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1 /* Decimal 64-bit format module for the decNumber C Library.
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2 Copyright (C) 2005, 2007, 2009 Free Software Foundation, Inc.
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3 Contributed by IBM Corporation. Author Mike Cowlishaw.
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4
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5 This file is part of GCC.
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6
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7 GCC is free software; you can redistribute it and/or modify it under
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8 the terms of the GNU General Public License as published by the Free
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9 Software Foundation; either version 3, or (at your option) any later
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10 version.
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11
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12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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13 WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 Under Section 7 of GPL version 3, you are granted additional
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18 permissions described in the GCC Runtime Library Exception, version
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19 3.1, as published by the Free Software Foundation.
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20
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21 You should have received a copy of the GNU General Public License and
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22 a copy of the GCC Runtime Library Exception along with this program;
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23 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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24 <http://www.gnu.org/licenses/>. */
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25
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26 /* ------------------------------------------------------------------ */
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27 /* Decimal 64-bit format module */
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28 /* ------------------------------------------------------------------ */
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29 /* This module comprises the routines for decimal64 format numbers. */
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30 /* Conversions are supplied to and from decNumber and String. */
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31 /* */
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32 /* This is used when decNumber provides operations, either for all */
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33 /* operations or as a proxy between decNumber and decSingle. */
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34 /* */
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35 /* Error handling is the same as decNumber (qv.). */
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36 /* ------------------------------------------------------------------ */
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37 #include <string.h> /* [for memset/memcpy] */
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38 #include <stdio.h> /* [for printf] */
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39
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40 #include "dconfig.h" /* GCC definitions */
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41 #define DECNUMDIGITS 16 /* make decNumbers with space for 16 */
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42 #include "decNumber.h" /* base number library */
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43 #include "decNumberLocal.h" /* decNumber local types, etc. */
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44 #include "decimal64.h" /* our primary include */
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45
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46 /* Utility routines and tables [in decimal64.c]; externs for C++ */
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47 extern const uInt COMBEXP[32], COMBMSD[32];
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48 extern const uShort DPD2BIN[1024];
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49 extern const uShort BIN2DPD[1000];
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50 extern const uByte BIN2CHAR[4001];
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51
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52 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
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53 extern void decDigitsToDPD(const decNumber *, uInt *, Int);
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54
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55 #if DECTRACE || DECCHECK
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56 void decimal64Show(const decimal64 *); /* for debug */
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57 extern void decNumberShow(const decNumber *); /* .. */
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58 #endif
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59
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60 /* Useful macro */
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61 /* Clear a structure (e.g., a decNumber) */
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62 #define DEC_clear(d) memset(d, 0, sizeof(*d))
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63
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64 /* define and include the tables to use for conversions */
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65 #define DEC_BIN2CHAR 1
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66 #define DEC_DPD2BIN 1
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67 #define DEC_BIN2DPD 1 /* used for all sizes */
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68 #include "decDPD.h" /* lookup tables */
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69
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70 /* ------------------------------------------------------------------ */
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71 /* decimal64FromNumber -- convert decNumber to decimal64 */
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72 /* */
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73 /* ds is the target decimal64 */
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74 /* dn is the source number (assumed valid) */
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75 /* set is the context, used only for reporting errors */
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76 /* */
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77 /* The set argument is used only for status reporting and for the */
