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1 /* Software floating-point emulation.
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2 Basic two-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_2(X) _FP_W_TYPE X##_f0, X##_f1
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35 #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
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36 #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
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37 #define _FP_FRAC_HIGH_2(X) (X##_f1)
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38 #define _FP_FRAC_LOW_2(X) (X##_f0)
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39 #define _FP_FRAC_WORD_2(X,w) (X##_f##w)
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40
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41 #define _FP_FRAC_SLL_2(X,N) \
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42 (void)(((N) < _FP_W_TYPE_SIZE) \
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43 ? ({ \
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44 if (__builtin_constant_p(N) && (N) == 1) \
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45 { \
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46 X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \
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47 X##_f0 += X##_f0; \
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48 } \
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49 else \
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50 { \
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51 X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
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52 X##_f0 <<= (N); \
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53 } \
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54 0; \
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55 }) \
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56 : ({ \
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57 X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
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58 X##_f0 = 0; \
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59 }))
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60
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61
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62 #define _FP_FRAC_SRL_2(X,N) \
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63 (void)(((N) < _FP_W_TYPE_SIZE) \
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64 ? ({ \
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65 X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
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66 X##_f1 >>= (N); \
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67 }) \
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68 : ({ \
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69 X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
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70 X##_f1 = 0; \
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71 }))
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72
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73 /* Right shift with sticky-lsb. */
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74 #define _FP_FRAC_SRST_2(X,S, N,sz) \
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75 (void)(((N) < _FP_W_TYPE_SIZE) \
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76 ? ({ \
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77 S = (__builtin_constant_p(N) && (N) == 1 \
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78 ? X##_f0 & 1 \
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79 : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \
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80 X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \
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81 X##_f1 >>= (N); \
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82 }) \
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83 : ({ \
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84 S = ((((N) == _FP_W_TYPE_SIZE \
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85 ? 0 \
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86 : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
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87 | X##_f0) != 0); \
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88 X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \
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89 X##_f1 = 0; \
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90 }))
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91
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92 #define _FP_FRAC_SRS_2(X,N,sz) \
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93 (void)(((N) < _FP_W_TYPE_SIZE) \
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94 ? ({ \
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95 X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \
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96 (__builtin_constant_p(N) && (N) == 1 \
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97 ? X##_f0 & 1 \
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98 : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
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99 X##_f1 >>= (N); \
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100 }) \
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101 : ({ \
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102 X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \
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103 ((((N) == _FP_W_TYPE_SIZE \
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104 ? 0 \
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105 : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
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106 | X##_f0) != 0)); \
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107 X##_f1 = 0; \
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108 }))
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109
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110 #define _FP_FRAC_ADDI_2(X,I) \
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111 __FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
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112
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113 #define _FP_FRAC_ADD_2(R,X,Y) \
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114 __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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115
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116 #define _FP_FRAC_SUB_2(R,X,Y) \
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117 __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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118
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119 #define _FP_FRAC_DEC_2(X,Y) \
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120 __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0)
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121
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122 #define _FP_FRAC_CLZ_2(R,X) \
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123 do { \
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124 if (X##_f1) \
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125 __FP_CLZ(R,X##_f1); \
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126 else \
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127 { \
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128 __FP_CLZ(R,X##_f0); \
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129 R += _FP_W_TYPE_SIZE; \
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130 } \
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131 } while(0)
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132
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133 /* Predicates */
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134 #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
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135 #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
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136 #define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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137 #define _FP_FRAC_CLEAR_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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138 #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
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139 #define _FP_FRAC_GT_2(X, Y) \
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140 (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
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141 #define _FP_FRAC_GE_2(X, Y) \
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142 (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
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143
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144 #define _FP_ZEROFRAC_2 0, 0
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145 #define _FP_MINFRAC_2 0, 1
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146 #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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147
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148 /*
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149 * Internals
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150 */
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151
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152 #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
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153
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154 #define __FP_CLZ_2(R, xh, xl) \
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155 do { \
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156 if (xh) \
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157 __FP_CLZ(R,xh); \
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158 else \
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159 { \
