1 | /* |
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2 | ** libgcc support for software floating point. |
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3 | ** Copyright (C) 1991 by Pipeline Associates, Inc. All rights reserved. |
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4 | ** Permission is granted to do *anything* you want with this file, |
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5 | ** commercial or otherwise, provided this message remains intact. So there! |
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6 | ** I would appreciate receiving any updates/patches/changes that anyone |
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7 | ** makes, and am willing to be the repository for said changes (am I |
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8 | ** making a big mistake?). |
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9 | |
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10 | Warning! Only single-precision is actually implemented. This file |
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11 | won't really be much use until double-precision is supported. |
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12 | |
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13 | However, once that is done, this file might eventually become a |
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14 | replacement for libgcc1.c. It might also make possible |
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15 | cross-compilation for an IEEE target machine from a non-IEEE |
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16 | host such as a VAX. |
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17 | |
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18 | If you'd like to work on completing this, please talk to rms@gnu.ai.mit.edu. |
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19 | |
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20 | |
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21 | ** |
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22 | ** Pat Wood |
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23 | ** Pipeline Associates, Inc. |
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24 | ** pipeline!phw@motown.com or |
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25 | ** sun!pipeline!phw or |
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26 | ** uunet!motown!pipeline!phw |
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27 | ** |
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28 | ** 05/01/91 -- V1.0 -- first release to gcc mailing lists |
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29 | ** 05/04/91 -- V1.1 -- added float and double prototypes and return values |
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30 | ** -- fixed problems with adding and subtracting zero |
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31 | ** -- fixed rounding in truncdfsf2 |
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32 | ** -- fixed SWAP define and tested on 386 |
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33 | */ |
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34 | |
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35 | /* |
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36 | ** The following are routines that replace the libgcc soft floating point |
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37 | ** routines that are called automatically when -msoft-float is selected. |
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38 | ** The support single and double precision IEEE format, with provisions |
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39 | ** for byte-swapped machines (tested on 386). Some of the double-precision |
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40 | ** routines work at full precision, but most of the hard ones simply punt |
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41 | ** and call the single precision routines, producing a loss of accuracy. |
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42 | ** long long support is not assumed or included. |
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43 | ** Overall accuracy is close to IEEE (actually 68882) for single-precision |
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44 | ** arithmetic. I think there may still be a 1 in 1000 chance of a bit |
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45 | ** being rounded the wrong way during a multiply. I'm not fussy enough to |
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46 | ** bother with it, but if anyone is, knock yourself out. |
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47 | ** |
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48 | ** Efficiency has only been addressed where it was obvious that something |
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49 | ** would make a big difference. Anyone who wants to do this right for |
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50 | ** best speed should go in and rewrite in assembler. |
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51 | ** |
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52 | ** I have tested this only on a 68030 workstation and 386/ix integrated |
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53 | ** in with -msoft-float. |
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54 | */ |
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55 | |
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56 | /* the following deal with IEEE single-precision numbers */ |
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57 | #define EXCESS 126 |
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58 | #define SIGNBIT 0x80000000 |
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59 | #define HIDDEN (1 << 23) |
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60 | #define SIGN(fp) ((fp) & SIGNBIT) |
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61 | #define EXP(fp) (((fp) >> 23) & 0xFF) |
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62 | #define MANT(fp) (((fp) & 0x7FFFFF) | HIDDEN) |
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63 | #define PACK(s,e,m) ((s) | ((e) << 23) | (m)) |
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64 | |
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65 | /* the following deal with IEEE double-precision numbers */ |
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66 | #define EXCESSD 1022 |
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67 | #define HIDDEND (1 << 20) |
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68 | #define EXPD(fp) (((fp.l.upper) >> 20) & 0x7FF) |
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69 | #define SIGND(fp) ((fp.l.upper) & SIGNBIT) |
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70 | #define MANTD(fp) (((((fp.l.upper) & 0xFFFFF) | HIDDEND) << 10) | \ |
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71 | (fp.l.lower >> 22)) |
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72 | |
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73 | /* define SWAP for 386/960 reverse-byte-order brain-damaged CPUs */ |
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74 | union double_long |
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75 | { |
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76 | double d; |
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77 | #ifdef SWAP |
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78 | struct { |
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79 | unsigned long lower; |
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80 | long upper; |
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81 | } l; |
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82 | #else |
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83 | struct { |
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84 | long upper; |
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85 | unsigned long lower; |
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86 | } l; |
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87 | #endif |
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88 | }; |
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89 | |
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90 | union float_long |
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91 | { |
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92 | float f; |
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93 | long l; |
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94 | }; |
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95 | |
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96 | /* add two floats */ |
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97 | float |
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98 | __addsf3 (float a1, float a2) |
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99 | { |
