1 /* ----------------------------------------------------------------------
2  * Project:      CMSIS DSP Library
3  * Title:        arm_sqrt_q31.c
4  * Description:  Q31 square root function
5  *
6  * $Date:        23 April 2021
7  * $Revision:    V1.9.0
8  *
9  * Target Processor: Cortex-M and Cortex-A cores
10  * -------------------------------------------------------------------- */
11 /*
12  * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
13  *
14  * SPDX-License-Identifier: Apache-2.0
15  *
16  * Licensed under the Apache License, Version 2.0 (the License); you may
17  * not use this file except in compliance with the License.
18  * You may obtain a copy of the License at
19  *
20  * www.apache.org/licenses/LICENSE-2.0
21  *
22  * Unless required by applicable law or agreed to in writing, software
23  * distributed under the License is distributed on an AS IS BASIS, WITHOUT
24  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
25  * See the License for the specific language governing permissions and
26  * limitations under the License.
27  */
28 
29 #include "dsp/fast_math_functions.h"
30 #include "arm_common_tables.h"
31 
32 #define Q28QUARTER 0x20000000
33 
34 /**
35   @ingroup groupFastMath
36  */
37 
38 /**
39   @addtogroup SQRT
40   @{
41  */
42 
43 /**
44   @brief         Q31 square root function.
45   @param[in]     in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF
46   @param[out]    pOut  points to square root of input value
47   @return        execution status
48                    - \ref ARM_MATH_SUCCESS        : input value is positive
49                    - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
50  */
51 
arm_sqrt_q31(q31_t in,q31_t * pOut)52 ARM_DSP_ATTRIBUTE arm_status arm_sqrt_q31(
53   q31_t in,
54   q31_t * pOut)
55 {
56   q31_t number, var1, signBits1 ,temp;
57 
58   number = in;
59 
60   /* If the input is a positive number then compute the signBits. */
61   if (number > 0)
62   {
63     signBits1 = __CLZ(number) - 1;
64 
65     /* Shift by the number of signBits1 */
66     if ((signBits1 % 2) == 0)
67     {
68       number = number << signBits1;
69     }
70     else
71     {
72       number = number << (signBits1 - 1);
73     }
74 
75     /* Start value for 1/sqrt(x) for the Newton iteration */
76     var1 = sqrt_initial_lut_q31[(number>> 26) - (Q28QUARTER >> 26)];
77 
78     /* 0.5 var1 * (3 - number * var1 * var1) */
79 
80     /* 1st iteration */
81 
82     temp = ((q63_t) var1 * var1) >> 28;
83     temp = ((q63_t) number * temp) >> 31;
84     temp = 0x30000000 - temp;
85     var1 = ((q63_t) var1 * temp) >> 29;
86 
87 
88     /* 2nd iteration */
89     temp = ((q63_t) var1 * var1) >> 28;
90     temp = ((q63_t) number * temp) >> 31;
91     temp = 0x30000000 - temp;
92     var1 = ((q63_t) var1 * temp) >> 29;
93 
94     /* 3nd iteration */
95     temp = ((q63_t) var1 * var1) >> 28;
96     temp = ((q63_t) number * temp) >> 31;
97     temp = 0x30000000 - temp;
98     var1 = ((q63_t) var1 * temp) >> 29;
99 
100     /* Multiply the inverse square root with the original value */
101     var1 = ((q31_t) (((q63_t) number * var1) >> 28));
102 
103     /* Shift the output down accordingly */
104     if ((signBits1 % 2) == 0)
105     {
106       var1 = var1 >> (signBits1 / 2);
107     }
108     else
109     {
110       var1 = var1 >> ((signBits1 - 1) / 2);
111     }
112     *pOut = var1;
113 
114     return (ARM_MATH_SUCCESS);
115   }
116   /* If the number is a negative number then store zero as its square root value */
117   else
118   {
119     *pOut = 0;
120 
121     if (number==0)
122     {
123        return (ARM_MATH_SUCCESS);
124     }
125     else
126     {
127        return (ARM_MATH_ARGUMENT_ERROR);
128     }
129   }
130 }
131 
132 /**
133   @} end of SQRT group
134  */
135