1 | /* Extended precision arithmetic functions for long double I/O. |
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2 | * This program has been placed in the public domain. |
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3 | */ |
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4 | |
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5 | #include <_ansi.h> |
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6 | #include <reent.h> |
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7 | #include <string.h> |
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8 | #include <stdlib.h> |
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9 | #include "mprec.h" |
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10 | |
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11 | /* These are the externally visible entries. */ |
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12 | /* linux name: long double _IO_strtold (char *, char **); */ |
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13 | long double _strtold (char *, char **); |
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14 | char *_ldtoa_r (struct _reent *, long double, int, int, int *, int *, |
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15 | char **); |
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16 | int _ldcheck (long double *); |
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17 | #if 0 |
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18 | void _IO_ldtostr (long double *, char *, int, int, char); |
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19 | #endif |
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20 | |
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21 | /* Number of 16 bit words in external x type format */ |
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22 | #define NE 10 |
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23 | |
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24 | /* Number of 16 bit words in internal format */ |
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25 | #define NI (NE+3) |
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26 | |
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27 | /* Array offset to exponent */ |
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28 | #define E 1 |
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29 | |
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30 | /* Array offset to high guard word */ |
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31 | #define M 2 |
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32 | |
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33 | /* Number of bits of precision */ |
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34 | #define NBITS ((NI-4)*16) |
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35 | |
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36 | /* Maximum number of decimal digits in ASCII conversion |
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37 | * = NBITS*log10(2) |
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38 | */ |
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39 | #define NDEC (NBITS*8/27) |
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40 | |
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41 | /* The exponent of 1.0 */ |
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42 | #define EXONE (0x3fff) |
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43 | |
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44 | /* Maximum exponent digits - base 10 */ |
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45 | #define MAX_EXP_DIGITS 5 |
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46 | |
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47 | /* Control structure for long double conversion including rounding precision values. |
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48 | * rndprc can be set to 80 (if NE=6), 64, 56, 53, or 24 bits. |
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49 | */ |
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50 | typedef struct |
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51 | { |
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52 | int rlast; |
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53 | int rndprc; |
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54 | int rw; |
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55 | int re; |
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56 | int outexpon; |
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57 | unsigned short rmsk; |
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58 | unsigned short rmbit; |
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59 | unsigned short rebit; |
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60 | unsigned short rbit[NI]; |
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61 | unsigned short equot[NI]; |
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62 | } LDPARMS; |
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63 | |
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64 | static void esub (const short unsigned int *a, const short unsigned int *b, |
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65 | short unsigned int *c, LDPARMS * ldp); |
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66 | static void emul (const short unsigned int *a, const short unsigned int *b, |
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67 | short unsigned int *c, LDPARMS * ldp); |
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68 | static void ediv (const short unsigned int *a, const short unsigned int *b, |
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69 | short unsigned int *c, LDPARMS * ldp); |
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70 | static int ecmp (const short unsigned int *a, const short unsigned int *b); |
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71 | static int enormlz (short unsigned int *x); |
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72 | static int eshift (short unsigned int *x, int sc); |
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73 | static void eshup1 (register short unsigned int *x); |
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74 | static void eshup8 (register short unsigned int *x); |
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75 | static void eshup6 (register short unsigned int *x); |
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76 | static void eshdn1 (register short unsigned int *x); |
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77 | static void eshdn8 (register short unsigned int *x); |
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78 | static void eshdn6 (register short unsigned int *x); |
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79 | static void eneg (short unsigned int *x); |
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80 | static void emov (register const short unsigned int *a, |
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81 | register short unsigned int *b); |
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82 | static void eclear (register short unsigned int *x); |
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83 | static void einfin (register short unsigned int *x, register LDPARMS * ldp); |
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84 | static void efloor (short unsigned int *x, short unsigned int *y, |
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85 | LDPARMS * ldp); |
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86 | static void etoasc (short unsigned int *x, char *string, int ndigs, |
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87 | int outformat, LDPARMS * ldp); |
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88 | |
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89 | union uconv |
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90 | { |
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91 | unsigned short pe; |
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92 | long double d; |
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93 | }; |
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94 | |
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95 | #if LDBL_MANT_DIG == 24 |
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96 | static void e24toe (short unsigned int *pe, short unsigned int *y, |
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97 | LDPARMS * ldp); |
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98 | #elif LDBL_MANT_DIG == 53 |
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99 | static void e53toe (short unsigned int *pe, short unsigned int *y, |
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100 | LDPARMS * ldp); |
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101 | #elif LDBL_MANT_DIG == 64 |
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102 | static void e64toe (short unsigned int *pe, short unsigned int *y, |
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103 | LDPARMS * ldp); |
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104 | #else |
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105 | static void e113toe (short unsigned int *pe, short unsigned int *y, |
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106 | LDPARMS * ldp); |
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107 | #endif |
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108 | |
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109 | /* econst.c */ |
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110 | /* e type constants used by high precision check routines */ |
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111 | |
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112 | #if NE == 10 |
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113 | /* 0.0 */ |
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114 | static const unsigned short ezero[NE] = { 0x0000, 0x0000, 0x0000, 0x0000, |
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115 | 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, |
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116 | }; |
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117 | |
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118 | /* 1.0E0 */ |
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119 | static const unsigned short eone[NE] = { 0x0000, 0x0000, 0x0000, 0x0000, |
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120 | 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff, |
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121 | }; |
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122 | |
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123 | #else |
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124 | |
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125 | /* 0.0 */ |
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126 | static const unsigned short ezero[NE] = { |
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127 | 0, 0000000, 0000000, 0000000, 0000000, 0000000, |
