1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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14 | Eval_multiply = ->
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15 | push(cadr(p1))
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16 | Eval()
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17 | p1 = cddr(p1)
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18 | while (iscons(p1))
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19 | push(car(p1))
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20 | Eval()
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21 | multiply()
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22 | p1 = cdr(p1)
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23 |
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24 |
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25 |
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26 |
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27 | multiply = ->
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28 | if (esc_flag)
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29 | stop("escape key stop")
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30 | if (isnum(stack[tos - 2]) && isnum(stack[tos - 1]))
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31 | multiply_numbers()
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32 | else
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33 | save()
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34 | yymultiply()
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35 | restore()
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36 |
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37 | yymultiply = ->
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38 | h = 0
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39 | i = 0
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40 | n = 0
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41 |
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42 |
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43 |
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44 | p2 = pop()
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45 | p1 = pop()
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46 |
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47 | h = tos
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48 |
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49 |
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50 |
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51 | if (iszero(p1) || iszero(p2))
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52 | if evaluatingAsFloats then push_double(0.0) else push(zero)
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53 | return
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54 |
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55 |
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56 |
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57 |
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58 | if (expanding && isadd(p1))
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59 | p1 = cdr(p1)
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60 | if evaluatingAsFloats then push_double(0.0) else push(zero)
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61 | while (iscons(p1))
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62 | push(car(p1))
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63 | push(p2)
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64 | multiply()
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65 | add()
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66 | p1 = cdr(p1)
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67 | return
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68 |
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69 | if (expanding && isadd(p2))
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70 | p2 = cdr(p2)
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71 | if evaluatingAsFloats then push_double(0.0) else push(zero)
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72 | while (iscons(p2))
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73 | push(p1)
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74 | push(car(p2))
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75 | multiply()
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76 | add()
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77 | p2 = cdr(p2)
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78 | return
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79 |
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80 |
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81 |
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82 | if (!istensor(p1) && istensor(p2))
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83 | push(p1)
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84 | push(p2)
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85 | scalar_times_tensor()
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86 | return
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87 |
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88 |
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89 |
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90 | if (istensor(p1) && !istensor(p2))
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91 | push(p1)
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92 | push(p2)
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93 | tensor_times_scalar()
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94 | return
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95 |
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96 |
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97 |
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98 | if (car(p1) == symbol(MULTIPLY))
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99 | p1 = cdr(p1)
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100 | else
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101 | push(p1)
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102 | list(1)
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103 | p1 = pop()
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104 |
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105 | if (car(p2) == symbol(MULTIPLY))
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106 | p2 = cdr(p2)
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107 | else
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108 | push(p2)
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109 | list(1)
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110 | p2 = pop()
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111 |
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112 |
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113 |
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114 | if (isnum(car(p1)) && isnum(car(p2)))
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115 | push(car(p1))
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116 | push(car(p2))
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117 | multiply_numbers()
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118 | p1 = cdr(p1)
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119 | p2 = cdr(p2)
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120 | else if (isnum(car(p1)))
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121 | push(car(p1))
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122 | p1 = cdr(p1)
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123 | else if (isnum(car(p2)))
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124 | push(car(p2))
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125 | p2 = cdr(p2)
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126 | else
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127 | if evaluatingAsFloats then push_double(1.0) else push(one)
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128 |
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129 | parse_p1()
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130 | parse_p2()
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131 |
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132 | while (iscons(p1) && iscons(p2))
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133 |
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134 |
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135 |
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136 |
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137 |
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138 |
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139 |
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140 |
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141 |
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142 |
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143 | if (caar(p1) == symbol(OPERATOR) && caar(p2) == symbol(OPERATOR))
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144 | push_symbol(OPERATOR)
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145 | push(cdar(p1))