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160 __FP_CLZ(R,xl); \
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161 R += _FP_W_TYPE_SIZE; \
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162 } \
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163 } while(0)
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164
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165 #if 0
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166
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167 #ifndef __FP_FRAC_ADDI_2
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168 #define __FP_FRAC_ADDI_2(xh, xl, i) \
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169 (xh += ((xl += i) < i))
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170 #endif
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171 #ifndef __FP_FRAC_ADD_2
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172 #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
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173 (rh = xh + yh + ((rl = xl + yl) < xl))
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174 #endif
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175 #ifndef __FP_FRAC_SUB_2
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176 #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
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177 (rh = xh - yh - ((rl = xl - yl) > xl))
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178 #endif
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179 #ifndef __FP_FRAC_DEC_2
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180 #define __FP_FRAC_DEC_2(xh, xl, yh, yl) \
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181 do { \
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182 UWtype _t = xl; \
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183 xh -= yh + ((xl -= yl) > _t); \
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184 } while (0)
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185 #endif
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186
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187 #else
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188
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189 #undef __FP_FRAC_ADDI_2
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190 #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
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191 #undef __FP_FRAC_ADD_2
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192 #define __FP_FRAC_ADD_2 add_ssaaaa
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193 #undef __FP_FRAC_SUB_2
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194 #define __FP_FRAC_SUB_2 sub_ddmmss
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195 #undef __FP_FRAC_DEC_2
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196 #define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl)
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197
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198 #endif
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199
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200 /*
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201 * Unpack the raw bits of a native fp value. Do not classify or
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202 * normalize the data.
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203 */
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204
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205 #define _FP_UNPACK_RAW_2(fs, X, val) \
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206 do { \
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207 union _FP_UNION_##fs _flo; _flo.flt = (val); \
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208 \
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209 X##_f0 = _flo.bits.frac0; \
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210 X##_f1 = _flo.bits.frac1; \
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211 X##_e = _flo.bits.exp; \
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212 X##_s = _flo.bits.sign; \
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213 } while (0)
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214
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215 #define _FP_UNPACK_RAW_2_P(fs, X, val) \
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216 do { \
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217 union _FP_UNION_##fs *_flo = \
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218 (union _FP_UNION_##fs *)(val); \
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219 \
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220 X##_f0 = _flo->bits.frac0; \
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221 X##_f1 = _flo->bits.frac1; \
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222 X##_e = _flo->bits.exp; \
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223 X##_s = _flo->bits.sign; \
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224 } while (0)
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225
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226
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227 /*
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228 * Repack the raw bits of a native fp value.
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229 */
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230
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231 #define _FP_PACK_RAW_2(fs, val, X) \
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232 do { \
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233 union _FP_UNION_##fs _flo; \
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234 \
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235 _flo.bits.frac0 = X##_f0; \
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236 _flo.bits.frac1 = X##_f1; \
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237 _flo.bits.exp = X##_e; \
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238 _flo.bits.sign = X##_s; \
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239 \
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240 (val) = _flo.flt; \
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241 } while (0)
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242
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243 #define _FP_PACK_RAW_2_P(fs, val, X) \
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244 do { \
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245 union _FP_UNION_##fs *_flo = \
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246 (union _FP_UNION_##fs *)(val); \
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247 \
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248 _flo->bits.frac0 = X##_f0; \
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249 _flo->bits.frac1 = X##_f1; \
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250 _flo->bits.exp = X##_e; \
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251 _flo->bits.sign = X##_s; \
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252 } while (0)
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253
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254
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255 /*
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256 * Multiplication algorithms:
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257 */
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258
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259 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
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260
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261 #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \
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262 do { \
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263 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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264 \
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265 doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
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266 doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
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267 doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
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268 doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
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269 \
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270 __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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271 _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \
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272 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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273 _FP_FRAC_WORD_4(_z,1)); \
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274 __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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275 _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \
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276 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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277 _FP_FRAC_WORD_4(_z,1)); \
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278 \
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279 /* Normalize since we know where the msb of the multiplicands \
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280 were (bit B), we know that the msb of the of the product is \
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281 at either 2B or 2B-1. */ \
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282 _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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283 R##_f0 = _FP_FRAC_WORD_4(_z,0); \
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284 R##_f1 = _FP_FRAC_WORD_4(_z,1); \
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285 } while (0)
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286
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287 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.
