diff options
Diffstat (limited to 'tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions')
8 files changed, 1816 insertions, 0 deletions
diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_f32.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_f32.c new file mode 100644 index 000000000..20a9f3657 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_f32.c @@ -0,0 +1,290 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_cos_f32.c +* +* Description: Fast cosine calculation for floating-point values. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" +/** + * @ingroup groupFastMath + */ + +/** + * @defgroup cos Cosine + * + * Computes the trigonometric cosine function using a combination of table lookup + * and cubic interpolation. There are separate functions for + * Q15, Q31, and floating-point data types. + * The input to the floating-point version is in radians while the + * fixed-point Q15 and Q31 have a scaled input with the range + * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a + * value of 2*pi wraps around to 0. + * + * The implementation is based on table lookup using 256 values together with cubic interpolation. + * The steps used are: + * -# Calculation of the nearest integer table index + * -# Fetch the four table values a, b, c, and d + * -# Compute the fractional portion (fract) of the table index. + * -# Calculation of wa, wb, wc, wd + * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code> + * + * where + * <pre> + * a=Table[index-1]; + * b=Table[index+0]; + * c=Table[index+1]; + * d=Table[index+2]; + * </pre> + * and + * <pre> + * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract; + * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1; + * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract; + * wd=(1/6)*fract.^3 - (1/6)*fract; + * </pre> + */ + + /** + * @addtogroup cos + * @{ + */ + + +/** +* \par +* <b>Example code for Generation of Cos Table:</b> +* <pre> +* tableSize = 256; +* for(n = -1; n < (tableSize + 2); n++) +* { +* cosTable[n+1]= cos(2*pi*n/tableSize); +* } </pre> +* where pi value is 3.14159265358979 +*/ + +static const float32_t cosTable[260] = { + 0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f, + 0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f, + 0.992479562759399410f, 0.989176511764526370f, + 0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f, + 0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f, + 0.949528157711029050f, 0.941544055938720700f, + 0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f, + 0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f, + 0.870086967945098880f, 0.857728600502014160f, + 0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f, + 0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f, + 0.757208824157714840f, 0.740951120853424070f, + 0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f, + 0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f, + 0.615231573581695560f, 0.595699310302734380f, + 0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f, + 0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f, + 0.449611335992813110f, 0.427555084228515630f, + 0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f, + 0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f, + 0.266712754964828490f, 0.242980182170867920f, + 0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f, + 0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f, + 0.073564566671848297f, 0.049067676067352295f, + 0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f, + -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f, + -0.122410677373409270f, -0.146730467677116390f, + -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f, + -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f, + -0.313681751489639280f, -0.336889863014221190f, + -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f, + -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f, + -0.492898195981979370f, -0.514102756977081300f, + -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f, + -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f, + -0.653172850608825680f, -0.671558976173400880f, + -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f, + -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f, + -0.788346409797668460f, -0.803207516670227050f, + -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f, + -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f, + -0.893224298954010010f, -0.903989315032958980f, + -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f, + -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f, + -0.963776051998138430f, -0.970031261444091800f, + -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f, + -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f, + -0.997290432453155520f, -0.998795449733734130f, + -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f, + -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f, + -0.992479562759399410f, -0.989176511764526370f, + -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f, + -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f, + -0.949528157711029050f, -0.941544055938720700f, + -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f, + -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f, + -0.870086967945098880f, -0.857728600502014160f, + -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f, + -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f, + -0.757208824157714840f, -0.740951120853424070f, + -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f, + -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f, + -0.615231573581695560f, -0.595699310302734380f, + -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f, + -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f, + -0.449611335992813110f, -0.427555084228515630f, + -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f, + -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f, + -0.266712754964828490f, -0.242980182170867920f, + -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f, + -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f, + -0.073564566671848297f, -0.049067676067352295f, + -0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f, + 0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f, + 0.122410677373409270f, 0.146730467677116390f, + 0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f, + 0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f, + 