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78 /* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */
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79 /* digits or an overflow is detected). If the exponent is out of the */
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80 /* valid range then Overflow or Underflow will be raised. */
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81 /* After Underflow a subnormal result is possible. */
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82 /* */
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83 /* DEC_Clamped is set if the number has to be 'folded down' to fit, */
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84 /* by reducing its exponent and multiplying the coefficient by a */
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85 /* power of ten, or if the exponent on a zero had to be clamped. */
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86 /* ------------------------------------------------------------------ */
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87 decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn,
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88 decContext *set) {
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89 uInt status=0; /* status accumulator */
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90 Int ae; /* adjusted exponent */
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91 decNumber dw; /* work */
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92 decContext dc; /* .. */
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93 uInt *pu; /* .. */
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94 uInt comb, exp; /* .. */
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95 uInt targar[2]={0, 0}; /* target 64-bit */
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96 #define targhi targar[1] /* name the word with the sign */
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97 #define targlo targar[0] /* and the other */
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98
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99 /* If the number has too many digits, or the exponent could be */
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100 /* out of range then reduce the number under the appropriate */
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101 /* constraints. This could push the number to Infinity or zero, */
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102 /* so this check and rounding must be done before generating the */
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103 /* decimal64] */
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104 ae=dn->exponent+dn->digits-1; /* [0 if special] */
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105 if (dn->digits>DECIMAL64_Pmax /* too many digits */
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106 || ae>DECIMAL64_Emax /* likely overflow */
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107 || ae<DECIMAL64_Emin) { /* likely underflow */
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108 decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [no traps] */
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109 dc.round=set->round; /* use supplied rounding */
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110 decNumberPlus(&dw, dn, &dc); /* (round and check) */
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111 /* [this changes -0 to 0, so enforce the sign...] */
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112 dw.bits|=dn->bits&DECNEG;
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113 status=dc.status; /* save status */
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114 dn=&dw; /* use the work number */
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115 } /* maybe out of range */
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116
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117 if (dn->bits&DECSPECIAL) { /* a special value */
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118 if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
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119 else { /* sNaN or qNaN */
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120 if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */
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121 && (dn->digits<DECIMAL64_Pmax)) { /* coefficient fits */
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122 decDigitsToDPD(dn, targar, 0);
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123 }
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124 if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
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125 else targhi|=DECIMAL_sNaN<<24;
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126 } /* a NaN */
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127 } /* special */
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128
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129 else { /* is finite */
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130 if (decNumberIsZero(dn)) { /* is a zero */
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131 /* set and clamp exponent */
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132 if (dn->exponent<-DECIMAL64_Bias) {
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133 exp=0; /* low clamp */
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134 status|=DEC_Clamped;
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135 }
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136 else {
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137 exp=dn->exponent+DECIMAL64_Bias; /* bias exponent */
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138 if (exp>DECIMAL64_Ehigh) { /* top clamp */
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139 exp=DECIMAL64_Ehigh;
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140 status|=DEC_Clamped;
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141 }
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142 }
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143 comb=(exp>>5) & 0x18; /* msd=0, exp top 2 bits .. */
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144 }
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145 else { /* non-zero finite number */
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146 uInt msd; /* work */
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147 Int pad=0; /* coefficient pad digits */
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148
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149 /* the dn is known to fit, but it may need to be padded */
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150 exp=(uInt)(dn->exponent+DECIMAL64_Bias); /* bias exponent */
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151 if (exp>DECIMAL64_Ehigh) { /* fold-down case */
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152 pad=exp-DECIMAL64_Ehigh;