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146 | push(cdar(p2))
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147 | append()
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148 | cons()
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149 | p1 = cdr(p1)
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150 | p2 = cdr(p2)
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151 | parse_p1()
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152 | parse_p2()
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153 | continue
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154 |
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155 | switch (cmp_expr(p3, p4))
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156 | when -1
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157 | push(car(p1))
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158 | p1 = cdr(p1)
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159 | parse_p1()
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160 | when 1
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161 | push(car(p2))
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162 | p2 = cdr(p2)
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163 | parse_p2()
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164 | when 0
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165 | combine_factors(h)
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166 | p1 = cdr(p1)
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167 | p2 = cdr(p2)
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168 | parse_p1()
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169 | parse_p2()
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170 | else
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171 | stop("internal error 2")
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172 |
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173 |
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174 |
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175 | while (iscons(p1))
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176 | push(car(p1))
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177 | p1 = cdr(p1)
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178 |
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179 | while (iscons(p2))
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180 | push(car(p2))
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181 | p2 = cdr(p2)
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182 |
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183 |
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184 |
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185 |
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186 |
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187 |
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188 |
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189 |
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190 |
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191 | __normalize_radical_factors(h)
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192 |
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193 |
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194 |
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195 |
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196 |
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197 |
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198 |
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199 |
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200 |
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201 |
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202 | if (expanding)
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203 | for i in [h...tos]
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204 | if (isadd(stack[i]))
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205 | multiply_all(tos - h)
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206 | return
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207 |
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208 |
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209 |
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210 | n = tos - h
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211 |
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212 | if (n == 1)
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213 | return
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214 |
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215 |
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216 |
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217 | if (isrational(stack[h]) && equaln(stack[h], 1))
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218 | if (n == 2)
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219 | p7 = pop()
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220 | pop()
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221 | push(p7)
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222 | else
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223 | stack[h] = symbol(MULTIPLY)
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224 | list(n)
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225 | return
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226 |
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227 | list(n)
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228 | p7 = pop()
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229 | push_symbol(MULTIPLY)
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230 | push(p7)
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231 | cons()
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232 |
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233 |
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234 |
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235 |
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236 |
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237 |
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238 |
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239 |
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240 |
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241 | parse_p1 = ->
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242 | p3 = car(p1)
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243 | p5 = if evaluatingAsFloats then one_as_double else one
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244 | if (car(p3) == symbol(POWER))
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245 | p5 = caddr(p3)
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246 | p3 = cadr(p3)
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247 |
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248 |
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249 |
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250 |
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251 |
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252 |
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253 |
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254 |
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255 |
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256 | parse_p2 = ->
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257 | p4 = car(p2)
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258 | p6 = if evaluatingAsFloats then one_as_double else one
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259 | if (car(p4) == symbol(POWER))
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260 | p6 = caddr(p4)
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261 | p4 = cadr(p4)
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262 |
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263 |
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264 | combine_factors = (h) ->
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265 | push(p4)
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266 | push(p5)
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267 | push(p6)
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268 | add()
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269 | power()
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270 | p7 = pop()
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271 | if (isnum(p7))
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272 | push(stack[h])
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273 | push(p7)
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274 | multiply_numbers()
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275 | stack[h] = pop()
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276 | else if (car(p7) == symbol(MULTIPLY))
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277 |
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278 | if (isnum(cadr(p7)) && cdddr(p7) == symbol(NIL))
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279 | push(stack[h])
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280 | push(cadr(p7))
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281 | multiply_numbers()
