Mercurial > hg > octave-nkf
annotate liboctave/oct-inttypes.cc @ 12278:52f6f2989fcd release-3-4-x
don't let uninitialized values escape from DNEUPD
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 28 Jan 2011 14:05:59 -0500 |
parents | 12df7854fa7c |
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5072 | 1 /* |
2 | |
11523 | 3 Copyright (C) 2004-2011 John W. Eaton |
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4 Copyright (C) 2008-2009 Jaroslav Hajek |
5072 | 5 |
6 This file is part of Octave. | |
7 | |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
5072 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
5072 | 21 |
22 */ | |
23 | |
24 #ifdef HAVE_CONFIG_H | |
25 #include <config.h> | |
26 #endif | |
27 | |
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28 #include "lo-error.h" |
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29 |
5072 | 30 #include "oct-inttypes.h" |
31 | |
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32 template<class T> |
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33 const octave_int<T> octave_int<T>::zero (static_cast<T> (0)); |
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34 |
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35 template<class T> |
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36 const octave_int<T> octave_int<T>::one (static_cast<T> (1)); |
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37 |
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38 // define type names. |
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39 #define DECLARE_OCTAVE_INT_TYPENAME(TYPE, TYPENAME) \ |
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40 template <> \ |
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41 OCTAVE_API const char * \ |
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42 octave_int<TYPE>::type_name () { return TYPENAME; } |
5072 | 43 |
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44 DECLARE_OCTAVE_INT_TYPENAME (int8_t, "int8") |
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45 DECLARE_OCTAVE_INT_TYPENAME (int16_t, "int16") |
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46 DECLARE_OCTAVE_INT_TYPENAME (int32_t, "int32") |
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47 DECLARE_OCTAVE_INT_TYPENAME (int64_t, "int64") |
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48 DECLARE_OCTAVE_INT_TYPENAME (uint8_t, "uint8") |
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49 DECLARE_OCTAVE_INT_TYPENAME (uint16_t, "uint16") |
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50 DECLARE_OCTAVE_INT_TYPENAME (uint32_t, "uint32") |
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51 DECLARE_OCTAVE_INT_TYPENAME (uint64_t, "uint64") |
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52 |
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53 #ifndef OCTAVE_INT_USE_LONG_DOUBLE |
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54 |
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55 // Define comparison operators |
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56 |
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57 template <class xop> |
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58 bool |
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59 octave_int_cmp_op::emulate_mop (uint64_t x, double y) |
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60 { |
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61 static const double xxup = std::numeric_limits<uint64_t>::max (); |
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62 // This converts to the nearest double. Unless there's an equality, the |
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63 // result is clear. |
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64 double xx = x; |
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65 if (xx != y) |
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66 return xop::op (xx, y); |
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67 else |
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68 { |
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69 // If equality occured we compare as integers. |
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70 if (xx == xxup) |
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71 return xop::gtval; |
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72 else |
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73 return xop::op (x, static_cast<uint64_t> (xx)); |
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74 } |
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75 } |
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76 |
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77 template <class xop> |
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78 bool |
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79 octave_int_cmp_op::emulate_mop (int64_t x, double y) |
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80 { |
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81 static const double xxup = std::numeric_limits<int64_t>::max (); |
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82 static const double xxlo = std::numeric_limits<int64_t>::min (); |
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83 // This converts to the nearest double. Unless there's an equality, the |
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84 // result is clear. |
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85 double xx = x; |
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86 if (xx != y) |
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87 return xop::op (xx, y); |
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88 else |
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89 { |
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90 // If equality occured we compare as integers. |
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91 if (xx == xxup) |
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92 return xop::gtval; |
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93 else if (xx == xxlo) |
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94 return xop::ltval; |
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95 else |
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96 return xop::op (x, static_cast<int64_t> (xx)); |
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97 } |
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98 |
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99 } |
5072 | 100 |
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101 // We define double-int operations by reverting the operator |
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102 |
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103 // A trait class reverting the operator |
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104 template <class xop> |
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105 class rev_op |
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106 { |
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107 public: |
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108 typedef xop op; |
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109 }; |
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110 |
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111 #define DEFINE_REVERTED_OPERATOR(OP1,OP2) \ |
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112 template <> \ |
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113 class rev_op<octave_int_cmp_op::OP1> \ |
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114 { \ |
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115 public: \ |
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116 typedef octave_int_cmp_op::OP2 op; \ |
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117 } |
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118 |
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119 DEFINE_REVERTED_OPERATOR(lt,gt); |
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120 DEFINE_REVERTED_OPERATOR(gt,lt); |