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153 exp=DECIMAL64_Ehigh; /* [to maximum] */
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154 status|=DEC_Clamped;
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155 }
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156
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157 /* fastpath common case */
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158 if (DECDPUN==3 && pad==0) {
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159 uInt dpd[6]={0,0,0,0,0,0};
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160 uInt i;
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161 Int d=dn->digits;
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162 for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];
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163 targlo =dpd[0];
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164 targlo|=dpd[1]<<10;
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165 targlo|=dpd[2]<<20;
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166 if (dn->digits>6) {
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167 targlo|=dpd[3]<<30;
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168 targhi =dpd[3]>>2;
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169 targhi|=dpd[4]<<8;
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170 }
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171 msd=dpd[5]; /* [did not really need conversion] */
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172 }
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173 else { /* general case */
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174 decDigitsToDPD(dn, targar, pad);
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175 /* save and clear the top digit */
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176 msd=targhi>>18;
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177 targhi&=0x0003ffff;
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178 }
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179
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180 /* create the combination field */
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181 if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);
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182 else comb=((exp>>5) & 0x18) | msd;
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183 }
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184 targhi|=comb<<26; /* add combination field .. */
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185 targhi|=(exp&0xff)<<18; /* .. and exponent continuation */
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186 } /* finite */
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187
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188 if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
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189
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190 /* now write to storage; this is now always endian */
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191 pu=(uInt *)d64->bytes; /* overlay */
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192 if (DECLITEND) {
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193 pu[0]=targar[0]; /* directly store the low int */
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194 pu[1]=targar[1]; /* then the high int */
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195 }
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196 else {
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197 pu[0]=targar[1]; /* directly store the high int */
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198 pu[1]=targar[0]; /* then the low int */
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199 }
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200
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201 if (status!=0) decContextSetStatus(set, status); /* pass on status */
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202 /* decimal64Show(d64); */
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203 return d64;
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204 } /* decimal64FromNumber */
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205
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206 /* ------------------------------------------------------------------ */
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207 /* decimal64ToNumber -- convert decimal64 to decNumber */
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208 /* d64 is the source decimal64 */
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209 /* dn is the target number, with appropriate space */
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210 /* No error is possible. */
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211 /* ------------------------------------------------------------------ */
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212 decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) {
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213 uInt msd; /* coefficient MSD */
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214 uInt exp; /* exponent top two bits */
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215 uInt comb; /* combination field */
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216 const uInt *pu; /* work */
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217 Int need; /* .. */
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218 uInt sourar[2]; /* source 64-bit */
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219 #define sourhi sourar[1] /* name the word with the sign */
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220 #define sourlo sourar[0] /* and the lower word */
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221
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222 /* load source from storage; this is endian */
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223 pu=(const uInt *)d64->bytes; /* overlay */
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224 if (DECLITEND) {
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225 sourlo=pu[0]; /* directly load the low int */
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226 sourhi=pu[1]; /* then the high int */
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227 }
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228 else {
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229 sourhi=pu[0]; /* directly load the high int */
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230 sourlo=pu[1]; /* then the low int */
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231 }
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232
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233 comb=(sourhi>>26)&0x1f; /* combination field */
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234
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235 decNumberZero(dn); /* clean number */
