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1 /* ----------------------------------------------------------------------
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2 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.
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3 *
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4 * $Date: 19. October 2015
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5 * $Revision: V.1.4.5 a
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6 *
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7 * Project: CMSIS DSP Library
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8 * Title: arm_sqrt_q31.c
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9 *
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10 * Description: Q31 square root function.
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11 *
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12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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13 *
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14 * Redistribution and use in source and binary forms, with or without
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15 * modification, are permitted provided that the following conditions
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16 * are met:
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17 * - Redistributions of source code must retain the above copyright
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18 * notice, this list of conditions and the following disclaimer.
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19 * - Redistributions in binary form must reproduce the above copyright
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20 * notice, this list of conditions and the following disclaimer in
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21 * the documentation and/or other materials provided with the
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22 * distribution.
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23 * - Neither the name of ARM LIMITED nor the names of its contributors
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24 * may be used to endorse or promote products derived from this
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25 * software without specific prior written permission.
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26 *
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27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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38 * POSSIBILITY OF SUCH DAMAGE.
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39 * -------------------------------------------------------------------- */
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40 #include "arm_math.h"
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41 #include "arm_common_tables.h"
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42
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43 /**
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44 * @ingroup groupFastMath
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45 */
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46
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47 /**
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48 * @addtogroup SQRT
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49 * @{
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50 */
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51
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52 /**
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53 * @brief Q31 square root function.
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54 * @param[in] in input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
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55 * @param[out] *pOut square root of input value.
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56 * @return The function returns ARM_MATH_SUCCESS if the input value is positive
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57 * and ARM_MATH_ARGUMENT_ERROR if the input is negative. For
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58 * negative inputs, the function returns *pOut = 0.
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59 */
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60
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61 arm_status arm_sqrt_q31(
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62 q31_t in,
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63 q31_t * pOut)
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64 {
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65 q31_t number, temp1, bits_val1, var1, signBits1, half;
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66 float32_t temp_float1;
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67 union
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68 {
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69 q31_t fracval;
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70 float32_t floatval;
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71 } tempconv;
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72
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73 number = in;
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74
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75 /* If the input is a positive number then compute the signBits. */
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76 if(number > 0)
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77 {
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78 signBits1 = __CLZ(number) - 1;
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79
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80 /* Shift by the number of signBits1 */
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81 if((signBits1 % 2) == 0)
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82 {
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83 number = number << signBits1;
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84 }
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85 else
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86 {
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87 number = number << (signBits1 - 1);
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88 }
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89
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90 /* Calculate half value of the number */
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91 half = number >> 1;
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92 /* Store the number for later use */
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93 temp1 = number;
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94
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95 /*Convert to float */
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96 temp_float1 = number * 4.6566128731e-010f;
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97 /*Store as integer */
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98 tempconv.floatval = temp_float1;
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99 bits_val1 = tempconv.fracval;
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100 /* Subtract the shifted value from the magic number to give intial guess */
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101 bits_val1 = 0x5f3759df - (bits_val1 >> 1); /* gives initial guess */
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102 /* Store as float */
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103 tempconv.fracval = bits_val1;
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104 temp_float1 = tempconv.floatval;
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105 /* Convert to integer format */
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106 var1 = (q31_t) (temp_float1 * 1073741824);
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107
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108 /* 1st iteration */
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109 var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
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110 ((q31_t)
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111 ((((q31_t)
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112 (((q63_t) var1 * var1) >> 31)) *
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113 (q63_t) half) >> 31))) >> 31)) << 2;
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114 /* 2nd iteration */
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115 var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
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116 ((q31_t)
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117 ((((q31_t)
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118 (((q63_t) var1 * var1) >> 31)) *
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119 (q63_t) half) >> 31))) >> 31)) << 2;
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120 /* 3rd iteration */
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121 var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
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122 ((q31_t)
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123 ((((q31_t)
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124 (((q63_t) var1 * var1) >> 31)) *
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125 (q63_t) half) >> 31))) >> 31)) << 2;
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126
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127 /* Multiply the inverse square root with the original value */
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128 var1 = ((q31_t) (((q63_t) temp1 * var1) >> 31)) << 1;
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129
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130 /* Shift the output down accordingly */
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131 if((signBits1 % 2) == 0)
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132 {
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133 var1 = var1 >> (signBits1 / 2);
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134 }
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135 else
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136 {
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137 var1 = var1 >> ((signBits1 - 1) / 2);
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138 }
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139 *pOut = var1;
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140
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141 return (ARM_MATH_SUCCESS);
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142 }
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143 /* If the number is a negative number then store zero as its square root value */
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144 else
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145 {
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146 *pOut = 0;
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147 return (ARM_MATH_ARGUMENT_ERROR);
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148 }
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149 }
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150
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151 /**
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152 * @} end of SQRT group
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153 */
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