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+/* ----------------------------------------------------------------------
+* 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
+ */