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100 | register long mant1, mant2; |
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101 | register union float_long fl1, fl2; |
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102 | register int exp1, exp2; |
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103 | int sign = 0; |
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104 | |
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105 | fl1.f = a1; |
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106 | fl2.f = a2; |
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107 | |
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108 | /* check for zero args */ |
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109 | if (!fl1.l) |
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110 | return (fl2.f); |
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111 | if (!fl2.l) |
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112 | return (fl1.f); |
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113 | |
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114 | exp1 = EXP (fl1.l); |
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115 | exp2 = EXP (fl2.l); |
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116 | |
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117 | if (exp1 > exp2 + 25) |
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118 | return (fl1.l); |
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119 | if (exp2 > exp1 + 25) |
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120 | return (fl2.l); |
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121 | |
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122 | /* do everything in excess precision so's we can round later */ |
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123 | mant1 = MANT (fl1.l) << 6; |
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124 | mant2 = MANT (fl2.l) << 6; |
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125 | |
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126 | if (SIGN (fl1.l)) |
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127 | mant1 = -mant1; |
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128 | if (SIGN (fl2.l)) |
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129 | mant2 = -mant2; |
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130 | |
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131 | if (exp1 > exp2) |
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132 | { |
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133 | mant2 >>= exp1 - exp2; |
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134 | } |
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135 | else |
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136 | { |
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137 | mant1 >>= exp2 - exp1; |
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138 | exp1 = exp2; |
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139 | } |
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140 | mant1 += mant2; |
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141 | |
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142 | if (mant1 < 0) |
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143 | { |
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144 | mant1 = -mant1; |
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145 | sign = SIGNBIT; |
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146 | } |
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147 | else if (!mant1) |
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148 | return (0); |
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149 | |
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150 | /* normalize up */ |
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151 | while (!(mant1 & 0xE0000000)) |
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152 | { |
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153 | mant1 <<= 1; |
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154 | exp1--; |
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155 | } |
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156 | |
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157 | /* normalize down? */ |
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158 | if (mant1 & (1 << 30)) |
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159 | { |
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160 | mant1 >>= 1; |
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161 | exp1++; |
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162 | } |
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163 | |
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164 | /* round to even */ |
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165 | mant1 += (mant1 & 0x40) ? 0x20 : 0x1F; |
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166 | |
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167 | /* normalize down? */ |
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168 | if (mant1 & (1 << 30)) |
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169 | { |
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170 | mant1 >>= 1; |
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171 | exp1++; |
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172 | } |
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173 | |
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174 | /* lose extra precision */ |
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175 | mant1 >>= 6; |
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176 | |
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177 | /* turn off hidden bit */ |
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178 | mant1 &= ~HIDDEN; |
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179 | |
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180 | /* pack up and go home */ |
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181 | fl1.l = PACK (sign, exp1, mant1); |
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182 | return (fl1.f); |
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183 | } |
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184 | |
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185 | /* subtract two floats */ |
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186 | float |
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187 | __subsf3 (float a1, float a2) |
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188 | { |
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189 | register union float_long fl1, fl2; |
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190 | |
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191 | fl1.f = a1; |
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192 | fl2.f = a2; |
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193 | |
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194 | /* check for zero args */ |
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195 | if (!fl2.l) |
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196 | return (fl1.f); |
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197 | if (!fl1.l) |
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198 | return (-fl2.f); |
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199 | |
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200 | /* twiddle sign bit and add */ |
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201 | fl2.l ^= SIGNBIT; |
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202 | return __addsf3 (a1, fl2.f); |
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203 | } |
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204 | |
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205 | /* compare two floats */ |
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206 | long |
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207 | __cmpsf2 (float a1, float a2) |
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208 | { |
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209 | register union float_long fl1, fl2; |
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210 | |
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211 | fl1.f = a1; |
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212 | fl2.f = a2; |
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213 | |
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214 | if (SIGN (fl1.l) && SIGN (fl2.l)) |
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215 | { |
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216 | fl1.l ^= SIGNBIT; |
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217 | fl2.l ^= SIGNBIT; |
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218 | } |
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219 | if (fl1.l < fl2.l) |
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220 | return (-1); |
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221 | if (fl1.l > fl2.l) |
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222 | return (1); |
