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1 /* Software floating-point emulation.
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2 Basic four-word fraction declaration and manipulation.
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3 Copyright (C) 1997,1998,1999,2006,2007 Free Software Foundation, Inc.
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4 This file is part of the GNU C Library.
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5 Contributed by Richard Henderson (rth@cygnus.com),
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6 Jakub Jelinek (jj@ultra.linux.cz),
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7 David S. Miller (davem@redhat.com) and
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8 Peter Maydell (pmaydell@chiark.greenend.org.uk).
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9
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10 The GNU C Library is free software; you can redistribute it and/or
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11 modify it under the terms of the GNU Lesser General Public
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12 License as published by the Free Software Foundation; either
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13 version 2.1 of the License, or (at your option) any later version.
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14
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15 In addition to the permissions in the GNU Lesser General Public
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16 License, the Free Software Foundation gives you unlimited
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17 permission to link the compiled version of this file into
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18 combinations with other programs, and to distribute those
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19 combinations without any restriction coming from the use of this
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20 file. (The Lesser General Public License restrictions do apply in
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21 other respects; for example, they cover modification of the file,
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22 and distribution when not linked into a combine executable.)
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23
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24 The GNU C Library is distributed in the hope that it will be useful,
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25 but WITHOUT ANY WARRANTY; without even the implied warranty of
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26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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27 Lesser General Public License for more details.
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28
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29 You should have received a copy of the GNU Lesser General Public
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30 License along with the GNU C Library; if not, write to the Free
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31 Software Foundation, 51 Franklin Street, Fifth Floor, Boston,
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32 MA 02110-1301, USA. */
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33
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34 #define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4]
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35 #define _FP_FRAC_COPY_4(D,S) \
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36 (D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \
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37 D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
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38 #define _FP_FRAC_SET_4(X,I) __FP_FRAC_SET_4(X, I)
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39 #define _FP_FRAC_HIGH_4(X) (X##_f[3])
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40 #define _FP_FRAC_LOW_4(X) (X##_f[0])
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41 #define _FP_FRAC_WORD_4(X,w) (X##_f[w])
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42
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43 #define _FP_FRAC_SLL_4(X,N) \
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44 do { \
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45 _FP_I_TYPE _up, _down, _skip, _i; \
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46 _skip = (N) / _FP_W_TYPE_SIZE; \
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47 _up = (N) % _FP_W_TYPE_SIZE; \
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48 _down = _FP_W_TYPE_SIZE - _up; \
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49 if (!_up) \
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50 for (_i = 3; _i >= _skip; --_i) \
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51 X##_f[_i] = X##_f[_i-_skip]; \
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52 else \
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53 { \
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54 for (_i = 3; _i > _skip; --_i) \
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55 X##_f[_i] = X##_f[_i-_skip] << _up \
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56 | X##_f[_i-_skip-1] >> _down; \
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57 X##_f[_i--] = X##_f[0] << _up; \
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58 } \
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59 for (; _i >= 0; --_i) \
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60 X##_f[_i] = 0; \
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61 } while (0)
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62
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63 /* This one was broken too */
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64 #define _FP_FRAC_SRL_4(X,N) \
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65 do { \
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66 _FP_I_TYPE _up, _down, _skip, _i; \
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67 _skip = (N) / _FP_W_TYPE_SIZE; \
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68 _down = (N) % _FP_W_TYPE_SIZE; \
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69 _up = _FP_W_TYPE_SIZE - _down; \
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70 if (!_down) \
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71 for (_i = 0; _i <= 3-_skip; ++_i) \
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72 X##_f[_i] = X##_f[_i+_skip]; \
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73 else \
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74 { \
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75 for (_i = 0; _i < 3-_skip; ++_i) \
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76 X##_f[_i] = X##_f[_i+_skip] >> _down \
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77 | X##_f[_i+_skip+1] << _up; \
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78 X##_f[_i++] = X##_f[3] >> _down; \
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79 } \
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80 for (; _i < 4; ++_i) \
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81 X##_f[_i] = 0; \
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82 } while (0)
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83
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84
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85 /* Right shift with sticky-lsb.
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86 * What this actually means is that we do a standard right-shift,
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87 * but that if any of the bits that fall off the right hand side
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88 * were one then we always set the LSbit.