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121 DEFINE_REVERTED_OPERATOR(le,ge); |
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122 DEFINE_REVERTED_OPERATOR(ge,le); |
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123 |
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124 template <class xop> |
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125 bool |
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126 octave_int_cmp_op::emulate_mop (double x, uint64_t y) |
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127 { |
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128 typedef typename rev_op<xop>::op rop; |
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129 return mop<rop> (y, x); |
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130 } |
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131 |
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132 template <class xop> |
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133 bool |
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134 octave_int_cmp_op::emulate_mop (double x, int64_t y) |
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135 { |
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136 typedef typename rev_op<xop>::op rop; |
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137 return mop<rop> (y, x); |
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138 } |
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139 |
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140 |
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141 // Define handlers for int64 multiplication |
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142 |
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143 template <> |
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144 uint64_t |
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145 octave_int_arith_base<uint64_t, false>::mul (uint64_t x, uint64_t y) |
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146 { |
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147 // Get upper words |
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148 uint64_t ux = x >> 32, uy = y >> 32; |
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149 uint64_t res; |
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150 if (ux) |
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151 { |
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152 if (uy) |
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153 goto overflow; |
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154 else |
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155 { |
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156 uint64_t ly = static_cast<uint32_t> (y), uxly = ux*ly; |
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157 if (uxly >> 32) |
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158 goto overflow; |
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159 uxly <<= 32; // never overflows |
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160 uint64_t lx = static_cast<uint32_t> (x), lxly = lx*ly; |
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161 res = add (uxly, lxly); |
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162 } |
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163 } |
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164 else if (uy) |
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165 { |
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166 uint64_t lx = static_cast<uint32_t> (x), uylx = uy*lx; |
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167 if (uylx >> 32) |
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168 goto overflow; |
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169 uylx <<= 32; // never overflows |
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170 uint64_t ly = static_cast<uint32_t> (y), lylx = ly*lx; |
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171 res = add (uylx, lylx); |
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172 } |
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173 else |
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174 { |
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175 uint64_t lx = static_cast<uint32_t> (x); |
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176 uint64_t ly = static_cast<uint32_t> (y); |
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177 res = lx*ly; |
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178 } |
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179 |
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180 return res; |
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181 |
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182 overflow: |
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183 return max_val (); |
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184 } |
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185 |
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186 template <> |
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187 int64_t |
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188 octave_int_arith_base<int64_t, true>::mul (int64_t x, int64_t y) |
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189 { |
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190 // The signed case is far worse. The problem is that |
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191 // even if neither integer fits into signed 32-bit range, the result may |
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192 // still be OK. Uh oh. |
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193 |
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194 // Essentially, what we do is compute sign, multiply absolute values |
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195 // (as above) and impose the sign. |
8333 | 196 // FIXME -- can we do something faster if we HAVE_FAST_INT_OPS? |
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197 |
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198 uint64_t usx = octave_int_abs (x), usy = octave_int_abs (y); |
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199 bool positive = (x < 0) == (y < 0); |
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200 |
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201 // Get upper words |
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202 uint64_t ux = usx >> 32, uy = usy >> 32; |
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203 uint64_t res; |
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204 if (ux) |
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205 { |
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206 if (uy) |
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207 goto overflow; |
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208 else |
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209 { |
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210 uint64_t ly = static_cast<uint32_t> (usy), uxly = ux*ly; |
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211 if (uxly >> 32) |
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212 goto overflow; |
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213 uxly <<= 32; // never overflows |
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214 uint64_t lx = static_cast<uint32_t> (usx), lxly = lx*ly; |
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215 res = uxly + lxly; |
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216 if (res < uxly) |
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217 goto overflow; |
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218 } |
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219 } |
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220 else if (uy) |
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221 { |
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222 uint64_t lx = static_cast<uint32_t> (usx), uylx = uy*lx; |
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223 if (uylx >> 32) |
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224 goto overflow; |