0.313681751489639280f, 0.336889863014221190f, + 0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f, + 0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f, + 0.492898195981979370f, 0.514102756977081300f, + 0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f, + 0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f, + 0.653172850608825680f, 0.671558976173400880f, + 0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f, + 0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f, + 0.788346409797668460f, 0.803207516670227050f, + 0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f, + 0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f, + 0.893224298954010010f, 0.903989315032958980f, + 0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f, + 0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f, + 0.963776051998138430f, 0.970031261444091800f, + 0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f, + 0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f, + 0.997290432453155520f, 0.998795449733734130f, + 0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f, + 0.998795449733734130f +}; + +/** + * @brief Fast approximation to the trigonometric cosine function for floating-point data. + * @param[in] x input value in radians. + * @return cos(x). + */ + + +float32_t arm_cos_f32( + float32_t x) +{ + float32_t cosVal, fract, in; + int32_t index; + uint32_t tableSize = (uint32_t) TABLE_SIZE; + float32_t wa, wb, wc, wd; + float32_t a, b, c, d; + float32_t *tablePtr; + int32_t n; + float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2; + float32_t oneminusfractby2; + float32_t frby2xfrsq, frby6xfrsq; + + /* input x is in radians */ + /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */ + in = x * 0.159154943092f; + + /* Calculation of floor value of input */ + n = (int32_t) in; + + /* Make negative values towards -infinity */ + if(x < 0.0f) + { + n = n - 1; + } + + /* Map input value to [0 1] */ + in = in - (float32_t) n; + + /* Calculation of index of the table */ + index = (uint32_t) (tableSize * in); + + /* fractional value calculation */ + fract = ((float32_t) tableSize * in) - (float32_t) index; + + /* Checking min and max index of table */ + if(index < 0) + { + index = 0; + } + else if(index > 256) + { + index = 256; + } + + /* Initialise table pointer */ + tablePtr = (float32_t *) & cosTable[index]; + + /* Read four nearest values of input value from the cos table */ + a = tablePtr[0]; + b = tablePtr[1]; + c = tablePtr[2]; + d = tablePtr[3]; + + /* Cubic interpolation process */ + fractsq = fract * fract; + fractby2 = fract * 0.5f; + fractby6 = fract * 0.166666667f; + fractby3 = fract * 0.3333333333333f; + fractsqby2 = fractsq * 0.5f; + frby2xfrsq = (fractby2) * fractsq; + frby6xfrsq = (fractby6) * fractsq; + oneminusfractby2 = 1.0f - fractby2; + wb = fractsqby2 - fractby3; + wc = (fractsqby2 + fract); + wa = wb - frby6xfrsq; + wb = frby2xfrsq - fractsq; + cosVal = wa * a; + wc = wc - frby2xfrsq; + wd = (frby6xfrsq) - fractby6; + wb = wb + oneminusfractby2; + + /* Calculate cos value */ + cosVal = (cosVal + (b * wb)) + ((c * wc) + (d * wd)); + + /* Return the output value */ + return (cosVal); + +} + +/** + * @} end of cos group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_q15.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_q15.c new file mode 100644 index 000000000..ffc0929f7 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_q15.c @@ -0,0 +1,214 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_cos_q15.c +* +* Description: Fast cosine calculation for Q15 values. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupFastMath + */ + + /** + * @addtogroup cos + * @{ + */ + +/** +* \par + * Table values are in Q15 (1.15 fixed-point format) and generation is done in + * three steps. First, generate cos values in floating point: + * <pre> + * tableSize = 256; + * for(n = -1; n < (tableSize + 1); n++) + * { + * cosTable[n+1]= cos(2*pi*n/tableSize); + * } </pre> + * where pi value is 3.14159265358979 + * \par + * Second, convert floating-point to Q15 (fixed-point): + * (cosTable[i] * pow(2, 15)) + * \par + * Finally, round to the nearest integer value: + * cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5); +*/ + +static const q15_t cosTableQ15[259] = { + 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d, + 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885, + 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca, + 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7, + 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40, + 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba, + 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a, + 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648, + 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38, + 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1, + 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32, + 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a, + 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930, + 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a, + 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6, + 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027, + 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163, + 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b, + 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236, + 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129, + 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0, + 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946, + 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6, + 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8, + 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8, + 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f, + 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce, + 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6, + 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0, + 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6, + 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a, + 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9, + 0x7ff6, 0x7fff, 0x7ff6 +}; + + +/** + * @brief Fast approximation to the trigonometric cosine function for Q15 data. + * @param[in] x Scaled input value in radians. + * @return cos(x). + * + * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian + * value in the range [0 2*pi). + */ + +q15_t arm_cos_q15( + q15_t x) +{ + q31_t cosVal; /* Temporary variable for output */ + q15_t *tablePtr; /* Pointer to table */ + q15_t in, in2; /* Temporary variables for input */ + q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ + q15_t a, b, c, d; /* Four nearest output values */ + q15_t fract, fractCube, fractSquare; /* Variables for fractional value */ + q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */ + q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */ + int32_t index; /* Index variable */ + + in = x; + + /* Calculate the nearest index */ + index = (int32_t) in / tableSpacing; + + /* Calculate the nearest value of input */ + in2 = (q15_t) index *tableSpacing; + + /* Calculation of fractional value */ + fract = (in - in2) << 8; + + /* fractSquare = fract * fract */ + fractSquare = (q15_t) ((fract * fract) >> 15); + + /* fractCube = fract * fract * fract */ + fractCube = (q15_t) ((fractSquare * fract) >> 15); + + /* Checking min and max index of table */ + if(index < 0) + { + index = 0; + } + else if(index > 256) + { + index = 256; + } + + /* Initialise table pointer */ + tablePtr = (q15_t *) & cosTableQ15[index]; + + /* Cubic interpolation process */ + /* Calculation of wa */ + /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */ + wa = (q31_t) oneBy6 *fractCube; + wa += (q31_t) 0x2AAA *fract; + wa = -(wa >> 15); + wa += (fractSquare >> 1u); + + /* Read first nearest value of output from the cos table */ + a = *tablePtr++; + + /* cosVal = a * wa */ + cosVal = a * wa; + + /* Calculation of wb */ + wb = (((fractCube >> 1u) - fractSquare) - (fract >> 1u)) + 0x7FFF; + + /* Read second nearest value of output from the cos table */ + b = *tablePtr++; + + /* cosVal += b*wb */ + cosVal += b * wb; + + /* Calculation of wc */ + wc = -(q31_t) fractCube + fractSquare; + wc = (wc >> 1u) + fract; + + /* Read third nearest value of output from the cos table */ + c = *tablePtr++; + + /* cosVal += c*wc */ + cosVal += c * wc; + + /* Calculation of wd */ + /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ + fractCube = fractCube - fract; + wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15)); + + /* Read fourth nearest value of output from the cos table */ + d = *tablePtr++; + + /* cosVal += d*wd; */ + cosVal += d * wd; + + /* Convert output value in 1.15(q15) format and saturate */ + cosVal = __SSAT((cosVal >> 15), 16); + + /* Return the output value in 1.15(q15) format */ + return ((q15_t) cosVal); + +} + +/** + * @} end of cos group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_q31.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_q31.c new file mode 100644 index 000000000..9ae4b5f80 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_cos_q31.c @@ -0,0 +1,249 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_cos_q31.c +* +* Description: Fast cosine calculation for Q31 values. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupFastMath + */ + + /** + * @addtogroup cos + * @{ + */ + +/** + * \par + * Table values are in Q31 (1.31 fixed-point format) and generation is done in + * three steps. First, generate cos values in floating point: + * <pre> + * tableSize = 256; + * for(n = -1; n < (tableSize + 1); n++) + * { + * cosTable[n+1]= cos(2*pi*n/tableSize); + * } </pre> + * where pi value is 3.14159265358979 + * \par + * Second, convert floating-point to Q31 (Fixed point): + * (cosTable[i] * pow(2, 31)) + * \par + * Finally, round to the nearest integer value: + * cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5); + */ + + +static const q31_t cosTableQ31[259] = { + 0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f, + 0x7f0991c4, 0x7e9d55fc, + 0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b, + 0x798a23b1, 0x78848414, + 0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6, + 0x6f5f02b2, 0x6dca0d14, + 0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac, + 0x60ec3830, 0x5ed77c8a, + 0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94, + 0x4ebfe8a5, 0x4c3fdff4, + 0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70, + 0x398cdd32, 0x36ba2014, + 0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e, + 0x2223a4c5, 0x1f19f97b, + 0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e, + 0x96a9049, 0x647d97c, + 0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5, + 0xed37ef91, + 0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2, + 0xd7d946d8, 0xd4e0cb15, + 0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590, + 0xc0e8b648, 0xbe31e19b, + 0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c, + 0xac64d510, 0xaa0a5b2e, + 0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54, + 0x9b1776da, 0x99307ee0, + 0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a, + 0x8daad37b, 0x8c4a142f, + 0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5, + 0x84a2fc62, 0x83d60412, + 0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971, + 0x8058c94c, 0x80277872, + 0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971, + 0x80f66e3c, 0x8162aa04, + 0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5, + 0x8675dc4f, 0x877b7bec, + 0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a, + 0x90a0fd4e, 0x9235f2ec, + 0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54, + 0x9f13c7d0, 0xa1288376, + 0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c, + 0xb140175b, 0xb3c0200c, + 0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590, + 0xc67322ce, 0xc945dfec, + 0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2, + 0xdddc5b3b, 0xe0e60685, + 0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2, + 0xf6956fb7, 0xf9b82684, + 0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b, + 0x12c8106f, + 0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e, + 0x2826b928, 0x2b1f34eb, + 0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70, + 0x3f1749b8, 0x41ce1e65, + 0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94, + 0x539b2af0, 0x55f5a4d2, + 0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac, + 0x64e88926, 0x66cf8120, + 0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6, + 0x72552c85, 0x73b5ebd1, + 0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b, + 0x7b5d039e, 0x7c29fbee, + 0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f, + 0x7fa736b4, 0x7fd8878e, + 0x7ff62182, 0x7fffffff, 0x7ff62182 +}; + +/** + * @brief Fast approximation to the trigonometric cosine function for Q31 data. + * @param[in] x