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89 */
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90 #define _FP_FRAC_SRST_4(X,S,N,size) \
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91 do { \
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92 _FP_I_TYPE _up, _down, _skip, _i; \
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93 _FP_W_TYPE _s; \
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94 _skip = (N) / _FP_W_TYPE_SIZE; \
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95 _down = (N) % _FP_W_TYPE_SIZE; \
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96 _up = _FP_W_TYPE_SIZE - _down; \
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97 for (_s = _i = 0; _i < _skip; ++_i) \
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98 _s |= X##_f[_i]; \
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99 if (!_down) \
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100 for (_i = 0; _i <= 3-_skip; ++_i) \
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101 X##_f[_i] = X##_f[_i+_skip]; \
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102 else \
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103 { \
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104 _s |= X##_f[_i] << _up; \
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105 for (_i = 0; _i < 3-_skip; ++_i) \
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106 X##_f[_i] = X##_f[_i+_skip] >> _down \
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107 | X##_f[_i+_skip+1] << _up; \
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108 X##_f[_i++] = X##_f[3] >> _down; \
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109 } \
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110 for (; _i < 4; ++_i) \
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111 X##_f[_i] = 0; \
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112 S = (_s != 0); \
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113 } while (0)
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114
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115 #define _FP_FRAC_SRS_4(X,N,size) \
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116 do { \
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117 int _sticky; \
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118 _FP_FRAC_SRST_4(X, _sticky, N, size); \
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119 X##_f[0] |= _sticky; \
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120 } while (0)
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121
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122 #define _FP_FRAC_ADD_4(R,X,Y) \
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123 __FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
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124 X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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125 Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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126
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127 #define _FP_FRAC_SUB_4(R,X,Y) \
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128 __FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
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129 X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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130 Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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131
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132 #define _FP_FRAC_DEC_4(X,Y) \
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133 __FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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134 Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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135
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136 #define _FP_FRAC_ADDI_4(X,I) \
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137 __FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
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138
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139 #define _FP_ZEROFRAC_4 0,0,0,0
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140 #define _FP_MINFRAC_4 0,0,0,1
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141 #define _FP_MAXFRAC_4 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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142
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143 #define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
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144 #define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE)X##_f[3] < 0)
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145 #define _FP_FRAC_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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146 #define _FP_FRAC_CLEAR_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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147
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148 #define _FP_FRAC_EQ_4(X,Y) \
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149 (X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \
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150 && X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
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151
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152 #define _FP_FRAC_GT_4(X,Y) \
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153 (X##_f[3] > Y##_f[3] || \
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154 (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \
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155 (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \
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156 (X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0]) \
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157 )) \
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158 )) \
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159 )
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160
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161 #define _FP_FRAC_GE_4(X,Y) \
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162 (X##_f[3] > Y##_f[3] || \
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163 (X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \
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164 (X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \
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165 (X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0]) \
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166 )) \
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167 )) \
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168 )
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169
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170
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171 #define _FP_FRAC_CLZ_4(R,X) \
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172 do { \
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173 if (X##_f[3]) \
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174 { \
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175 __FP_CLZ(R,X##_f[3]); \
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176 } \
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177 else if (X##_f[2]) \
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178 { \
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179 __FP_CLZ(R,X##_f[2]); \
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180 R += _FP_W_TYPE_SIZE; \
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181 } \
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182 else if (X##_f[1]) \
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183 { \
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184 __FP_CLZ(R,X##_f[1]); \
