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111
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1 /* Software floating-point emulation.
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2 Basic one-word fraction declaration and manipulation.
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145
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3 Copyright (C) 1997-2019 Free Software Foundation, Inc.
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111
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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, see
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31 <http://www.gnu.org/licenses/>. */
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32
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33 #ifndef SOFT_FP_OP_1_H
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34 #define SOFT_FP_OP_1_H 1
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35
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36 #define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f _FP_ZERO_INIT
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37 #define _FP_FRAC_COPY_1(D, S) (D##_f = S##_f)
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38 #define _FP_FRAC_SET_1(X, I) (X##_f = I)
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39 #define _FP_FRAC_HIGH_1(X) (X##_f)
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40 #define _FP_FRAC_LOW_1(X) (X##_f)
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41 #define _FP_FRAC_WORD_1(X, w) (X##_f)
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42
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43 #define _FP_FRAC_ADDI_1(X, I) (X##_f += I)
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44 #define _FP_FRAC_SLL_1(X, N) \
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45 do \
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46 { \
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47 if (__builtin_constant_p (N) && (N) == 1) \
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48 X##_f += X##_f; \
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49 else \
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50 X##_f <<= (N); \
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51 } \
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52 while (0)
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53 #define _FP_FRAC_SRL_1(X, N) (X##_f >>= N)
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54
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55 /* Right shift with sticky-lsb. */
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56 #define _FP_FRAC_SRST_1(X, S, N, sz) __FP_FRAC_SRST_1 (X##_f, S, (N), (sz))
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57 #define _FP_FRAC_SRS_1(X, N, sz) __FP_FRAC_SRS_1 (X##_f, (N), (sz))
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58
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59 #define __FP_FRAC_SRST_1(X, S, N, sz) \
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60 do \
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61 { \
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62 S = (__builtin_constant_p (N) && (N) == 1 \
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63 ? X & 1 \
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64 : (X << (_FP_W_TYPE_SIZE - (N))) != 0); \
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65 X = X >> (N); \
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66 } \
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67 while (0)
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68
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69 #define __FP_FRAC_SRS_1(X, N, sz) \
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70 (X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1 \
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71 ? X & 1 \
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72 : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
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73
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74 #define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f)
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75 #define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f)
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76 #define _FP_FRAC_DEC_1(X, Y) (X##_f -= Y##_f)
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77 #define _FP_FRAC_CLZ_1(z, X) __FP_CLZ ((z), X##_f)
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78
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79 /* Predicates. */
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80 #define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE) X##_f < 0)
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81 #define _FP_FRAC_ZEROP_1(X) (X##_f == 0)
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82 #define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs)
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83 #define _FP_FRAC_CLEAR_OVERP_1(fs, X) (X##_f &= ~_FP_OVERFLOW_##fs)
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84 #define _FP_FRAC_HIGHBIT_DW_1(fs, X) (X##_f & _FP_HIGHBIT_DW_##fs)
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85 #define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f)
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86 #define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f)
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87 #define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f)
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88
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89 #define _FP_ZEROFRAC_1 0
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90 #define _FP_MINFRAC_1 1
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91 #define _FP_MAXFRAC_1 (~(_FP_WS_TYPE) 0)
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92
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93 /* Unpack the raw bits of a native fp value. Do not classify or
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94 normalize the data. */
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95
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96 #define _FP_UNPACK_RAW_1(fs, X, val) \
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97 do \
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98 { \
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99 union _FP_UNION_##fs _FP_UNPACK_RAW_1_flo; \
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100 _FP_UNPACK_RAW_1_flo.flt = (val); \
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101 \
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102 X##_f = _FP_UNPACK_RAW_1_flo.bits.frac; \
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103 X##_e = _FP_UNPACK_RAW_1_flo.bits.exp; \
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104 X##_s = _FP_UNPACK_RAW_1_flo.bits.sign; \
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105 } \
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106 while (0)
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107
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108 #define _FP_UNPACK_RAW_1_P(fs, X, val) \
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109 do \
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110 { \
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111 union _FP_UNION_##fs *_FP_UNPACK_RAW_1_P_flo \
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112 = (union _FP_UNION_##fs *) (val); \
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113 \
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114 X##_f = _FP_UNPACK_RAW_1_P_flo->bits.frac; \
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115 X##_e = _FP_UNPACK_RAW_1_P_flo->bits.exp; \
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116 X##_s = _FP_UNPACK_RAW_1_P_flo->bits.sign; \
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117 } \
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118 while (0)
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119
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120 /* Repack the raw bits of a native fp value. */
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121
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122 #define _FP_PACK_RAW_1(fs, val, X) \
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123 do \
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124 { \
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125 union _FP_UNION_##fs _FP_PACK_RAW_1_flo; \
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126 \
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127 _FP_PACK_RAW_1_flo.bits.frac = X##_f; \
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128 _FP_PACK_RAW_1_flo.bits.exp = X##_e; \
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129 _FP_PACK_RAW_1_flo.bits.sign = X##_s; \
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130 \
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131 (val) = _FP_PACK_RAW_1_flo.flt; \
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132 } \
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133 while (0)
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134
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135 #define _FP_PACK_RAW_1_P(fs, val, X) \
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136 do \
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137 { \
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138 union _FP_UNION_##fs *_FP_PACK_RAW_1_P_flo \
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139 = (union _FP_UNION_##fs *) (val); \
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140 \
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141 _FP_PACK_RAW_1_P_flo->bits.frac = X##_f; \
