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math: Add power scalar and base 2 log function
fix point math power function having negative and positive values of base and exponent as function argument. power_int32() support only integer base and exponential value and it does not support fractional values for base and exponent. fix point math base 2 logarithm function using a short lookup tables Signed-off-by: ShriramShastry <malladi.sastry@intel.com>
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‎src/include/sof/math/base2log.h‎

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/* SPDX-License-Identifier: BSD-3-Clause
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*
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* Copyright(c) 2021 Intel Corporation. All rights reserved.
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*
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* Author: Shriram Shastry <malladi.sastry@linux.intel.com>
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*
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*/
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#ifndef __SOF_MATH_BASE_TWO_LOGARITHM_H__
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#define __SOF_MATH_BASE_TWO_LOGARITHM_H__
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/* Include Files */
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#include <stdint.h>
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/* Function Declarations */
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int32_t base2_logarithm(uint32_t u);
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#endif

‎src/include/sof/math/power.h‎

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/* SPDX-License-Identifier: BSD-3-Clause
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*
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* Copyright(c) 2021 Intel Corporation. All rights reserved.
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*
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* Author: Shriram Shastry <malladi.sastry@linux.intel.com>
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*
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*/
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#ifndef __SOF_MATH_POWER_H__
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#define __SOF_MATH_POWER_H__
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/* Include Files */
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#include <stdint.h>
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/* Function Declarations */
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int32_t power_int32(int32_t b, int32_t e);
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#endif

‎src/math/CMakeLists.txt‎

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@@ -14,6 +14,14 @@ if(CONFIG_MATH_DECIBELS)
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add_local_sources(sof decibels.c)
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endif()
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if(CONFIG_POWER_FIXED)
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add_local_sources(sof power.c)
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endif()
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if(CONFIG_BINARY_LOGARITHM_FIXED)
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add_local_sources(sof base2log.c)
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endif()
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if(CONFIG_MATH_FIR)
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add_local_sources(sof fir_generic.c fir_hifi2ep.c fir_hifi3.c)
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endif()

‎src/math/Kconfig‎

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@@ -9,6 +9,28 @@ config CORDIC_FIXED
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Select this to enable sin(), cos(), asin(), acos(),
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and cexp() functions as 16 bit and 32 bit versions.
1111

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config POWER_FIXED
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bool "Power function"
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default n
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help
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This option builds the 32 bit power_int32(). A power represents repeated
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multiplication of the same number. power_int32() calculates the power
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raised to the base value. The power function works for even, odd and
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fractional base and exponent argument.Operating range of power_int32()
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with base having values from -32 to + 32 . Exponent values range from
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-3 to +3. Power out MIN/MAX range is -/+32768.
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config BINARY_LOGARITHM_FIXED
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bool "Binary Logarithm function"
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default n
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help
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This option builds Binary Logarithm function (log2n) is the logarithm to
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the base 2. The binary logarithm of x is the power to which the number 2
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must be raised to obtain the value x. Base 2 logarithm function is implemented
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with a short lookup table. (log2n) operates for a range of 32 bit width size
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i.e. 1 to 4294967295.
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config NUMBERS_GCD
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bool "Greatest common divisor"
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default n

