1 | /* ix87 specific implementation of pow function.
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2 | Copyright (C) 1996, 1997, 1998, 1999, 2001, 2004 Free Software Foundation
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3 | This file is part of the GNU C Library.
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4 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
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5 |
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6 | The GNU C Library is free software; you can redistribute it and/or
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7 | modify it under the terms of the GNU Lesser General Public
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8 | License as published by the Free Software Foundation; either
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9 | version 2.1 of the License, or (at your option) any later version.
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10 |
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11 | The GNU C Library is distributed in the hope that it will be useful,
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12 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 | Lesser General Public License for more details.
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15 |
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16 | You should have received a copy of the GNU Lesser General Public
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17 | License along with the GNU C Library; if not, write to the Free
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18 | Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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19 | 02111-1307 USA. */
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20 |
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21 | /*
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22 | * Oracle LGPL Disclaimer: For the avoidance of doubt, except that if any license choice
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23 | * other than GPL or LGPL is available it will apply instead, Oracle elects to use only
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24 | * the Lesser General Public License version 2.1 (LGPLv2) at this time for any software where
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25 | * a choice of LGPL license versions is made available with the language indicating
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26 | * that LGPLv2 or any later version may be used, or where a choice of which version
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27 | * of the LGPL is applied is otherwise unspecified.
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28 | */
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29 |
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30 | /*#include <machine/asm.h>*/
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31 | #include <iprt/cdefs.h>
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32 |
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33 | #define ALIGNARG(log2) 1<<log2
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34 | #define ASM_TYPE_DIRECTIVE(name,typearg) .type name,typearg;
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35 | #define ASM_SIZE_DIRECTIVE(name) .size name,.-name;
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36 | #define ASM_GLOBAL_DIRECTIVE .global
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37 |
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38 | #define C_LABEL(name) name:
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39 | #define C_SYMBOL_NAME(name) name
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40 |
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41 | #define ENTRY(name) \
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42 | ASM_GLOBAL_DIRECTIVE C_SYMBOL_NAME(name); \
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43 | ASM_TYPE_DIRECTIVE (C_SYMBOL_NAME(name),@function) \
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44 | .align ALIGNARG(4); \
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45 | C_LABEL(name)
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46 |
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47 | #undef END
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48 | #define END(name) \
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49 | ASM_SIZE_DIRECTIVE(name)
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50 |
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51 |
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52 | #ifdef __ELF__
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53 | .section .rodata
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54 | #else
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55 | .text
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56 | #endif
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57 |
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58 | .align ALIGNARG(4)
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59 | ASM_TYPE_DIRECTIVE(infinity,@object)
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60 | inf_zero:
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61 | infinity:
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62 | .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
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63 | ASM_SIZE_DIRECTIVE(infinity)
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64 | ASM_TYPE_DIRECTIVE(zero,@object)
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65 | zero: .double 0.0
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66 | ASM_SIZE_DIRECTIVE(zero)
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67 | ASM_TYPE_DIRECTIVE(minf_mzero,@object)
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68 | minf_mzero:
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69 | minfinity:
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70 | .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
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71 | mzero:
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72 | .byte 0, 0, 0, 0, 0, 0, 0, 0x80
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73 | ASM_SIZE_DIRECTIVE(minf_mzero)
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74 | ASM_TYPE_DIRECTIVE(one,@object)
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75 | one: .double 1.0
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76 | ASM_SIZE_DIRECTIVE(one)
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77 | ASM_TYPE_DIRECTIVE(limit,@object)
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78 | limit: .double 0.29
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79 | ASM_SIZE_DIRECTIVE(limit)
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80 | ASM_TYPE_DIRECTIVE(p63,@object)
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81 | p63:
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82 | .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
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83 | ASM_SIZE_DIRECTIVE(p63)
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84 |
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85 | //#ifdef PIC
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86 | //#define MO(op) op##(%rip)
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87 | //#else
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88 | #define MO(op) op
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89 | //#endif
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90 |
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91 | .text
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92 | /*ENTRY(__ieee754_powl)*/
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93 | ENTRY(RT_NOCRT(powl))
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94 |
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95 | fldt 24(%rsp) // y
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96 | fxam
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97 |
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98 |
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99 | fnstsw
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100 | movb %ah, %dl
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101 | andb $0x45, %ah
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102 | cmpb $0x40, %ah // is y == 0 ?
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103 | je 11f
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104 |
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105 | cmpb $0x05, %ah // is y == ±inf ?
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106 | je 12f
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107 |
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108 | cmpb $0x01, %ah // is y == NaN ?