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282 | stack[h] = pop()
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283 | push(caddr(p7))
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284 | else
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285 | push(p7)
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286 | else
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287 | push(p7)
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288 |
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289 | gp = [
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290 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
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291 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
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292 | [0,0,1,-6,-7,-8,-3,-4,-5,13,14,15,-16,9,10,11,-12],
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293 | [0,0,6,-1,-11,10,-2,-15,14,12,-5,4,-9,16,-8,7,-13],
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294 | [0,0,7,11,-1,-9,15,-2,-13,5,12,-3,-10,8,16,-6,-14],
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295 | [0,0,8,-10,9,-1,-14,13,-2,-4,3,12,-11,-7,6,16,-15],
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296 | [0,0,3,2,15,-14,1,11,-10,16,-8,7,13,12,-5,4,9],
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297 | [0,0,4,-15,2,13,-11,1,9,8,16,-6,14,5,12,-3,10],
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298 | [0,0,5,14,-13,2,10,-9,1,-7,6,16,15,-4,3,12,11],
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299 | [0,0,13,12,-5,4,16,-8,7,-1,-11,10,-3,-2,-15,14,-6],
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300 | [0,0,14,5,12,-3,8,16,-6,11,-1,-9,-4,15,-2,-13,-7],
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301 | [0,0,15,-4,3,12,-7,6,16,-10,9,-1,-5,-14,13,-2,-8],
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302 | [0,0,16,-9,-10,-11,-13,-14,-15,-3,-4,-5,1,-6,-7,-8,2],
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303 | [0,0,9,-16,8,-7,-12,5,-4,-2,-15,14,6,-1,-11,10,3],
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304 | [0,0,10,-8,-16,6,-5,-12,3,15,-2,-13,7,11,-1,-9,4],
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305 | [0,0,11,7,-6,-16,4,-3,-12,-14,13,-2,8,-10,9,-1,5],
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306 | [0,0,12,13,14,15,9,10,11,-6,-7,-8,-2,-3,-4,-5,-1]
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307 | ]
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308 |
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309 |
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310 |
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311 |
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312 | combine_gammas = (h) ->
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313 | n = gp[Math.floor(p1.gamma)][Math.floor(p2.gamma)]
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314 | if (n < 0)
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315 | n = -n
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316 | push(stack[h])
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317 | negate()
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318 | stack[h] = pop()
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319 | if (n > 1)
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320 | push(_gamma[n])
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321 |
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322 |
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323 |
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324 | multiply_noexpand = ->
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325 | prev_expanding = expanding
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326 | expanding = 0
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327 | multiply()
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328 | expanding = prev_expanding
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329 |
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330 |
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331 |
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332 |
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333 | multiply_all = (n) ->
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334 | i = 0
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335 | if (n == 1)
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336 | return
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337 | if (n == 0)
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338 | push if evaluatingAsFloats then one_as_double else one
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339 | return
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340 | h = tos - n
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341 | push(stack[h])
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342 | for i in [1...n]
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343 | push(stack[h + i])
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344 | multiply()
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345 | stack[h] = pop()
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346 | moveTos h + 1
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347 |
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348 |
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349 | multiply_all_noexpand = (n) ->
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350 | prev_expanding = expanding
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351 | expanding = 0
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352 | multiply_all(n)
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353 | expanding = prev_expanding
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354 |
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355 |
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356 |
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357 |
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358 |
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359 |
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360 |
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361 |
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362 |
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363 |
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364 |
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365 | divide = ->
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366 | if (isnum(stack[tos - 2]) && isnum(stack[tos - 1]))
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367 | divide_numbers()
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368 | else
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369 | inverse()
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370 | multiply()
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371 |
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372 |
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373 | inverse = ->
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374 | if (isnum(stack[tos - 1]))
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375 | invert_number()
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376 | else
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377 | push_integer(-1)
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378 | power()
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379 |
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380 | reciprocate = ->
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381 | inverse()
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382 |
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383 | negate = ->
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384 | if (isnum(stack[tos - 1]))
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385 | negate_number()
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386 | else
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387 | if evaluatingAsFloats then push_double(-1.0) else push_integer(-1)
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388 | multiply()
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389 |
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390 | negate_expand = ->
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391 | prev_expanding = expanding
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392 | expanding = 1
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393 | negate()
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394 | expanding = prev_expanding
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395 |
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396 | negate_noexpand = ->
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397 | prev_expanding = expanding
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398 | expanding = 0
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399 | negate()
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400 | expanding = prev_expanding
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401 |
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402 |
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403 |