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288 Do only 3 multiplications instead of four. This one is for machines
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289 where multiplication is much more expensive than subtraction. */
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290
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291 #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \
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292 do { \
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293 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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294 _FP_W_TYPE _d; \
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295 int _c1, _c2; \
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296 \
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297 _b_f0 = X##_f0 + X##_f1; \
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298 _c1 = _b_f0 < X##_f0; \
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299 _b_f1 = Y##_f0 + Y##_f1; \
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300 _c2 = _b_f1 < Y##_f0; \
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301 doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
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302 doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \
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303 doit(_c_f1, _c_f0, X##_f1, Y##_f1); \
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304 \
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305 _b_f0 &= -_c2; \
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306 _b_f1 &= -_c1; \
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307 __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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308 _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \
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309 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \
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310 __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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311 _b_f0); \
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312 __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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313 _b_f1); \
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314 __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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315 _FP_FRAC_WORD_4(_z,1), \
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316 0, _d, _FP_FRAC_WORD_4(_z,0)); \
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317 __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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318 _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \
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319 __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \
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320 _c_f1, _c_f0, \
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321 _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \
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322 \
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323 /* Normalize since we know where the msb of the multiplicands \
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|
324 were (bit B), we know that the msb of the of the product is \
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325 at either 2B or 2B-1. */ \
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326 _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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327 R##_f0 = _FP_FRAC_WORD_4(_z,0); \
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328 R##_f1 = _FP_FRAC_WORD_4(_z,1); \
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329 } while (0)
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330
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331 #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \
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332 do { \
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333 _FP_FRAC_DECL_4(_z); \
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334 _FP_W_TYPE _x[2], _y[2]; \
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335 _x[0] = X##_f0; _x[1] = X##_f1; \
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336 _y[0] = Y##_f0; _y[1] = Y##_f1; \
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337 \
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338 mpn_mul_n(_z_f, _x, _y, 2); \
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339 \
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340 /* Normalize since we know where the msb of the multiplicands \
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341 were (bit B), we know that the msb of the of the product is \
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342 at either 2B or 2B-1. */ \
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343 _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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344 R##_f0 = _z_f[0]; \
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345 R##_f1 = _z_f[1]; \
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346 } while (0)
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347
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348 /* Do at most 120x120=240 bits multiplication using double floating
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349 point multiplication. This is useful if floating point
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350 multiplication has much bigger throughput than integer multiply.
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351 It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
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352 between 106 and 120 only.