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223 | return (0); |
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224 | } |
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225 | |
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226 | /* multiply two floats */ |
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227 | float |
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228 | __mulsf3 (float a1, float a2) |
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229 | { |
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230 | register union float_long fl1, fl2; |
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231 | register unsigned long result; |
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232 | register int exp; |
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233 | int sign; |
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234 | |
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235 | fl1.f = a1; |
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236 | fl2.f = a2; |
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237 | |
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238 | if (!fl1.l || !fl2.l) |
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239 | return (0); |
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240 | |
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241 | /* compute sign and exponent */ |
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242 | sign = SIGN (fl1.l) ^ SIGN (fl2.l); |
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243 | exp = EXP (fl1.l) - EXCESS; |
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244 | exp += EXP (fl2.l); |
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245 | |
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246 | fl1.l = MANT (fl1.l); |
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247 | fl2.l = MANT (fl2.l); |
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248 | |
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249 | /* the multiply is done as one 16x16 multiply and two 16x8 multiples */ |
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250 | result = (fl1.l >> 8) * (fl2.l >> 8); |
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251 | result += ((fl1.l & 0xFF) * (fl2.l >> 8)) >> 8; |
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252 | result += ((fl2.l & 0xFF) * (fl1.l >> 8)) >> 8; |
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253 | |
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254 | if (result & 0x80000000) |
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255 | { |
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256 | /* round */ |
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257 | result += 0x80; |
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258 | result >>= 8; |
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259 | } |
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260 | else |
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261 | { |
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262 | /* round */ |
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263 | result += 0x40; |
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264 | result >>= 7; |
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265 | exp--; |
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266 | } |
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267 | |
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268 | result &= ~HIDDEN; |
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269 | |
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270 | /* pack up and go home */ |
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271 | fl1.l = PACK (sign, exp, result); |
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272 | return (fl1.f); |
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273 | } |
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274 | |
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275 | /* divide two floats */ |
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276 | float |
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277 | __divsf3 (float a1, float a2) |
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278 | { |
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279 | register union float_long fl1, fl2; |
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280 | register int result; |
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281 | register int mask; |
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282 | register int exp, sign; |
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283 | |
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284 | fl1.f = a1; |
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285 | fl2.f = a2; |
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286 | |
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287 | /* subtract exponents */ |
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288 | exp = EXP (fl1.l) - EXP (fl2.l) + EXCESS; |
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289 | |
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290 | /* compute sign */ |
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291 | sign = SIGN (fl1.l) ^ SIGN (fl2.l); |
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292 | |
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293 | /* divide by zero??? */ |
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294 | if (!fl2.l) |
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295 | /* return NaN or -NaN */ |
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296 | return (sign ? 0xFFFFFFFF : 0x7FFFFFFF); |
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297 | |
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298 | /* numerator zero??? */ |
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299 | if (!fl1.l) |
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300 | return (0); |
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301 | |
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302 | /* now get mantissas */ |
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303 | fl1.l = MANT (fl1.l); |
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304 | fl2.l = MANT (fl2.l); |
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305 | |
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306 | /* this assures we have 25 bits of precision in the end */ |
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307 | if (fl1.l < fl2.l) |
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308 | { |
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309 | fl1.l <<= 1; |
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310 | exp--; |
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311 | } |
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312 | |
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313 | /* now we perform repeated subtraction of fl2.l from fl1.l */ |
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314 | mask = 0x1000000; |
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315 | result = 0; |
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316 | while (mask) |
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317 | { |
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318 | if (fl1.l >= fl2.l) |
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319 | { |
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320 | result |= mask; |
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321 | fl1.l -= fl2.l; |
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322 | } |
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323 | fl1.l <<= 1; |
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324 | mask >>= 1; |
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325 | } |
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326 | |
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327 | /* round */ |
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328 | result += 1; |
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329 | |
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330 | /* normalize down */ |
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331 | exp++; |
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332 | result >>= 1; |
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333 | |
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334 | result &= ~HIDDEN; |
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335 | |
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336 | /* pack up and go home */ |
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337 | fl1.l = PACK (sign, exp, result); |
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338 | return (fl1.f); |
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339 | } |
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340 | |
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341 | /* convert int to double */ |