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404 |
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405 |
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406 |
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407 |
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408 |
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409 |
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410 |
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411 |
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412 |
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413 |
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414 |
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415 |
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416 |
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417 |
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418 |
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419 |
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420 |
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421 |
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422 |
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423 |
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424 |
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425 |
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426 |
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427 |
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428 |
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429 |
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430 |
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431 |
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432 |
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433 |
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434 |
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435 |
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436 | __normalize_radical_factors = (h) ->
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437 |
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438 | i = 0
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439 |
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440 |
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441 | if (isplusone(stack[h]) || isminusone(stack[h]) || isdouble(stack[h]))
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442 | return
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443 |
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444 |
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445 |
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446 | for i in [(h + 1)...tos]
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447 | if (__is_radical_number(stack[i]))
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448 | break
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449 |
|
450 | if (i == tos)
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451 | return
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452 |
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453 |
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454 |
|
455 | save()
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456 |
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457 |
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458 |
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459 | push(stack[h])
|
460 | mp_numerator()
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461 |
|
462 | p1 = pop();
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463 |
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464 | for i in [(h + 1)...tos]
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465 |
|
466 | if (isplusone(p1) || isminusone(p1))
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467 | break
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468 |
|
469 | if (!__is_radical_number(stack[i]))
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470 | continue
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471 |
|
472 | p3 = cadr(stack[i]);
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473 | p4 = caddr(stack[i]);
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474 |
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475 |
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476 |
|
477 | if (!isnegativenumber(p4))
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478 | continue
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479 |
|
480 |
|
481 |
|
482 | push(p1);
|
483 | push(p3);
|
484 | divide()
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485 |
|
486 | p5 = pop();
|
487 |
|
488 | if (!isinteger(p5))
|
489 | continue
|
490 |
|
491 |
|
492 |
|
493 | p1 = p5;
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494 |
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495 |
|
496 |
|
497 | push_symbol(POWER)
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498 | push(p3);
|
499 | push if evaluatingAsFloats then one_as_double else one
|
500 | push(p4);
|
501 | add()
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502 | list(3)
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503 | stack[i] = pop()
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504 |
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505 |
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506 |
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507 | push(stack[h])
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508 | mp_denominator()
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509 |
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510 | p2 = pop();
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511 |
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512 | for i in [(h + 1)...tos]
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513 |
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514 | if (isplusone(p2))
|
515 | break
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516 |
|
517 | if (!__is_radical_number(stack[i]))
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518 | continue
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519 |
|
520 | p3 = cadr(stack[i]);
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521 | p4 = caddr(stack[i]);
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522 |
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523 |
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524 |
|
525 | if (isnegativenumber(p4))
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526 | continue
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527 |
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528 |
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529 |
|
530 | push(p2);
|
531 | push(p3);
|
532 | divide()
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533 |
|
534 | p5 = pop();
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535 |
|
536 | if (!isinteger(p5))
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537 | continue
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538 |
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539 |
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540 |
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541 |
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542 |
|
543 | p2 = p5;
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544 |
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545 |
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546 |
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547 | push_symbol(POWER)
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548 | push(p3);
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549 | push(p4);
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550 |
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551 |
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552 | push(one)
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553 | subtract()
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554 |
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555 | if dontCreateNewRadicalsInDenominatorWhenEvalingMultiplication
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556 | if (isinteger(p3) and !isinteger(stack[tos-1]) and isnegativenumber(stack[tos - 1]))
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557 |
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558 |
|
559 |
|
560 |
|
561 |
|
562 |
|
563 |
|
564 | pop()
|
565 | pop()
|
566 | pop()
|
567 |
|
568 | push(p1);
|
569 | push(p3);
|
570 | divide()
|
571 | p1 = pop()
|
572 |
|
573 | break
|
574 |
|
575 |
|
576 | list(3)
|
577 | stack[i] = pop()
|
578 |
|
579 |
|
580 |
|
581 | push(p1);
|
582 | push(p2);
|
583 | divide()
|
584 | stack[h] = pop()
|
585 |
|
586 | restore()
|
587 |
|
588 |
|
589 |
|
590 |
|
591 | __is_radical_number = (p) ->
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592 |
|
593 |
|
594 | if (car(p) == symbol(POWER) && isnum(cadr(p)) && isnum(caddr(p)) && !isminusone(cadr(p)))
|
595 | return 1
|
596 | else
|
597 | return 0
|
598 |
|
599 |
|
600 |
|
601 |
|
602 |
|
603 |
|
604 |
|
605 |
|
606 |
|
607 |
|
608 |
|
609 |
|
610 |
|
611 |
|
612 |
|
613 |
|
614 |
|
615 |
|
616 |
|
617 |
|