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353 Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
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354 SETFETZ is a macro which will disable all FPU exceptions and set rounding
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355 towards zero, RESETFE should optionally reset it back. */
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356
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357 #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \
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358 do { \
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359 static const double _const[] = { \
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360 /* 2^-24 */ 5.9604644775390625e-08, \
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361 /* 2^-48 */ 3.5527136788005009e-15, \
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362 /* 2^-72 */ 2.1175823681357508e-22, \
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363 /* 2^-96 */ 1.2621774483536189e-29, \
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364 /* 2^28 */ 2.68435456e+08, \
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365 /* 2^4 */ 1.600000e+01, \
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366 /* 2^-20 */ 9.5367431640625e-07, \
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367 /* 2^-44 */ 5.6843418860808015e-14, \
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368 /* 2^-68 */ 3.3881317890172014e-21, \
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369 /* 2^-92 */ 2.0194839173657902e-28, \
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370 /* 2^-116 */ 1.2037062152420224e-35}; \
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371 double _a240, _b240, _c240, _d240, _e240, _f240, \
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372 _g240, _h240, _i240, _j240, _k240; \
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373 union { double d; UDItype i; } _l240, _m240, _n240, _o240, \
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374 _p240, _q240, _r240, _s240; \
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375 UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \
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376 \
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377 if (wfracbits < 106 || wfracbits > 120) \
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378 abort(); \
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379 \
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380 setfetz; \
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381 \
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382 _e240 = (double)(long)(X##_f0 & 0xffffff); \
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383 _j240 = (double)(long)(Y##_f0 & 0xffffff); \
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384 _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \
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385 _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \
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386 _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \
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387 _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \
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|
|
388 _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \
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|
|
389 _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \
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|
|
390 _a240 = (double)(long)(X##_f1 >> 32); \
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|
|
391 _f240 = (double)(long)(Y##_f1 >> 32); \
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|
|
392 _e240 *= _const[3]; \
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|
|
393 _j240 *= _const[3]; \
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|
|
394 _d240 *= _const[2]; \
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|
|
395 _i240 *= _const[2]; \
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|
|
396 _c240 *= _const[1]; \
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|
|
397 _h240 *= _const[1]; \
|
|
|
398 _b240 *= _const[0]; \
|
|
|
399 _g240 *= _const[0]; \
|
|
|
400 _s240.d = _e240*_j240;\
|
|
|
401 _r240.d = _d240*_j240 + _e240*_i240;\
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|
|
402 _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\
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|
|
403 _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\
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|
|
404 _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\
|
|
|
405 _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \
|
|
|
406 _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \
|
|
|
407 _l240.d = _a240*_g240 + _b240*_f240; \
|
|
|
408 _k240 = _a240*_f240; \
|
|
|
409 _r240.d += _s240.d; \