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128 | }; |
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129 | |
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130 | /* 1.0E0 */ |
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131 | static const unsigned short eone[NE] = { |
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132 | 0, 0000000, 0000000, 0000000, 0100000, 0x3fff, |
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133 | }; |
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134 | |
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135 | #endif |
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136 | |
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137 | /* Debugging routine for displaying errors */ |
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138 | #ifdef DEBUG |
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139 | /* Notice: the order of appearance of the following |
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140 | * messages is bound to the error codes defined |
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141 | * in mconf.h. |
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142 | */ |
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143 | static const char *const ermsg[7] = { |
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144 | "unknown", /* error code 0 */ |
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145 | "domain", /* error code 1 */ |
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146 | "singularity", /* et seq. */ |
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147 | "overflow", |
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148 | "underflow", |
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149 | "total loss of precision", |
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150 | "partial loss of precision" |
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151 | }; |
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152 | |
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153 | #define mtherr(name, code) printf( "\n%s %s error\n", name, ermsg[code] ); |
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154 | #else |
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155 | #define mtherr(name, code) |
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156 | #endif |
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157 | |
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158 | /* ieee.c |
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159 | * |
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160 | * Extended precision IEEE binary floating point arithmetic routines |
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161 | * |
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162 | * Numbers are stored in C language as arrays of 16-bit unsigned |
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163 | * short integers. The arguments of the routines are pointers to |
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164 | * the arrays. |
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165 | * |
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166 | * |
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167 | * External e type data structure, simulates Intel 8087 chip |
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168 | * temporary real format but possibly with a larger significand: |
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169 | * |
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170 | * NE-1 significand words (least significant word first, |
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171 | * most significant bit is normally set) |
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172 | * exponent (value = EXONE for 1.0, |
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173 | * top bit is the sign) |
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174 | * |
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175 | * |
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176 | * Internal data structure of a number (a "word" is 16 bits): |
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177 | * |
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178 | * ei[0] sign word (0 for positive, 0xffff for negative) |
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179 | * ei[1] biased exponent (value = EXONE for the number 1.0) |
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180 | * ei[2] high guard word (always zero after normalization) |
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181 | * ei[3] |
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182 | * to ei[NI-2] significand (NI-4 significand words, |
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183 | * most significant word first, |
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184 | * most significant bit is set) |
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185 | * ei[NI-1] low guard word (0x8000 bit is rounding place) |
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186 | * |
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187 | * |
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188 | * |
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189 | * Routines for external format numbers |
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190 | * |
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191 | * asctoe( string, e ) ASCII string to extended double e type |
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192 | * asctoe64( string, &d ) ASCII string to long double |
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193 | * asctoe53( string, &d ) ASCII string to double |
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194 | * asctoe24( string, &f ) ASCII string to single |
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195 | * asctoeg( string, e, prec, ldp ) ASCII string to specified precision |
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196 | * e24toe( &f, e, ldp ) IEEE single precision to e type |
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197 | * e53toe( &d, e, ldp ) IEEE double precision to e type |
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198 | * e64toe( &d, e, ldp ) IEEE long double precision to e type |
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199 | * e113toe( &d, e, ldp ) IEEE long double precision to e type |
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200 | * eabs(e) absolute value |
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201 | * eadd( a, b, c ) c = b + a |
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202 | * eclear(e) e = 0 |
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203 | * ecmp (a, b) Returns 1 if a > b, 0 if a == b, |
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204 | * -1 if a < b, -2 if either a or b is a NaN. |
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205 | * ediv( a, b, c, ldp ) c = b / a |
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206 | * efloor( a, b, ldp ) truncate to integer, toward -infinity |
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207 | * efrexp( a, exp, s ) extract exponent and significand |
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208 | * eifrac( e, &l, frac ) e to long integer and e type fraction |
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209 | * euifrac( e, &l, frac ) e to unsigned long integer and e type fraction |
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210 | * einfin( e, ldp ) set e to infinity, leaving its sign alone |
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211 | * eldexp( a, n, b ) multiply by 2**n |
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212 | * emov( a, b ) b = a |
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213 | * emul( a, b, c, ldp ) c = b * a |
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214 | * eneg(e) e = -e |
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215 | * eround( a, b ) b = nearest integer value to a |
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216 | * esub( a, b, c, ldp ) c = b - a |
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217 | * e24toasc( &f, str, n ) single to ASCII string, n digits after decimal |
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218 | * e53toasc( &d, str, n ) double to ASCII string, n digits after decimal |
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219 | * e64toasc( &d, str, n ) long double to ASCII string |
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220 | * etoasc(e,str,n,fmt,ldp)e to ASCII string, n digits after decimal |
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221 | * etoe24( e, &f ) convert e type to IEEE single precision |
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222 | * etoe53( e, &d ) convert e type to IEEE double precision |
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223 | * etoe64( e, &d ) convert e type to IEEE long double precision |
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224 | * ltoe( &l, e ) long (32 bit) integer to e type |
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225 | * ultoe( &l, e ) unsigned long (32 bit) integer to e type |
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226 | * eisneg( e ) 1 if sign bit of e != 0, else 0 |
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227 | * eisinf( e ) 1 if e has maximum exponent (non-IEEE) |
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228 | * or is infinite (IEEE) |
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229 | * eisnan( e ) 1 if e is a NaN |
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230 | * esqrt( a, b ) b = square root of a |
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231 | * |
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232 | * |
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233 | * Routines for internal format numbers |
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234 | * |
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235 | * eaddm( ai, bi ) add significands, bi = bi + ai |
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236 | * ecleaz(ei) ei = 0 |
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237 | * ecleazs(ei) set ei = 0 but leave its sign alone |
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238 | * ecmpm( ai, bi ) compare significands, return 1, 0, or -1 |
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239 | * edivm( ai, bi, ldp ) divide significands, bi = bi / ai |
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240 | * emdnorm(ai,l,s,exp,ldp) normalize and round off |
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241 | * emovi( a, ai ) convert external a to internal ai |
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242 | * emovo( ai, a, ldp ) convert internal ai to external a |
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243 | * emovz( ai, bi ) bi = ai, low guard word of bi = 0 |
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244 | * emulm( ai, bi, ldp ) multiply significands, bi = bi * ai |