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342 | double |
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343 | __floatsidf (register long a1) |
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344 | { |
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345 | register int sign = 0, exp = 31 + EXCESSD; |
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346 | union double_long dl; |
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347 | |
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348 | if (!a1) |
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349 | { |
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350 | dl.l.upper = dl.l.lower = 0; |
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351 | return (dl.d); |
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352 | } |
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353 | |
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354 | if (a1 < 0) |
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355 | { |
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356 | sign = SIGNBIT; |
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357 | a1 = -a1; |
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358 | } |
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359 | |
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360 | while (a1 < 0x1000000) |
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361 | { |
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362 | a1 <<= 4; |
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363 | exp -= 4; |
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364 | } |
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365 | |
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366 | while (a1 < 0x40000000) |
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367 | { |
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368 | a1 <<= 1; |
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369 | exp--; |
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370 | } |
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371 | |
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372 | /* pack up and go home */ |
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373 | dl.l.upper = sign; |
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374 | dl.l.upper |= exp << 20; |
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375 | dl.l.upper |= (a1 >> 10) & ~HIDDEND; |
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376 | dl.l.lower = a1 << 22; |
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377 | |
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378 | return (dl.d); |
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379 | } |
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380 | |
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381 | /* negate a float */ |
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382 | float |
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383 | __negsf2 (float a1) |
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384 | { |
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385 | register union float_long fl1; |
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386 | |
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387 | fl1.f = a1; |
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388 | if (!fl1.l) |
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389 | return (0); |
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390 | |
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391 | fl1.l ^= SIGNBIT; |
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392 | return (fl1.f); |
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393 | } |
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394 | |
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395 | /* negate a double */ |
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396 | double |
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397 | __negdf2 (double a1) |
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398 | { |
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399 | register union double_long dl1; |
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400 | |
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401 | dl1.d = a1; |
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402 | |
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403 | if (!dl1.l.upper && !dl1.l.lower) |
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404 | return (dl1.d); |
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405 | |
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406 | dl1.l.upper ^= SIGNBIT; |
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407 | return (dl1.d); |
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408 | } |
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409 | |
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410 | /* convert float to double */ |
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411 | double |
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412 | __extendsfdf2 (float a1) |
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413 | { |
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414 | register union float_long fl1; |
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415 | register union double_long dl; |
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416 | register int exp; |
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417 | |
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418 | fl1.f = a1; |
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419 | |
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420 | if (!fl1.l) |
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421 | { |
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422 | dl.l.upper = dl.l.lower = 0; |
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423 | return (dl.d); |
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424 | } |
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425 | |
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426 | dl.l.upper = SIGN (fl1.l); |
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427 | exp = EXP (fl1.l) - EXCESS + EXCESSD; |
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428 | dl.l.upper |= exp << 20; |
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429 | dl.l.upper |= (MANT (fl1.l) & ~HIDDEN) >> 3; |
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430 | dl.l.lower = MANT (fl1.l) << 29; |
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431 | |
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432 | return (dl.d); |
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433 | } |
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434 | |
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435 | /* convert double to float */ |
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436 | float |
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437 | __truncdfsf2 (double a1) |
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438 | { |
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439 | register int exp; |
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440 | register long mant; |
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441 | register union float_long fl; |
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442 | register union double_long dl1; |
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443 | |
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444 | dl1.d = a1; |
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445 | |
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446 | if (!dl1.l.upper && !dl1.l.lower) |
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447 | return (0); |
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448 | |
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449 | exp = EXPD (dl1) - EXCESSD + EXCESS; |
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450 | |
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451 | /* shift double mantissa 6 bits so we can round */ |
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452 | mant = MANTD (dl1) >> 6; |
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453 | |
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454 | /* now round and shift down */ |
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455 | mant += 1; |
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456 | mant >>= 1; |
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457 | |
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458 | /* did the round overflow? */ |
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459 | if (mant & 0xFF000000) |
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460 | { |
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461 | mant >>= 1; |
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462 | exp++; |
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463 | } |
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464 | |
