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1983
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1 /* Numeric types for XEmacs using the MP library.
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2 Copyright (C) 2004 Jerry James.
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3
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4 This file is part of XEmacs.
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5
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6 XEmacs is free software; you can redistribute it and/or modify it
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7 under the terms of the GNU General Public License as published by the
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8 Free Software Foundation; either version 2, or (at your option) any
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9 later version.
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10
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11 XEmacs is distributed in the hope that it will be useful, but WITHOUT
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12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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14 for more details.
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15
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16 You should have received a copy of the GNU General Public License
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17 along with XEmacs; see the file COPYING. If not, write to
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18 the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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19 Boston, MA 02111-1307, USA. */
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20
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21 /* Synched up with: Not in FSF. */
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22
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23 #include <config.h>
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24 #include <limits.h>
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25 #include <math.h>
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26 #include "lisp.h"
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27
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28 static MINT *bignum_bytesize, *bignum_long_sign_bit, *bignum_one, *bignum_two;
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29 MINT *bignum_zero, *intern_bignum;
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30 MINT *bignum_min_int, *bignum_max_int, *bignum_max_uint;
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31 MINT *bignum_min_long, *bignum_max_long, *bignum_max_ulong;
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32 short div_rem;
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33
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34 char *
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35 bignum_to_string (bignum b, int base)
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36 {
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37 REGISTER unsigned int i;
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38 unsigned int bufsize = 128U, index = 0U;
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39 int sign;
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40 char *buffer = xnew_array (char, 128), *retval;
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41 MINT *quo = MP_ITOM (0);
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42 short rem;
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43
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44 /* FIXME: signal something if base is < 2 or doesn't fit into a short. */
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45
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46 /* Save the sign for later */
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47 sign = MP_MCMP (b, bignum_zero);
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48
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49 if (sign == 0)
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50 {
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51 XREALLOC_ARRAY (buffer, char, 2);
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52 buffer[0] = '0';
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53 buffer[1] = '\0';
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54 return buffer;
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55 }
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56 /* Copy abs(b) into quo for destructive modification */
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57 else if (sign < 0)
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58 MP_MSUB (bignum_zero, b, quo);
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59 else
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60 MP_MOVE (b, quo);
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61
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62 quo = MP_ITOM (0);
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63
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64 /* Loop over the digits of b (in BASE) and place each one into buffer */
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65 for (i = 0U; MP_MCMP(quo, bignum_zero) > 0; i++)
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66 {
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67 MP_SDIV (quo, base, quo, &rem);
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68 if (index == bufsize)
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69 {
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70 bufsize <<= 1;
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71 XREALLOC_ARRAY (buffer, char, bufsize);
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72 }
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73 buffer[index++] = rem < 10 ? rem + '0' : rem - 10 + 'a';
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74 }
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75 MP_MFREE (quo);
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76
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77 /* Reverse the digits, maybe add a minus sign, and add a null terminator */
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78 bufsize = index + (sign < 0 ? 1 : 0) + 1;
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79 retval = xnew_array (char, bufsize);
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80 if (sign < 0)
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81 {
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82 retval[0] = '-';
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83 i = 1;
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84 }
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85 else
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86 i = 0;
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87 for (; i < bufsize - 1; i++)
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88 retval[i] = buffer[--index];
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89 retval[bufsize - 1] = '\0';
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90 xfree (buffer, char *);
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91 return retval;
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92 }
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93
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94 #define BIGNUM_TO_TYPE(type,accumtype) do { \
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95 MP_MULT (b, quo, quo); \
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96 for (i = 0U; i < sizeof(type); i++) \
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97 { \
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98 MP_SDIV (quo, 256, quo, &rem); \
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99 retval |= ((accumtype) rem) << (8 * i); \
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100 } \
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101 MP_MFREE (quo); \
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102 } while (0)
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103
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104 int
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105 bignum_to_int (bignum b)
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106 {
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107 short rem, sign;
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108 unsigned int retval = 0;
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109 REGISTER unsigned int i;
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110 MINT *quo;
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111
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112 sign = MP_MCMP (b, bignum_zero) < 0 ? -1 : 1;
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113 quo = MP_ITOM (sign);
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114 BIGNUM_TO_TYPE (int, unsigned int);
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115 return ((int) retval) * sign;
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116 }
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117
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118 unsigned int
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119 bignum_to_uint (bignum b)
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120 {
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121 short rem;
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122 unsigned int retval = 0U;
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123 REGISTER unsigned int i;
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124 MINT *quo;
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125
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126 quo = MP_ITOM (MP_MCMP (b, bignum_zero) < 0 ? -1 : 1);
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127 BIGNUM_TO_TYPE (unsigned int, unsigned int);