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225 uylx <<= 32; // never overflows |
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226 uint64_t ly = static_cast<uint32_t> (usy), lylx = ly*lx; |
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227 res = uylx + lylx; |
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228 if (res < uylx) |
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229 goto overflow; |
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230 } |
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231 else |
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232 { |
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233 uint64_t lx = static_cast<uint32_t> (usx); |
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234 uint64_t ly = static_cast<uint32_t> (usy); |
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235 res = lx*ly; |
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236 } |
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237 |
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238 if (positive) |
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239 { |
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240 if (res > static_cast<uint64_t> (max_val ())) |
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241 { |
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242 return max_val (); |
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243 } |
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244 else |
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245 return static_cast<int64_t> (res); |
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246 } |
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247 else |
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248 { |
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249 if (res > static_cast<uint64_t> (-min_val ())) |
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250 { |
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251 return min_val (); |
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252 } |
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253 else |
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254 return -static_cast<int64_t> (res); |
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255 } |
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256 |
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257 |
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258 overflow: |
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259 return positive ? max_val () : min_val (); |
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260 |
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261 } |
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262 |
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263 #define INT_DOUBLE_BINOP_DECL(OP,SUFFIX) \ |
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264 template <> \ |
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265 OCTAVE_API octave_ ## SUFFIX \ |
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266 operator OP (const octave_ ## SUFFIX & x, const double& y) |
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267 |
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268 #define DOUBLE_INT_BINOP_DECL(OP,SUFFIX) \ |
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269 template <> \ |
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270 OCTAVE_API octave_ ## SUFFIX \ |
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271 operator OP (const double& x, const octave_ ## SUFFIX & y) |
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272 |
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273 INT_DOUBLE_BINOP_DECL (+, uint64) |
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274 { |
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275 return (y < 0) ? x - octave_uint64(-y) : x + octave_uint64(y); |
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276 } |
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277 |
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278 DOUBLE_INT_BINOP_DECL (+, uint64) |
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279 { return y + x; } |
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280 |
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281 INT_DOUBLE_BINOP_DECL (+, int64) |
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282 { |
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283 if (fabs (y) < static_cast<double> (octave_int64::max ())) |
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284 return x + octave_int64 (y); |
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285 else |
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286 { |
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287 // If the number is within the int64 range (the most common case, |
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288 // probably), the above will work as expected. If not, it's more |
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289 // complicated - as long as y is within _twice_ the signed range, the |
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290 // result may still be an integer. An instance of such an operation is |
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291 // 3*2**62 + (1+intmin('int64')) that should yield int64(2**62) + 1. So |
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292 // what we do is to try to convert y/2 and add it twice. Note that if y/2 |
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293 // overflows, the result must overflow as well, and that y/2 cannot be a |
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294 // fractional number. |
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295 octave_int64 y2 (y / 2); |
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296 return (x + y2) + y2; |
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297 } |
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298 } |
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299 |
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300 DOUBLE_INT_BINOP_DECL (+, int64) |
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301 { |
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302 return y + x; |
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303 } |
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304 |
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305 INT_DOUBLE_BINOP_DECL (-, uint64) |
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306 { |
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307 return x + (-y); |
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308 } |
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310 DOUBLE_INT_BINOP_DECL (-, uint64) |
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311 { |
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312 if (x <= static_cast<double> (octave_uint64::max ())) |
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313 return octave_uint64(x) - y; |
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314 else |
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315 { |
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316 // Again a trick to get the corner cases right. Things like |
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317 // 3**2**63 - intmax('uint64') should produce the correct result, i.e. |
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318 // int64(2**63) + 1. |
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319 const double p2_64 = std::pow (2.0, 64); |
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320 if (y.bool_value ()) |
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321 { |
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322 const uint64_t p2_64my = (~y.value ()) + 1; // Equals 2**64 - y |
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323 return octave_uint64 (x - p2_64) + octave_uint64 (p2_64my); |
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324 } |
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325 else |