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465 | mant &= ~HIDDEN; |
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466 | |
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467 | /* pack up and go home */ |
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468 | fl.l = PACK (SIGND (dl1), exp, mant); |
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469 | return (fl.f); |
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470 | } |
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471 | |
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472 | /* compare two doubles */ |
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473 | long |
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474 | __cmpdf2 (double a1, double a2) |
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475 | { |
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476 | register union double_long dl1, dl2; |
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477 | |
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478 | dl1.d = a1; |
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479 | dl2.d = a2; |
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480 | |
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481 | if (SIGND (dl1) && SIGND (dl2)) |
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482 | { |
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483 | dl1.l.upper ^= SIGNBIT; |
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484 | dl2.l.upper ^= SIGNBIT; |
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485 | } |
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486 | if (dl1.l.upper < dl2.l.upper) |
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487 | return (-1); |
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488 | if (dl1.l.upper > dl2.l.upper) |
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489 | return (1); |
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490 | if (dl1.l.lower < dl2.l.lower) |
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491 | return (-1); |
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492 | if (dl1.l.lower > dl2.l.lower) |
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493 | return (1); |
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494 | return (0); |
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495 | } |
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496 | |
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497 | /* convert double to int */ |
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498 | long |
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499 | __fixdfsi (double a1) |
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500 | { |
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501 | register union double_long dl1; |
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502 | register int exp; |
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503 | register long l; |
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504 | |
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505 | dl1.d = a1; |
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506 | |
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507 | if (!dl1.l.upper && !dl1.l.lower) |
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508 | return (0); |
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509 | |
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510 | exp = EXPD (dl1) - EXCESSD - 31; |
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511 | l = MANTD (dl1); |
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512 | |
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513 | if (exp > 0) |
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514 | return (0x7FFFFFFF | SIGND (dl1)); /* largest integer */ |
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515 | |
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516 | /* shift down until exp = 0 or l = 0 */ |
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517 | if (exp < 0 && exp > -32 && l) |
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518 | l >>= -exp; |
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519 | else |
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520 | return (0); |
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521 | |
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522 | return (SIGND (dl1) ? -l : l); |
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523 | } |
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524 | |
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525 | /* convert double to unsigned int */ |
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526 | unsigned |
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527 | long __fixunsdfsi (double a1) |
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528 | { |
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529 | register union double_long dl1; |
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530 | register int exp; |
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531 | register unsigned long l; |
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532 | |
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533 | dl1.d = a1; |
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534 | |
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535 | if (!dl1.l.upper && !dl1.l.lower) |
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536 | return (0); |
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537 | |
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538 | exp = EXPD (dl1) - EXCESSD - 32; |
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539 | l = (((((dl1.l.upper) & 0xFFFFF) | HIDDEND) << 11) | (dl1.l.lower >> 21)); |
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540 | |
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541 | if (exp > 0) |
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542 | return (0xFFFFFFFF); /* largest integer */ |
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543 | |
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544 | /* shift down until exp = 0 or l = 0 */ |
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545 | if (exp < 0 && exp > -32 && l) |
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546 | l >>= -exp; |
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547 | else |
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548 | return (0); |
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549 | |
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550 | return (l); |
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551 | } |
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552 | |
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553 | /* For now, the hard double-precision routines simply |
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554 | punt and do it in single */ |
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555 | /* addtwo doubles */ |
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556 | double |
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557 | __adddf3 (double a1, double a2) |
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558 | { |
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559 | return ((float) a1 + (float) a2); |
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560 | } |
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561 | |
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562 | /* subtract two doubles */ |
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563 | double |
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564 | __subdf3 (double a1, double a2) |
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565 | { |
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566 | return ((float) a1 - (float) a2); |
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567 | } |
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568 | |
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569 | /* multiply two doubles */ |
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570 | double |
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571 | __muldf3 (double a1, double a2) |
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572 | { |
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573 | return ((float) a1 * (float) a2); |
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574 | } |
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575 | |
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576 | /* divide two doubles */ |
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577 | double |
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578 | __divdf3 (double a1, double a2) |
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579 | { |
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580 | return ((float) a1 / (float) a2); |
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581 | } |
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