Scaled input value in radians. + * @return cos(x). + * + * The Q31 input value is in the range [0 +0.9999] and is mapped to a radian + * value in the range [0 2*pi). + */ + +q31_t arm_cos_q31( + q31_t x) +{ + q31_t cosVal, in, in2; /* Temporary variables for input, output */ + q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ + q31_t a, b, c, d; /* Four nearest output values */ + q31_t *tablePtr; /* Pointer to table */ + q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */ + q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */ + q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */ + q31_t temp; /* Temporary variable for intermediate process */ + int32_t index; /* Index variable */ + + in = x; + + /* Calculate the nearest index */ + index = in / tableSpacing; + + /* Calculate the nearest value of input */ + in2 = ((q31_t) index) * tableSpacing; + + /* Calculation of fractional value */ + fract = (in - in2) << 8; + + /* fractSquare = fract * fract */ + fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32)); + fractSquare = fractSquare << 1; + + /* fractCube = fract * fract * fract */ + fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32)); + fractCube = fractCube << 1; + + /* Checking min and max index of table */ + if(index < 0) + { + index = 0; + } + else if(index > 256) + { + index = 256; + } + + /* Initialise table pointer */ + tablePtr = (q31_t *) & cosTableQ31[index]; + + /* Cubic interpolation process */ + /* Calculation of wa */ + /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */ + wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); + temp = 0x2AAAAAAA; + wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32); + wa = -(wa << 1u); + wa += (fractSquare >> 1u); + + /* Read first nearest value of output from the cos table */ + a = *tablePtr++; + + /* cosVal = a*wa */ + cosVal = ((q31_t) (((q63_t) a * wa) >> 32)); + + /* q31(1.31) Fixed point value of 1 */ + temp = 0x7FFFFFFF; + + /* Calculation of wb */ + wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp; + /* Read second nearest value of output from the cos table */ + b = *tablePtr++; + + /* cosVal += b*wb */ + cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32); + + /* Calculation of wc */ + wc = -fractCube + fractSquare; + wc = (wc >> 1u) + fract; + /* Read third nearest values of output value from the cos table */ + c = *tablePtr++; + + /* cosVal += c*wc */ + cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32); + + /* Calculation of wd */ + /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ + fractCube = fractCube - fract; + wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); + wd = (wd << 1u); + + /* Read fourth nearest value of output from the cos table */ + d = *tablePtr++; + + /* cosVal += d*wd; */ + cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32); + + + /* convert cosVal in 2.30 format to 1.31 format */ + return (__QADD(cosVal, cosVal)); + +} + +/** + * @} end of cos group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_f32.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_f32.c new file mode 100644 index 000000000..038229f06 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_f32.c @@ -0,0 +1,291 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_sin_f32.c +* +* Description: Fast sine calculation for floating-point values. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupFastMath + */ + +/** + * @defgroup sin Sine + * + * Computes the trigonometric sine function using a combination of table lookup + * and cubic interpolation. There are separate functions for + * Q15, Q31, and floating-point data types. + * The input to the floating-point version is in radians while the + * fixed-point Q15 and Q31 have a scaled input with the range + * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a + * value of 2*pi wraps around to 0. + * + * The implementation is based on table lookup using 256 values together with cubic interpolation. + * The steps used are: + * -# Calculation of the nearest integer table index + * -# Fetch the four table values a, b, c, and d + * -# Compute the fractional portion (fract) of the table index. + * -# Calculation of wa, wb, wc, wd + * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code> + * + * where + * <pre> + * a=Table[index-1]; + * b=Table[index+0]; + * c=Table[index+1]; + * d=Table[index+2]; + * </pre> + * and + * <pre> + * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract; + * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1; + * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract; + * wd=(1/6)*fract.^3 - (1/6)*fract; + * </pre> + */ + +/** + * @addtogroup sin + * @{ + */ + + +/** + * \par + * Example code for the generation of the floating-point sine table: + * <pre> + * tableSize = 256; + * for(n = -1; n < (tableSize + 1); n++) + * { + * sinTable[n+1]=sin(2*pi*n/tableSize); + * }</pre> + * \par + * where pi value is 3.14159265358979 + */ + +static const float32_t sinTable[259] = { + -0.024541229009628296f, 0.000000000000000000f, 0.024541229009628296f, + 0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f, + 0.122410677373409270f, 0.146730467677116390f, + 0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f, + 0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f, + 0.313681751489639280f, 0.336889863014221190f, + 0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f, + 0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f, + 0.492898195981979370f, 0.514102756977081300f, + 0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f, + 0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f, + 0.653172850608825680f, 0.671558976173400880f, + 0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f, + 0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f, + 0.788346409797668460f, 0.803207516670227050f, + 0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f, + 0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f, + 0.893224298954010010f, 0.903989315032958980f, + 0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f, + 0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f, + 0.963776051998138430f, 0.970031261444091800f, + 0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f, + 0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f, + 0.997290432453155520f, 0.998795449733734130f, + 0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f, + 0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f, + 