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185 R += _FP_W_TYPE_SIZE*2; \
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186 } \
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187 else \
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188 { \
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189 __FP_CLZ(R,X##_f[0]); \
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190 R += _FP_W_TYPE_SIZE*3; \
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191 } \
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192 } while(0)
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193
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194
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195 #define _FP_UNPACK_RAW_4(fs, X, val) \
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196 do { \
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197 union _FP_UNION_##fs _flo; _flo.flt = (val); \
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198 X##_f[0] = _flo.bits.frac0; \
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199 X##_f[1] = _flo.bits.frac1; \
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200 X##_f[2] = _flo.bits.frac2; \
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201 X##_f[3] = _flo.bits.frac3; \
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202 X##_e = _flo.bits.exp; \
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203 X##_s = _flo.bits.sign; \
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204 } while (0)
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205
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206 #define _FP_UNPACK_RAW_4_P(fs, X, val) \
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207 do { \
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208 union _FP_UNION_##fs *_flo = \
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209 (union _FP_UNION_##fs *)(val); \
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210 \
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211 X##_f[0] = _flo->bits.frac0; \
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212 X##_f[1] = _flo->bits.frac1; \
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213 X##_f[2] = _flo->bits.frac2; \
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214 X##_f[3] = _flo->bits.frac3; \
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215 X##_e = _flo->bits.exp; \
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216 X##_s = _flo->bits.sign; \
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217 } while (0)
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218
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219 #define _FP_PACK_RAW_4(fs, val, X) \
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220 do { \
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221 union _FP_UNION_##fs _flo; \
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222 _flo.bits.frac0 = X##_f[0]; \
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223 _flo.bits.frac1 = X##_f[1]; \
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224 _flo.bits.frac2 = X##_f[2]; \
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225 _flo.bits.frac3 = X##_f[3]; \
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226 _flo.bits.exp = X##_e; \
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227 _flo.bits.sign = X##_s; \
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228 (val) = _flo.flt; \
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229 } while (0)
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230
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231 #define _FP_PACK_RAW_4_P(fs, val, X) \
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232 do { \
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233 union _FP_UNION_##fs *_flo = \
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234 (union _FP_UNION_##fs *)(val); \
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235 \
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236 _flo->bits.frac0 = X##_f[0]; \
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237 _flo->bits.frac1 = X##_f[1]; \
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238 _flo->bits.frac2 = X##_f[2]; \
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239 _flo->bits.frac3 = X##_f[3]; \
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240 _flo->bits.exp = X##_e; \
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241 _flo->bits.sign = X##_s; \
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242 } while (0)
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243
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244 /*
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245 * Multiplication algorithms:
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246 */
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247
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248 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
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249
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250 #define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \
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251 do { \
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252 _FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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253 _FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f); \
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254 \
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255 doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
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256 doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]); \
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257 doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]); \
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258 doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]); \
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259 doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]); \
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260 doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]); \
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261 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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262 _FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0, \
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263 0,0,_FP_FRAC_WORD_8(_z,1)); \
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264 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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265 _FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0, \
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266 _FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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267 _FP_FRAC_WORD_8(_z,1)); \
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268 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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269 _FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0, \
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270 0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2)); \
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271 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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272 _FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0, \
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273 _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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274 _FP_FRAC_WORD_8(_z,2)); \
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275 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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276 _FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0, \