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326 return octave_uint64 (p2_64); |
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327 } |
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328 } |
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329 |
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330 INT_DOUBLE_BINOP_DECL (-, int64) |
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331 { |
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332 return x + (-y); |
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333 } |
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334 |
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335 DOUBLE_INT_BINOP_DECL (-, int64) |
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336 { |
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337 static const bool twosc = (std::numeric_limits<int64_t>::min () |
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338 < -std::numeric_limits<int64_t>::max ()); |
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339 // In case of symmetric integers (not two's complement), this will probably |
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340 // be eliminated at compile time. |
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341 if (twosc && y.value () == std::numeric_limits<int64_t>::min ()) |
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342 { |
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343 return octave_int64 (x + std::pow(2.0, 63)); |
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344 } |
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345 else |
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346 return x + (-y); |
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347 } |
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349 // NOTE: |
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350 // Emulated mixed multiplications are tricky due to possible precision loss. |
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351 // Here, after sorting out common cases for speed, we follow the strategy |
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352 // of converting the double number into the form sign * 64-bit integer* 2**exponent, |
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353 // multiply the 64-bit integers to get a 128-bit number, split that number into 32-bit words |
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354 // and form 4 double-valued summands (none of which loases precision), then convert these |
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355 // into integers and sum them. Though it is not immediately obvious, this should work |
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356 // even w.r.t. rounding (none of the summands lose precision). |
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357 |
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358 // Multiplies two unsigned 64-bit ints to get a 128-bit number represented |
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359 // as four 32-bit words. |
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360 static void |
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361 umul128 (uint64_t x, uint64_t y, uint32_t w[4]) |
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362 { |
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363 uint64_t lx = static_cast<uint32_t> (x), ux = x >> 32; |
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364 uint64_t ly = static_cast<uint32_t> (y), uy = y >> 32; |
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365 uint64_t a = lx * ly; |
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366 w[0] = a; a >>= 32; |
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367 uint64_t uxly = ux*ly, uylx = uy*lx; |
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368 a += static_cast<uint32_t> (uxly); uxly >>= 32; |
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369 a += static_cast<uint32_t> (uylx); uylx >>= 32; |
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370 w[1] = a; a >>= 32; |
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371 uint64_t uxuy = ux * uy; |
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372 a += uxly; a += uylx; a += uxuy; |
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373 w[2] = a; a >>= 32; |
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374 w[3] = a; |
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375 } |
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376 |
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377 // Splits a double into bool sign, unsigned 64-bit mantissa and int exponent |
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378 static void |
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379 dblesplit (double x, bool& sign, uint64_t& mtis, int& exp) |
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380 { |
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381 sign = x < 0; x = fabs (x); |
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382 x = frexp (x, &exp); |
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383 exp -= 52; |
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384 mtis = static_cast<uint64_t> (ldexp (x, 52)); |
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385 } |
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386 |
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387 // Gets a double number from a 32-bit unsigned integer mantissa, exponent and sign. |
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388 static double |
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389 dbleget (bool sign, uint32_t mtis, int exp) |
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390 { |
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391 double x = ldexp (static_cast<double> (mtis), exp); |
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392 return sign ? -x : x; |
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393 } |
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394 |
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395 |
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396 INT_DOUBLE_BINOP_DECL (*, uint64) |
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397 { |
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398 if (y >= 0 && y < octave_uint64::max () && y == xround (y)) |
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399 { |
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400 return x * octave_uint64 (static_cast<uint64_t> (y)); |
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401 } |
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402 else if (y == 0.5) |
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403 { |
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404 return x / octave_uint64 (static_cast<uint64_t> (2)); |
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405 } |
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406 else if (y < 0 || xisnan (y) || xisinf (y)) |
8185
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407 { |
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408 return octave_uint64 (x.value () * y); |
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409 } |
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410 else |
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411 { |
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412 bool sign; |
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413 uint64_t my; |
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414 int e; |
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415 dblesplit (y, sign, my, e); |
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416 uint32_t w[4]; |
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417 umul128 (x.value (), my, w); |
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418 octave_uint64 res = octave_uint64::zero; |
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419 for (short i = 0; i < 4; i++) |
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420 { |
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421 res += octave_uint64 (dbleget (sign, w[i], e)); |