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245 | * enormlz(ei) left-justify the significand |
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246 | * eshdn1( ai ) shift significand and guards down 1 bit |
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247 | * eshdn8( ai ) shift down 8 bits |
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248 | * eshdn6( ai ) shift down 16 bits |
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249 | * eshift( ai, n ) shift ai n bits up (or down if n < 0) |
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250 | * eshup1( ai ) shift significand and guards up 1 bit |
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251 | * eshup8( ai ) shift up 8 bits |
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252 | * eshup6( ai ) shift up 16 bits |
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253 | * esubm( ai, bi ) subtract significands, bi = bi - ai |
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254 | * |
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255 | * |
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256 | * The result is always normalized and rounded to NI-4 word precision |
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257 | * after each arithmetic operation. |
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258 | * |
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259 | * Exception flags are NOT fully supported. |
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260 | * |
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261 | * Define USE_INFINITY in mconf.h for support of infinity; otherwise a |
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262 | * saturation arithmetic is implemented. |
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263 | * |
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264 | * Define NANS for support of Not-a-Number items; otherwise the |
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265 | * arithmetic will never produce a NaN output, and might be confused |
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266 | * by a NaN input. |
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267 | * If NaN's are supported, the output of ecmp(a,b) is -2 if |
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268 | * either a or b is a NaN. This means asking if(ecmp(a,b) < 0) |
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269 | * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than |
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270 | * if in doubt. |
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271 | * Signaling NaN's are NOT supported; they are treated the same |
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272 | * as quiet NaN's. |
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273 | * |
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274 | * Denormals are always supported here where appropriate (e.g., not |
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275 | * for conversion to DEC numbers). |
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276 | */ |
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277 | |
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278 | /* |
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279 | * Revision history: |
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280 | * |
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281 | * 5 Jan 84 PDP-11 assembly language version |
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282 | * 6 Dec 86 C language version |
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283 | * 30 Aug 88 100 digit version, improved rounding |
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284 | * 15 May 92 80-bit long double support |
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285 | * 22 Nov 00 Revised to fit into newlib by Jeff Johnston <jjohnstn@redhat.com> |
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286 | * |
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287 | * Author: S. L. Moshier. |
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288 | * |
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289 | * Copyright (c) 1984,2000 S.L. Moshier |
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290 | * |
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291 | * Permission to use, copy, modify, and distribute this software for any |
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292 | * purpose without fee is hereby granted, provided that this entire notice |
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293 | * is included in all copies of any software which is or includes a copy |
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294 | * or modification of this software and in all copies of the supporting |
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295 | * documentation for such software. |
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296 | * |
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297 | * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED |
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298 | * WARRANTY. IN PARTICULAR, THE AUTHOR MAKES NO REPRESENTATION |
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299 | * OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS |
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300 | * SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. |
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301 | * |
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302 | */ |
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303 | |
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304 | #include <stdio.h> |
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305 | /* #include "\usr\include\stdio.h" */ |
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306 | /*#include "ehead.h"*/ |
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307 | /*#include "mconf.h"*/ |
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308 | /* mconf.h |
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309 | * |
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310 | * Common include file for math routines |
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311 | * |
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312 | * |
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313 | * |
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314 | * SYNOPSIS: |
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315 | * |
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316 | * #include "mconf.h" |
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317 | * |
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318 | * |
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319 | * |
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320 | * DESCRIPTION: |
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321 | * |
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322 | * This file contains definitions for error codes that are |
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323 | * passed to the common error handling routine mtherr() |
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324 | * (which see). |
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325 | * |
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326 | * The file also includes a conditional assembly definition |
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327 | * for the type of computer arithmetic (IEEE, DEC, Motorola |
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328 | * IEEE, or UNKnown). |
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329 | * |
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330 | * For Digital Equipment PDP-11 and VAX computers, certain |
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331 | * IBM systems, and others that use numbers with a 56-bit |
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332 | * significand, the symbol DEC should be defined. In this |
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333 | * mode, most floating point constants are given as arrays |
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334 | * of octal integers to eliminate decimal to binary conversion |
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335 | * errors that might be introduced by the compiler. |
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336 | * |
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337 | * For computers, such as IBM PC, that follow the IEEE |
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338 | * Standard for Binary Floating Point Arithmetic (ANSI/IEEE |
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339 | * Std 754-1985), the symbol IBMPC should be defined. These |
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340 | * numbers have 53-bit significands. In this mode, constants |
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341 | * are provided as arrays of hexadecimal 16 bit integers. |
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342 | * |
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343 | * To accommodate other types of computer arithmetic, all |
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344 | * constants are also provided in a normal decimal radix |
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345 | * which one can hope are correctly converted to a suitable |
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346 | * format by the available C language compiler. To invoke |
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347 | * this mode, the symbol UNK is defined. |
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348 | * |
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349 | * An important difference among these modes is a predefined |
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350 | * set of machine arithmetic constants for each. The numbers |
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351 | * MACHEP (the machine roundoff error), MAXNUM (largest number |
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352 | * represented), and several other parameters are preset by |
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353 | * the configuration symbol. Check the file const.c to |
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354 | * ensure that these values are correct for your computer. |
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355 | * |
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356 | * For ANSI C compatibility, define ANSIC equal to 1. Currently |
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357 | * this affects only the atan2() function and others that use it. |
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358 | */ |
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359 | |
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360 | /* Constant definitions for math error conditions |
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361 | */ |
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362 | |
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363 | #define DOMAIN 1 /* argument domain error */ |
