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annotate libtwamr/oper_32b.c @ 553:ebcf414b7d99

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doc/TFO-transform: describe details for FRv1, both modes
author Mychaela Falconia <falcon@freecalypso.org>
date Mon, 07 Oct 2024 08:24:24 +0000
parents 54f6bc41ed10
children
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1 /*****************************************************************************
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2 * *
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3 * This file contains operations in double precision. *
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4 * These operations are not standard double precision operations. *
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5 * They are used where single precision is not enough but the full 32 bits *
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6 * precision is not necessary. For example, the function Div_32() has a *
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7 * 24 bits precision which is enough for our purposes. *
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8 * *
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9 * The double precision numbers use a special representation: *
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10 * *
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11 * L_32 = hi<<16 + lo<<1 *
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12 * *
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13 * L_32 is a 32 bit integer. *
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14 * hi and lo are 16 bit signed integers. *
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15 * As the low part also contains the sign, this allows fast multiplication. *
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16 * *
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17 * 0x8000 0000 <= L_32 <= 0x7fff fffe. *
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18 * *
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19 * We will use DPF (Double Precision Format )in this file to specify *
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20 * this special format. *
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21 *****************************************************************************
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22 */
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23
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24 #include "typedef.h"
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25 #include "namespace.h"
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26 #include "basic_op.h"
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27 #include "oper_32b.h"
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28 #include "no_count.h"
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29
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30 /*****************************************************************************
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31 * *
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32 * Function L_Extract() *
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33 * *
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34 * Extract from a 32 bit integer two 16 bit DPF. *
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35 * *
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36 * Arguments: *
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37 * *
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38 * L_32 : 32 bit integer. *
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39 * 0x8000 0000 <= L_32 <= 0x7fff ffff. *
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40 * hi : b16 to b31 of L_32 *
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41 * lo : (L_32 - hi<<16)>>1 *
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42 *****************************************************************************
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43 */
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44
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45 void L_Extract (Word32 L_32, Word16 *hi, Word16 *lo)
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46 {
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47 *hi = extract_h (L_32);
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48 *lo = extract_l (L_msu (L_shr (L_32, 1), *hi, 16384));
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49 return;
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50 }
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51
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52 /*****************************************************************************
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53 * *
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54 * Function L_Comp() *
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55 * *
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56 * Compose from two 16 bit DPF a 32 bit integer. *
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57 * *
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58 * L_32 = hi<<16 + lo<<1 *
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59 * *
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60 * Arguments: *
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61 * *
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62 * hi msb *
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63 * lo lsf (with sign) *
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64 * *
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65 * Return Value : *
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66 * *
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67 * 32 bit long signed integer (Word32) whose value falls in the *
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68 * range : 0x8000 0000 <= L_32 <= 0x7fff fff0. *
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69 * *
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70 *****************************************************************************
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71 */
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72
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73 Word32 L_Comp (Word16 hi, Word16 lo)
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74 {
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75 Word32 L_32;
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76
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77 L_32 = L_deposit_h (hi);
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78 return (L_mac (L_32, lo, 1)); /* = hi<<16 + lo<<1 */
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79 }
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80
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81 /*****************************************************************************
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82 * Function Mpy_32() *
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83 * *
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84 * Multiply two 32 bit integers (DPF). The result is divided by 2**31 *
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85 * *
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86 * L_32 = (hi1*hi2)<<1 + ( (hi1*lo2)>>15 + (lo1*hi2)>>15 )<<1 *
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87 * *
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88 * This operation can also be viewed as the multiplication of two Q31 *
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89 * number and the result is also in Q31. *
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90 * *
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91 * Arguments: *
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92 * *
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93 * hi1 hi part of first number *
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94 * lo1 lo part of first number *
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95 * hi2 hi part of second number *
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96 * lo2 lo part of second number *
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97 * *
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98 *****************************************************************************
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99 */
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100