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422 e += 32; |
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423 } |
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424 return res; |
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425 } |
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426 } |
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427 |
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428 DOUBLE_INT_BINOP_DECL (*, uint64) |
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429 { return y * x; } |
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430 |
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431 INT_DOUBLE_BINOP_DECL (*, int64) |
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432 { |
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433 if (fabs (y) < octave_int64::max () && y == xround (y)) |
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434 { |
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435 return x * octave_int64 (static_cast<int64_t> (y)); |
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436 } |
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437 else if (fabs (y) == 0.5) |
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438 { |
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439 return x / octave_int64 (static_cast<uint64_t> (4*y)); |
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440 } |
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441 else if (xisnan (y) || xisinf (y)) |
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442 { |
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443 return octave_int64 (x.value () * y); |
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444 } |
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445 else |
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446 { |
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447 bool sign; |
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448 uint64_t my; |
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449 int e; |
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450 dblesplit (y, sign, my, e); |
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451 uint32_t w[4]; |
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452 sign = (sign != (x.value () < 0)); |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
|
453 umul128 (octave_int_abs (x.value ()), my, w); |
8185
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454 octave_int64 res = octave_int64::zero; |
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455 for (short i = 0; i < 4; i++) |
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456 { |
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457 res += octave_int64 (dbleget (sign, w[i], e)); |
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458 e += 32; |
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|
459 } |
8185
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|
460 return res; |
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461 } |
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462 } |
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463 |
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464 DOUBLE_INT_BINOP_DECL (*, int64) |
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465 { return y * x; } |
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466 |
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467 DOUBLE_INT_BINOP_DECL (/, uint64) |
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468 { |
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469 return octave_uint64 (x / static_cast<double> (y)); |
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470 } |
5072 | 471 |
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472 DOUBLE_INT_BINOP_DECL (/, int64) |
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473 { |
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474 return octave_int64 (x / static_cast<double> (y)); |
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475 } |
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476 |
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477 INT_DOUBLE_BINOP_DECL (/, uint64) |
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478 { |
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479 if (y >= 0 && y < octave_uint64::max () && y == xround (y)) |
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|
480 { |
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481 return x / octave_uint64 (y); |
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482 } |
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483 else |
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484 return x * (1.0/y); |
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485 } |
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|
486 |
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487 INT_DOUBLE_BINOP_DECL (/, int64) |
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|
488 { |
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489 if (fabs (y) < octave_int64::max () && y == xround (y)) |
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490 { |
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491 return x / octave_int64 (y); |
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492 } |
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493 else |
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494 return x * (1.0/y); |
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495 } |
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496 |
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497 #define INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP,T1,T2) \ |
9237
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Add missing xxx_API decoration and remove misplaced ones
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|
498 template OCTAVE_API bool \ |
8856
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8797
diff
changeset
|
499 octave_int_cmp_op::emulate_mop<octave_int_cmp_op::OP> (T1 x, T2 y) |
8185
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500 |
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501 #define INSTANTIATE_INT64_DOUBLE_CMP_OP(OP) \ |
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502 INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP, double, int64_t); \ |
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503 INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP, double, uint64_t); \ |
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504 INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP, int64_t, double); \ |
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505 INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP, uint64_t, double) |
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506 |
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507 INSTANTIATE_INT64_DOUBLE_CMP_OP(lt); |
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508 INSTANTIATE_INT64_DOUBLE_CMP_OP(le); |
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509 INSTANTIATE_INT64_DOUBLE_CMP_OP(gt); |
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510 INSTANTIATE_INT64_DOUBLE_CMP_OP(ge); |
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511 INSTANTIATE_INT64_DOUBLE_CMP_OP(eq); |
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512 INSTANTIATE_INT64_DOUBLE_CMP_OP(ne); |
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513 |
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514 #endif |
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515 |
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516 //template <class T> |
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517 //bool |
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518 //xisnan (const octave_int<T>&) |
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519 //{ |
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520 // return false; |
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521 //} |
5072 | 522 |