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364 | #define SING 2 /* argument singularity */ |
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365 | #define OVERFLOW 3 /* overflow range error */ |
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366 | #define UNDERFLOW 4 /* underflow range error */ |
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367 | #define TLOSS 5 /* total loss of precision */ |
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368 | #define PLOSS 6 /* partial loss of precision */ |
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369 | |
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370 | #define EDOM 33 |
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371 | #define ERANGE 34 |
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372 | |
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373 | typedef struct |
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374 | { |
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375 | double r; |
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376 | double i; |
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377 | } cmplx; |
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378 | |
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379 | /* Type of computer arithmetic */ |
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380 | |
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381 | #ifndef DEC |
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382 | #ifdef __IEEE_LITTLE_ENDIAN |
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383 | #define IBMPC 1 |
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384 | #else /* !__IEEE_LITTLE_ENDIAN */ |
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385 | #define MIEEE 1 |
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386 | #endif /* !__IEEE_LITTLE_ENDIAN */ |
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387 | #endif /* !DEC */ |
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388 | |
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389 | /* Define 1 for ANSI C atan2() function |
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390 | * See atan.c and clog.c. |
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391 | */ |
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392 | #define ANSIC 1 |
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393 | |
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394 | /*define VOLATILE volatile*/ |
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395 | #define VOLATILE |
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396 | |
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397 | #define NANS |
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398 | #define USE_INFINITY |
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399 | |
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400 | /* NaN's require infinity support. */ |
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401 | #ifdef NANS |
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402 | #ifndef INFINITY |
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403 | #define USE_INFINITY |
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404 | #endif |
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405 | #endif |
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406 | |
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407 | /* This handles 64-bit long ints. */ |
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408 | #define LONGBITS (8 * sizeof(long)) |
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409 | |
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410 | |
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411 | static void eaddm (short unsigned int *x, short unsigned int *y); |
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412 | static void esubm (short unsigned int *x, short unsigned int *y); |
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413 | static void emdnorm (short unsigned int *s, int lost, int subflg, |
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414 | long int exp, int rcntrl, LDPARMS * ldp); |
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415 | static int asctoeg (char *ss, short unsigned int *y, int oprec, |
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416 | LDPARMS * ldp); |
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417 | static void enan (short unsigned int *nan, int size); |
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418 | #if LDBL_MANT_DIG == 24 |
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419 | static void toe24 (short unsigned int *x, short unsigned int *y); |
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420 | #elif LDBL_MANT_DIG == 53 |
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421 | static void toe53 (short unsigned int *x, short unsigned int *y); |
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422 | #elif LDBL_MANT_DIG == 64 |
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423 | static void toe64 (short unsigned int *a, short unsigned int *b); |
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424 | #else |
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425 | static void toe113 (short unsigned int *a, short unsigned int *b); |
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426 | #endif |
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427 | static void eiremain (short unsigned int *den, short unsigned int *num, |
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428 | LDPARMS * ldp); |
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429 | static int ecmpm (register short unsigned int *a, |
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430 | register short unsigned int *b); |
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431 | static int edivm (short unsigned int *den, short unsigned int *num, |
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432 | LDPARMS * ldp); |
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433 | static int emulm (short unsigned int *a, short unsigned int *b, |
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434 | LDPARMS * ldp); |
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435 | static int eisneg (const short unsigned int *x); |
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436 | static int eisinf (const short unsigned int *x); |
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437 | static void emovi (const short unsigned int *a, short unsigned int *b); |
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438 | static void emovo (short unsigned int *a, short unsigned int *b, |
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439 | LDPARMS * ldp); |
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440 | static void emovz (register short unsigned int *a, |
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441 | register short unsigned int *b); |
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442 | static void ecleaz (register short unsigned int *xi); |
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443 | static void eadd1 (const short unsigned int *a, const short unsigned int *b, |
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444 | short unsigned int *c, int subflg, LDPARMS * ldp); |
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445 | static int eisnan (const short unsigned int *x); |
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446 | static int eiisnan (short unsigned int *x); |
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447 | |
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448 | #ifdef DEC |
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449 | static void etodec (), todec (), dectoe (); |
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450 | #endif |
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451 | |
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452 | /* |
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453 | ; Clear out entire external format number. |
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454 | ; |
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455 | ; unsigned short x[]; |
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456 | ; eclear( x ); |
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457 | */ |
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458 | |
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459 | static void |
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460 | eclear (register short unsigned int *x) |
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461 | { |
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462 | register int i; |
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463 | |
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464 | for (i = 0; i < NE; i++) |
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465 | *x++ = 0; |
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466 | } |
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467 | |
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468 | |
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469 | |
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470 | /* Move external format number from a to b. |
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471 | * |
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472 | * emov( a, b ); |
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473 | */ |
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474 | |
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475 | static void |
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476 | emov (register const short unsigned int *a, register short unsigned int *b) |
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477 | { |
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478 | register int i; |
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479 | |
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480 | for (i = 0; i < NE; i++) |
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481 | *b++ = *a++; |
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482 | } |
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483 | |
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484 | |
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485 | /* |
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486 | ; Negate external format number |
---|
487 | ; |
---|
488 | ; unsigned short x[NE]; |
---|
489 | ; eneg( x ); |
---|
490 | */ |
---|
491 | |
---|
492 | static void |
---|
493 | eneg (short unsigned int *x) |
---|
494 | { |
---|
495 | |
---|
496 | #ifdef NANS |
---|
497 | if (eisnan (x)) |
---|
498 | return; |
---|
499 | #endif |
---|
500 | x[NE - 1] ^= 0x8000; /* Toggle the sign bit */ |
---|
501 | } |
---|
502 | |
---|
503 | |
---|
504 | |
---|
505 | /* Return 1 if external format number is negative, |
---|
506 | * else return zero. |
---|
507 | */ |
---|
508 | static int |
---|
509 | eisneg (const short unsigned int *x) |
---|
510 | { |
---|
511 | |
---|
512 | #ifdef NANS |
---|
513 | if (eisnan (x)) |