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128 return retval;
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129 }
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130
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131 long
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132 bignum_to_long (bignum b)
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133 {
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134 short rem, sign;
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135 unsigned long retval = 0L;
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136 REGISTER unsigned int i;
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137 MINT *quo;
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138
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139 sign = MP_MCMP (b, bignum_zero) < 0 ? -1 : 1;
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140 quo = MP_ITOM (sign);
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141 BIGNUM_TO_TYPE (long, unsigned long);
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142 return ((long) retval) * sign;
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143 }
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144
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145 unsigned long
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146 bignum_to_ulong (bignum b)
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147 {
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148 short rem;
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149 unsigned long retval = 0UL;
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150 REGISTER unsigned int i;
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151 MINT *quo;
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152
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153 quo = MP_ITOM (MP_MCMP (b, bignum_zero) < 0 ? -1 : 1);
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154 BIGNUM_TO_TYPE (unsigned long, unsigned long);
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155 return retval;
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156 }
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157
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158 double
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159 bignum_to_double (bignum b)
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160 {
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161 short rem, sign;
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1990
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162 double retval = 0.0, factor = 1.0;
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1983
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163 REGISTER unsigned int i;
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164 MINT *quo;
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165
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166 sign = MP_MCMP (b, bignum_zero) < 0 ? -1 : 1;
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167 quo = MP_ITOM (sign);
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168 MP_MULT (b, quo, quo);
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1990
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169 for (i = 0U; MP_MCMP (quo, bignum_zero) > 0; i++)
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1983
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170 {
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171 MP_SDIV (quo, 256, quo, &rem);
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1990
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172 retval += rem * factor;
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173 factor *= 256.0;
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1983
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174 }
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175 MP_MFREE (quo);
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176 return retval * sign;
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177 }
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178
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179 static short
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180 char_to_number (char c)
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181 {
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182 if (c >= '0' && c <= '9')
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183 return c - '0';
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184 if (c >= 'a' && c <= 'z')
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185 return c - 'a' + 10;
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186 if (c >= 'A' && c <= 'Z')
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187 return c - 'A' + 10;
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188 return -1;
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189 }
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190
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191 int
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192 bignum_set_string (bignum b, const char *s, int base)
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193 {
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194 MINT *mbase;
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195 short digit;
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196
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197 if (base == 0)
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198 {
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199 if (s[0] == '0' && (s[1] == 'x' || s[1] == 'X'))
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200 {
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201 base = 16;
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202 s += 2;
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203 }
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204 else if (*s == '0')
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205 {
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206 base = 8;
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207 s++;
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208 }
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209 else
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210 base = 10;
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211 }
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212
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213 /* FIXME: signal something if base is < 2 or doesn't fit into a short. */
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214
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215 mbase = MP_ITOM ((short) base);
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216 MP_MOVE (bignum_zero, b);
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217
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218 for (digit = char_to_number (*s); digit >= 0 && digit < base;
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219 digit = char_to_number (*++s))
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220 {
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221 MINT *temp;
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222
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223 MP_MULT (b, mbase, b);
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224 temp = MP_ITOM (digit);
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225 MP_MADD (b, temp, b);
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226 MP_MFREE (temp);
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227 }
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228
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229 return (digit >= 0) ? -1 : 0;
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230 }
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231
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232 void
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233 bignum_set_long (MINT *b, long l)
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234 {
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235 /* Negative l is hard, not least because -LONG_MIN == LONG_MIN. We pretend
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236 that l is unsigned, then subtract off the amount equal to the sign bit. */
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237 bignum_set_ulong (b, (unsigned long) l);
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238 if (l < 0L)
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239 MP_MSUB (b, bignum_long_sign_bit, b);
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240 }
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241
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242 void
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243 bignum_set_ulong (bignum b, unsigned long l)
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244 {
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245 REGISTER unsigned int i;
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246 MINT *multiplier = MP_ITOM (1);
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247
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248 MP_MOVE (bignum_zero, b);
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249 for (i = 0UL; l > 0UL; l >>= 8, i++)
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250 {
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251 MINT *temp = MP_ITOM ((short) (l & 255));
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252 MP_MULT (multiplier, temp, temp);
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253 MP_MADD (b, temp, b);
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254 MP_MULT (multiplier, bignum_bytesize, multiplier);
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255 MP_MFREE (temp);
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256 }
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257 MP_MFREE (multiplier);