0.992479562759399410f, 0.989176511764526370f, + 0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f, + 0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f, + 0.949528157711029050f, 0.941544055938720700f, + 0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f, + 0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f, + 0.870086967945098880f, 0.857728600502014160f, + 0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f, + 0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f, + 0.757208824157714840f, 0.740951120853424070f, + 0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f, + 0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f, + 0.615231573581695560f, 0.595699310302734380f, + 0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f, + 0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f, + 0.449611335992813110f, 0.427555084228515630f, + 0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f, + 0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f, + 0.266712754964828490f, 0.242980182170867920f, + 0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f, + 0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f, + 0.073564566671848297f, 0.049067676067352295f, + 0.024541229009628296f, 0.000000000000000122f, -0.024541229009628296f, + -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f, + -0.122410677373409270f, -0.146730467677116390f, + -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f, + -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f, + -0.313681751489639280f, -0.336889863014221190f, + -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f, + -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f, + -0.492898195981979370f, -0.514102756977081300f, + -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f, + -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f, + -0.653172850608825680f, -0.671558976173400880f, + -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f, + -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f, + -0.788346409797668460f, -0.803207516670227050f, + -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f, + -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f, + -0.893224298954010010f, -0.903989315032958980f, + -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f, + -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f, + -0.963776051998138430f, -0.970031261444091800f, + -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f, + -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f, + -0.997290432453155520f, -0.998795449733734130f, + -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f, + -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f, + -0.992479562759399410f, -0.989176511764526370f, + -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f, + -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f, + -0.949528157711029050f, -0.941544055938720700f, + -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f, + -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f, + -0.870086967945098880f, -0.857728600502014160f, + -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f, + -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f, + -0.757208824157714840f, -0.740951120853424070f, + -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f, + -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f, + -0.615231573581695560f, -0.595699310302734380f, + -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f, + -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f, + -0.449611335992813110f, -0.427555084228515630f, + -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f, + -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f, + -0.266712754964828490f, -0.242980182170867920f, + -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f, + -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f, + -0.073564566671848297f, -0.049067676067352295f, + -0.024541229009628296f, -0.000000000000000245f, 0.024541229009628296f +}; + + +/** + * @brief Fast approximation to the trigonometric sine function for floating-point data. + * @param[in] x input value in radians. + * @return sin(x). + */ + +float32_t arm_sin_f32( + float32_t x) +{ + float32_t sinVal, fract, in; /* Temporary variables for input, output */ + int32_t index; /* Index variable */ + uint32_t tableSize = (uint32_t) TABLE_SIZE; /* Initialise tablesize */ + float32_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ + float32_t a, b, c, d; /* Four nearest output values */ + float32_t *tablePtr; /* Pointer to table */ + int32_t n; + float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2; + float32_t oneminusfractby2; + float32_t frby2xfrsq, frby6xfrsq; + + /* input x is in radians */ + /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */ + in = x * 0.159154943092f; + + /* Calculation of floor value of input */ + n = (int32_t) in; + + /* Make negative values towards -infinity */ + if(x < 0.0f) + { + n = n - 1; + } + + /* Map input value to [0 1] */ + in = in - (float32_t) n; + + /* Calculation of index of the table */ + index = (uint32_t) (tableSize * in); + + /* fractional value calculation */ + fract = ((float32_t) tableSize * in) - (float32_t) index; + + /* Checking min and max index of table */ + if(index < 0) + { + index = 0; + } + else if(index > 256) + { + index = 256; + } + + /* Initialise table pointer */ + tablePtr = (float32_t *) & sinTable[index]; + + /* Read four nearest values of input value from the sin table */ + a = tablePtr[0]; + b = tablePtr[1]; + c = tablePtr[2]; + d = tablePtr[3]; + + /* Cubic interpolation process */ + fractsq = fract * fract; + fractby2 = fract * 0.5f; + fractby6 = fract * 0.166666667f; + fractby3 = fract * 0.3333333333333f; + fractsqby2 = fractsq * 0.5f; + frby2xfrsq = (fractby2) * fractsq; + frby6xfrsq = (fractby6) * fractsq; + oneminusfractby2 = 1.0f - fractby2; + wb = fractsqby2 - fractby3; + wc = (fractsqby2 + fract); + wa = wb - frby6xfrsq; + wb = frby2xfrsq - fractsq; + sinVal = wa * a; + wc = wc - frby2xfrsq; + wd = (frby6xfrsq) - fractby6; + wb = wb + oneminusfractby2; + + /* Calculate sin value */ + sinVal = (sinVal + (b * wb)) + ((c * wc) + (d * wd)); + + /* Return the output value */ + return (sinVal); + +} + +/** + * @} end of sin group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_q15.