---|
514 | return (0); |
---|
515 | #endif |
---|
516 | if (x[NE - 1] & 0x8000) |
---|
517 | return (1); |
---|
518 | else |
---|
519 | return (0); |
---|
520 | } |
---|
521 | |
---|
522 | |
---|
523 | /* Return 1 if external format number has maximum possible exponent, |
---|
524 | * else return zero. |
---|
525 | */ |
---|
526 | static int |
---|
527 | eisinf (const short unsigned int *x) |
---|
528 | { |
---|
529 | |
---|
530 | if ((x[NE - 1] & 0x7fff) == 0x7fff) |
---|
531 | { |
---|
532 | #ifdef NANS |
---|
533 | if (eisnan (x)) |
---|
534 | return (0); |
---|
535 | #endif |
---|
536 | return (1); |
---|
537 | } |
---|
538 | else |
---|
539 | return (0); |
---|
540 | } |
---|
541 | |
---|
542 | /* Check if e-type number is not a number. |
---|
543 | */ |
---|
544 | static int |
---|
545 | eisnan (const short unsigned int *x) |
---|
546 | { |
---|
547 | |
---|
548 | #ifdef NANS |
---|
549 | int i; |
---|
550 | /* NaN has maximum exponent */ |
---|
551 | if ((x[NE - 1] & 0x7fff) != 0x7fff) |
---|
552 | return (0); |
---|
553 | /* ... and non-zero significand field. */ |
---|
554 | for (i = 0; i < NE - 1; i++) |
---|
555 | { |
---|
556 | if (*x++ != 0) |
---|
557 | return (1); |
---|
558 | } |
---|
559 | #endif |
---|
560 | return (0); |
---|
561 | } |
---|
562 | |
---|
563 | /* |
---|
564 | ; Fill entire number, including exponent and significand, with |
---|
565 | ; largest possible number. These programs implement a saturation |
---|
566 | ; value that is an ordinary, legal number. A special value |
---|
567 | ; "infinity" may also be implemented; this would require tests |
---|
568 | ; for that value and implementation of special rules for arithmetic |
---|
569 | ; operations involving inifinity. |
---|
570 | */ |
---|
571 | |
---|
572 | static void |
---|
573 | einfin (register short unsigned int *x, register LDPARMS * ldp) |
---|
574 | { |
---|
575 | register int i; |
---|
576 | |
---|
577 | #ifdef USE_INFINITY |
---|
578 | for (i = 0; i < NE - 1; i++) |
---|
579 | *x++ = 0; |
---|
580 | *x |= 32767; |
---|
581 | ldp = ldp; |
---|
582 | #else |
---|
583 | for (i = 0; i < NE - 1; i++) |
---|
584 | *x++ = 0xffff; |
---|
585 | *x |= 32766; |
---|
586 | if (ldp->rndprc < NBITS) |
---|
587 | { |
---|
588 | if (ldp->rndprc == 113) |
---|
589 | { |
---|
590 | *(x - 9) = 0; |
---|
591 | *(x - 8) = 0; |
---|
592 | } |
---|
593 | if (ldp->rndprc == 64) |
---|
594 | { |
---|
595 | *(x - 5) = 0; |
---|
596 | } |
---|
597 | if (ldp->rndprc == 53) |
---|
598 | { |
---|
599 | *(x - 4) = 0xf800; |
---|
600 | } |
---|
601 | else |
---|
602 | { |
---|
603 | *(x - 4) = 0; |
---|
604 | *(x - 3) = 0; |
---|
605 | *(x - 2) = 0xff00; |
---|
606 | } |
---|
607 | } |
---|
608 | #endif |
---|
609 | } |
---|
610 | |
---|
611 | /* Move in external format number, |
---|
612 | * converting it to internal format. |
---|
613 | */ |
---|
614 | static void |
---|
615 | emovi (const short unsigned int *a, short unsigned int *b) |
---|
616 | { |
---|
617 | register const unsigned short *p; |
---|
618 | register unsigned short *q; |
---|
619 | int i; |
---|
620 | |
---|
621 | q = b; |
---|
622 | p = a + (NE - 1); /* point to last word of external number */ |
---|
623 | /* get the sign bit */ |
---|
624 | if (*p & 0x8000) |
---|
625 | *q++ = 0xffff; |
---|
626 | else |
---|
627 | *q++ = 0; |
---|
628 | /* get the exponent */ |
---|
629 | *q = *p--; |
---|
630 | *q++ &= 0x7fff; /* delete the sign bit */ |
---|
631 | #ifdef USE_INFINITY |
---|
632 | if ((*(q - 1) & 0x7fff) == 0x7fff) |
---|
633 | { |
---|
634 | #ifdef NANS |
---|
635 | if (eisnan (a)) |
---|
636 | { |
---|
637 | *q++ = 0; |
---|
638 | for (i = 3; i < NI; i++) |
---|
639 | *q++ = *p--; |
---|
640 | return; |
---|
641 | } |
---|
642 | #endif |
---|
643 | for (i = 2; i < NI; i++) |
---|
644 | *q++ = 0; |
---|
645 | return; |
---|
646 | } |
---|
647 | #endif |
---|
648 | /* clear high guard word */ |
---|
649 | *q++ = 0; |
---|
650 | /* move in the significand */ |
---|
651 | for (i = 0; i < NE - 1; i++) |
---|
652 | *q++ = *p--; |
---|
653 | /* clear low guard word */ |
---|
654 | *q = 0; |
---|
655 | } |
---|
656 | |
---|
657 | |
---|
658 | /* Move internal format number out, |
---|
659 | * converting it to external format. |
---|
660 | */ |
---|
661 | static void |
---|
662 | emovo (short unsigned int *a, short unsigned int *b, LDPARMS * ldp) |
---|
663 | { |
---|
664 | register unsigned short *p, *q; |
---|
665 | unsigned short i; |
---|
666 | |
---|
667 | p = a; |
---|
668 | q = b + (NE - 1); /* point to output exponent */ |
---|
669 | /* combine sign and exponent */ |
---|
670 | i = *p++; |
---|
671 | if (i) |
---|
672 | *q-- = *p++ | 0x8000; |
---|
673 | else |
---|
674 | *q-- = *p++; |
---|
675 | #ifdef USE_INFINITY |
---|
676 | if (*(p - 1) == 0x7fff) |
---|
677 | { |
---|
678 | #ifdef NANS |
---|
679 | if (eiisnan (a)) |
---|
680 | { |
---|
681 | enan (b, NBITS); |
---|
682 | return; |
---|
683 | } |
---|
684 | #endif |
---|
685 | einfin (b, ldp); |
---|
686 | return; |
---|
687 | } |
---|
688 | #endif |
---|
689 | /* skip over guard word */ |
---|
690 | ++p; |
---|
691 | /* move the significand */ |
---|
692 | for (i = 0; i < NE - 1; i++) |
---|
693 | *q-- = *p++; |
---|
694 | } |
---|
695 | |
---|
696 | |
---|
697 | /* Clear out internal format number. |
---|
698 | */ |
---|
699 | |
---|
700 | static void |
---|
701 | ecleaz (register short unsigned int *xi) |
---|
702 | { |
---|
703 | register int i; |
---|
704 | |
---|
705 | for (i = 0; i < NI; i++) |
---|
706 | *xi++ = 0; |
---|
707 | } |
---|
708 | |
---|
709 | /* same, but don't touch the sign. */ |
---|
710 | |
---|
711 | static void |
---|
712 | ecleazs (register short unsigned int *xi) |
---|
713 | { |
---|
714 | register int i; |
---|
715 | |
---|
716 | ++xi; |
---|
717 | for (i = 0; i < NI - 1; i++) |
---|
718 | *xi++ = 0; |
---|
719 | } |
---|
720 | |
---|
721 | |
---|
722 | |
---|
723 | |
---|
724 | /* Move internal format number from a to b. |
---|
725 | */ |
---|
726 | static void |
---|
727 | emovz (register short unsigned int *a, register short unsigned int *b) |
---|
728 | { |
---|
729 | register int i; |
---|
730 | |
---|
731 | for (i = 0; i < NI - 1; i++) |
---|
732 | *b++ = *a++; |
---|
733 | /* clear low guard word */ |
---|
734 | *b = 0; |
---|
735 | } |
---|
736 | |
---|
737 | /* Return nonzero if internal format number is a NaN. |
---|
738 | */ |
---|
739 | |
---|
740 | static int |
---|
741 | eiisnan (short unsigned int *x) |
---|
742 | { |
---|
743 | int i; |
---|
744 | |
---|
745 | if ((x[E] & 0x7fff) == 0x7fff) |
---|
746 | { |
---|
747 | for (i = M + 1; i < NI; i++) |
---|
748 | { |
---|
749 | if (x[i] != 0) |
---|
750 | return (1); |
---|
751 | } |
---|
752 | } |
---|
753 | return (0); |
---|
754 | } |
---|
755 | |
---|
756 | #if LDBL_MANT_DIG == 64 |
---|
757 | |
---|
758 | /* Return nonzero if internal format number is infinite. */ |
---|
759 | static int |
---|
760 | eiisinf (unsigned short x[]) |
---|
761 | { |
---|
762 | |
---|
763 | #ifdef NANS |
---|
764 | if (eiisnan (x)) |
---|
765 | return (0); |
---|
766 | #endif |
---|
767 | if ((x[E] & 0x7fff) == 0x7fff) |
---|
768 | return (1); |
---|
769 | return (0); |
---|
770 | } |
---|
771 | #endif /* LDBL_MANT_DIG == 64 */ |
---|
772 | |
---|
773 | /* |
---|
774 | ; Compare significands of numbers in internal format. |
---|
775 | ; Guard words are included in the comparison. |
---|
776 | ; |
---|
777 | ; unsigned short a[NI], b[NI]; |
---|
778 | ; cmpm( a, b ); |
---|
779 | ; |
---|
780 | ; for the significands: |
---|
781 | ; returns +1 if a > b |
---|
782 | ; 0 if a == b |
---|
783 | ; -1 if a < b |
---|
784 | */ |
---|
785 | static int |
---|
786 | ecmpm (register short unsigned int *a, register short unsigned int *b) |
---|
787 | { |
---|
788 | int i; |
---|
789 | |
---|
790 | a += M; /* skip up to significand area */ |
---|
791 | b += M; |
---|
792 | for (i = M; i < NI; i++) |
---|
793 | { |
---|
794 | if (*a++ != *b++) |
---|
795 | goto difrnt; |
---|
796 | } |
---|
797 | return (0); |
---|
798 | |
---|
799 | difrnt: |
---|
800 | if (*(--a) > *(--b)) |
---|
801 | return (1); |
---|
802 | else |
---|
803 | return (-1); |
---|
804 | } |
---|
805 | |
---|
806 | |
---|
807 | /* |
---|
808 | ; Shift significand down by 1 bit |
---|
809 | */ |
---|
810 | |
---|
811 | static void |
---|
812 | eshdn1 (register short unsigned int *x) |
---|
813 | { |
---|
814 | register unsigned short bits; |
---|
815 | int i; |
---|
816 | |
---|
817 | x += M; /* point to significand area */ |
---|
818 | |
---|
819 | bits = 0; |
---|
820 | for (i = M; i < NI; i++) |
---|
821 | { |
---|
822 | if (*x & 1) |
---|
823 | bits |= 1; |
---|
824 | *x >>= 1; |
---|
825 | if (bits & 2) |
---|
826 | *x |= 0x8000; |
---|
827 | bits <<= 1; |
---|
828 | ++x; |
---|
829 | } |
---|
830 | } |
---|
831 | |
---|
832 | |
---|
833 | |
---|
834 | /* |
---|
835 | ; Shift significand up by 1 bit |
---|
836 | */ |
---|
837 | |
---|
838 | static void |
---|
839 | eshup1 (register short unsigned int *x) |
---|
840 | { |
---|
841 | register unsigned short bits; |
---|
842 | int i; |
---|
843 | |
---|
844 | x += NI - 1; |
---|
845 | bits = 0; |
---|
846 | |
---|
847 | for (i = M; i < NI; i++) |
---|
848 | { |
---|
849 | if (*x & 0x8000) |
---|
850 | bits |= 1; |
---|
851 | *x <<= 1; |
---|
852 | if (bits & 2) |
---|
853 | *x |= 1; |
---|
854 | bits <<= 1; |
---|
855 | --x; |
---|
856 | } |
---|
857 | } |
---|
858 | |
---|
859 | |
---|
860 | |
---|
861 | /* |
---|
862 | ; Shift significand down by 8 bits |
---|
863 | */ |
---|
864 | |
---|
865 | static void |
---|
866 | eshdn8 (register short unsigned int *x) |
---|
867 | { |
---|
868 | register unsigned short newbyt, oldbyt; |
---|
869 | int i; |
---|
870 | |
---|
871 | x += M; |
---|
872 | oldbyt = 0; |
---|
873 | for (i = M; i < NI; i++) |
---|
874 | { |
---|
875 | newbyt = *x << 8; |
---|
876 | *x >>= 8; |
---|
877 | *x |= oldbyt; |
---|
878 | oldbyt = newbyt; |
---|
879 | ++x; |
---|
880 | } |
---|
881 | } |
---|
882 | |
---|
883 | /* |
---|
884 | ; Shift significand up by 8 bits |
---|
885 | */ |
---|
886 | |
---|
887 | static void |
---|
888 | eshup8 (register short unsigned int *x) |
---|
889 | { |
---|
890 | int i; |
---|
891 | register unsigned short newbyt, oldbyt; |
---|
892 | |
---|
893 | x += NI - 1; |
---|
894 | oldbyt = 0; |
---|
895 | |
---|
896 | for (i = M; i < NI; i++) |
---|
897 | { |
---|
898 | newbyt = *x >> 8; |
---|
899 | *x <<= 8; |
---|
900 | *x |= oldbyt; |
---|
901 | oldbyt = newbyt; |
---|
902 | --x; |
---|
903 | } |
---|
904 | } |
---|
905 | |
---|
906 | /* |
---|
907 | ; Shift significand up by 16 bits |
---|
908 | */ |
---|
909 | |
---|
910 | static void |
---|
911 | eshup6 (register short unsigned int *x) |
---|
912 | { |
---|
913 | int i; |
---|
914 | register unsigned short *p; |
---|
915 | |
---|
916 | p = x + M; |
---|
917 | x += M + 1; |
---|
918 | |
---|
919 | for (i = M; i < NI - 1; i++) |
---|
920 | *p++ = *x++; |
---|
921 | |
---|
922 | *p = 0; |
---|
923 | } |
---|
924 | |
---|
925 | /* |
---|
926 | ; Shift significand down by 16 bits |
---|
927 | */ |
---|
928 | |
---|
929 | static void |
---|
930 | eshdn6 (register short unsigned int *x) |
---|
931 | { |
---|
932 | int i; |
---|
933 | register unsigned short *p; |