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258 }
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259
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260 void
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261 bignum_set_double (bignum b, double d)
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262 {
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263 REGISTER unsigned int i;
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264 int negative = (d < 0) ? 1 : 0;
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265 MINT *multiplier = MP_ITOM (1);
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266
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267 MP_MOVE (bignum_zero, b);
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268 if (negative)
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269 d = -d;
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270 for (i = 0UL; d > 0.0; d /= 256, i++)
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271 {
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272 MINT *temp = MP_ITOM ((short) fmod (d, 256.0));
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273 MP_MULT (multiplier, temp, temp);
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274 MP_MADD (b, temp, b);
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275 MP_MULT (multiplier, bignum_bytesize, multiplier);
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276 MP_MFREE (temp);
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277 }
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278 MP_MFREE (multiplier);
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279 if (negative)
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280 MP_MSUB (bignum_zero, b, b);
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281 }
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282
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283 /* Return nonzero if b1 is exactly divisible by b2 */
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284 int
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285 bignum_divisible_p (bignum b1, bignum b2)
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286 {
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287 int retval;
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288 MINT *rem = MP_ITOM (0);
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289 MP_MDIV (b1, b2, intern_bignum, rem);
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290 retval = (MP_MCMP (rem, bignum_zero) == 0);
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291 MP_MFREE (rem);
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292 return retval;
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293 }
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294
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295 void bignum_ceil (bignum quotient, bignum N, bignum D)
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296 {
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297 MP_MDIV (N, D, quotient, intern_bignum);
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298 if (MP_MCMP (intern_bignum, bignum_zero) > 0 &&
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299 MP_MCMP (quotient, bignum_zero) > 0)
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300 MP_MADD (quotient, bignum_one, quotient);
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301 }
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302
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303 void bignum_floor (bignum quotient, bignum N, bignum D)
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304 {
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305 MP_MDIV (N, D, quotient, intern_bignum);
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306 if (MP_MCMP (intern_bignum, bignum_zero) > 0 &&
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307 MP_MCMP (quotient, bignum_zero) < 0)
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308 MP_MSUB (quotient, bignum_one, quotient);
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309 }
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310
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311 /* RESULT = N to the POWth power */
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312 void
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313 bignum_pow (bignum result, bignum n, unsigned long pow)
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314 {
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315 MP_MOVE (bignum_one, result);
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316 for ( ; pow > 0UL; pow--)
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317 MP_MULT (result, n, result);
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318 }
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319
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320 /* lcm(b1,b2) = b1 * b2 / gcd(b1, b2) */
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321 void
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322 bignum_lcm (bignum result, bignum b1, bignum b2)
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323 {
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324 MP_MULT (b1, b2, result);
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325 MP_GCD (b1, b2, intern_bignum);
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326 MP_MDIV (result, intern_bignum, result, intern_bignum);
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327 }
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328
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329 /* FIXME: We can't handle negative args, so right now we just make them
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330 positive before doing anything else. How should we really handle negative
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331 args? */
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332 #define bignum_bit_op(result, b1, b2, op) \
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333 REGISTER unsigned int i; \
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334 MINT *multiplier = MP_ITOM (1), *n1 = MP_ITOM (0), *n2 = MP_ITOM (0); \
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335 \
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336 if (MP_MCMP (bignum_zero, b1) > 0) \
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337 MP_MSUB (bignum_zero, b1, n1); \
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338 else \
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339 MP_MOVE (b1, n1); \
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340 if (MP_MCMP (bignum_zero, b2) > 0) \
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341 MP_MSUB (bignum_zero, b2, n2); \
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342 else \
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343 MP_MOVE (b2, n2); \
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344 \
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345 MP_MOVE (bignum_zero, result); \
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346 \
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347 for (i = 0UL; MP_MCMP (bignum_zero, n1) < 0 && \
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348 MP_MCMP (bignum_zero, n2) < 0; i++) \
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349 { \
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350 short byte1, byte2; \
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351 MINT *temp; \
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352 \
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353 MP_SDIV (n1, 256, n1, &byte1); \
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354 MP_SDIV (n2, 256, n2, &byte2); \
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355 temp = MP_ITOM (byte1 op byte2); \
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356 MP_MULT (multiplier, temp, temp); \
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357 MP_MADD (result, temp, result); \
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358 MP_MULT (multiplier, bignum_bytesize, multiplier); \
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359 MP_MFREE (temp); \
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360 } \
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361 MP_MFREE (n2); \
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362 MP_MFREE (n1); \
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363 MP_MFREE (multiplier)
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364
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365 void
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366 bignum_and (bignum result, bignum b1, bignum b2)
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367 {
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368 bignum_bit_op (result, b1, b2, &);
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369 }
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370
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371 void
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372 bignum_ior (bignum result, bignum b1, bignum b2)
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373 {
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374 bignum_bit_op (result, b1, b2, |);
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375 }
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376
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377 void
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378 bignum_xor (bignum result, bignum b1, bignum b2)
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379 {
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380 bignum_bit_op (result, b1, b2, ^);
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381 }
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382
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383 /* NOT is not well-defined for bignums ... where do you stop flipping bits?