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523 template <class T> |
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524 octave_int<T> |
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525 pow (const octave_int<T>& a, const octave_int<T>& b) |
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526 { |
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527 octave_int<T> retval; |
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528 |
8864 | 529 octave_int<T> zero = static_cast<T> (0); |
530 octave_int<T> one = static_cast<T> (1); | |
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531 |
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532 if (b == zero || a == one) |
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533 retval = one; |
8864 | 534 else if (b < zero) |
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535 { |
8864 | 536 if (a == -one) |
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537 retval = (b.value () % 2) ? a : one; |
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538 else |
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539 retval = zero; |
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540 } |
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541 else |
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542 { |
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543 octave_int<T> a_val = a; |
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544 T b_val = b; // no need to do saturation on b |
5072 | 545 |
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546 retval = a; |
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547 |
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548 b_val -= 1; |
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549 |
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550 while (b_val != 0) |
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551 { |
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552 if (b_val & 1) |
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553 retval = retval * a_val; |
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554 |
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555 b_val = b_val >> 1; |
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556 |
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557 if (b_val) |
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558 a_val = a_val * a_val; |
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559 } |
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560 } |
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561 |
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562 return retval; |
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563 } |
5072 | 564 |
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565 template <class T> |
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566 octave_int<T> |
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567 pow (const double& a, const octave_int<T>& b) |
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568 { return octave_int<T> (pow (a, b.double_value ())); } |
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569 |
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570 template <class T> |
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571 octave_int<T> |
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572 pow (const octave_int<T>& a, const double& b) |
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573 { |
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574 return ((b >= 0 && b < std::numeric_limits<T>::digits && b == xround (b)) |
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575 ? pow (a, octave_int<T> (static_cast<T> (b))) |
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576 : octave_int<T> (pow (a.double_value (), b))); |
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577 } |
5072 | 578 |
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579 template <class T> |
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580 octave_int<T> |
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581 powf (const float& a, const octave_int<T>& b) |
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582 { return octave_int<T> (pow (a, b.float_value ())); } |
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583 |
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584 template <class T> |
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585 octave_int<T> |
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586 powf (const octave_int<T>& a, const float& b) |
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587 { |
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588 return ((b >= 0 && b < std::numeric_limits<T>::digits && b == xround (b)) |
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589 ? pow (a, octave_int<T> (static_cast<T> (b))) |
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590 : octave_int<T> (pow (a.double_value (), static_cast<double> (b)))); |
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591 } |
5072 | 592 |
593 #define INSTANTIATE_INTTYPE(T) \ | |
6108 | 594 template class OCTAVE_API octave_int<T>; \ |
595 template OCTAVE_API octave_int<T> pow (const octave_int<T>&, const octave_int<T>&); \ | |
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596 template OCTAVE_API octave_int<T> pow (const double&, const octave_int<T>&); \ |
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597 template OCTAVE_API octave_int<T> pow (const octave_int<T>&, const double&); \ |
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598 template OCTAVE_API octave_int<T> powf (const float&, const octave_int<T>&); \ |
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599 template OCTAVE_API octave_int<T> powf (const octave_int<T>&, const float&); \ |
6108 | 600 template OCTAVE_API octave_int<T> \ |
5072 | 601 bitshift (const octave_int<T>&, int, const octave_int<T>&); \ |
602 | |
5828 | 603 INSTANTIATE_INTTYPE (int8_t); |
604 INSTANTIATE_INTTYPE (int16_t); | |
605 INSTANTIATE_INTTYPE (int32_t); | |
606 INSTANTIATE_INTTYPE (int64_t); | |
5072 | 607 |
5828 | 608 INSTANTIATE_INTTYPE (uint8_t); |
609 INSTANTIATE_INTTYPE (uint16_t); | |
610 INSTANTIATE_INTTYPE (uint32_t); | |
611 INSTANTIATE_INTTYPE (uint64_t); | |
5072 | 612 |
613 | |
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614 // Tests follow. |
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615 |
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616 /* |
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617 |
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618 %!assert(intmax("int64")/intmin("int64"),int64(-1)) |
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619 %!assert(intmin("int64")/int64(-1),intmax("int64")) |
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620 %!assert(int64(2**63),intmax("int64")) |
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621 %!assert(uint64(2**64),intmax("uint64")) |
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622 %!test |
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623 %! a = 1.9*2^61; b = uint64(a); b++; assert(b > a) |
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624 %!test |
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625 %! a = -1.9*2^61; b = int64(a); b++; assert(b > a) |
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626 %!test |
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627 %! a = int64(-2**60) + 2; assert(1.25*a == (5*a)/4) |
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628 %!test |
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629 %! a = uint64(2**61) + 2; assert(1.25*a == (5*a)/4) |
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630 %!assert(int32(2**31+0.5),intmax('int32')) |
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631 %!assert(int32(-2**31-0.5),intmin('int32')) |
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632 %!assert((int64(2**62)+1)**1, int64(2**62)+1) |
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633 %!assert((int64(2**30)+1)**2, int64(2**60+2**31) + 1) |
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634 */ |