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236 if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */
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237
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238 msd=COMBMSD[comb]; /* decode the combination field */
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239 exp=COMBEXP[comb]; /* .. */
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240
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241 if (exp==3) { /* is a special */
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242 if (msd==0) {
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243 dn->bits|=DECINF;
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244 return dn; /* no coefficient needed */
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245 }
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246 else if (sourhi&0x02000000) dn->bits|=DECSNAN;
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247 else dn->bits|=DECNAN;
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248 msd=0; /* no top digit */
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249 }
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250 else { /* is a finite number */
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251 dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */
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252 }
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253
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254 /* get the coefficient */
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255 sourhi&=0x0003ffff; /* clean coefficient continuation */
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256 if (msd) { /* non-zero msd */
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257 sourhi|=msd<<18; /* prefix to coefficient */
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258 need=6; /* process 6 declets */
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259 }
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260 else { /* msd=0 */
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261 if (!sourhi) { /* top word 0 */
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262 if (!sourlo) return dn; /* easy: coefficient is 0 */
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263 need=3; /* process at least 3 declets */
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264 if (sourlo&0xc0000000) need++; /* process 4 declets */
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265 /* [could reduce some more, here] */
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266 }
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267 else { /* some bits in top word, msd=0 */
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268 need=4; /* process at least 4 declets */
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269 if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */
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270 }
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271 } /*msd=0 */
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272
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273 decDigitsFromDPD(dn, sourar, need); /* process declets */
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274 return dn;
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275 } /* decimal64ToNumber */
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276
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277
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278 /* ------------------------------------------------------------------ */
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279 /* to-scientific-string -- conversion to numeric string */
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280 /* to-engineering-string -- conversion to numeric string */
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281 /* */
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282 /* decimal64ToString(d64, string); */
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283 /* decimal64ToEngString(d64, string); */
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284 /* */
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285 /* d64 is the decimal64 format number to convert */
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286 /* string is the string where the result will be laid out */
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287 /* */
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288 /* string must be at least 24 characters */
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289 /* */
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290 /* No error is possible, and no status can be set. */
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291 /* ------------------------------------------------------------------ */
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292 char * decimal64ToEngString(const decimal64 *d64, char *string){
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293 decNumber dn; /* work */
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294 decimal64ToNumber(d64, &dn);
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295 decNumberToEngString(&dn, string);
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296 return string;
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297 } /* decimal64ToEngString */
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298
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299 char * decimal64ToString(const decimal64 *d64, char *string){
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300 uInt msd; /* coefficient MSD */
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301 Int exp; /* exponent top two bits or full */
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302 uInt comb; /* combination field */
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303 char *cstart; /* coefficient start */
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304 char *c; /* output pointer in string */
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305 const uInt *pu; /* work */
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306 char *s, *t; /* .. (source, target) */
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307 Int dpd; /* .. */
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308 Int pre, e; /* .. */
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309 const uByte *u; /* .. */
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310
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311 uInt sourar[2]; /* source 64-bit */
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312 #define sourhi sourar[1] /* name the word with the sign */
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313 #define sourlo sourar[0] /* and the lower word */
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314
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315 /* load source from storage; this is endian */
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316 pu=(const uInt *)d64->bytes; /* overlay */