‎src/math/base2log.c‎

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// SPDX-License-Identifier: BSD-3-Clause
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//
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// Copyright(c) 2021 Intel Corporation. All rights reserved.
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//
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// Author: Shriram Shastry <malladi.sastry@linux.intel.com>
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//
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//
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/* Include Files */
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#include <sof/math/base2log.h>
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/* Defines Constant*/
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#define BASE2LOG_WRAP_SCHAR_BITS 0xFF
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#define BASE2LOG_UPPERBYTES 0xFFFFFF
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#define BASE2LOG_WORDLENGTH 0x1F
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/**
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* Base-2 logarithm log2(n)
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*
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* Y = (u) computes the base-2 logarithm of
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* u using lookup table.
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* input u must be scalar/real number and positive
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*
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* +------------------+-----------------+--------+--------+
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* | u | y (returntype) | u | y |
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* +----+-----+-------+----+----+-------+--------+--------+
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* |WLen| FLen|Signbit|WLen|FLen|Signbit| Qformat| Qformat|
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* +----+-----+-------+----+----+-------+--------+--------+
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* | 32 | 0 | 0 | 32 | 16 | 0 | 32.0 | 16.16 |
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* +------------------+-----------------+--------+--------+
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*
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* Arguments : uint32_t u
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* u input range [1 to 4294967295]
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*
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* Return Type : int32_t y
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* y output range [0 to 32]
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*
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*/
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int32_t base2_logarithm(uint32_t u)
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{
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static const int32_t iv1[129] = {
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0, 736, 1466, 2190, 2909, 3623, 4331, 5034, 5732, 6425, 7112, 7795,
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8473, 9146, 9814, 10477, 11136, 11791, 12440, 13086, 13727, 14363, 14996, 15624,
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16248, 16868, 17484, 18096, 18704, 19308, 19909, 20505, 21098, 21687, 22272, 22854,
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23433, 24007, 24579, 25146, 25711, 26272, 26830, 27384, 27936, 28484, 29029, 29571,
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30109, 30645, 31178, 31707, 32234, 32758, 33279, 33797, 34312, 34825, 35334, 35841,
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36346, 36847, 37346, 37842, 38336, 38827, 39316, 39802, 40286, 40767, 41246, 41722,
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42196, 42667, 43137, 43603, 44068, 44530, 44990, 45448, 45904, 46357, 46809, 47258,
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47705, 48150, 48593, 49034, 49472, 49909, 50344, 50776, 51207, 51636, 52063, 52488,
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52911, 53332, 53751, 54169, 54584, 54998, 55410, 55820, 56229, 56635, 57040, 57443,
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57845, 58245, 58643, 59039, 59434, 59827, 60219, 60609, 60997, 61384, 61769, 62152,
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62534, 62915, 63294, 63671, 64047, 64421, 64794, 65166, 65536};
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static const int8_t iv[256] = {
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8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
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2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
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uint64_t v;
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uint32_t x;
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int32_t a_i;
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int32_t l1_i;
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int32_t s_v;
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int32_t l2_i;
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int32_t l3_i;
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int num_left_shifts;
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int shift_factor;
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unsigned int slice_temp;
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/* Skipping for-loop */
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/* Unroll the loop so there will be no branching. */
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/* Loop unroll execute 20% faster (CPU cycle count )than for loop */
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/* Every iteration, look for leading zeros are in the high */
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/* byte of V, and shift them out to the left. Continue with the */
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/* shifted V for as many bytes as it has. */
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/* The index is the high byte of the input plus 1 to make it a */
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/* one-based index. */
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/* Index into the number-of-leading-zeros lookup table. This lookup */
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/* table takes in a byte and returns the number of leading zeros in the */
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/* binary representation. */
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shift_factor = iv[u >> 24];
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/* Left-shift out all the leading zeros in the high byte. */
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v = (uint64_t)u << shift_factor;
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/* Update the total number of left-shifts */
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num_left_shifts = shift_factor;
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shift_factor = iv[v >> 24];
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/* Left-shift out all the leading zeros in the high byte. */
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v <<= shift_factor;
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/* Update the total number of left-shifts */
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num_left_shifts += shift_factor;
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shift_factor = iv[v >> 24];
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/* Left-shift out all the leading zeros in the high byte. */
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v <<= shift_factor;
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/* Update the total number of left-shifts */
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num_left_shifts += shift_factor;
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shift_factor = iv[v >> 24];
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/* Left-shift out all the leading zeros in the high byte. */
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/* Update the total number of left-shifts */
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num_left_shifts += shift_factor;
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/* The input has been left-shifted so the most-significant-bit is a 1. */
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/* Reinterpret the output as unsigned with one integer bit, so */
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/* that 1 <= x < 2. */
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x = (uint32_t)v << shift_factor;
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/* Let Q = int(u). Then u = Q*2^(-u_fraction_length), */
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/* and x = Q*2^num_left_shifts * 2^(1-word_length). Therefore, */
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/* u = x*2^n, where n is defined as: */
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/* Extract the high byte of x */
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/* Convert the high byte into an index for lookup table */
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slice_temp = (v << shift_factor) >> 24;
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/* Interpolate between points. */
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/* The upper byte was used for the index into lookup table */
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/* The remaining bits make up the fraction between points. */
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a_i = BASE2LOG_WORDLENGTH - num_left_shifts;
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a_i <<= 16;
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l1_i = iv1[(BASE2LOG_WRAP_SCHAR_BITS & ((x >> 24) + 129)) - 1];
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s_v = a_i + l1_i;
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l2_i = iv1[(BASE2LOG_WRAP_SCHAR_BITS & (slice_temp + 130)) - 1];
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l3_i = iv1[(slice_temp - 127) - 1];
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return s_v + (((x & BASE2LOG_UPPERBYTES) * (int64_t)(l2_i - l3_i)) >> 24);
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}
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‎src/math/power.c‎