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384 We just flip until we see the last one. This is probably a bad idea. */
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385 void
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386 bignum_not (bignum result, bignum b)
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387 {
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388 REGISTER unsigned int i;
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389 MINT *multiplier = MP_ITOM (1), *n = MP_ITOM (0);
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390
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391 if (MP_MCMP (bignum_zero, b) > 0)
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392 MP_MSUB (bignum_zero, b, n);
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393 else
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394 MP_MOVE (b, n);
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395
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396 MP_MOVE (bignum_zero, result);
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397
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398 for (i = 0UL; MP_MCMP (bignum_zero, n) < 0; i++)
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399 {
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400 short byte;
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401 MINT *temp;
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402
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403 MP_SDIV (n, 256, n, &byte);
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404 temp = MP_ITOM (~byte);
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405 MP_MULT (multiplier, temp, temp);
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406 MP_MADD (result, temp, result);
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407 MP_MULT (multiplier, bignum_bytesize, multiplier);
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408 MP_MFREE (temp);
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409 }
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410 MP_MFREE (n);
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411 MP_MFREE (multiplier);
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412 }
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413
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414 void
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415 bignum_setbit (bignum b, unsigned long bit)
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416 {
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417 bignum_pow (intern_bignum, bignum_two, bit);
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418 bignum_ior (b, b, intern_bignum);
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419 }
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420
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421 /* This is so evil, even I feel queasy. */
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422 void
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423 bignum_clrbit (bignum b, unsigned long bit)
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424 {
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425 MINT *num = MP_ITOM (0);
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426
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427 /* See if the bit is already set, and subtract it off if not */
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428 MP_MOVE (b, intern_bignum);
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429 bignum_pow (num, bignum_two, bit);
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430 bignum_ior (intern_bignum, intern_bignum, num);
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431 if (MP_MCMP (b, intern_bignum) == 0)
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432 MP_MSUB (b, num, b);
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433 MP_MFREE (num);
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434 }
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435
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436 int
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437 bignum_testbit (bignum b, unsigned long bit)
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438 {
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439 bignum_pow (intern_bignum, bignum_two, bit);
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440 bignum_and (intern_bignum, b, intern_bignum);
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441 return MP_MCMP (intern_bignum, bignum_zero);
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442 }
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443
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444 void
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445 bignum_lshift (bignum result, bignum b, unsigned long bits)
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446 {
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447 bignum_pow (intern_bignum, bignum_two, bits);
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448 MP_MULT (b, intern_bignum, result);
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449 }
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450
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451 void
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452 bignum_rshift (bignum result, bignum b, unsigned long bits)
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453 {
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454 bignum_pow (intern_bignum, bignum_two, bits);
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455 MP_MDIV (b, intern_bignum, result, intern_bignum);
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456 }
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457
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458 void bignum_random_seed(unsigned long seed)
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459 {
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460 /* FIXME: Implement me */
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461 }
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462
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463 void bignum_random(bignum result, bignum limit)
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464 {
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465 /* FIXME: Implement me */
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466 MP_MOVE (bignum_zero, result);
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467 }
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468
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469 void
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470 init_number_mp ()
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471 {
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472 REGISTER unsigned int i;
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473
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474 bignum_zero = MP_ITOM (0);
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475 bignum_one = MP_ITOM (1);
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476 bignum_two = MP_ITOM (2);
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477
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478 /* intern_bignum holds throwaway values from macro expansions in
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479 number-mp.h. Its value is immaterial. */
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480 intern_bignum = MP_ITOM (0);
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481
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482 /* bignum_bytesize holds the number of bits in a byte. */
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483 bignum_bytesize = MP_ITOM (256);
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484
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485 /* bignum_long_sign_bit holds an adjustment for negative longs. */
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486 bignum_long_sign_bit = MP_ITOM (256);
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487 for (i = 1UL; i < sizeof (long); i++)
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488 MP_MULT (bignum_bytesize, bignum_long_sign_bit, bignum_long_sign_bit);
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489
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490 /* The MP interface only supports turning short ints into MINTs, so we have
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491 to set these the hard way. */
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492
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493 bignum_min_int = MP_ITOM (0);
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494 bignum_set_long (bignum_min_int, INT_MIN);
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495
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496 bignum_max_int = MP_ITOM (0);
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497 bignum_set_long (bignum_max_int, INT_MAX);
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498
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499 bignum_max_uint = MP_ITOM (0);
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500 bignum_set_ulong (bignum_max_uint, UINT_MAX);
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501
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502 bignum_min_long = MP_ITOM (0);
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503 bignum_set_long (bignum_min_long, LONG_MIN);
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504
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505 bignum_max_long = MP_ITOM (0);
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506 bignum_set_long (bignum_max_long, LONG_MAX);
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507
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508 bignum_max_ulong = MP_ITOM (0);
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509 bignum_set_ulong (bignum_max_ulong, ULONG_MAX);
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510 }
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