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317 if (DECLITEND) {
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318 sourlo=pu[0]; /* directly load the low int */
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319 sourhi=pu[1]; /* then the high int */
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320 }
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321 else {
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322 sourhi=pu[0]; /* directly load the high int */
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323 sourlo=pu[1]; /* then the low int */
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324 }
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325
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326 c=string; /* where result will go */
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327 if (((Int)sourhi)<0) *c++='-'; /* handle sign */
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328
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329 comb=(sourhi>>26)&0x1f; /* combination field */
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330 msd=COMBMSD[comb]; /* decode the combination field */
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331 exp=COMBEXP[comb]; /* .. */
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332
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333 if (exp==3) {
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334 if (msd==0) { /* infinity */
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335 strcpy(c, "Inf");
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336 strcpy(c+3, "inity");
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337 return string; /* easy */
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338 }
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339 if (sourhi&0x02000000) *c++='s'; /* sNaN */
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340 strcpy(c, "NaN"); /* complete word */
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341 c+=3; /* step past */
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342 if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; /* zero payload */
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343 /* otherwise drop through to add integer; set correct exp */
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344 exp=0; msd=0; /* setup for following code */
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345 }
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346 else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;
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347
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348 /* convert 16 digits of significand to characters */
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349 cstart=c; /* save start of coefficient */
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350 if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */
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351
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352 /* Now decode the declets. After extracting each one, it is */
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353 /* decoded to binary and then to a 4-char sequence by table lookup; */
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354 /* the 4-chars are a 1-char length (significant digits, except 000 */
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355 /* has length 0). This allows us to left-align the first declet */
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356 /* with non-zero content, then remaining ones are full 3-char */
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357 /* length. We use fixed-length memcpys because variable-length */
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358 /* causes a subroutine call in GCC. (These are length 4 for speed */
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359 /* and are safe because the array has an extra terminator byte.) */
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360 #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
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361 if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
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362 else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
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363
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364 dpd=(sourhi>>8)&0x3ff; /* declet 1 */
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365 dpd2char;
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366 dpd=((sourhi&0xff)<<2) | (sourlo>>30); /* declet 2 */
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367 dpd2char;
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368 dpd=(sourlo>>20)&0x3ff; /* declet 3 */
|
|
|
369 dpd2char;
|
|
|
370 dpd=(sourlo>>10)&0x3ff; /* declet 4 */
|
|
|
371 dpd2char;
|
|
|
372 dpd=(sourlo)&0x3ff; /* declet 5 */
|
|
|
373 dpd2char;
|
|
|
374
|
|
|
375 if (c==cstart) *c++='0'; /* all zeros -- make 0 */
|
|
|
376
|
|
|
377 if (exp==0) { /* integer or NaN case -- easy */
|
|
|
378 *c='\0'; /* terminate */
|
|
|
379 return string;
|
|
|
380 }
|
|
|
381
|
|
|
382 /* non-0 exponent */
|
|
|
383 e=0; /* assume no E */
|
|
|
384 pre=c-cstart+exp;
|
|
|
385 /* [here, pre-exp is the digits count (==1 for zero)] */
|
|
|
386 if (exp>0 || pre<-5) { /* need exponential form */
|
|
|
387 e=pre-1; /* calculate E value */
|
|
|
388 pre=1; /* assume one digit before '.' */
|
|
|
389 } /* exponential form */
|
|
|
390
|
|
|
391 /* modify the coefficient, adding 0s, '.', and E+nn as needed */
|
|
|
392 s=c-1; /* source (LSD) */
|
|
|
393 if (pre>0) { /* ddd.ddd (plain), perhaps with E */
|
|
|
394 char *dotat=cstart+pre;
|
|
|
395 if (dotat<c) { /* if embedded dot needed... */
|
|
|
396 t=c; /* target */
|
|
|
397 for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
|
|
|
398 *t='.'; /* insert the dot */
|
|
|
399 c++; /* length increased by one */
|
|
|
400 }
|
|
|
401
|
|
|
402 /* finally add the E-part, if needed; it will never be 0, and has */
|
|
|
403 /* a maximum length of 3 digits */
|
|
|
404 if (e!=0) {
|
|
|
405 *c++='E'; /* starts with E */
|
|
|
406 *c++='+'; /* assume positive */
|
|
|
407 if (e<0) {
|
|
|
408 *(c-1)='-'; /* oops, need '-' */
|
|
|
409 e=-e; /* uInt, please */
|
|
|
410 }
|
|
|
411 u=&BIN2CHAR[e*4]; /* -> length byte */
|
|
|
412 memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */
|
|
|
413 c+=*u; /* bump pointer appropriately */
|
|
|
414 }
|
|
|
415 *c='\0'; /* add terminator */
|
|
|
416 /*printf("res %s\n", string); */
|
|
|
417 return string;
|
|
|
418 } /* pre>0 */
|
|
|
419
|
|
|
420 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
|
|
|
421 t=c+1-pre;
|
|
|
422 *(t+1)='\0'; /* can add terminator now */
|
|
|
423 for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */
|
|
|
424 c=cstart;
|
|
|
425 *c++='0'; /* always starts with 0. */
|
|
|
426 *c++='.';
|
|
|
427 for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */
|
|
|