|
|
|
410 _q240.d += _r240.d; \
|
|
|
411 _p240.d += _q240.d; \
|
|
|
412 _o240.d += _p240.d; \
|
|
|
413 _n240.d += _o240.d; \
|
|
|
414 _m240.d += _n240.d; \
|
|
|
415 _l240.d += _m240.d; \
|
|
|
416 _k240 += _l240.d; \
|
|
|
417 _s240.d -= ((_const[10]+_s240.d)-_const[10]); \
|
|
|
418 _r240.d -= ((_const[9]+_r240.d)-_const[9]); \
|
|
|
419 _q240.d -= ((_const[8]+_q240.d)-_const[8]); \
|
|
|
420 _p240.d -= ((_const[7]+_p240.d)-_const[7]); \
|
|
|
421 _o240.d += _const[7]; \
|
|
|
422 _n240.d += _const[6]; \
|
|
|
423 _m240.d += _const[5]; \
|
|
|
424 _l240.d += _const[4]; \
|
|
|
425 if (_s240.d != 0.0) _y240 = 1; \
|
|
|
426 if (_r240.d != 0.0) _y240 = 1; \
|
|
|
427 if (_q240.d != 0.0) _y240 = 1; \
|
|
|
428 if (_p240.d != 0.0) _y240 = 1; \
|
|
|
429 _t240 = (DItype)_k240; \
|
|
|
430 _u240 = _l240.i; \
|
|
|
431 _v240 = _m240.i; \
|
|
|
432 _w240 = _n240.i; \
|
|
|
433 _x240 = _o240.i; \
|
|
|
434 R##_f1 = (_t240 << (128 - (wfracbits - 1))) \
|
|
|
435 | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \
|
|
|
436 R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \
|
|
|
437 | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \
|
|
|
438 | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \
|
|
|
439 | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \
|
|
|
440 | _y240; \
|
|
|
441 resetfe; \
|
|
|
442 } while (0)
|
|
|
443
|
|
|
444 /*
|
|
|
445 * Division algorithms:
|
|
|
446 */
|
|
|
447
|
|
|
448 #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \
|
|
|
449 do { \
|
|
|
450 _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \
|
|
|
451 if (_FP_FRAC_GT_2(X, Y)) \
|
|
|
452 { \
|
|
|
453 _n_f2 = X##_f1 >> 1; \
|
|
|
454 _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
|
|
|
455 _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
|
|
|
456 } \
|
|
|
457 else \
|
|
|
458 { \
|
|
|
459 R##_e--; \
|
|
|
460 _n_f2 = X##_f1; \
|
|
|
461 _n_f1 = X##_f0; \
|
|
|
462 _n_f0 = 0; \
|
|
|
463 } \
|
|
|
464 \
|
|
|
465 /* Normalize, i.e. make the most significant bit of the \
|
|
|
466 denominator set. */ \
|
|
|
467 _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \
|
|
|
468 \
|
|
|
469 udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \
|
|
|
470 umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \
|
|
|
471 _r_f0 = _n_f0; \
|
|
|
472 if (_FP_FRAC_GT_2(_m, _r)) \
|
|
|
473 { \
|
|
|
474 R##_f1--; \
|
|
|
475 _FP_FRAC_ADD_2(_r, Y, _r); \
|
|
|
476 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
|
|
477 { \
|
|
|
478 R##_f1--; \
|
|
|
479 _FP_FRAC_ADD_2(_r, Y, _r); \
|
|
|
480 } \
|
|
|
481 } \
|
|
|
482 _FP_FRAC_DEC_2(_r, _m); \
|
|
|
483 \
|
|
|
484 if (_r_f1 == Y##_f1) \
|
|
|
485 { \
|
|
|
486 /* This is a special case, not an optimization \
|
|
|
487 (_r/Y##_f1 would not fit into UWtype). \
|
|
|
488 As _r is guaranteed to be < Y, R##_f0 can be either \
|
|
|
489 (UWtype)-1 or (UWtype)-2. But as we know what kind \
|
|
|
490 of bits it is (sticky, guard, round), we don't care. \
|
|
|
491 We also don't care what the reminder is, because the \
|
|
|
492 guard bit will be set anyway. -jj */ \
|
|
|
493 R##_f0 = -1; \
|
|
|
494 } \
|
|
|
495 else \
|
|
|
496 { \
|
|
|
497 udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \
|
|
|
498 umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \
|
|
|
499 _r_f0 = 0; \
|
|
|
500 if (_FP_FRAC_GT_2(_m, _r)) \
|
|
|
501 { \
|
|
|
502 R##_f0--; \
|
|
|
503 _FP_FRAC_ADD_2(_r, Y, _r); \
|
|
|
504 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
|
|
505 { \
|
|
|
506 R##_f0--; \
|
|
|
507 _FP_FRAC_ADD_2(_r, Y, _r); \
|
|
|
508 } \
|
|
|
509 } \
|
|
|
510 if (!_FP_FRAC_EQ_2(_r, _m)) \
|
|
|
511 R##_f0 |= _FP_WORK_STICKY; \
|
|
|
512 } \
|
|
|
513 } while (0)
|
|
|
514
|
|
|
515
|
|
|
516 #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
|
|
|
517 do { \
|
|
|
518 _FP_W_TYPE _x[4], _y[2], _z[4]; \
|
|
|
519 _y[0] = Y##_f0; _y[1] = Y##_f1; \
|
|
|
520 _x[0] = _x[3] = 0; \
|
|
|
521 if (_FP_FRAC_GT_2(X, Y)) \
|
|
|
522 { \
|
|
|
523 R##_e++; \
|
|
|
524 _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \
|
|
|
525 X##_f1 >> (_FP_W_TYPE_SIZE - \
|
|
|
526 (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \
|
|
|
527 _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \
|
|
|
528 } \
|
|
|
529 else \
|
|
|
530 { \
|
|
|
531 _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \
|
|
|
532 X##_f1 >> (_FP_W_TYPE_SIZE - \
|
|
|
533 (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \
|
|
|
534 _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \
|
|
|
535 } \
|
|
|
536 \
|
|
|
537 (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
|
|
|
538 R##_f1 = _z[1]; \
|
|
|
539 R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \
|
|
|
540 } while (0)
|
|
|
541
|
|
|
542
|
|
|
543 /*
|
|
|
544 * Square root algorithms:
|
|
|
545 * We have just one right now, maybe Newton approximation
|
|
|
546 * should be added for those machines where division is fast.