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101 Word32 Mpy_32 (Word16 hi1, Word16 lo1, Word16 hi2, Word16 lo2)
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102 {
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103 Word32 L_32;
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104
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105 L_32 = L_mult (hi1, hi2);
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106 L_32 = L_mac (L_32, mult (hi1, lo2), 1);
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107 L_32 = L_mac (L_32, mult (lo1, hi2), 1);
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108
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109 return (L_32);
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110 }
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111
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112 /*****************************************************************************
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113 * Function Mpy_32_16() *
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114 * *
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115 * Multiply a 16 bit integer by a 32 bit (DPF). The result is divided *
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116 * by 2**15 *
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117 * *
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118 * *
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119 * L_32 = (hi1*lo2)<<1 + ((lo1*lo2)>>15)<<1 *
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120 * *
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121 * Arguments: *
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122 * *
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123 * hi hi part of 32 bit number. *
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124 * lo lo part of 32 bit number. *
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125 * n 16 bit number. *
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126 * *
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127 *****************************************************************************
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128 */
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129
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130 Word32 Mpy_32_16 (Word16 hi, Word16 lo, Word16 n)
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131 {
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132 Word32 L_32;
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133
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134 L_32 = L_mult (hi, n);
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135 L_32 = L_mac (L_32, mult (lo, n), 1);
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136
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137 return (L_32);
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138 }
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139
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140 /*****************************************************************************
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141 * *
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142 * Function Name : Div_32 *
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143 * *
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144 * Purpose : *
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145 * Fractional integer division of two 32 bit numbers. *
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146 * L_num / L_denom. *
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147 * L_num and L_denom must be positive and L_num < L_denom. *
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148 * L_denom = denom_hi<<16 + denom_lo<<1 *
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149 * denom_hi is a normalize number. *
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150 * *
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151 * Inputs : *
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152 * *
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153 * L_num *
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154 * 32 bit long signed integer (Word32) whose value falls in the *
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155 * range : 0x0000 0000 < L_num < L_denom *
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156 * *
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157 * L_denom = denom_hi<<16 + denom_lo<<1 (DPF) *
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158 * *
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159 * denom_hi *
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160 * 16 bit positive normalized integer whose value falls in the *
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161 * range : 0x4000 < hi < 0x7fff *
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162 * denom_lo *
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163 * 16 bit positive integer whose value falls in the *
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164 * range : 0 < lo < 0x7fff *
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165 * *
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166 * Return Value : *
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167 * *
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168 * L_div *
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169 * 32 bit long signed integer (Word32) whose value falls in the *
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170 * range : 0x0000 0000 <= L_div <= 0x7fff ffff. *
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171 * *
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172 * Algorithm: *
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173 * *
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174 * - find = 1/L_denom. *
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175 * First approximation: approx = 1 / denom_hi *
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176 * 1/L_denom = approx * (2.0 - L_denom * approx ) *
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177 * *
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178 * - result = L_num * (1/L_denom) *
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179 *****************************************************************************
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180 */
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181
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182 Word32 Div_32 (Word32 L_num, Word16 denom_hi, Word16 denom_lo)
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183 {
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184 Word16 approx, hi, lo, n_hi, n_lo;
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185 Word32 L_32;
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186
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187 /* First approximation: 1 / L_denom = 1/denom_hi */
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188
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189 approx = div_s ((Word16) 0x3fff, denom_hi);
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190
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191 /* 1/L_denom = approx * (2.0 - L_denom * approx) */
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192
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193 L_32 = Mpy_32_16 (denom_hi, denom_lo, approx);
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194
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195 L_32 = L_sub ((Word32) 0x7fffffffL, L_32);
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196
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197 L_Extract (L_32, &hi, &lo);
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198
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199 L_32 = Mpy_32_16 (hi, lo, approx);
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200
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201 /* L_num * (1/L_denom) */
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202
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203 L_Extract (L_32, &hi, &lo);
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204 L_Extract (L_num, &n_hi, &n_lo);
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205 L_32 = Mpy_32 (n_hi, n_lo, hi, lo);
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206 L_32 = L_shl (L_32, 2);
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207
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208 return (L_32);
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209 }