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109 | je 30f
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110 |
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111 | fldt 8(%rsp) // x : y
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112 |
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113 | fxam
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114 | fnstsw
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115 | movb %ah, %dh
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116 | andb $0x45, %ah
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117 | cmpb $0x40, %ah
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118 | je 20f // x is ±0
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119 |
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120 | cmpb $0x05, %ah
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121 | je 15f // x is ±inf
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122 |
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123 | fxch // y : x
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124 |
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125 | /* fistpll raises invalid exception for |y| >= 1L<<63. */
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126 | fldl MO(p63) // 1L<<63 : y : x
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127 | fld %st(1) // y : 1L<<63 : y : x
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128 | fabs // |y| : 1L<<63 : y : x
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129 | fcomip %st(1), %st // 1L<<63 : y : x
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130 | fstp %st(0) // y : x
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131 | jnc 2f
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132 |
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133 | /* First see whether `y' is a natural number. In this case we
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134 | can use a more precise algorithm. */
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135 | fld %st // y : y : x
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136 | fistpll -8(%rsp) // y : x
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137 | fildll -8(%rsp) // int(y) : y : x
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138 | fucomip %st(1),%st // y : x
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139 | jne 2f
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140 |
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141 | /* OK, we have an integer value for y. */
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142 | mov -8(%rsp),%eax
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143 | mov -4(%rsp),%edx
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144 | orl $0, %edx
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145 | fstp %st(0) // x
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146 | jns 4f // y >= 0, jump
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147 | fdivrl MO(one) // 1/x (now referred to as x)
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148 | negl %eax
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149 | adcl $0, %edx
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150 | negl %edx
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151 | 4: fldl MO(one) // 1 : x
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152 | fxch
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153 |
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154 | 6: shrdl $1, %edx, %eax
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155 | jnc 5f
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156 | fxch
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157 | fmul %st(1) // x : ST*x
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158 | fxch
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159 | 5: fmul %st(0), %st // x*x : ST*x
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160 | shrl $1, %edx
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161 | movl %eax, %ecx
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162 | orl %edx, %ecx
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163 | jnz 6b
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164 | fstp %st(0) // ST*x
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165 | ret
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166 |
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167 | /* y is ±NAN */
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168 | 30: fldt 8(%rsp) // x : y
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169 | fldl MO(one) // 1.0 : x : y
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170 | fucomip %st(1),%st // x : y
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171 | je 31f
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172 | fxch // y : x
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173 | 31: fstp %st(1)
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174 | ret
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175 |
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176 | .align ALIGNARG(4)
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177 | 2: /* y is a real number. */
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178 | fxch // x : y
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179 | fldl MO(one) // 1.0 : x : y
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180 | fld %st(1) // x : 1.0 : x : y
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181 | fsub %st(1) // x-1 : 1.0 : x : y
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182 | fabs // |x-1| : 1.0 : x : y
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183 | fcompl MO(limit) // 1.0 : x : y
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184 | fnstsw
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185 | fxch // x : 1.0 : y
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186 | test $4500,%eax
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187 | jz 7f
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188 | fsub %st(1) // x-1 : 1.0 : y
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189 | fyl2xp1 // log2(x) : y
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190 | jmp 8f
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191 |
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192 | 7: fyl2x // log2(x) : y
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193 | 8: fmul %st(1) // y*log2(x) : y
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194 | fxam
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195 | fnstsw
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196 | andb $0x45, %ah
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197 | cmpb $0x05, %ah // is y*log2(x) == ±inf ?
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198 | je 28f
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199 | fst %st(1) // y*log2(x) : y*log2(x)
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200 | frndint // int(y*log2(x)) : y*log2(x)
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201 | fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
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202 | fxch // fract(y*log2(x)) : int(y*log2(x))
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203 | f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
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204 | faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
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205 | fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
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206 | fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
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207 | ret
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208 |
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209 | 28: fstp %st(1) // y*log2(x)
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210 | fldl MO(one) // 1 : y*log2(x)
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211 | fscale // 2^(y*log2(x)) : y*log2(x)
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212 | fstp %st(1) // 2^(y*log2(x))
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213 | ret
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214 |
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215 | // pow(x,±0) = 1
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216 | .align ALIGNARG(4)
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217 | 11: fstp %st(0) // pop y
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218 | fldl MO(one)
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219 | ret
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220 |
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221 | // y == ±inf
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222 | .align ALIGNARG(4)
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223 | 12: fstp %st(0) // pop y
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224 | fldt 8(%rsp) // x
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225 | fabs
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226 | fcompl MO(one) // < 1, == 1, or > 1
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227 | fnstsw
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228 | andb $0x45, %ah
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229 | cmpb $0x45, %ah
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230 | je 13f // jump if x is NaN
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231 |
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232 | cmpb $0x40, %ah
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233 | je 14f // jump if |x| == 1
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234 |
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235 | shlb $1, %ah
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236 | xorb %ah, %dl
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237 | andl $2, %edx
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238 | #ifdef PIC
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239 | lea inf_zero(%rip),%rcx
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240 | fldl (%rcx, %rdx, 4)
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241 | #else
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242 | fldl inf_zero(,%rdx, 4)
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243 | #endif
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244 | ret
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245 |
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246 | .align ALIGNARG(4)
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247 | 14: fldl MO(one)
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248 | ret
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249 |
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250 | .align ALIGNARG(4)
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251 | 13: fldt 8(%rsp) // load x == NaN
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252 | ret
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253 |
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254 | .align ALIGNARG(4)
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255 | // x is ±inf
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256 | 15: fstp %st(0) // y
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257 | testb $2, %dh
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258 | jz 16f // jump if x == +inf
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259 |
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260 | // We must find out whether y is an odd integer.