428 /*printf("res %s\n", string); */
|
|
|
429 return string;
|
|
|
430 } /* decimal64ToString */
|
|
|
431
|
|
|
432 /* ------------------------------------------------------------------ */
|
|
|
433 /* to-number -- conversion from numeric string */
|
|
|
434 /* */
|
|
|
435 /* decimal64FromString(result, string, set); */
|
|
|
436 /* */
|
|
|
437 /* result is the decimal64 format number which gets the result of */
|
|
|
438 /* the conversion */
|
|
|
439 /* *string is the character string which should contain a valid */
|
|
|
440 /* number (which may be a special value) */
|
|
|
441 /* set is the context */
|
|
|
442 /* */
|
|
|
443 /* The context is supplied to this routine is used for error handling */
|
|
|
444 /* (setting of status and traps) and for the rounding mode, only. */
|
|
|
445 /* If an error occurs, the result will be a valid decimal64 NaN. */
|
|
|
446 /* ------------------------------------------------------------------ */
|
|
|
447 decimal64 * decimal64FromString(decimal64 *result, const char *string,
|
|
|
448 decContext *set) {
|
|
|
449 decContext dc; /* work */
|
|
|
450 decNumber dn; /* .. */
|
|
|
451
|
|
|
452 decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */
|
|
|
453 dc.round=set->round; /* use supplied rounding */
|
|
|
454
|
|
|
455 decNumberFromString(&dn, string, &dc); /* will round if needed */
|
|
|
456
|
|
|
457 decimal64FromNumber(result, &dn, &dc);
|
|
|
458 if (dc.status!=0) { /* something happened */
|
|
|
459 decContextSetStatus(set, dc.status); /* .. pass it on */
|
|
|
460 }
|
|
|
461 return result;
|
|
|
462 } /* decimal64FromString */
|
|
|
463
|
|
|
464 /* ------------------------------------------------------------------ */
|
|
|
465 /* decimal64IsCanonical -- test whether encoding is canonical */
|
|
|
466 /* d64 is the source decimal64 */
|
|
|
467 /* returns 1 if the encoding of d64 is canonical, 0 otherwise */
|
|
|
468 /* No error is possible. */
|
|
|
469 /* ------------------------------------------------------------------ */
|
|
|
470 uint32_t decimal64IsCanonical(const decimal64 *d64) {
|
|
|
471 decNumber dn; /* work */
|
|
|
472 decimal64 canon; /* .. */
|
|
|
473 decContext dc; /* .. */
|
|
|
474 decContextDefault(&dc, DEC_INIT_DECIMAL64);
|
|
|
475 decimal64ToNumber(d64, &dn);
|
|
|
476 decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
|
|
|
477 return memcmp(d64, &canon, DECIMAL64_Bytes)==0;
|
|
|
478 } /* decimal64IsCanonical */
|
|
|
479
|
|
|
480 /* ------------------------------------------------------------------ */
|
|
|
481 /* decimal64Canonical -- copy an encoding, ensuring it is canonical */
|
|
|
482 /* d64 is the source decimal64 */
|
|
|
483 /* result is the target (may be the same decimal64) */
|
|
|
484 /* returns result */
|
|
|
485 /* No error is possible. */
|
|
|
486 /* ------------------------------------------------------------------ */
|
|
|
487 decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {
|
|
|
488 decNumber dn; /* work */
|
|
|
489 decContext dc; /* .. */
|
|
|
490 decContextDefault(&dc, DEC_INIT_DECIMAL64);
|
|
|
491 decimal64ToNumber(d64, &dn);
|
|
|
492 decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */
|
|
|
493 return result;
|
|
|
494 } /* decimal64Canonical */
|
|
|
495
|
|
|
496 #if DECTRACE || DECCHECK
|
|
|
497 /* Macros for accessing decimal64 fields. These assume the
|
|
|
498 argument is a reference (pointer) to the decimal64 structure,
|
|
|
499 and the decimal64 is in network byte order (big-endian) */
|
|
|
500 /* Get sign */
|
|
|
501 #define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7)
|
|
|
502
|
|
|
503 /* Get combination field */
|
|
|
504 #define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2)
|
|
|
505
|
|
|
506 /* Get exponent continuation [does not remove bias] */
|
|
|
507 #define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \
|
|
|
508 | ((unsigned)(d)->bytes[1]>>2))
|
|
|
509
|
|
|
510 /* Set sign [this assumes sign previously 0] */
|
|
|
511 #define decimal64SetSign(d, b) { \
|
|
|
512 (d)->bytes[0]|=((unsigned)(b)<<7);}
|
|
|
513
|
|
|
514 /* Set exponent continuation [does not apply bias] */
|
|
|
515 /* This assumes range has been checked and exponent previously 0; */
|
|
|
516 /* type of exponent must be unsigned */
|
|
|
517 #define decimal64SetExpCon(d, e) { \
|
|
|
518 (d)->bytes[0]|=(uint8_t)((e)>>6); \
|
|
|
519 (d)->bytes[1]|=(uint8_t)(((e)&0x3F)<<2);}
|
|
|
520
|
|
|
521 /* ------------------------------------------------------------------ */
|
|
|
522 /* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */
|
|
|
523 /* d64 -- the number to show */
|
|
|
524 /* ------------------------------------------------------------------ */
|
|
|
525 /* Also shows sign/cob/expconfields extracted */
|
|
|
526 void decimal64Show(const decimal64 *d64) {
|
|
|
527 char buf[DECIMAL64_Bytes*2+1];
|
|
|
528 Int i, j=0;
|
|
|
529
|
|
|
530 if (DECLITEND) {
|
|
|
531 for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
|
|
|
532 sprintf(&buf[j], "%02x", d64->bytes[7-i]);
|
|
|
533 }
|
|
|
534 printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
|
|
|
535 d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,
|
|
|
536 ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));
|
|
|
537 }
|
|
|
538 else { /* big-endian */
|
|
|
539 for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
|
|
|
540 sprintf(&buf[j], "%02x", d64->bytes[i]);
|
|
|
541 }
|
|
|
542 printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
|
|
|
543 decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));
|
|
|
544 }
|
|
|
545 } /* decimal64Show */
|
|
|
546 #endif
|
|
|
547
|
|
|
548 /* ================================================================== */
|
|
|
549 /* Shared utility routines and tables */
|
|
|
550 /* ================================================================== */
|
|
|
551 /* define and include the conversion tables to use for shared code */
|
|
|
552 #if DECDPUN==3
|
|
|
553 #define DEC_DPD2BIN 1
|
|
|
554 #else
|
|
|
555 #define DEC_DPD2BCD 1
|
|
|
556 #endif
|
|
|
557 #include "decDPD.h" /* lookup tables */
|
|
|
558
|
|
|
559 /* The maximum number of decNumberUnits needed for a working copy of */
|
|
|
560 /* the units array is the ceiling of digits/DECDPUN, where digits is */
|
|
|
561 /* the maximum number of digits in any of the formats for which this */
|
|
|
562 /* is used. decimal128.h must not be included in this module, so, as */
|
|
|
563 /* a very special case, that number is defined as a literal here. */
|
|
|
564 #define DECMAX754 34
|
|
|
565 #define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)
|
|
|
566
|
|
|
567 /* ------------------------------------------------------------------ */
|
|
|
568 /* Combination field lookup tables (uInts to save measurable work) */
|
|
|
569 /* */
|
|
|
570 /* COMBEXP - 2-bit most-significant-bits of exponent */
|
|
|
571 /* [11 if an Infinity or NaN] */
|
|
|
572 /* COMBMSD - 4-bit most-significant-digit */
|
|
|
573 /* [0=Infinity, 1=NaN if COMBEXP=11] */
|
|
|
574 /* */
|
|
|
575 /* Both are indexed by the 5-bit combination field (0-31) */