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142 _FP_PACK_RAW_1_P_flo->bits.exp = X##_e; \
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143 _FP_PACK_RAW_1_P_flo->bits.sign = X##_s; \
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144 } \
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145 while (0)
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146
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147
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148 /* Multiplication algorithms: */
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149
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150 /* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
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151 multiplication immediately. */
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152
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153 #define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \
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154 do \
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155 { \
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156 R##_f = X##_f * Y##_f; \
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157 } \
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158 while (0)
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159
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160 #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \
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161 do \
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162 { \
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163 _FP_MUL_MEAT_DW_1_imm ((wfracbits), R, X, Y); \
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164 /* Normalize since we know where the msb of the multiplicands \
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165 were (bit B), we know that the msb of the of the product is \
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166 at either 2B or 2B-1. */ \
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167 _FP_FRAC_SRS_1 (R, (wfracbits)-1, 2*(wfracbits)); \
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168 } \
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169 while (0)
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170
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171 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
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172
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173 #define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \
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174 do \
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175 { \
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176 doit (R##_f1, R##_f0, X##_f, Y##_f); \
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177 } \
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178 while (0)
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179
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180 #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \
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181 do \
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182 { \
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183 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_wide_Z); \
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184 _FP_MUL_MEAT_DW_1_wide ((wfracbits), _FP_MUL_MEAT_1_wide_Z, \
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185 X, Y, doit); \
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186 /* Normalize since we know where the msb of the multiplicands \
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187 were (bit B), we know that the msb of the of the product is \
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188 at either 2B or 2B-1. */ \
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189 _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_wide_Z, (wfracbits)-1, \
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190 2*(wfracbits)); \
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191 R##_f = _FP_MUL_MEAT_1_wide_Z_f0; \
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192 } \
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193 while (0)
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194
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195 /* Finally, a simple widening multiply algorithm. What fun! */
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196
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197 #define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \
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198 do \
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199 { \
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200 _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_xh, _FP_MUL_MEAT_DW_1_hard_xl; \
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201 _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_yh, _FP_MUL_MEAT_DW_1_hard_yl; \
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202 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_1_hard_a); \
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203 \
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204 /* Split the words in half. */ \
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205 _FP_MUL_MEAT_DW_1_hard_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \
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206 _FP_MUL_MEAT_DW_1_hard_xl \
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207 = X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
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208 _FP_MUL_MEAT_DW_1_hard_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \
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209 _FP_MUL_MEAT_DW_1_hard_yl \
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210 = Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
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211 \
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212 /* Multiply the pieces. */ \
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213 R##_f0 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yl; \
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214 _FP_MUL_MEAT_DW_1_hard_a_f0 \
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215 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yl; \
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216 _FP_MUL_MEAT_DW_1_hard_a_f1 \
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217 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yh; \
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218 R##_f1 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yh; \
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219 \
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220 /* Reassemble into two full words. */ \
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221 if ((_FP_MUL_MEAT_DW_1_hard_a_f0 += _FP_MUL_MEAT_DW_1_hard_a_f1) \
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222 < _FP_MUL_MEAT_DW_1_hard_a_f1) \
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223 R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2); \
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224 _FP_MUL_MEAT_DW_1_hard_a_f1 \
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225 = _FP_MUL_MEAT_DW_1_hard_a_f0 >> (_FP_W_TYPE_SIZE/2); \
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226 _FP_MUL_MEAT_DW_1_hard_a_f0 \
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227 = _FP_MUL_MEAT_DW_1_hard_a_f0 << (_FP_W_TYPE_SIZE/2); \
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228 _FP_FRAC_ADD_2 (R, R, _FP_MUL_MEAT_DW_1_hard_a); \
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229 } \
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230 while (0)
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231
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232 #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \
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233 do \
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234 { \
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235 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_hard_z); \
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236 _FP_MUL_MEAT_DW_1_hard ((wfracbits), \
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237 _FP_MUL_MEAT_1_hard_z, X, Y); \
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238 \
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239 /* Normalize. */ \
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240 _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_hard_z, \
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241 (wfracbits) - 1, 2*(wfracbits)); \
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242 R##_f = _FP_MUL_MEAT_1_hard_z_f0; \
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243 } \
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244 while (0)
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245
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246
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247 /* Division algorithms: */
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248
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249 /* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
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250 division immediately. Give this macro either _FP_DIV_HELP_imm for
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251 C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you
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252 choose will depend on what the compiler does with divrem4. */
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253