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// SPDX-License-Identifier: BSD-3-Clause
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//
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// Copyright(c) 2021 Intel Corporation. All rights reserved.
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//
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// Author: Shriram Shastry <malladi.sastry@linux.intel.com>
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// Seppo Ingalsuo <seppo.ingalsuo@linux.intel.com>
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//
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/* Include Files */
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#include <sof/audio/format.h>
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#include <sof/trace/trace.h>
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#include <sof/math/power.h>
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#include <sof/lib/uuid.h>
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#include <ipc/trace.h>
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#include <user/trace.h>
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#include <stdint.h>
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/* d23cf8d0-8dfe-497c-8202-5f909cf72735 */
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DECLARE_SOF_UUID("math_power", math_power_uuid, 0xd23cf8d0, 0x8dfe, 0x497c,
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0x82, 0x02, 0x5f, 0x90, 0x9c, 0xf7, 0x27, 0x35);
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DECLARE_TR_CTX(math_power_tr, SOF_UUID(math_power_uuid), LOG_LEVEL_INFO);
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/* define constant */
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#define POWER_MAX_LIMIT 0x8000
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/* Function Definitions */
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/**
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* Arguments : int32_t b
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* base input range [-32 to +32]
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*
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* : int32_t e
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* exponent input range [ -3 to +3 ]
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*
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* Return Type : int32_t
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* power output range [-32768 to + 32768]
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* ATTENTION - FRACTIONAL EXPONENTIAL IS NOT SUPPORTED
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* +------------------+------------------+------------------+--------+--------+--------+
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* | base | exponent | power(returntype)| b | e | p |
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* +----+-----+-------+----+-----+-------+----+----+--------+--------+--------+--------+
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* |WLen| FLen|Signbit|WLen| FLen|Signbit|WLen|FLen|Signbit | Qformat| Qformat| Qformat|
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* +----+-----+-------+----+-----+-------+----+----+--------+--------+--------+--------+
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* | 32 | 25 | 1 | 32 | 29 | 1 | 32 | 15 | 1 | 6.26 | 2.30 | 16.16 |
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* +------------------+------------------+------------------+--------+--------+--------+
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*/
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int32_t power_int32(int32_t b, int32_t e)
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{
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int32_t i;
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int32_t k;
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int32_t multiplier;
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int32_t p;
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p = POWER_MAX_LIMIT;
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if (e < 0) {
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e = -e;
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if (b) {
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multiplier = (int32_t)((1LL << 50) / (int64_t)b);
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} else {
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multiplier = INT32_MAX;
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tr_err(&math_power_tr, "power_int32(): Divide by zero error.");
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}
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} else {
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multiplier = b;
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}
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i = e >> 29;
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for (k = 0; k < i; k++)
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p = sat_int32((((p * (int64_t)multiplier) >> 24) + 1) >> 1);
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return p;
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}

‎test/cmocka/include/log2_tables.h‎

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/* SPDX-License-Identifier: BSD-3-Clause
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*
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* Copyright(c) 2021 Intel Corporation. All rights reserved.
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*
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* Author: Shriram Shastry <malladi.sastry@linux.intel.com>
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*/
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/* Include Files */
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#include <stdint.h>
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/* Reference table generated by Matlab log2() */
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static const double log2_lookup_table[] = {
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0.0000000000000000, 25.3706434118312352, 26.3706433952040058, 26.9556058903827527,
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27.3706433868903893, 27.6925714801150313, 27.9556058848403417, 28.1779983053850174,
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28.3706433827335829, 28.5405683837140280, 28.6925714767895848, 28.8300750002372048,
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28.9556058820691362, 29.0710830992759028, 29.1779983030096979, 29.2775339764022569,
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29.3706433806551779, 29.4581062237394029, 29.5405683837140280, 29.6185708955208291,
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29.6925714767895848, 29.7629608045226277, 29.8300750002372048, 29.8942053375254808,
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29.9556058820691362, 30.0144995710118572, 30.0710830992759028, 30.1255308832035382,
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30.1779983030096979, 30.2286243759977573, 30.2775339764022569, 30.3248396911091014,
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30.3706433806551779, 30.4150374999506496, 30.4581062217832610, 30.4999263974219978,
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30.5405683818665565, 30.5800967460032638, 30.6185708937705954, 30.6560455991443810,
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30.6925714751268615, 30.7281953848170275, 30.7629608029390802, 30.7969081348255926,
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30.8300749987256388, 30.8624964763844254, 30.8942053360796365, 30.9252322316694972,
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30.9556058806835352, 30.9853532240493088, 31.0144995703467679, 31.0430687225044153,
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31.0710830986363931, 31.0985638350223041, 31.1255308825877144, 31.1520030939153152,
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31.1779983024158689, 31.2035333944917532, 31.2286243754244062, 31.2532864296295223,
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31.2775339758480158, 31.3013807177751282, 31.3248396905727375, 31.3479233036602380,
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31.3706433801355793, 31.3930111931400511, 31.4150374994467967, 31.4367325705235530,
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31.4581062212942228, 31.4791678368007908, 31.4999263969469325, 31.5203904994865773,
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31.5405683814046895, 31.5604679388234146, 31.5800967455538810, 31.5994620704028364,
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31.6185708933330361, 31.6374299205673069, 31.6560455987180411, 31.6744241280167067,
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31.6925714747111797, 31.7104933826930484, 31.7281953844114852, 31.7456828115263257,
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31.7629608029390802, 31.7800343162793943, 31.7969081348255926, 31.8135868759544458,
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31.8300749987256388, 31.8463768110377572, 31.8624964763844254, 31.8784380202372049,
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31.8942053360796365, 31.9098021911151051, 31.9252322316694972, 31.9404989883079118,
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31.9556058806835352, 31.9705562221352224, 31.9853532240493088, 31.9999999996640980};

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