|
|
|
576 /* ------------------------------------------------------------------ */
|
|
|
577 const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,
|
|
|
578 1, 1, 1, 1, 1, 1, 1, 1,
|
|
|
579 2, 2, 2, 2, 2, 2, 2, 2,
|
|
|
580 0, 0, 1, 1, 2, 2, 3, 3};
|
|
|
581 const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7,
|
|
|
582 0, 1, 2, 3, 4, 5, 6, 7,
|
|
|
583 0, 1, 2, 3, 4, 5, 6, 7,
|
|
|
584 8, 9, 8, 9, 8, 9, 0, 1};
|
|
|
585
|
|
|
586 /* ------------------------------------------------------------------ */
|
|
|
587 /* decDigitsToDPD -- pack coefficient into DPD form */
|
|
|
588 /* */
|
|
|
589 /* dn is the source number (assumed valid, max DECMAX754 digits) */
|
|
|
590 /* targ is 1, 2, or 4-element uInt array, which the caller must */
|
|
|
591 /* have cleared to zeros */
|
|
|
592 /* shift is the number of 0 digits to add on the right (normally 0) */
|
|
|
593 /* */
|
|
|
594 /* The coefficient must be known small enough to fit. The full */
|
|
|
595 /* coefficient is copied, including the leading 'odd' digit. This */
|
|
|
596 /* digit is retrieved and packed into the combination field by the */
|
|
|
597 /* caller. */
|
|
|
598 /* */
|
|
|
599 /* The target uInts are altered only as necessary to receive the */
|
|
|
600 /* digits of the decNumber. When more than one uInt is needed, they */
|
|
|
601 /* are filled from left to right (that is, the uInt at offset 0 will */
|
|
|
602 /* end up with the least-significant digits). */
|
|
|
603 /* */
|
|
|
604 /* shift is used for 'fold-down' padding. */
|
|
|
605 /* */
|
|
|
606 /* No error is possible. */
|
|
|
607 /* ------------------------------------------------------------------ */
|
|
|
608 #if DECDPUN<=4
|
|
|
609 /* Constant multipliers for divide-by-power-of five using reciprocal */
|
|
|
610 /* multiply, after removing powers of 2 by shifting, and final shift */
|
|
|
611 /* of 17 [we only need up to **4] */
|
|
|
612 static const uInt multies[]={131073, 26215, 5243, 1049, 210};
|
|
|
613 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
|
|
|
614 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
|
|
|
615 #endif
|
|
|
616 void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {
|
|
|
617 Int cut; /* work */
|
|
|
618 Int n; /* output bunch counter */
|
|
|
619 Int digits=dn->digits; /* digit countdown */
|
|
|
620 uInt dpd; /* densely packed decimal value */
|
|
|
621 uInt bin; /* binary value 0-999 */
|
|
|
622 uInt *uout=targ; /* -> current output uInt */
|
|
|
623 uInt uoff=0; /* -> current output offset [from right] */
|
|
|
624 const Unit *inu=dn->lsu; /* -> current input unit */
|
|
|
625 Unit uar[DECMAXUNITS]; /* working copy of units, iff shifted */
|
|
|
626 #if DECDPUN!=3 /* not fast path */
|
|
|
627 Unit in; /* current unit */
|
|
|
628 #endif
|
|
|
629
|
|
|
630 if (shift!=0) { /* shift towards most significant required */
|
|
|
631 /* shift the units array to the left by pad digits and copy */
|
|
|
632 /* [this code is a special case of decShiftToMost, which could */
|
|
|
633 /* be used instead if exposed and the array were copied first] */
|
|
|
634 const Unit *source; /* .. */
|
|
|
635 Unit *target, *first; /* .. */
|
|
|
636 uInt next=0; /* work */
|
|
|
637
|
|
|
638 source=dn->lsu+D2U(digits)-1; /* where msu comes from */
|
|
|
639 target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */
|
|
|
640 cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
|
|
|
641 if (cut==0) { /* unit-boundary case */
|
|
|
642 for (; source>=dn->lsu; source--, target--) *target=*source;
|
|
|
643 }
|
|
|
644 else {
|
|
|
645 first=uar+D2U(digits+shift)-1; /* where msu will end up */
|
|
|
646 for (; source>=dn->lsu; source--, target--) {
|
|
|
647 /* split the source Unit and accumulate remainder for next */
|
|
|
648 #if DECDPUN<=4
|
|
|
649 uInt quot=QUOT10(*source, cut);
|
|
|
650 uInt rem=*source-quot*DECPOWERS[cut];
|
|
|
651 next+=quot;
|
|
|
652 #else
|
|
|
653 uInt rem=*source%DECPOWERS[cut];
|
|
|
654 next+=*source/DECPOWERS[cut];
|
|
|
655 #endif
|
|
|
656 if (target<=first) *target=(Unit)next; /* write to target iff valid */
|
|
|
657 next=rem*DECPOWERS[DECDPUN-cut]; /* save remainder for next Unit */
|
|
|
658 }
|
|
|
659 } /* shift-move */
|
|
|
660 /* propagate remainder to one below and clear the rest */
|
|
|
661 for (; target>=uar; target--) {
|
|
|
662 *target=(Unit)next;
|
|
|
663 next=0;
|
|
|
664 }
|
|
|
665 digits+=shift; /* add count (shift) of zeros added */
|
|
|
666 inu=uar; /* use units in working array */
|
|
|
667 }
|
|
|
668
|
|
|
669 /* now densely pack the coefficient into DPD declets */
|
|
|
670
|
|
|
671 #if DECDPUN!=3 /* not fast path */
|
|
|
672 in=*inu; /* current unit */
|
|
|
673 cut=0; /* at lowest digit */
|
|
|
674 bin=0; /* [keep compiler quiet] */
|
|
|
675 #endif
|
|
|
676
|
|
|
677 for(n=0; digits>0; n++) { /* each output bunch */
|
|
|
678 #if DECDPUN==3 /* fast path, 3-at-a-time */
|
|
|
679 bin=*inu; /* 3 digits ready for convert */
|
|
|
680 digits-=3; /* [may go negative] */
|
|
|
681 inu++; /* may need another */
|
|
|
682
|
|
|
683 #else /* must collect digit-by-digit */
|
|
|
684 Unit dig; /* current digit */
|
|
|
685 Int j; /* digit-in-declet count */
|
|
|
686 for (j=0; j<3; j++) {
|
|
|
687 #if DECDPUN<=4
|
|
|
688 Unit temp=(Unit)((uInt)(in*6554)>>16);
|
|
|
689 dig=(Unit)(in-X10(temp));
|
|
|
690 in=temp;
|
|
|
691 #else
|
|
|
692 dig=in%10;
|
|
|
693 in=in/10;
|
|
|
694 #endif
|
|
|
695 if (j==0) bin=dig;
|
|
|
696 else if (j==1) bin+=X10(dig);
|
|
|
697 else /* j==2 */ bin+=X100(dig);
|
|
|
698 digits--;
|
|
|
699 if (digits==0) break; /* [also protects *inu below] */
|
|
|
700 cut++;
|
|
|
701 if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
|
|
|
702 }
|
|
|
703 #endif
|
|
|
704 /* here there are 3 digits in bin, or have used all input digits */
|
|
|
705
|
|
|
706 dpd=BIN2DPD[bin];
|
|
|
707
|
|
|
708 /* write declet to uInt array */
|
|
|
709 *uout|=dpd<<uoff;
|
|
|
710 uoff+=10;
|
|
|
711 if (uoff<32) continue; /* no uInt boundary cross */
|
|
|
712 uout++;
|
|
|
713 uoff-=32;
|
|
|
714 *uout|=dpd>>(10-uoff); /* collect top bits */
|
|
|
715 } /* n declets */
|
|
|
716 return;
|
|
|
717 } /* decDigitsToDPD */
|
|
|
718
|
|
|
719 /* ------------------------------------------------------------------ */
|
|
|
720 /* decDigitsFromDPD -- unpack a format's coefficient */
|
|
|
721 /* */
|
|
|
722 /* dn is the target number, with 7, 16, or 34-digit space. */
|
|
|
723 /* sour is a 1, 2, or 4-element uInt array containing only declets */
|
|
|
724 /* declets is the number of (right-aligned) declets in sour to */
|
|
|
725 /* be processed. This may be 1 more than the obvious number in */
|
|
|
726 /* a format, as any top digit is prefixed to the coefficient */
|
|
|
727 /* continuation field. It also may be as small as 1, as the */
|
|
|
728 /* caller may pre-process leading zero declets. */
|
|
|
729 /* */
|
|
|
730 /* When doing the 'extra declet' case care is taken to avoid writing */
|
|
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731 /* extra digits when there are leading zeros, as these could overflow */