---|
934 | |
---|
935 | x += NI - 1; |
---|
936 | p = x + 1; |
---|
937 | |
---|
938 | for (i = M; i < NI - 1; i++) |
---|
939 | *(--p) = *(--x); |
---|
940 | |
---|
941 | *(--p) = 0; |
---|
942 | } |
---|
943 | |
---|
944 | /* |
---|
945 | ; Add significands |
---|
946 | ; x + y replaces y |
---|
947 | */ |
---|
948 | |
---|
949 | static void |
---|
950 | eaddm (short unsigned int *x, short unsigned int *y) |
---|
951 | { |
---|
952 | register unsigned long a; |
---|
953 | int i; |
---|
954 | unsigned int carry; |
---|
955 | |
---|
956 | x += NI - 1; |
---|
957 | y += NI - 1; |
---|
958 | carry = 0; |
---|
959 | for (i = M; i < NI; i++) |
---|
960 | { |
---|
961 | a = (unsigned long) (*x) + (unsigned long) (*y) + carry; |
---|
962 | if (a & 0x10000) |
---|
963 | carry = 1; |
---|
964 | else |
---|
965 | carry = 0; |
---|
966 | *y = (unsigned short) a; |
---|
967 | --x; |
---|
968 | --y; |
---|
969 | } |
---|
970 | } |
---|
971 | |
---|
972 | /* |
---|
973 | ; Subtract significands |
---|
974 | ; y - x replaces y |
---|
975 | */ |
---|
976 | |
---|
977 | static void |
---|
978 | esubm (short unsigned int *x, short unsigned int *y) |
---|
979 | { |
---|
980 | unsigned long a; |
---|
981 | int i; |
---|
982 | unsigned int carry; |
---|
983 | |
---|
984 | x += NI - 1; |
---|
985 | y += NI - 1; |
---|
986 | carry = 0; |
---|
987 | for (i = M; i < NI; i++) |
---|
988 | { |
---|
989 | a = (unsigned long) (*y) - (unsigned long) (*x) - carry; |
---|
990 | if (a & 0x10000) |
---|
991 | carry = 1; |
---|
992 | else |
---|
993 | carry = 0; |
---|
994 | *y = (unsigned short) a; |
---|
995 | --x; |
---|
996 | --y; |
---|
997 | } |
---|
998 | } |
---|
999 | |
---|
1000 | |
---|
1001 | /* Divide significands */ |
---|
1002 | |
---|
1003 | |
---|
1004 | /* Multiply significand of e-type number b |
---|
1005 | by 16-bit quantity a, e-type result to c. */ |
---|
1006 | |
---|
1007 | static void |
---|
1008 | m16m (short unsigned int a, short unsigned int *b, short unsigned int *c) |
---|
1009 | { |
---|
1010 | register unsigned short *pp; |
---|
1011 | register unsigned long carry; |
---|
1012 | unsigned short *ps; |
---|
1013 | unsigned short p[NI]; |
---|
1014 | unsigned long aa, m; |
---|
1015 | int i; |
---|
1016 | |
---|
1017 | aa = a; |
---|
1018 | pp = &p[NI - 2]; |
---|
1019 | *pp++ = 0; |
---|
1020 | *pp = 0; |
---|
1021 | ps = &b[NI - 1]; |
---|
1022 | |
---|
1023 | for (i = M + 1; i < NI; i++) |
---|
1024 | { |
---|
1025 | if (*ps == 0) |
---|
1026 | { |
---|
1027 | --ps; |
---|
1028 | --pp; |
---|
1029 | *(pp - 1) = 0; |
---|
1030 | } |
---|
1031 | else |
---|
1032 | { |
---|
1033 | m = (unsigned long) aa **ps--; |
---|
1034 | carry = (m & 0xffff) + *pp; |
---|
1035 | *pp-- = (unsigned short) carry; |
---|
1036 | carry = (carry >> 16) + (m >> 16) + *pp; |
---|
1037 | *pp = (unsigned short) carry; |
---|
1038 | *(pp - 1) = carry >> 16; |
---|
1039 | } |
---|
1040 | } |
---|
1041 | for (i = M; i < NI; i++) |
---|
1042 | c[i] = p[i]; |
---|
1043 | } |
---|
1044 | |
---|
1045 | |
---|
1046 | /* Divide significands. Neither the numerator nor the denominator |
---|
1047 | is permitted to have its high guard word nonzero. */ |
---|
1048 | |
---|
1049 | |
---|
1050 | static int |
---|
1051 | edivm (short unsigned int *den, short unsigned int *num, LDPARMS * ldp) |
---|
1052 | { |
---|
1053 | int i; |
---|
1054 | register unsigned short *p; |
---|
1055 | unsigned long tnum; |
---|
1056 | unsigned short j, tdenm, tquot; |
---|
1057 | unsigned short tprod[NI + 1]; |
---|
1058 | unsigned short *equot = ldp->equot; |
---|
1059 | |
---|
1060 | p = &equot[0]; |
---|
1061 | *p++ = num[0]; |
---|
1062 | *p++ = num[1]; |
---|
1063 | |
---|
1064 | for (i = M; i < NI; i++) |
---|
1065 | { |
---|
1066 | *p++ = 0; |
---|
1067 | } |
---|
1068 | eshdn1 (num); |
---|
1069 | tdenm = den[M + 1]; |
---|
1070 | for (i = M; i < NI; i++) |
---|
1071 | { |
---|
1072 | /* Find trial quotient digit (the radix is 65536). */ |
---|
1073 | tnum = (((unsigned long) num[M]) << 16) + num[M + 1]; |
---|
1074 | |
---|
1075 | /* Do not execute the divide instruction if it will overflow. */ |
---|
1076 | if ((tdenm * 0xffffUL) < tnum) |
---|
1077 | tquot = 0xffff; |
---|
1078 | else |
---|
1079 | tquot = tnum / tdenm; |
---|
1080 | |
---|
1081 | /* Prove that the divide worked. */ |
---|
1082 | /* |
---|
1083 | tcheck = (unsigned long )tquot * tdenm; |
---|
1084 | if( tnum - tcheck > tdenm ) |
---|
1085 | tquot = 0xffff; |
---|
1086 | */ |
---|
1087 | /* Multiply denominator by trial quotient digit. */ |
---|
1088 | m16m (tquot, den, tprod); |
---|
1089 | /* The quotient digit may have been overestimated. */ |
---|
1090 | if (ecmpm (tprod, num) > 0) |
---|
1091 | { |
---|
1092 | tquot -= 1; |
---|
1093 | esubm (den, tprod); |
---|
1094 | if (ecmpm (tprod, num) > 0) |
---|
1095 | { |
---|
1096 | tquot -= 1; |
---|
1097 | esubm (den, tprod); |
---|
1098 | } |
---|
1099 | } |
---|
1100 | /* |
---|
1101 | if( ecmpm( tprod, num ) > 0 ) |
---|
1102 | { |
---|
1103 | eshow( "tprod", tprod ); |
---|
1104 | eshow( "num ", num ); |
---|
1105 | printf( "tnum = %08lx, tden = %04x, tquot = %04x\n", |
---|
1106 | tnum, den[M+1], tquot ); |
---|
1107 | } |
---|
1108 | */ |
---|
1109 | esubm (tprod, num); |
---|
1110 | /* |
---|
1111 | if( ecmpm( num, den ) >= 0 ) |
---|
1112 | { |
---|
1113 | eshow( "num ", num ); |
---|
1114 | eshow( "den ", den ); |
---|
1115 | printf( "tnum = %08lx, tden = %04x, tquot = %04x\n", |
---|
1116 | tnum, den[M+1], tquot ); |
---|
1117 | } |
---|
1118 | */ |
---|
1119 | equot[i] = tquot; |
---|
1120 | eshup6 (num); |
---|
1121 | } |
---|
1122 | /* test for nonzero remainder after roundoff bit */ |
---|
1123 | p = &num[M]; |
---|
1124 | j = 0; |
---|
1125 | for (i = M; i < NI; i++) |
---|
1126 | { |
---|
1127 | j |= *p++; |
---|
1128 | } |
---|
1129 | if (j) |
---|
1130 | j = 1; |
---|
1131 | |
---|
1132 | for (i = 0; i < NI; i++) |
---|
1133 | num[i] = equot[i]; |
---|
1134 | |
---|
1135 | return ((int) j); |
---|
1136 | } |
---|
1137 | |
---|
1138 | |
---|
1139 | |
---|
1140 | /* Multiply significands */ |
---|
1141 | static int |
---|
1142 | emulm (short unsigned int *a, short unsigned int *b, LDPARMS * ldp) |
---|
1143 | { |
---|
1144 | unsigned short *p, *q; |
---|
1145 | unsigned short pprod[NI]; |
---|
1146 | unsigned short j; |
---|
1147 | int i; |
---|
1148 | unsigned short *equot = ldp->equot; |
---|
1149 | |
---|
1150 | equot[0] = b[0]; |
---|
1151 | equot[1] = b[1]; |
---|
1152 | for (i = M; i < NI; i++) |
---|
1153 | equot[i] = 0; |
---|
1154 | |
---|
1155 | j = 0; |
---|
1156 | p = &a[NI - 1]; |
---|
1157 | q = &equot[NI - 1]; |
---|
1158 | for (i = M + 1; i < NI; i++) |
---|
1159 | { |
---|
1160 | if (*p == 0) |
---|
1161 | { |
---|
1162 | --p; |
---|
1163 | } |
---|
1164 | else |
---|
1165 | { |
---|
1166 | m16m (*p--, b, pprod); |
---|
1167 | eaddm (pprod, equot); |
---|
1168 | } |
---|
1169 | j |= *q; |
---|
1170 | eshdn6 (equot); |
---|
1171 | } |
---|
1172 | |
---|
1173 | for (i = 0; i < NI; i++) |
---|
1174 | b[i] = equot[i]; |
---|
1175 | |
---|
1176 | /* return flag for lost nonzero bits */ |
---|
1177 | return ((int) j); |
---|
1178 | } |
---|
1179 | |
---|
1180 | |
---|
1181 | /* |
---|
1182 | static void eshow(str, x) |
---|
1183 | char *str; |
---|
1184 | unsigned short *x; |
---|
1185 | { |
---|
1186 | int i; |
---|
1187 | |
---|
1188 | printf( "%s ", str ); |
---|
1189 | for( i=0; i<NI; i++ ) |
---|
1190 | printf( "%04x ", *x++ ); |
---|
1191 | printf( "\n" ); |
---|
1192 | } |
---|
1193 | */ |
---|
1194 | |
---|
1195 | |
---|
1196 | /* |
---|
1197 | * Normalize and round off. |
---|
1198 | * |
---|
1199 | * The internal format number to be rounded is "s". |
---|
1200 | * Input "lost" indicates whether the number is exact. |
---|
1201 | * This is the so-called sticky bit. |
---|
1202 | * |
---|
1203 | * Input "subflg" indicates whether the number was obtained |
---|
1204 | * by a subtraction operation. In that case if lost is nonzero |
---|
1205 | * then the number is slightly smaller than indicated. |
---|
1206 | * |
---|
1207 | * Input "exp" is the biased exponent, which may be negative. |
---|
1208 | * the exponent field of "s" is ignored but is replaced by |
---|
1209 | * "exp" as adjusted by normalization and rounding. |
---|
1210 | * |
---|
1211 | * Input "rcntrl" is the rounding control. |
---|
1212 | */ |
---|
1213 | |
---|
1214 | |
---|
1215 | static void |
---|
1216 | emdnorm (short unsigned int *s, int lost, int subflg, long int exp, |
---|
1217 | int rcntrl, LDPARMS * ldp) |
---|
1218 | { |
---|
1219 | int i, j; |
---|
1220 | unsigned short r; |
---|
1221 | |
---|
1222 | /* Normalize */ |
---|
1223 | j = enormlz (s); |
---|
1224 | |
---|
1225 | /* a blank significand could mean either zero or infinity. */ |
---|
1226 | #ifndef USE_INFINITY |
---|
1227 | if (j > NBITS) |
---|
1228 | { |
---|
1229 | ecleazs (s); |
---|
1230 | return; |
---|
1231 | } |
---|
1232 | #endif |
---|
1233 | exp -= j; |
---|
1234 | #ifndef USE_INFINITY |
---|
1235 | if (exp >= 32767L) |
---|
1236 | goto overf; |
---|
1237 | #else |
---|
1238 | if ((j > NBITS) && (exp < 32767L)) |
---|
1239 | { |
---|
1240 | ecleazs (s); |
---|
1241 | return; |
---|
1242 | } |
---|
1243 | #endif |
---|
1244 | if (exp < 0L) |
---|
1245 | { |
---|
1246 | if (exp > (long) (-NBITS - 1)) |
---|
1247 | { |
---|
1248 | j = (int) exp; |
---|
1249 | i = eshift (s, j); |
---|
1250 | if (i) |
---|
1251 | lost = 1; |
---|
1252 | } |
---|
1253 | else |
---|
1254 | { |
---|
1255 | ecleazs (s); |
---|
1256 | return; |
---|
1257 | } |
---|
1258 | } |
---|
1259 | /* Round off, unless told not to by rcntrl. */ |
---|
1260 | if (rcntrl == 0) |
---|
1261 | goto mdfin; |
---|
1262 | /* Set up rounding parameters if the control register changed. */ |
---|
1263 | if (ldp->rndprc != ldp->rlast) |
---|
1264 | { |
---|
1265 | ecleaz (ldp->rbit); |
---|
1266 | switch (ldp->rndprc) |
---|
1267 | { |
---|
1268 | default: |
---|
1269 | case NBITS: |
---|
1270 | ldp->rw = NI - 1; /* low guard word */ |
---|
1271 | ldp->rmsk = 0xffff; |
---|
1272 | ldp->rmbit = 0x8000; |
---|
1273 | ldp->rebit = 1; |
---|
1274 | ldp->re = ldp->rw - 1; |
---|
1275 | break; |
---|
1276 | case 113: |
---|
1277 | ldp->rw = 10; |
---|
1278 | ldp->rmsk = 0x7fff; |
---|
1279 | ldp->rmbit = 0x4000; |
---|
1280 | ldp->rebit = 0x8000; |
---|
1281 | ldp->re = ldp->rw; |
---|
1282 | break; |
---|
1283 | case 64: |
---|
1284 | ldp->rw = 7; |
---|
1285 | ldp->rmsk = 0xffff; |
---|
1286 | ldp->rmbit = 0x8000; |
---|
1287 | ldp->rebit = 1; |
---|
1288 | ldp->re = ldp->rw - 1; |
---|
1289 | break; |
---|
1290 | /* For DEC arithmetic */ |
---|
1291 | case 56: |
---|
1292 | ldp->rw = 6; |
---|
1293 | ldp->rmsk = 0xff; |
---|
1294 | ldp->rmbit = 0x80; |
---|
1295 | ldp->rebit = 0x100; |
---|
1296 | ldp->re = ldp->rw; |
---|
1297 | break; |
---|
1298 | case 53: |
---|
1299 | ldp->rw = 6; |
---|
1300 | ldp->rmsk = 0x7ff; |
---|
1301 | ldp->rmbit = 0x0400; |
---|
1302 | ldp->rebit = 0x800; |
---|
1303 | ldp->re = ldp->rw; |
---|
1304 | break; |
---|
1305 | case 24: |
---|
1306 | ldp->rw = 4; |
---|
1307 | ldp->rmsk = 0xff; |
---|
1308 | ldp->rmbit = 0x80; |
---|
1309 | ldp->rebit = 0x100; |
---|
1310 | ldp->re = ldp->rw; |