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277 _FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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278 _FP_FRAC_WORD_8(_z,2)); \
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279 doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]); \
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280 doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]); \
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281 doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]); \
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282 doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]); \
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283 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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284 _FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0, \
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285 0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3)); \
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286 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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287 _FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0, \
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288 _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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289 _FP_FRAC_WORD_8(_z,3)); \
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290 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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291 _FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0, \
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292 _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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293 _FP_FRAC_WORD_8(_z,3)); \
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294 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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295 _FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0, \
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296 _FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
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297 _FP_FRAC_WORD_8(_z,3)); \
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298 doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]); \
|
|
|
299 doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]); \
|
|
|
300 doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]); \
|
|
|
301 doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]); \
|
|
|
302 doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]); \
|
|
|
303 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
|
|
304 _FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0, \
|
|
|
305 0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4)); \
|
|
|
306 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
|
|
307 _FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0, \
|
|
|
308 _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
|
|
309 _FP_FRAC_WORD_8(_z,4)); \
|
|
|
310 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
|
|
311 _FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0, \
|
|
|
312 _FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
|
|
313 _FP_FRAC_WORD_8(_z,4)); \
|
|
|
314 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
|
|
315 _FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0, \
|
|
|
316 0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5)); \
|
|
|
317 __FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
|
|
318 _FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0, \
|
|
|
319 _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
|
|
320 _FP_FRAC_WORD_8(_z,5)); \
|
|
|
321 doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]); \
|
|
|
322 __FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
|
|
323 _b_f1,_b_f0, \
|
|
|
324 _FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6)); \
|
|
|
325 \
|
|
|
326 /* Normalize since we know where the msb of the multiplicands \
|
|
|
327 were (bit B), we know that the msb of the of the product is \
|
|
|
328 at either 2B or 2B-1. */ \
|
|
|
329 _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \
|
|
|
330 __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \
|
|
|
331 _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \
|
|
|
332 } while (0)
|
|
|
333
|
|
|
334 #define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \
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|
|
335 do { \
|
|
|
336 _FP_FRAC_DECL_8(_z); \
|
|
|
337 \
|
|
|
338 mpn_mul_n(_z_f, _x_f, _y_f, 4); \
|
|
|
339 \
|
|
|
340 /* Normalize since we know where the msb of the multiplicands \
|
|
|
341 were (bit B), we know that the msb of the of the product is \
|
|
|
342 at either 2B or 2B-1. */ \
|
|
|
343 _FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \
|
|
|
344 __FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \
|
|
|
345 _FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \
|
|
|
346 } while (0)
|
|
|
347
|
|
|
348 /*
|
|
|
349 * Helper utility for _FP_DIV_MEAT_4_udiv:
|
|
|
350 * pppp = m * nnn
|
|
|
351 */
|
|
|
352 #define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0) \
|
|
|
353 do { \
|
|
|
354 UWtype _t; \
|
|
|
355 umul_ppmm(p1,p0,m,n0); \
|
|
|
356 umul_ppmm(p2,_t,m,n1); \
|
|
|
357 __FP_FRAC_ADDI_2(p2,p1,_t); \
|
|
|
358 umul_ppmm(p3,_t,m,n2); \
|
|
|
359 __FP_FRAC_ADDI_2(p3,p2,_t); \
|
|
|
360 } while (0)
|
|
|
361
|
|
|
362 /*
|
|
|
363 * Division algorithms:
|
|
|
364 */
|
|
|
365
|
|
|
366 #define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \
|
|
|
367 do { \
|
|
|
368 int _i; \
|
|
|
369 _FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m); \
|
|
|
370 _FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4); \
|
|
|
371 if (_FP_FRAC_GT_4(X, Y)) \
|
|
|
372 { \
|
|
|
373 _n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \
|
|
|
374 _FP_FRAC_SRL_4(X, 1); \
|
|
|
375 } \
|
|
|
376 else \
|
|
|
377 R##_e--; \
|
|
|
378 \
|
|
|
379 /* Normalize, i.e. make the most significant bit of the \
|
|
|
380 denominator set. */ \
|
|
|
381 _FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs); \
|
|
|
382 \
|
|
|
383 for (_i = 3; ; _i--) \
|
|
|
384 { \
|
|
|
385 if (X##_f[3] == Y##_f[3]) \
|
|
|
386 { \
|
|
|
387 /* This is a special case, not an optimization \
|
|
|
388 (X##_f[3]/Y##_f[3] would not fit into UWtype). \
|
|
|
389 As X## is guaranteed to be < Y, R##_f[_i] can be either \
|
|
|
390 (UWtype)-1 or (UWtype)-2. */ \
|
|
|
391 R##_f[_i] = -1; \
|
|
|
392 if (!_i) \
|
|
|
393 break; \
|
|
|
394 __FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
|
|
|
395 Y##_f[2], Y##_f[1], Y##_f[0], 0, \
|
|
|
396 X##_f[2], X##_f[1], X##_f[0], _n_f[_i]); \
|
|
|
397 _FP_FRAC_SUB_4(X, Y, X); \
|
|
|
398 if (X##_f[3] > Y##_f[3]) \
|
|
|
399 { \
|
|
|
400 R##_f[_i] = -2; \
|
|
|
401 _FP_FRAC_ADD_4(X, Y, X); \
|
|
|
402 } \
|
|
|
403 } \
|
|
|
404 else \
|
|
|
405 { \
|
|
|
406 udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \
|
|
|
407 umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0], \
|
|
|
408 R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]); \
|
|
|
409 X##_f[2] = X##_f[1]; \
|
|
|
410 X##_f[1] = X##_f[0]; \
|
|
|
411 X##_f[0] = _n_f[_i]; \
|
|
|
412 if (_FP_FRAC_GT_4(_m, X)) \
|
|
|
413 { \
|
|
|
414 R##_f[_i]--; \
|
|
|
415 _FP_FRAC_ADD_4(X, Y, X); \
|
|
|
416 if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X)) \
|
|
|
417 { \
|
|
|
418 R##_f[_i]--; \
|
|
|
419 _FP_FRAC_ADD_4(X, Y, X); \
|
|
|
420 } \
|
|
|
421 } \
|
|
|
422 _FP_FRAC_DEC_4(X, _m); \
|
|
|
423 if (!_i) \
|
|
|
424 { \
|
|
|
425 if (!_FP_FRAC_EQ_4(X, _m)) \
|
|
|
426 R##_f[0] |= _FP_WORK_STICKY; \
|
|
|
427 break; \
|
|
|
428 } \
|
|
|
429 } \
|
|
|
430 } \
|
|
|
431 } while (0)
|
|
|
432
|
|
|
433
|
|
|
434 /*
|
|
|
435 * Square root algorithms:
|
|
|
436 * We have just one right now, maybe Newton approximation
|
|
|
437 * should be added for those machines where division is fast.