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732 /* the units array when DECDPUN is not 3. */
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|
|
733 /* */
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|
734 /* The target uInts are used only as necessary to process declets */
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735 /* declets into the decNumber. When more than one uInt is needed, */
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|
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736 /* they are used from left to right (that is, the uInt at offset 0 */
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737 /* provides the least-significant digits). */
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|
|
738 /* */
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|
739 /* dn->digits is set, but not the sign or exponent. */
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740 /* No error is possible [the redundant 888 codes are allowed]. */
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|
741 /* ------------------------------------------------------------------ */
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742 void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {
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743
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744 uInt dpd; /* collector for 10 bits */
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745 Int n; /* counter */
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|
746 Unit *uout=dn->lsu; /* -> current output unit */
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747 Unit *last=uout; /* will be unit containing msd */
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|
|
748 const uInt *uin=sour; /* -> current input uInt */
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|
749 uInt uoff=0; /* -> current input offset [from right] */
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|
750
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751 #if DECDPUN!=3
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752 uInt bcd; /* BCD result */
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753 uInt nibble; /* work */
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754 Unit out=0; /* accumulator */
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755 Int cut=0; /* power of ten in current unit */
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756 #endif
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|
757 #if DECDPUN>4
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758 uInt const *pow; /* work */
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|
|
759 #endif
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760
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|
761 /* Expand the densely-packed integer, right to left */
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|
762 for (n=declets-1; n>=0; n--) { /* count down declets of 10 bits */
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763 dpd=*uin>>uoff;
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|
|
764 uoff+=10;
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|
|
765 if (uoff>32) { /* crossed uInt boundary */
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|
|
766 uin++;
|
|
|
767 uoff-=32;
|
|
|
768 dpd|=*uin<<(10-uoff); /* get waiting bits */
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|
769 }
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|
|
770 dpd&=0x3ff; /* clear uninteresting bits */
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|
|
771
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|
|
772 #if DECDPUN==3
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|
|
773 if (dpd==0) *uout=0;
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|
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774 else {
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|
775 *uout=DPD2BIN[dpd]; /* convert 10 bits to binary 0-999 */
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|
|
776 last=uout; /* record most significant unit */
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|
777 }
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|
|
778 uout++;
|
|
|
779 } /* n */
|
|
|
780
|
|
|
781 #else /* DECDPUN!=3 */
|
|
|
782 if (dpd==0) { /* fastpath [e.g., leading zeros] */
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|
|
783 /* write out three 0 digits (nibbles); out may have digit(s) */
|
|
|
784 cut++;
|
|
|
785 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
|
786 if (n==0) break; /* [as below, works even if MSD=0] */
|
|
|
787 cut++;
|
|
|
788 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
|
789 cut++;
|
|
|
790 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
|
791 continue;
|
|
|
792 }
|
|
|
793
|
|
|
794 bcd=DPD2BCD[dpd]; /* convert 10 bits to 12 bits BCD */
|
|
|
795
|
|
|
796 /* now accumulate the 3 BCD nibbles into units */
|
|
|
797 nibble=bcd & 0x00f;
|
|
|
798 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
|
|
799 cut++;
|
|
|
800 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
|
801 bcd>>=4;
|
|
|
802
|
|
|
803 /* if this is the last declet and the remaining nibbles in bcd */
|
|
|
804 /* are 00 then process no more nibbles, because this could be */
|
|
|
805 /* the 'odd' MSD declet and writing any more Units would then */
|
|
|
806 /* overflow the unit array */
|
|
|
807 if (n==0 && !bcd) break;
|
|
|
808
|
|
|
809 nibble=bcd & 0x00f;
|
|
|
810 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
|
|
811 cut++;
|
|
|
812 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
|
813 bcd>>=4;
|
|
|
814
|
|
|
815 nibble=bcd & 0x00f;
|
|
|
816 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
|
|
817 cut++;
|
|
|
818 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
|
819 } /* n */
|
|
|
820 if (cut!=0) { /* some more left over */
|
|
|
821 *uout=out; /* write out final unit */
|
|
|
822 if (out) last=uout; /* and note if non-zero */
|
|
|
823 }
|
|
|
824 #endif
|
|
|
825
|
|
|
826 /* here, last points to the most significant unit with digits; */
|
|
|
827 /* inspect it to get the final digits count -- this is essentially */
|
|
|
828 /* the same code as decGetDigits in decNumber.c */
|
|
|
829 dn->digits=(last-dn->lsu)*DECDPUN+1; /* floor of digits, plus */
|
|
|
830 /* must be at least 1 digit */
|
|
|
831 #if DECDPUN>1
|
|
|
832 if (*last<10) return; /* common odd digit or 0 */
|
|
|
833 dn->digits++; /* must be 2 at least */
|
|
|
834 #if DECDPUN>2
|
|
|
835 if (*last<100) return; /* 10-99 */
|
|
|
836 dn->digits++; /* must be 3 at least */
|
|
|
837 #if DECDPUN>3
|
|
|
838 if (*last<1000) return; /* 100-999 */
|
|
|
839 dn->digits++; /* must be 4 at least */
|
|
|
840 #if DECDPUN>4
|
|
|
841 for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
|
|
|
842 #endif
|
|
|
843 #endif
|
|
|
844 #endif
|
|
|
845 #endif
|
|
|
846 return;
|
|
|
847 } /*decDigitsFromDPD */
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