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254 #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \
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255 do \
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256 { \
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257 _FP_W_TYPE _FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r; \
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258 X##_f <<= (X##_f < Y##_f \
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259 ? R##_e--, _FP_WFRACBITS_##fs \
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260 : _FP_WFRACBITS_##fs - 1); \
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261 doit (_FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r, X##_f, Y##_f); \
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262 R##_f = _FP_DIV_MEAT_1_imm_q | (_FP_DIV_MEAT_1_imm_r != 0); \
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263 } \
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264 while (0)
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265
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266 /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
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267 that may be useful in this situation. This first is for a primitive
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268 that requires normalization, the second for one that does not. Look
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269 for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */
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270
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271 #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \
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272 do \
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273 { \
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274 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nh; \
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275 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nl; \
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276 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_q; \
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277 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_r; \
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278 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_y; \
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279 \
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280 /* Normalize Y -- i.e. make the most significant bit set. */ \
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281 _FP_DIV_MEAT_1_udiv_norm_y = Y##_f << _FP_WFRACXBITS_##fs; \
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282 \
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283 /* Shift X op correspondingly high, that is, up one full word. */ \
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284 if (X##_f < Y##_f) \
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285 { \
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286 R##_e--; \
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287 _FP_DIV_MEAT_1_udiv_norm_nl = 0; \
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288 _FP_DIV_MEAT_1_udiv_norm_nh = X##_f; \
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289 } \
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290 else \
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291 { \
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292 _FP_DIV_MEAT_1_udiv_norm_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \
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293 _FP_DIV_MEAT_1_udiv_norm_nh = X##_f >> 1; \
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294 } \
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295 \
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296 udiv_qrnnd (_FP_DIV_MEAT_1_udiv_norm_q, \
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297 _FP_DIV_MEAT_1_udiv_norm_r, \
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298 _FP_DIV_MEAT_1_udiv_norm_nh, \
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299 _FP_DIV_MEAT_1_udiv_norm_nl, \
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300 _FP_DIV_MEAT_1_udiv_norm_y); \
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301 R##_f = (_FP_DIV_MEAT_1_udiv_norm_q \
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302 | (_FP_DIV_MEAT_1_udiv_norm_r != 0)); \
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303 } \
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304 while (0)
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305
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306 #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \
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307 do \
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308 { \
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309 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl; \
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310 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r; \
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311 if (X##_f < Y##_f) \
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312 { \
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313 R##_e--; \
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314 _FP_DIV_MEAT_1_udiv_nl = X##_f << _FP_WFRACBITS_##fs; \
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315 _FP_DIV_MEAT_1_udiv_nh = X##_f >> _FP_WFRACXBITS_##fs; \
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316 } \
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317 else \
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318 { \
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319 _FP_DIV_MEAT_1_udiv_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \
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320 _FP_DIV_MEAT_1_udiv_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
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321 } \
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322 udiv_qrnnd (_FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r, \
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323 _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl, \
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324 Y##_f); \
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325 R##_f = _FP_DIV_MEAT_1_udiv_q | (_FP_DIV_MEAT_1_udiv_r != 0); \
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326 } \
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327 while (0)
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328
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329
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330 /* Square root algorithms:
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331 We have just one right now, maybe Newton approximation
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332 should be added for those machines where division is fast. */
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333
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334 #define _FP_SQRT_MEAT_1(R, S, T, X, q) \
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335 do \
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336 { \
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337 while ((q) != _FP_WORK_ROUND) \
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338 { \
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339 T##_f = S##_f + (q); \
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340 if (T##_f <= X##_f) \
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341 { \
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342 S##_f = T##_f + (q); \
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343 X##_f -= T##_f; \
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344 R##_f += (q); \
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345 } \
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346 _FP_FRAC_SLL_1 (X, 1); \
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347 (q) >>= 1; \
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348 } \
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349 if (X##_f) \
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350 { \
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351 if (S##_f < X##_f) \
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352 R##_f |= _FP_WORK_ROUND; \
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353 R##_f |= _FP_WORK_STICKY; \
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354 } \
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355 } \
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356 while (0)
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357
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358 /* Assembly/disassembly for converting to/from integral types.
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359 No shifting or overflow handled here. */
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360
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361 #define _FP_FRAC_ASSEMBLE_1(r, X, rsize) ((r) = X##_f)
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362 #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = (r))
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363
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364
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365 /* Convert FP values between word sizes. */
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366
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367 #define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f)
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368
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369 #endif /* !SOFT_FP_OP_1_H */
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