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_q15.c new file mode 100644 index 000000000..6bbacc634 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_q15.c @@ -0,0 +1,216 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_sin_q15.c +* +* Description: Fast sine calculation for Q15 values. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupFastMath + */ + + /** + * @addtogroup sin + * @{ + */ + + +/** +* \par + * Table values are in Q15 (1.15 fixed-point format) and generation is done in + * three steps. First, generate sin values in floating point: + * <pre> + * tableSize = 256; + * for(n = -1; n < (tableSize + 1); n++) + * { + * sinTable[n+1]= sin(2*pi*n/tableSize); + * } </pre> + * where pi value is 3.14159265358979 + * \par + * Second, convert floating-point to Q15 (fixed-point): + * (sinTable[i] * pow(2, 15)) + * \par + * Finally, round to the nearest integer value: + * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5); +*/ + +static const q15_t sinTableQ15[259] = { + 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8, + 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f, + 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce, + 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6, + 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0, + 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6, + 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a, + 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9, + 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d, + 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885, + 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca, + 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7, + 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40, + 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba, + 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a, + 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648, + 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38, + 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1, + 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32, + 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a, + 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930, + 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a, + 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6, + 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027, + 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163, + 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b, + 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236, + 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129, + 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0, + 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946, + 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6, + 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8, + 0xfcdc, 0x0, 0x324 +}; + + +/** + * @brief Fast approximation to the trigonometric sine function for Q15 data. + * @param[in] x Scaled input value in radians. + * @return sin(x). + * + * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi). + */ + +q15_t arm_sin_q15( + q15_t x) +{ + q31_t sinVal; /* Temporary variables output */ + q15_t *tablePtr; /* Pointer to table */ + q15_t fract, in, in2; /* Temporary variables for input, output */ + q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ + q15_t a, b, c, d; /* Four nearest output values */ + q15_t fractCube, fractSquare; /* Temporary values for fractional value */ + q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */ + q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */ + int32_t index; /* Index variable */ + + in = x; + + /* Calculate the nearest index */ + index = (int32_t) in / tableSpacing; + + /* Calculate the nearest value of input */ + in2 = (q15_t) ((index) * tableSpacing); + + /* Calculation of fractional value */ + fract = (in - in2) << 8; + + /* fractSquare = fract * fract */ + fractSquare = (q15_t) ((fract * fract) >> 15); + + /* fractCube = fract * fract * fract */ + fractCube = (q15_t) ((fractSquare * fract) >> 15); + + /* Checking min and max index of table */ + if(index < 0) + { + index = 0; + } + else if(index > 256) + { + index = 256; + } + + /* Initialise table pointer */ + tablePtr = (q15_t *) & sinTableQ15[index]; + + /* Cubic interpolation process */ + /* Calculation of wa */ + /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */ + wa = (q31_t) oneBy6 *fractCube; + wa += (q31_t) 0x2AAA *fract; + wa = -(wa >> 15); + wa += ((q31_t) fractSquare >> 1u); + + /* Read first nearest value of output from the sin table */ + a = *tablePtr++; + + /* sinVal = a * wa */ + sinVal = a * wa; + + /* Calculation of wb */ + wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) - + (((q31_t) fract >> 1u) - 0x7FFF); + + /* Read second nearest value of output from the sin table */ + b = *tablePtr++; + + /* sinVal += b*wb */ + sinVal += b * wb; + + + /* Calculation of wc */ + wc = -(q31_t) fractCube + fractSquare; + wc = (wc >> 1u) + fract; + + /* Read third nearest value of output from the sin table */ + c = *tablePtr++; + + /* sinVal += c*wc */ + sinVal += c * wc; + + /* Calculation of wd */ + /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ + fractCube = fractCube - fract; + wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15)); + + /* Read fourth nearest value of output from the sin table */ + d = *tablePtr++; + + /* sinVal += d*wd; */ + sinVal += d * wd; + + /* Convert output value in 1.15(q15) format and saturate */ + sinVal = __SSAT((sinVal >> 15), 16); + + /* Return the output value in 1.15(q15) format */ + return ((q15_t) sinVal); + +} + +/** + * @} end of sin group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_q31.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_q31.c new file mode 100644 index 000000000..034a3b42c --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sin_q31.c @@ -0,0 +1,248 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_sin_q31.c +* +* Description: Fast sine calculation for Q31 values. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupFastMath + */ + + /** + * @addtogroup sin + * @{ + */ + +/** + * \par + * Table values are in Q31 (1.31 fixed-point format) and generation is done in + * three steps. First, generate sin values in floating point: + * <pre> + * tableSize = 256; + * for(n = -1; n < (tableSize + 1); n++) + * { + * sinTable[n+1]= sin(2*pi*n/tableSize); + * } </pre> + * where pi value is 3.14159265358979 + * \par + * Second, convert floating-point to Q31 (Fixed point): + * (sinTable[i] * pow(2, 31)) + * \par + * Finally, round to the nearest integer value: + * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5); + */ + +static const q31_t sinTableQ31[259] = { + 0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b, + 0x12c8106f, + 0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e, + 0x2826b928, 0x2b1f34eb, + 0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70, + 0x3f1749b8, 0x41ce1e65, + 0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94, + 0x539b2af0, 0x55f5a4d2, + 0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac, + 0x64e88926, 0x66cf8120, + 0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6, + 0x72552c85, 0x73b5ebd1, + 0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b, + 0x7b5d039e, 0x7c29fbee, + 0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f, + 0x7fa736b4, 0x7fd8878e, + 0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f, + 0x7f0991c4, 0x7e9d55fc, + 0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b, + 0x798a23b1, 0x78848414, + 0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6, + 0x6f5f02b2, 0x6dca0d14, + 0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac, + 0x60ec3830, 0x5ed77c8a, + 0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94, + 0x4ebfe8a5, 0x4c3fdff4, + 0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70, + 0x398cdd32, 0x36ba2014, + 0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e, + 0x2223a4c5, 0x1f19f97b, + 0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e, + 0x96a9049, 0x647d97c, + 0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5, + 0xed37ef91, + 0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2, + 0xd7d946d8, 0xd4e0cb15, + 0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590, + 0xc0e8b648, 0xbe31e19b, + 0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c, + 0xac64d510, 0xaa0a5b2e, + 0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54, + 0x9b1776da, 0x99307ee0, + 0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a, + 0x8daad37b, 0x8c4a142f, + 0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5, + 0x84a2fc62, 0x83d60412, + 0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971, + 0x8058c94c, 0x80277872, + 0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971, + 0x80f66e3c, 0x8162aa04, + 0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5, + 0x8675dc4f, 0x877b7bec, + 0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a, + 0x90a0fd4e, 0x9235f2ec, + 0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54, + 0x9f13c7d0, 0xa1288376, + 0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c, + 0xb140175b, 0xb3c0200c, + 0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590, + 0xc67322ce, 0xc945dfec, + 0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2, + 0xdddc5b3b, 0xe0e60685, + 0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2, + 0xf6956fb7, 0xf9b82684, + 0xfcdbd541, 0x0, 0x3242abf +}; + + +/** + * @brief Fast approximation to the trigonometric sine function for Q31 data. + * @param[in] x Scaled input value in radians. + * @return sin(x). + * + * The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi). */ + +q31_t arm_sin_q31( + q31_t x) +{ + q31_t sinVal, in, in2; /* Temporary variables for input, output */ + int32_t index; /* Index variables */ + q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ + q31_t a, b, c, d; /* Four nearest output values */ + q31_t *tablePtr; /* Pointer to table */ + q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */ + q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */ + q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */ + q31_t temp; /* Temporary variable for intermediate process */ + + in = x; + + /* Calculate the nearest index */ + index = (uint32_t) in / (uint32_t) tableSpacing; + + /* Calculate the nearest value of input */ + in2 = (q31_t) index *tableSpacing; + + /* Calculation of fractional value */ + fract = (in - in2) << 8; + + /* fractSquare = fract * fract */ + fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32)); + fractSquare = fractSquare << 1; + + /* fractCube = fract * fract * fract */ + fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32)); + fractCube = fractCube << 1; + + /* Checking min and max index of table */ + if(index < 0) + { + index = 0; + } + else if(index > 256) + { + index = 256; + } + + /* Initialise table pointer */ + tablePtr = (q31_t *) & sinTableQ31[index]; + + /* Cubic interpolation process */ + /* Calculation of wa */ + /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */ + wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); + temp = 0x2AAAAAAA; + wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32); + wa = -(wa << 1u); + wa += (fractSquare >> 1u); + + /* Read first nearest value of output from the sin table */ + a = *tablePtr++; + + /* sinVal = a*wa */ + sinVal = ((q31_t) (((q63_t) a * wa) >> 32)); + + /* q31(1.31) Fixed point value of 1 */ + temp = 0x7FFFFFFF; + + /* Calculation of wb */ + wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp; + + /* Read second nearest value of output from the sin table */ + b = *tablePtr++; + + /* sinVal += b*wb */ + sinVal = (q31_t) ((((q63_t) sinVal << 32) + (q63_t) b * (wb)) >> 32); + + /* Calculation of wc */ + wc = -fractCube + fractSquare; + wc = (wc >> 1u) + fract; + + /* Read third nearest value of output from the sin table */ + c = *tablePtr++; + + /* sinVal += c*wc */ + sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) c * wc)) >> 32); + + /* Calculation of wd */ + /* wd = (oneBy6) * fractCube - (oneBy6) * fract; */ + fractCube = fractCube - fract; + wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); + wd = (wd << 1u); + + /* Read fourth nearest value of output from the sin table */ + d = *tablePtr++; + + /* sinVal += d*wd; */ + sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) d * wd)) >> 32); + + /* convert sinVal in 2.30 format to 1.31 format */ + return (__QADD(sinVal, sinVal)); + +} + +/** + * @} end of sin group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sqrt_q15.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sqrt_q15.c new file mode 100644 index 000000000..07b5a90c1 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sqrt_q15.c @@ -0,0 +1,155 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_sqrt_q15.c +* +* Description: Q15 square root function. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ +#include "arm_math.h" +#include "arm_common_tables.h" + + +/** + * @ingroup groupFastMath + */ + +/** + * @addtogroup SQRT + * @{ + */ + + /** + * @brief Q15 square root function. + * @param[in] in input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF. + * @param[out] *pOut square root of input value. + * @return The function returns ARM_MATH_SUCCESS if the input value is positive + * and ARM_MATH_ARGUMENT_ERROR if the input is negative. For + * negative inputs, the function returns *pOut = 0. + */ + +arm_status arm_sqrt_q15( + q15_t in, + q15_t * pOut) +{ + q15_t number, temp1, var1, signBits1, half; + q31_t bits_val1; + float32_t temp_float1; + union + { + q31_t fracval; + float32_t floatval; + } tempconv; + + number = in; + + /* If the input is a positive number then compute the signBits. */ + if(number > 0) + { + signBits1 = __CLZ(number) - 17; + + /* Shift by the number of signBits1 */ + if((signBits1 % 2) == 0) + { + number = number << signBits1; + } + else + { + number = number << (signBits1 - 1); + } + + /* Calculate half value of the number */ + half = number >> 1; + /* Store the number for later use */ + temp1 = number; + + /*Convert to float */ + temp_float1 = number * 3.051757812500000e-005f; + /*Store as integer */ + tempconv.floatval = temp_float1; + bits_val1 = tempconv.fracval; + /* Subtract the shifted value from the magic number to give intial guess */ + bits_val1 = 0x5f3759df - (bits_val1 >> 1); // gives initial guess + /* Store as float */ + tempconv.fracval = bits_val1; + temp_float1 = tempconv.floatval; + /* Convert to integer format */ + var1 = (q31_t) (temp_float1 * 16384); + + /* 1st iteration */ + var1 = ((q15_t) ((q31_t) var1 * (0x3000 - + ((q15_t) + ((((q15_t) + (((q31_t) var1 * var1) >> 15)) * + (q31_t) half) >> 15))) >> 15)) << 2; + /* 2nd iteration */ + var1 = ((q15_t) ((q31_t) var1 * (0x3000 - + ((q15_t) + ((((q15_t) + (((q31_t) var1 * var1) >> 15)) * + (q31_t) half) >> 15))) >> 15)) << 2; + /* 3rd iteration */ + var1 = ((q15_t) ((q31_t) var1 * (0x3000 - + ((q15_t) + ((((q15_t) + (((q31_t) var1 * var1) >> 15)) * + (q31_t) half) >> 15))) >> 15)) << 2; + + /* Multiply the inverse square root with the original value */ + var1 = ((q15_t) (((q31_t) temp1 * var1) >> 15)) << 1; + + /* Shift the output down accordingly */ + if((signBits1 % 2) == 0) + { + var1 = var1 >> (signBits1 / 2); + } + else + { + var1 = var1 >> ((signBits1 - 1) / 2); + } + *pOut = var1; + + return (ARM_MATH_SUCCESS); + } + /* If the number is a negative number then store zero as its square root value */ + else + { + *pOut = 0; + return (ARM_MATH_ARGUMENT_ERROR); + } +} + +/** + * @} end of SQRT group + */ diff --git a/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sqrt_q31.c b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sqrt_q31.c new file mode 100644 index 000000000..7217834a8 --- /dev/null +++ b/tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FastMathFunctions/arm_sqrt_q31.c @@ -0,0 +1,153 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2013 ARM Limited. All rights reserved. +* +* $Date: 17. January 2013 +* $Revision: V1.4.1 +* +* Project: CMSIS DSP Library +* Title: arm_sqrt_q31.c +* +* Description: Q31 square root function. +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* - Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* - Redistributions in binary form must reproduce the above copyright +* notice, this list of conditions and the following disclaimer in +* the documentation and/or other materials provided with the +* distribution. +* - Neither the name of ARM LIMITED nor the names of its contributors +* may be used to endorse or promote products derived from this +* software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +* POSSIBILITY OF SUCH DAMAGE. +* -------------------------------------------------------------------- */ +#include "arm_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupFastMath + */ + +/** + * @addtogroup SQRT + * @{ + */ + +/** + * @brief Q31 square root function. + * @param[in] in input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF. + * @param[out] *pOut square root of input value. + * @return The function returns ARM_MATH_SUCCESS if the input value is positive + * and ARM_MATH_ARGUMENT_ERROR if the input is negative. For + * negative inputs, the function returns *pOut = 0. + */ + +arm_status arm_sqrt_q31( + q31_t in, + q31_t * pOut) +{ + q31_t number, temp1, bits_val1, var1, signBits1, half; + float32_t temp_float1; + union + { + q31_t fracval; + float32_t floatval; + } tempconv; + + number = in; + + /* If the input is a positive number then compute the signBits. */ + if(number > 0) + { + signBits1 = __CLZ(number) - 1; + + /* Shift by the number of signBits1 */ + if((signBits1 % 2) == 0) + { + number = number << signBits1; + } + else + { + number = number << (signBits1 - 1); + } + + /* Calculate half value of the number */ + half = number >> 1; + /* Store the number for later use */ + temp1 = number; + + /*Convert to float */ + temp_float1 = number * 4.6566128731e-010f; + /*Store as integer */ + tempconv.floatval = temp_float1; + bits_val1 = tempconv.fracval; + /* Subtract the shifted value from the magic number to give intial guess */ + bits_val1 = 0x5f3759df - (bits_val1 >> 1); // gives initial guess + /* Store as float */ + tempconv.fracval = bits_val1; + temp_float1 = tempconv.floatval; + /* Convert to integer format */ + var1 = (q31_t) (temp_float1 * 1073741824); + + /* 1st iteration */ + var1 = ((q31_t) ((q63_t) var1 * (0x30000000 - + ((q31_t) + ((((q31_t) + (((q63_t) var1 * var1) >> 31)) * + (q63_t) half) >> 31))) >> 31)) << 2; + /* 2nd iteration */ + var1 = ((q31_t) ((q63_t) var1 * (0x30000000 - + ((q31_t) + ((((q31_t) + (((q63_t) var1 * var1) >> 31)) * + (q63_t) half) >> 31))) >> 31)) << 2; + /* 3rd iteration */ + var1 = ((q31_t) ((q63_t) var1 * (0x30000000 - + ((q31_t) + ((((q31_t) + (((q63_t) var1 * var1) >> 31)) * + (q63_t) half) >> 31))) >> 31)) << 2; + + /* Multiply the inverse square root with the original value */ + var1 = ((q31_t) (((q63_t) temp1 * var1) >> 31)) << 1; + + /* Shift the output down accordingly */ + if((signBits1 % 2) == 0) + { + var1 = var1 >> (signBits1 / 2); + } + else + { + var1 = var1 >> ((signBits1 - 1) / 2); + } + *pOut = var1; + + return (ARM_MATH_SUCCESS); + } + /* If the number is a negative number then store zero as its square root value */ + else + { + *pOut = 0; + return (ARM_MATH_ARGUMENT_ERROR); + } +} + +/** + * @} end of SQRT group + */ |