0, 20) */
-#define SOFM_EXP_MINUS_100_Q24		-1677721600	/* Q_CONVERT_FLOAT(-100.0, 24) */
-#define SOFM_EXP_LOG10_DIV20_Q27	 15452387	/* Q_CONVERT_FLOAT(0.1151292546, 27) */
+/**
+ * Calculates exponent function exp(x) = e^x with accurate and efficient technique that
+ * includes range reduction operations, approximation with Taylor series, and reconstruction
+ * operations to compensate the range reductions.
+ * @param	x	The input argument as Q4.28 from -8 to +8
+ * @return		The calculated e^x value as Q13.19 from 3.3546e-04 to 2981.0
+ */
+int32_t sofm_exp_approx(int32_t x);
 
-#endif
+/**
+ * Calculated exponent function exp(x) = e^x by using sofm_exp_approx(). The input range for
+ * large arguments is internally reduced to -8 to +8 with rule exp(x) = exp(x/2) * exp(x/2)
+ * and reconstructed back. This function is essentially a wrapper for compatibility with
+ * existing usage of exp() function and Q-format choice. Note that the return value saturates
+ * to INT32_MAX with input arguments larger than 7.6246.
+ * @param	x	The input argument as Q5.27 from -16 to +16
+ * @return		The calculated e^x value as Q12.20
+ */
+int32_t sofm_exp_fixed(int32_t x);
 
-#define SOFM_EXP_BIT_MASK_LOW_Q27P5 0x0000000008000000
-#define SOFM_EXP_BIT_MASK_Q62P2 0x4000000000000000LL
-#define SOFM_EXP_QUOTIENT_SCALE 0x40000000
-#define SOFM_EXP_TERMS_Q23P9 0x800000
-#define SOFM_EXP_LSHIFT_BITS 0x2000
 
-int32_t sofm_exp_int32(int32_t x);
-int32_t sofm_exp_fixed(int32_t x);
+/**
+ * Converts a decibels value to liner amplitude lin = 10^(db/20) value with optimized
+ * equation exp(db * log(10)/20). Note that due to range limitation of sofm_exp_fixed()
+ * the output saturates to maximum with about +66 dB input.
+ * @param	db	Decibels value in Q8.24 format, from -128 to +66.226
+ * @return		Linear value in Q12.20 format, from 3.9811e-07 to 2048
+ */
 int32_t sofm_db2lin_fixed(int32_t db);
 
 #endif /* __SOFM_EXP_FCN_H__ */