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261 | fld %st // y : y
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262 | fistpll -8(%rsp) // y
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263 | fildll -8(%rsp) // int(y) : y
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264 | fucomip %st(1),%st
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265 | ffreep %st // <empty>
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266 | jne 17f
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267 |
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268 | // OK, the value is an integer, but is it odd?
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269 | mov -8(%rsp), %eax
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270 | mov -4(%rsp), %edx
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271 | andb $1, %al
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272 | jz 18f // jump if not odd
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273 | // It's an odd integer.
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274 | shrl $31, %edx
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275 | #ifdef PIC
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276 | lea minf_mzero(%rip),%rcx
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277 | fldl (%rcx, %rdx, 8)
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278 | #else
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279 | fldl minf_mzero(,%rdx, 8)
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280 | #endif
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281 | ret
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282 |
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283 | .align ALIGNARG(4)
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284 | 16: fcompl MO(zero)
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285 | fnstsw
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286 | shrl $5, %eax
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287 | andl $8, %eax
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288 | #ifdef PIC
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289 | lea inf_zero(%rip),%rcx
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290 | fldl (%rcx, %rax, 1)
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291 | #else
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292 | fldl inf_zero(,%rax, 1)
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293 | #endif
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294 | ret
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295 |
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296 | .align ALIGNARG(4)
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297 | 17: shll $30, %edx // sign bit for y in right position
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298 | 18: shrl $31, %edx
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299 | #ifdef PIC
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300 | lea inf_zero(%rip),%rcx
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301 | fldl (%rcx, %rdx, 8)
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302 | #else
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303 | fldl inf_zero(,%rdx, 8)
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304 | #endif
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305 | ret
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306 |
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307 | .align ALIGNARG(4)
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308 | // x is ±0
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309 | 20: fstp %st(0) // y
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310 | testb $2, %dl
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311 | jz 21f // y > 0
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312 |
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313 | // x is ±0 and y is < 0. We must find out whether y is an odd integer.
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314 | testb $2, %dh
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315 | jz 25f
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316 |
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317 | fld %st // y : y
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318 | fistpll -8(%rsp) // y
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319 | fildll -8(%rsp) // int(y) : y
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320 | fucomip %st(1),%st
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321 | ffreep %st // <empty>
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322 | jne 26f
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323 |
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324 | // OK, the value is an integer, but is it odd?
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325 | mov -8(%rsp),%eax
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326 | mov -4(%rsp),%edx
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327 | andb $1, %al
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328 | jz 27f // jump if not odd
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329 | // It's an odd integer.
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330 | // Raise divide-by-zero exception and get minus infinity value.
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331 | fldl MO(one)
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332 | fdivl MO(zero)
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333 | fchs
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334 | ret
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335 |
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336 | 25: fstp %st(0)
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337 | 26:
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338 | 27: // Raise divide-by-zero exception and get infinity value.
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339 | fldl MO(one)
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340 | fdivl MO(zero)
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341 | ret
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342 |
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343 | .align ALIGNARG(4)
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344 | // x is ±0 and y is > 0. We must find out whether y is an odd integer.
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345 | 21: testb $2, %dh
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346 | jz 22f
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347 |
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348 | fld %st // y : y
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349 | fistpll -8(%rsp) // y
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350 | fildll -8(%rsp) // int(y) : y
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351 | fucomip %st(1),%st
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352 | ffreep %st // <empty>
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353 | jne 23f
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354 |
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355 | // OK, the value is an integer, but is it odd?
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356 | mov -8(%rsp),%eax
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357 | mov -4(%rsp),%edx
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358 | andb $1, %al
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359 | jz 24f // jump if not odd
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360 | // It's an odd integer.
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361 | fldl MO(mzero)
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362 | ret
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363 |
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364 | 22: fstp %st(0)
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365 | 23:
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366 | 24: fldl MO(zero)
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367 | ret
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368 |
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369 | /*END(__ieee754_powl)*/
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370 | END(RT_NOCRT(powl))
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371 |
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