|
|
|
438 */
|
|
|
439
|
|
|
440 #define _FP_SQRT_MEAT_4(R, S, T, X, q) \
|
|
|
441 do { \
|
|
|
442 while (q) \
|
|
|
443 { \
|
|
|
444 T##_f[3] = S##_f[3] + q; \
|
|
|
445 if (T##_f[3] <= X##_f[3]) \
|
|
|
446 { \
|
|
|
447 S##_f[3] = T##_f[3] + q; \
|
|
|
448 X##_f[3] -= T##_f[3]; \
|
|
|
449 R##_f[3] += q; \
|
|
|
450 } \
|
|
|
451 _FP_FRAC_SLL_4(X, 1); \
|
|
|
452 q >>= 1; \
|
|
|
453 } \
|
|
|
454 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
|
|
455 while (q) \
|
|
|
456 { \
|
|
|
457 T##_f[2] = S##_f[2] + q; \
|
|
|
458 T##_f[3] = S##_f[3]; \
|
|
|
459 if (T##_f[3] < X##_f[3] || \
|
|
|
460 (T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \
|
|
|
461 { \
|
|
|
462 S##_f[2] = T##_f[2] + q; \
|
|
|
463 S##_f[3] += (T##_f[2] > S##_f[2]); \
|
|
|
464 __FP_FRAC_DEC_2(X##_f[3], X##_f[2], \
|
|
|
465 T##_f[3], T##_f[2]); \
|
|
|
466 R##_f[2] += q; \
|
|
|
467 } \
|
|
|
468 _FP_FRAC_SLL_4(X, 1); \
|
|
|
469 q >>= 1; \
|
|
|
470 } \
|
|
|
471 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
|
|
472 while (q) \
|
|
|
473 { \
|
|
|
474 T##_f[1] = S##_f[1] + q; \
|
|
|
475 T##_f[2] = S##_f[2]; \
|
|
|
476 T##_f[3] = S##_f[3]; \
|
|
|
477 if (T##_f[3] < X##_f[3] || \
|
|
|
478 (T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] || \
|
|
|
479 (T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1])))) \
|
|
|
480 { \
|
|
|
481 S##_f[1] = T##_f[1] + q; \
|
|
|
482 S##_f[2] += (T##_f[1] > S##_f[1]); \
|
|
|
483 S##_f[3] += (T##_f[2] > S##_f[2]); \
|
|
|
484 __FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1], \
|
|
|
485 T##_f[3], T##_f[2], T##_f[1]); \
|
|
|
486 R##_f[1] += q; \
|
|
|
487 } \
|
|
|
488 _FP_FRAC_SLL_4(X, 1); \
|
|
|
489 q >>= 1; \
|
|
|
490 } \
|
|
|
491 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
|
|
492 while (q != _FP_WORK_ROUND) \
|
|
|
493 { \
|
|
|
494 T##_f[0] = S##_f[0] + q; \
|
|
|
495 T##_f[1] = S##_f[1]; \
|
|
|
496 T##_f[2] = S##_f[2]; \
|
|
|
497 T##_f[3] = S##_f[3]; \
|
|
|
498 if (_FP_FRAC_GE_4(X,T)) \
|
|
|
499 { \
|
|
|
500 S##_f[0] = T##_f[0] + q; \
|
|
|
501 S##_f[1] += (T##_f[0] > S##_f[0]); \
|
|
|
502 S##_f[2] += (T##_f[1] > S##_f[1]); \
|
|
|
503 S##_f[3] += (T##_f[2] > S##_f[2]); \
|
|
|
504 _FP_FRAC_DEC_4(X, T); \
|
|
|
505 R##_f[0] += q; \
|
|
|
506 } \
|
|
|
507 _FP_FRAC_SLL_4(X, 1); \
|
|
|
508 q >>= 1; \
|
|
|
509 } \
|
|
|
510 if (!_FP_FRAC_ZEROP_4(X)) \
|
|
|
511 { \
|
|
|
512 if (_FP_FRAC_GT_4(X,S)) \
|
|
|
513 R##_f[0] |= _FP_WORK_ROUND; \
|
|
|
514 R##_f[0] |= _FP_WORK_STICKY; \
|
|
|
515 } \
|
|
|
516 } while (0)
|
|
|
517
|
|
|
518
|
|
|
519 /*
|
|
|
520 * Internals
|
|
|
521 */
|
|
|
522
|
|
|
523 #define __FP_FRAC_SET_4(X,I3,I2,I1,I0) \
|
|
|
524 (X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
|
|
|
525
|
|
|
526 #ifndef __FP_FRAC_ADD_3
|
|
|
527 #define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \
|
|
|
528 do { \
|
|
|
529 _FP_W_TYPE _c1, _c2; \
|
|
|
530 r0 = x0 + y0; \
|
|
|
531 _c1 = r0 < x0; \
|
|
|
532 r1 = x1 + y1; \
|
|
|
533 _c2 = r1 < x1; \
|
|
|
534 r1 += _c1; \
|
|
|
535 _c2 |= r1 < _c1; \
|
|
|
536 r2 = x2 + y2 + _c2; \
|
|
|
537 } while (0)
|
|
|
538 #endif
|
|
|
539
|
|
|
540 #ifndef __FP_FRAC_ADD_4
|
|
|
541 #define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \
|
|
|
542 do { \
|
|
|
543 _FP_W_TYPE _c1, _c2, _c3; \
|
|
|
544 r0 = x0 + y0; \
|
|
|
545 _c1 = r0 < x0; \
|
|
|
546 r1 = x1 + y1; \
|
|
|
547 _c2 = r1 < x1; \
|
|
|
548 r1 += _c1; \
|
|
|
549 _c2 |= r1 < _c1; \
|
|
|
550 r2 = x2 + y2; \
|
|
|
551 _c3 = r2 < x2; \
|
|
|
552 r2 += _c2; \
|
|
|
553 _c3 |= r2 < _c2; \
|
|
|
554 r3 = x3 + y3 + _c3; \
|
|
|
555 } while (0)
|
|
|
556 #endif
|
|
|
557
|
|
|
558 #ifndef __FP_FRAC_SUB_3
|
|
|
559 #define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \
|
|
|
560 do { \
|
|
|
561 _FP_W_TYPE _c1, _c2; \
|
|
|
562 r0 = x0 - y0; \
|
|
|
563 _c1 = r0 > x0; \
|
|
|
564 r1 = x1 - y1; \
|
|
|
565 _c2 = r1 > x1; \
|
|
|
566 r1 -= _c1; \
|