---|
1311 | break; |
---|
1312 | } |
---|
1313 | ldp->rbit[ldp->re] = ldp->rebit; |
---|
1314 | ldp->rlast = ldp->rndprc; |
---|
1315 | } |
---|
1316 | |
---|
1317 | /* Shift down 1 temporarily if the data structure has an implied |
---|
1318 | * most significant bit and the number is denormal. |
---|
1319 | * For rndprc = 64 or NBITS, there is no implied bit. |
---|
1320 | * But Intel long double denormals lose one bit of significance even so. |
---|
1321 | */ |
---|
1322 | #if IBMPC |
---|
1323 | if ((exp <= 0) && (ldp->rndprc != NBITS)) |
---|
1324 | #else |
---|
1325 | if ((exp <= 0) && (ldp->rndprc != 64) && (ldp->rndprc != NBITS)) |
---|
1326 | #endif |
---|
1327 | { |
---|
1328 | lost |= s[NI - 1] & 1; |
---|
1329 | eshdn1 (s); |
---|
1330 | } |
---|
1331 | /* Clear out all bits below the rounding bit, |
---|
1332 | * remembering in r if any were nonzero. |
---|
1333 | */ |
---|
1334 | r = s[ldp->rw] & ldp->rmsk; |
---|
1335 | if (ldp->rndprc < NBITS) |
---|
1336 | { |
---|
1337 | i = ldp->rw + 1; |
---|
1338 | while (i < NI) |
---|
1339 | { |
---|
1340 | if (s[i]) |
---|
1341 | r |= 1; |
---|
1342 | s[i] = 0; |
---|
1343 | ++i; |
---|
1344 | } |
---|
1345 | } |
---|
1346 | s[ldp->rw] &= ~ldp->rmsk; |
---|
1347 | if ((r & ldp->rmbit) != 0) |
---|
1348 | { |
---|
1349 | if (r == ldp->rmbit) |
---|
1350 | { |
---|
1351 | if (lost == 0) |
---|
1352 | { /* round to even */ |
---|
1353 | if ((s[ldp->re] & ldp->rebit) == 0) |
---|
1354 | goto mddone; |
---|
1355 | } |
---|
1356 | else |
---|
1357 | { |
---|
1358 | if (subflg != 0) |
---|
1359 | goto mddone; |
---|
1360 | } |
---|
1361 | } |
---|
1362 | eaddm (ldp->rbit, s); |
---|
1363 | } |
---|
1364 | mddone: |
---|
1365 | #if IBMPC |
---|
1366 | if ((exp <= 0) && (ldp->rndprc != NBITS)) |
---|
1367 | #else |
---|
1368 | if ((exp <= 0) && (ldp->rndprc != 64) && (ldp->rndprc != NBITS)) |
---|
1369 | #endif |
---|
1370 | { |
---|
1371 | eshup1 (s); |
---|
1372 | } |
---|
1373 | if (s[2] != 0) |
---|
1374 | { /* overflow on roundoff */ |
---|
1375 | eshdn1 (s); |
---|
1376 | exp += 1; |
---|
1377 | } |
---|
1378 | mdfin: |
---|
1379 | s[NI - 1] = 0; |
---|
1380 | if (exp >= 32767L) |
---|
1381 | { |
---|
1382 | #ifndef USE_INFINITY |
---|
1383 | overf: |
---|
1384 | #endif |
---|
1385 | #ifdef USE_INFINITY |
---|
1386 | s[1] = 32767; |
---|
1387 | for (i = 2; i < NI - 1; i++) |
---|
1388 | s[i] = 0; |
---|
1389 | #else |
---|
1390 | s[1] = 32766; |
---|
1391 | s[2] = 0; |
---|
1392 | for (i = M + 1; i < NI - 1; i++) |
---|
1393 | s[i] = 0xffff; |
---|
1394 | s[NI - 1] = 0; |
---|
1395 | if ((ldp->rndprc < 64) || (ldp->rndprc == 113)) |
---|
1396 | { |
---|
1397 | s[ldp->rw] &= ~ldp->rmsk; |
---|
1398 | if (ldp->rndprc == 24) |
---|
1399 | { |
---|
1400 | s[5] = 0; |
---|
1401 | s[6] = 0; |
---|
1402 | } |
---|
1403 | } |
---|
1404 | #endif |
---|
1405 | return; |
---|
1406 | } |
---|
1407 | if (exp < 0) |
---|
1408 | s[1] = 0; |
---|
1409 | else |
---|
1410 | s[1] = (unsigned short) exp; |
---|
1411 | } |
---|
1412 | |
---|
1413 | |
---|
1414 | |
---|
1415 | /* |
---|
1416 | ; Subtract external format numbers. |
---|
1417 | ; |
---|
1418 | ; unsigned short a[NE], b[NE], c[NE]; |
---|
1419 | ; LDPARMS *ldp; |
---|
1420 | ; esub( a, b, c, ldp ); c = b - a |
---|
1421 | */ |
---|
1422 | |
---|
1423 | static void |
---|
1424 | esub (const short unsigned int *a, const short unsigned int *b, |
---|
1425 | short unsigned int *c, LDPARMS * ldp) |
---|
1426 | { |
---|
1427 | |
---|
1428 | #ifdef NANS |
---|
1429 | if (eisnan (a)) |
---|
1430 | { |
---|
1431 | emov (a, c); |
---|
1432 | return; |
---|
1433 | } |
---|
1434 | if (eisnan (b)) |
---|
1435 | { |
---|
1436 | emov (b, c); |
---|
1437 | return; |
---|
1438 | } |
---|
1439 | /* Infinity minus infinity is a NaN. |
---|
1440 | * Test for subtracting infinities of the same sign. |
---|
1441 | */ |
---|
1442 | if (eisinf (a) && eisinf (b) && ((eisneg (a) ^ eisneg (b)) == 0)) |
---|
1443 | { |
---|
1444 | mtherr ("esub", DOMAIN); |
---|
1445 | enan (c, NBITS); |
---|
1446 | return; |
---|
1447 | } |
---|
1448 | #endif |
---|
1449 | eadd1 (a, b, c, 1, ldp); |
---|
1450 | } |
---|
1451 | |
---|
1452 | |
---|
1453 | |
---|
1454 | static void |
---|
1455 | eadd1 (const short unsigned int *a, const short unsigned int *b, |
---|
1456 | short unsigned int *c, int subflg, LDPARMS * ldp) |
---|
1457 | { |
---|
1458 | unsigned short ai[NI], bi[NI], ci[NI]; |
---|
1459 | int i, lost, j, k; |
---|
1460 | long lt, lta, ltb; |
---|
1461 | |
---|
1462 | #ifdef USE_INFINITY |
---|
1463 | if (eisinf (a)) |
---|
1464 | { |
---|
1465 | emov (a, c); |
---|
1466 | if (subflg) |
---|
1467 | eneg (c); |
---|
1468 | return; |
---|
1469 | } |
---|
1470 | if (eisinf (b)) |
---|
1471 | { |
---|
1472 | emov (b, c); |
---|
1473 | return; |
---|
1474 | } |
---|
1475 | #endif |
---|
1476 | emovi (a, ai); |
---|
1477 | emovi (b, bi); |
---|
1478 | if (subflg) |
---|
1479 | ai[0] = ~ai[0]; |
---|
1480 | |
---|
1481 | /* compare exponents */ |
---|
1482 | lta = ai[E]; |
---|
1483 | ltb = bi[E]; |
---|
1484 | lt = lta - ltb; |
---|
1485 | if (lt > 0L) |
---|
1486 | { /* put the larger number in bi */ |
---|
1487 | emovz (bi, ci); |
---|
1488 | emovz (ai, bi); |
---|
1489 | emovz (ci, ai); |
---|
1490 | ltb = bi[E]; |
---|
1491 | lt = -lt; |
---|
1492 | } |
---|
1493 | lost = 0; |
---|
1494 | if (lt != 0L) |
---|
1495 | { |
---|
1496 | if (lt < (long) (-NBITS - 1)) |
---|
1497 | goto done; /* answer same as larger addend */ |
---|
1498 | k = (int) lt; |
---|
1499 | lost = eshift (ai, k); /* shift the smaller number down */ |
---|
1500 | } |
---|
1501 | else |
---|
1502 | { |
---|
1503 | /* exponents were the same, so must compare significands */ |
---|
1504 | i = ecmpm (ai, bi); |
---|
1505 | if (i == 0) |
---|
1506 | { /* the numbers are identical in magnitude */ |
---|
1507 | /* if different signs, result is zero */ |
---|
1508 | if (ai[0] != bi[0]) |
---|
1509 | { |
---|
1510 | eclear (c); |
---|
1511 | return; |
---|
1512 | } |
---|
1513 | /* if same sign, result is double */ |
---|
1514 | /* double denomalized tiny number */ |
---|
1515 | if ((bi[E] == 0) && ((bi[3] & 0x8000) == 0)) |
---|
1516 | { |
---|
1517 | eshup1 (bi); |
---|
1518 | goto done; |
---|
1519 | } |
---|
1520 | /* add 1 to exponent unless both are zero! */ |
---|
1521 | for (j = 1; j < NI - 1; j++) |
---|
1522 | { |
---|
1523 | if (bi[j] != 0) |
---|
1524 | { |
---|
1525 | /* This could overflow, but let emovo take care of that. */ |
---|
1526 | ltb += 1; |
---|
1527 | break; |
---|
1528 | } |
---|
1529 | } |
---|
1530 | bi[E] = (unsigned short) ltb; |
---|
1531 | goto done; |
---|
1532 | } |
---|
1533 | if (i > 0) |
---|
1534 | { /* put the larger number in bi */ |
---|
1535 | emovz (bi, ci); |
---|
1536 | emovz (ai, bi); |
---|
1537 | emovz (ci, ai); |
---|
1538 | } |
---|
1539 | } |
---|
1540 | if (ai[0] == bi[0]) |
---|
1541 | { |
---|
1542 | eaddm (ai, bi); |
---|
1543 | subflg = 0; |
---|
1544 | } |
---|
1545 | else |
---|
1546 | { |
---|
1547 | esubm (ai, bi); |
---|
1548 | subflg = 1; |
---|
1549 | } |
---|
1550 | emdnorm (bi, lost, subflg, ltb, 64, ldp); |
---|
1551 | |
---|
1552 | done: |
---|
1553 | emovo (bi, c, ldp); |
---|
1554 | } |
---|
1555 | |
---|
1556 | |
---|
1557 | |
---|
1558 | /* |
---|
1559 | ; Divide. |
---|
1560 | ; |
---|
1561 | ; unsigned short a[NE], b[NE], c[NE]; |
---|
1562 | ; LDPARMS *ldp; |
---|
1563 | ; ediv( a, b, c, ldp ); c = b / a |
---|
1564 | */ |
---|
1565 | static void |
---|
1566 | ediv (const short unsigned int *a, const short unsigned int *b, |
---|
1567 | short unsigned int *c, LDPARMS * ldp) |
---|
1568 | { |
---|
1569 | unsigned short ai[NI], bi[NI]; |
---|
1570 | int i; |
---|
1571 | long lt, lta, ltb; |
---|
1572 | |
---|
1573 | #ifdef NANS |
---|
1574 | /* Return any NaN input. */ |
---|
1575 | if (eisnan (a)) |
---|
1576 | { |
---|
1577 | emov (a, c); |
---|
1578 | return; |
---|
1579 | } |
---|
1580 | if (eisnan (b)) |
---|
1581 | { |
---|
1582 | emov (b, c); |
---|
1583 | return; |
---|
1584 | } |
---|
1585 | /* Zero over zero, or infinity over infinity, is a NaN. */ |
---|
1586 | if (((ecmp (a, ezero) == 0) && (ecmp (b, ezero) == 0)) |
---|
1587 | || (eisinf (a) && eisinf (b))) |
---|
1588 | { |
---|
1589 | mtherr ("ediv", DOMAIN); |
---|
1590 | enan (c, NBITS); |
---|
1591 | return; |
---|
1592 | } |
---|
1593 | #endif |
---|
1594 | /* Infinity over anything else is infinity. */ |
---|
1595 | #ifdef USE_INFINITY |
---|
1596 | if (eisinf (b)) |
---|
1597 | { |
---|
1598 | if (eisneg (a) ^ eisneg (b)) |
---|
1599 | *(c + (NE - 1)) = 0x8000; |
---|
1600 | else |
---|
1601 | *(c + (NE - 1)) = 0; |
---|
1602 | einfin (c, ldp); |
---|
1603 | return; |
---|
1604 | } |
---|
1605 | if (eisinf (a)) |
---|
1606 | { |
---|
1607 | eclear (c); |
---|
1608 | return; |
---|
1609 | } |
---|
1610 | #endif |
---|
1611 | emovi (a, ai); |
---|
1612 | emovi (b, bi); |
---|
1613 | lta = ai[E]; |
---|
1614 | ltb = bi[E]; |
---|
1615 | if (bi[E] == 0) |
---|
1616 | { /* See if numerator is zero. */ |
---|
1617 | for (i = 1; i < NI - 1; i++) |
---|
1618 | { |
---|
1619 | if (bi[i] != 0) |
---|
1620 | { |
---|
1621 | ltb -= enormlz (bi); |
---|
1622 | goto dnzro1; |
---|
1623 | } |
---|
1624 | } |
---|
1625 | eclear (c); |
---|
1626 | return; |
---|
1627 | } |
---|
1628 | dnzro1: |
---|
1629 | |
---|
1630 | if (ai[E] == 0) |
---|
1631 | { /* possible divide by zero */ |
---|
1632 | for (i = 1; i < NI - 1; i++) |
---|
1633 | { |
---|
1634 | if (ai[i] != 0) |
---|
1635 | { |
---|
1636 | lta -= enormlz (ai); |
---|
1637 | goto dnzro2; |
---|
1638 | } |
---|
1639 | } |
---|
1640 | if (ai[0] == bi[0]) |
---|
1641 | *(c + (NE - 1)) = 0; |
---|
1642 | else |
---|
1643 | *(c + (NE - 1)) = 0x8000; |
---|
1644 | einfin (c, ldp); |
---|
1645 | mtherr ("ediv", SING); |
---|
1646 | return; |
---|
1647 | } |
---|
1648 | dnzro2: |
---|
1649 | |
---|
1650 | i = edivm (ai, bi, ldp); |
---|
1651 | /* calculate exponent */ |
---|
1652 | lt = ltb - lta + EXONE; |
---|
1653 | emdnorm (bi, i, 0, lt, 64, ldp); |
---|
1654 | /* set the sign */ |
---|
1655 | if (ai[0] == bi[0]) |
---|
1656 | bi[0] = 0; |
---|
1657 | else |
---|
1658 | bi[0] = 0Xffff; |
---|
1659 | emovo (bi, c, ldp); |
---|
1660 | } |
---|
1661 | |
---|
1662 | |
---|
1663 | |
---|
1664 | /* |
---|
1665 | ; Multiply. |
---|
1666 | ; |
---|
1667 | ; unsigned short a[NE], b[NE], c[NE]; |
---|
1668 | ; LDPARMS *ldp |
---|
1669 | ; emul( a, b, c, ldp ); c = b * a |
---|
1670 | */ |
---|
1671 | static void |
---|
1672 | emul (const short unsigned int *a, const short unsigned int *b, |
---|
1673 | short unsigned int *c, LDPARMS * ldp) |
---|
1674 | { |
---|
1675 | unsigned short ai[NI], bi[NI]; |
---|
1676 | int i, j; |
---|
1677 | long lt, lta, ltb; |
---|
1678 | |
---|
1679 | #ifdef NANS |
---|
1680 | /* NaN times anything is the same NaN. */ |
---|
1681 | if (eisnan (a)) |
---|
1682 | { |
---|
1683 | emov (a, c); |
---|
1684 | return; |
---|
1685 | } |
---|
1686 | if (eisnan (b)) |
---|
1687 | { |
---|
1688 | emov (b, c); |
---|
1689 | return; |
---|
1690 | } |
---|
1691 | /* Zero times infinity is a NaN. */ |
---|
1692 | if ((eisinf (a) && (ecmp (b, ezero) == 0)) |
---|
1693 | || (eisinf (b) && (ecmp (a, ezero) == 0))) |