|
|
|
547 */
|
|
|
548
|
|
|
549 #define _FP_SQRT_MEAT_2(R, S, T, X, q) \
|
|
|
550 do { \
|
|
|
551 while (q) \
|
|
|
552 { \
|
|
|
553 T##_f1 = S##_f1 + q; \
|
|
|
554 if (T##_f1 <= X##_f1) \
|
|
|
555 { \
|
|
|
556 S##_f1 = T##_f1 + q; \
|
|
|
557 X##_f1 -= T##_f1; \
|
|
|
558 R##_f1 += q; \
|
|
|
559 } \
|
|
|
560 _FP_FRAC_SLL_2(X, 1); \
|
|
|
561 q >>= 1; \
|
|
|
562 } \
|
|
|
563 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
|
|
564 while (q != _FP_WORK_ROUND) \
|
|
|
565 { \
|
|
|
566 T##_f0 = S##_f0 + q; \
|
|
|
567 T##_f1 = S##_f1; \
|
|
|
568 if (T##_f1 < X##_f1 || \
|
|
|
569 (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \
|
|
|
570 { \
|
|
|
571 S##_f0 = T##_f0 + q; \
|
|
|
572 S##_f1 += (T##_f0 > S##_f0); \
|
|
|
573 _FP_FRAC_DEC_2(X, T); \
|
|
|
574 R##_f0 += q; \
|
|
|
575 } \
|
|
|
576 _FP_FRAC_SLL_2(X, 1); \
|
|
|
577 q >>= 1; \
|
|
|
578 } \
|
|
|
579 if (X##_f0 | X##_f1) \
|
|
|
580 { \
|
|
|
581 if (S##_f1 < X##_f1 || \
|
|
|
582 (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \
|
|
|
583 R##_f0 |= _FP_WORK_ROUND; \
|
|
|
584 R##_f0 |= _FP_WORK_STICKY; \
|
|
|
585 } \
|
|
|
586 } while (0)
|
|
|
587
|
|
|
588
|
|
|
589 /*
|
|
|
590 * Assembly/disassembly for converting to/from integral types.
|
|
|
591 * No shifting or overflow handled here.
|
|
|
592 */
|
|
|
593
|
|
|
594 #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
|
|
|
595 (void)((rsize <= _FP_W_TYPE_SIZE) \
|
|
|
596 ? ({ r = X##_f0; }) \
|
|
|
597 : ({ \
|
|
|
598 r = X##_f1; \
|
|
|
599 r <<= _FP_W_TYPE_SIZE; \
|
|
|
600 r += X##_f0; \
|
|
|
601 }))
|
|
|
602
|
|
|
603 #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
|
|
|
604 do { \
|
|
|
605 X##_f0 = r; \
|
|
|
606 X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
|
|
|
607 } while (0)
|
|
|
608
|
|
|
609 /*
|
|
|
610 * Convert FP values between word sizes
|
|
|
611 */
|
|
|
612
|
|
|
613 #define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0)
|
|
|
614
|
|
|
615 #define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0))
|
|
|
616
|
|
|
617 #define _FP_FRAC_COPY_2_2(D,S) _FP_FRAC_COPY_2(D,S)
|