|
|
567 _c2 |= _c1 && (y1 == x1); \
|
|
|
568 r2 = x2 - y2 - _c2; \
|
|
|
569 } while (0)
|
|
|
570 #endif
|
|
|
571
|
|
|
572 #ifndef __FP_FRAC_SUB_4
|
|
|
573 #define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \
|
|
|
574 do { \
|
|
|
575 _FP_W_TYPE _c1, _c2, _c3; \
|
|
|
576 r0 = x0 - y0; \
|
|
|
577 _c1 = r0 > x0; \
|
|
|
578 r1 = x1 - y1; \
|
|
|
579 _c2 = r1 > x1; \
|
|
|
580 r1 -= _c1; \
|
|
|
581 _c2 |= _c1 && (y1 == x1); \
|
|
|
582 r2 = x2 - y2; \
|
|
|
583 _c3 = r2 > x2; \
|
|
|
584 r2 -= _c2; \
|
|
|
585 _c3 |= _c2 && (y2 == x2); \
|
|
|
586 r3 = x3 - y3 - _c3; \
|
|
|
587 } while (0)
|
|
|
588 #endif
|
|
|
589
|
|
|
590 #ifndef __FP_FRAC_DEC_3
|
|
|
591 #define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0) \
|
|
|
592 do { \
|
|
|
593 UWtype _t0, _t1, _t2; \
|
|
|
594 _t0 = x0, _t1 = x1, _t2 = x2; \
|
|
|
595 __FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0); \
|
|
|
596 } while (0)
|
|
|
597 #endif
|
|
|
598
|
|
|
599 #ifndef __FP_FRAC_DEC_4
|
|
|
600 #define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0) \
|
|
|
601 do { \
|
|
|
602 UWtype _t0, _t1, _t2, _t3; \
|
|
|
603 _t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3; \
|
|
|
604 __FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0); \
|
|
|
605 } while (0)
|
|
|
606 #endif
|
|
|
607
|
|
|
608 #ifndef __FP_FRAC_ADDI_4
|
|
|
609 #define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i) \
|
|
|
610 do { \
|
|
|
611 UWtype _t; \
|
|
|
612 _t = ((x0 += i) < i); \
|
|
|
613 x1 += _t; _t = (x1 < _t); \
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614 x2 += _t; _t = (x2 < _t); \
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615 x3 += _t; \
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616 } while (0)
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617 #endif
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618
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619 /* Convert FP values between word sizes. This appears to be more
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620 * complicated than I'd have expected it to be, so these might be
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621 * wrong... These macros are in any case somewhat bogus because they
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622 * use information about what various FRAC_n variables look like
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623 * internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
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624 * the ones in op-2.h and op-1.h.
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625 */
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626 #define _FP_FRAC_COPY_1_4(D, S) (D##_f = S##_f[0])
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627
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628 #define _FP_FRAC_COPY_2_4(D, S) \
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629 do { \
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630 D##_f0 = S##_f[0]; \
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631 D##_f1 = S##_f[1]; \
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632 } while (0)
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633
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634 /* Assembly/disassembly for converting to/from integral types.
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635 * No shifting or overflow handled here.
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636 */
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637 /* Put the FP value X into r, which is an integer of size rsize. */
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638 #define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \
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639 do { \
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640 if (rsize <= _FP_W_TYPE_SIZE) \
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641 r = X##_f[0]; \
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642 else if (rsize <= 2*_FP_W_TYPE_SIZE) \
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643 { \
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644 r = X##_f[1]; \
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645 r <<= _FP_W_TYPE_SIZE; \
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646 r += X##_f[0]; \
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647 } \
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648 else \
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649 { \
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650 /* I'm feeling lazy so we deal with int == 3words (implausible)*/ \
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651 /* and int == 4words as a single case. */ \
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652 r = X##_f[3]; \
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653 r <<= _FP_W_TYPE_SIZE; \
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654 r += X##_f[2]; \
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655 r <<= _FP_W_TYPE_SIZE; \
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656 r += X##_f[1]; \
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657 r <<= _FP_W_TYPE_SIZE; \
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658 r += X##_f[0]; \
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659 } \
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660 } while (0)
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661
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662 /* "No disassemble Number Five!" */
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663 /* move an integer of size rsize into X's fractional part. We rely on
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664 * the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
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665 * having to mask the values we store into it.
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666 */
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667 #define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \
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668 do { \
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669 X##_f[0] = r; \
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670 X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
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671 X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
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672 X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
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673 } while (0);
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674
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675 #define _FP_FRAC_COPY_4_1(D, S) \
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676 do { \
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677 D##_f[0] = S##_f; \
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678 D##_f[1] = D##_f[2] = D##_f[3] = 0; \
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679 } while (0)
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680
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681 #define _FP_FRAC_COPY_4_2(D, S) \
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682 do { \
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683 D##_f[0] = S##_f0; \
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684 D##_f[1] = S##_f1; \
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685 D##_f[2] = D##_f[3] = 0; \
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686 } while (0)
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687
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688 #define _FP_FRAC_COPY_4_4(D,S) _FP_FRAC_COPY_4(D,S)
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