---|
1694 | { |
---|
1695 | mtherr ("emul", DOMAIN); |
---|
1696 | enan (c, NBITS); |
---|
1697 | return; |
---|
1698 | } |
---|
1699 | #endif |
---|
1700 | /* Infinity times anything else is infinity. */ |
---|
1701 | #ifdef USE_INFINITY |
---|
1702 | if (eisinf (a) || eisinf (b)) |
---|
1703 | { |
---|
1704 | if (eisneg (a) ^ eisneg (b)) |
---|
1705 | *(c + (NE - 1)) = 0x8000; |
---|
1706 | else |
---|
1707 | *(c + (NE - 1)) = 0; |
---|
1708 | einfin (c, ldp); |
---|
1709 | return; |
---|
1710 | } |
---|
1711 | #endif |
---|
1712 | emovi (a, ai); |
---|
1713 | emovi (b, bi); |
---|
1714 | lta = ai[E]; |
---|
1715 | ltb = bi[E]; |
---|
1716 | if (ai[E] == 0) |
---|
1717 | { |
---|
1718 | for (i = 1; i < NI - 1; i++) |
---|
1719 | { |
---|
1720 | if (ai[i] != 0) |
---|
1721 | { |
---|
1722 | lta -= enormlz (ai); |
---|
1723 | goto mnzer1; |
---|
1724 | } |
---|
1725 | } |
---|
1726 | eclear (c); |
---|
1727 | return; |
---|
1728 | } |
---|
1729 | mnzer1: |
---|
1730 | |
---|
1731 | if (bi[E] == 0) |
---|
1732 | { |
---|
1733 | for (i = 1; i < NI - 1; i++) |
---|
1734 | { |
---|
1735 | if (bi[i] != 0) |
---|
1736 | { |
---|
1737 | ltb -= enormlz (bi); |
---|
1738 | goto mnzer2; |
---|
1739 | } |
---|
1740 | } |
---|
1741 | eclear (c); |
---|
1742 | return; |
---|
1743 | } |
---|
1744 | mnzer2: |
---|
1745 | |
---|
1746 | /* Multiply significands */ |
---|
1747 | j = emulm (ai, bi, ldp); |
---|
1748 | /* calculate exponent */ |
---|
1749 | lt = lta + ltb - (EXONE - 1); |
---|
1750 | emdnorm (bi, j, 0, lt, 64, ldp); |
---|
1751 | /* calculate sign of product */ |
---|
1752 | if (ai[0] == bi[0]) |
---|
1753 | bi[0] = 0; |
---|
1754 | else |
---|
1755 | bi[0] = 0xffff; |
---|
1756 | emovo (bi, c, ldp); |
---|
1757 | } |
---|
1758 | |
---|
1759 | |
---|
1760 | |
---|
1761 | #if LDBL_MANT_DIG > 64 |
---|
1762 | static void |
---|
1763 | e113toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) |
---|
1764 | { |
---|
1765 | register unsigned short r; |
---|
1766 | unsigned short *e, *p; |
---|
1767 | unsigned short yy[NI]; |
---|
1768 | int denorm, i; |
---|
1769 | |
---|
1770 | e = pe; |
---|
1771 | denorm = 0; |
---|
1772 | ecleaz (yy); |
---|
1773 | #ifdef IBMPC |
---|
1774 | e += 7; |
---|
1775 | #endif |
---|
1776 | r = *e; |
---|
1777 | yy[0] = 0; |
---|
1778 | if (r & 0x8000) |
---|
1779 | yy[0] = 0xffff; |
---|
1780 | r &= 0x7fff; |
---|
1781 | #ifdef USE_INFINITY |
---|
1782 | if (r == 0x7fff) |
---|
1783 | { |
---|
1784 | #ifdef NANS |
---|
1785 | #ifdef IBMPC |
---|
1786 | for (i = 0; i < 7; i++) |
---|
1787 | { |
---|
1788 | if (pe[i] != 0) |
---|
1789 | { |
---|
1790 | enan (y, NBITS); |
---|
1791 | return; |
---|
1792 | } |
---|
1793 | } |
---|
1794 | #else /* !IBMPC */ |
---|
1795 | for (i = 1; i < 8; i++) |
---|
1796 | { |
---|
1797 | if (pe[i] != 0) |
---|
1798 | { |
---|
1799 | enan (y, NBITS); |
---|
1800 | return; |
---|
1801 | } |
---|
1802 | } |
---|
1803 | #endif /* !IBMPC */ |
---|
1804 | #endif /* NANS */ |
---|
1805 | eclear (y); |
---|
1806 | einfin (y, ldp); |
---|
1807 | if (*e & 0x8000) |
---|
1808 | eneg (y); |
---|
1809 | return; |
---|
1810 | } |
---|
1811 | #endif /* INFINITY */ |
---|
1812 | yy[E] = r; |
---|
1813 | p = &yy[M + 1]; |
---|
1814 | #ifdef IBMPC |
---|
1815 | for (i = 0; i < 7; i++) |
---|
1816 | *p++ = *(--e); |
---|
1817 | #else /* IBMPC */ |
---|
1818 | ++e; |
---|
1819 | for (i = 0; i < 7; i++) |
---|
1820 | *p++ = *e++; |
---|
1821 | #endif /* IBMPC */ |
---|
1822 | /* If denormal, remove the implied bit; else shift down 1. */ |
---|
1823 | if (r == 0) |
---|
1824 | { |
---|
1825 | yy[M] = 0; |
---|
1826 | } |
---|
1827 | else |
---|
1828 | { |
---|
1829 | yy[M] = 1; |
---|
1830 | eshift (yy, -1); |
---|
1831 | } |
---|
1832 | emovo (yy, y, ldp); |
---|
1833 | } |
---|
1834 | |
---|
1835 | /* move out internal format to ieee long double */ |
---|
1836 | static void |
---|
1837 | toe113 (short unsigned int *a, short unsigned int *b) |
---|
1838 | { |
---|
1839 | register unsigned short *p, *q; |
---|
1840 | unsigned short i; |
---|
1841 | |
---|
1842 | #ifdef NANS |
---|
1843 | if (eiisnan (a)) |
---|
1844 | { |
---|
1845 | enan (b, 113); |
---|
1846 | return; |
---|
1847 | } |
---|
1848 | #endif |
---|
1849 | p = a; |
---|
1850 | #ifdef MIEEE |
---|
1851 | q = b; |
---|
1852 | #else |
---|
1853 | q = b + 7; /* point to output exponent */ |
---|
1854 | #endif |
---|
1855 | |
---|
1856 | /* If not denormal, delete the implied bit. */ |
---|
1857 | if (a[E] != 0) |
---|
1858 | { |
---|
1859 | eshup1 (a); |
---|
1860 | } |
---|
1861 | /* combine sign and exponent */ |
---|
1862 | i = *p++; |
---|
1863 | #ifdef MIEEE |
---|
1864 | if (i) |
---|
1865 | *q++ = *p++ | 0x8000; |
---|
1866 | else |
---|
1867 | *q++ = *p++; |
---|
1868 | #else |
---|
1869 | if (i) |
---|
1870 | *q-- = *p++ | 0x8000; |
---|
1871 | else |
---|
1872 | *q-- = *p++; |
---|
1873 | #endif |
---|
1874 | /* skip over guard word */ |
---|
1875 | ++p; |
---|
1876 | /* move the significand */ |
---|
1877 | #ifdef MIEEE |
---|
1878 | for (i = 0; i < 7; i++) |
---|
1879 | *q++ = *p++; |
---|
1880 | #else |
---|
1881 | for (i = 0; i < 7; i++) |
---|
1882 | *q-- = *p++; |
---|
1883 | #endif |
---|
1884 | } |
---|
1885 | #endif /* LDBL_MANT_DIG > 64 */ |
---|
1886 | |
---|
1887 | |
---|
1888 | #if LDBL_MANT_DIG == 64 |
---|
1889 | static void |
---|
1890 | e64toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) |
---|
1891 | { |
---|
1892 | unsigned short yy[NI]; |
---|
1893 | unsigned short *p, *q, *e; |
---|
1894 | int i; |
---|
1895 | |
---|
1896 | e = pe; |
---|
1897 | p = yy; |
---|
1898 | |
---|
1899 | for (i = 0; i < NE - 5; i++) |
---|
1900 | *p++ = 0; |
---|
1901 | #ifdef IBMPC |
---|
1902 | for (i = 0; i < 5; i++) |
---|
1903 | *p++ = *e++; |
---|
1904 | #endif |
---|
1905 | #ifdef DEC |
---|
1906 | for (i = 0; i < 5; i++) |
---|
1907 | *p++ = *e++; |
---|
1908 | #endif |
---|
1909 | #ifdef MIEEE |
---|
1910 | p = &yy[0] + (NE - 1); |
---|
1911 | *p-- = *e++; |
---|
1912 | ++e; /* MIEEE skips over 2nd short */ |
---|
1913 | for (i = 0; i < 4; i++) |
---|
1914 | *p-- = *e++; |
---|
1915 | #endif |
---|
1916 | |
---|
1917 | #ifdef IBMPC |
---|
1918 | /* For Intel long double, shift denormal significand up 1 |
---|
1919 | -- but only if the top significand bit is zero. */ |
---|
1920 | if ((yy[NE - 1] & 0x7fff) == 0 && (yy[NE - 2] & 0x8000) == 0) |
---|
1921 | { |
---|
1922 | unsigned short temp[NI + 1]; |
---|
1923 | emovi (yy, temp); |
---|
1924 | eshup1 (temp); |
---|
1925 | emovo (temp, y, ldp); |
---|
1926 | return; |
---|
1927 | } |
---|
1928 | #endif |
---|
1929 | #ifdef USE_INFINITY |
---|
1930 | /* Point to the exponent field. */ |
---|
1931 | p = &yy[NE - 1]; |
---|
1932 | if ((*p & 0x7fff) == 0x7fff) |
---|
1933 | { |
---|
1934 | #ifdef NANS |
---|
1935 | #ifdef IBMPC |
---|
1936 | for (i = 0; i < 4; i++) |
---|
1937 | { |
---|
1938 | if ((i != 3 && pe[i] != 0) |
---|
1939 | /* Check for Intel long double infinity pattern. */ |
---|
1940 | || (i == 3 && pe[i] != 0x8000)) |
---|
1941 | { |
---|
1942 | enan (y, NBITS); |
---|
1943 | return; |
---|
1944 | } |
---|
1945 | } |
---|
1946 | #endif |
---|
1947 | #ifdef MIEEE |
---|
1948 | for (i = 2; i <= 5; i++) |
---|
1949 | { |
---|
1950 | if (pe[i] != 0) |
---|
1951 | { |
---|
1952 | enan (y, NBITS); |
---|
1953 | return; |
---|
1954 | } |
---|
1955 | } |
---|
1956 | #endif |
---|
1957 | #endif /* NANS */ |
---|
1958 | eclear (y); |
---|
1959 | einfin (y, ldp); |
---|
1960 | if (*p & 0x8000) |
---|
1961 | eneg (y); |
---|
1962 | return; |
---|
1963 | } |
---|
1964 | #endif /* USE_INFINITY */ |
---|
1965 | p = yy; |
---|
1966 | q = y; |
---|
1967 | for (i = 0; i < NE; i++) |
---|
1968 | *q++ = *p++; |
---|
1969 | } |
---|
1970 | |
---|
1971 | /* move out internal format to ieee long double */ |
---|
1972 | static void |
---|
1973 | toe64 (short unsigned int *a, short unsigned int *b) |
---|
1974 | { |
---|
1975 | register unsigned short *p, *q; |
---|
1976 | unsigned short i; |
---|
1977 | |
---|
1978 | #ifdef NANS |
---|
1979 | if (eiisnan (a)) |
---|
1980 | { |
---|
1981 | enan (b, 64); |
---|
1982 | return; |
---|
1983 | } |
---|
1984 | #endif |
---|
1985 | #ifdef IBMPC |
---|
1986 | /* Shift Intel denormal significand down 1. */ |
---|
1987 | if (a[E] == 0) |
---|
1988 | eshdn1 (a); |
---|
1989 | #endif |
---|
1990 | p = a; |
---|
1991 | #ifdef MIEEE |
---|
1992 | q = b; |
---|
1993 | #else |
---|
1994 | q = b + 4; /* point to output exponent */ |
---|
1995 | /* NOTE: Intel data type is 96 bits wide, clear the last word here. */ |
---|
1996 | *(q + 1) = 0; |
---|
1997 | #endif |
---|
1998 | |
---|
1999 | /* combine sign and exponent */ |
---|
2000 | i = *p++; |
---|
2001 | #ifdef MIEEE |
---|
2002 | if (i) |
---|
2003 | *q++ = *p++ | 0x8000; |
---|
2004 | else |
---|
2005 | *q++ = *p++; |
---|
2006 | *q++ = 0; /* leave 2nd short blank */ |
---|
2007 | #else |
---|
2008 | if (i) |
---|
2009 | *q-- = *p++ | 0x8000; |
---|
2010 | else |
---|
2011 | *q-- = *p++; |
---|
2012 | #endif |
---|
2013 | /* skip over guard word */ |
---|
2014 | ++p; |
---|
2015 | /* move the significand */ |
---|
2016 | #ifdef MIEEE |
---|
2017 | for (i = 0; i < 4; i++) |
---|
2018 | *q++ = *p++; |
---|
2019 | #else |
---|
2020 | #ifdef USE_INFINITY |
---|
2021 | #ifdef IBMPC |
---|
2022 | if (eiisinf (a)) |
---|
2023 | { |
---|
2024 | /* Intel long double infinity. */ |
---|
2025 | *q-- = 0x8000; |
---|
2026 | *q-- = 0; |
---|
2027 | *q-- = 0; |
---|
2028 | *q = 0; |
---|
2029 | return; |
---|
2030 | } |
---|
2031 | #endif /* IBMPC */ |
---|
2032 | #endif /* USE_INFINITY */ |
---|
2033 | for (i = 0; i < 4; i++) |
---|
2034 | *q-- = *p++; |
---|
2035 | #endif |
---|
2036 | } |
---|
2037 | |
---|
2038 | #endif /* LDBL_MANT_DIG == 64 */ |
---|
2039 | |
---|
2040 | #if LDBL_MANT_DIG == 53 |
---|
2041 | /* |
---|
2042 | ; Convert IEEE double precision to e type |
---|
2043 | ; double d; |
---|
2044 | ; unsigned short x[N+2]; |
---|
2045 | ; e53toe( &d, x ); |
---|
2046 | */ |
---|
2047 | static void |
---|
2048 | e53toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) |
---|
2049 | { |
---|
2050 | #ifdef DEC |
---|
2051 | |
---|
2052 | dectoe (pe, y); /* see etodec.c */ |
---|
2053 | |
---|
2054 | #else |
---|
2055 | |
---|
2056 | register unsigned short r; |
---|
2057 | register unsigned short *p, *e; |
---|
2058 | unsigned short yy[NI]; |
---|
2059 | int denorm, k; |
---|
2060 | |
---|
2061 | e = pe; |
---|
2062 | denorm = 0; /* flag if denormalized number */ |
---|
2063 | ecleaz (yy); |
---|
2064 | #ifdef IBMPC |
---|
2065 | e += 3; |
---|
2066 | #endif |
---|
2067 | #ifdef DEC |
---|
2068 | e += 3; |
---|
2069 | #endif |
---|
2070 | r = *e; |
---|
2071 | yy[0] = 0; |
---|
2072 | if (r & 0x8000) |
---|
2073 | yy[0] = 0xffff; |
---|
2074 | yy[M] = (r & 0x0f) | 0x10; |
---|
2075 | r &= ~0x800f; /* strip sign and 4 significand bits */ |
---|
2076 | #ifdef USE_INFINITY |
---|
2077 | if (r == 0x7ff0) |
---|
2078 | { |
---|
2079 | #ifdef NANS |
---|
2080 | #ifdef IBMPC |
---|
2081 | if (((pe[3] & 0xf) != 0) || (pe[2] != 0) |
---|
2082 | || (pe[1] != 0) || (pe[0] != 0)) |
---|
2083 | { |
---|
2084 | enan (y, NBITS); |
---|
2085 | return; |
---|
2086 | } |
---|
2087 | #else /* !IBMPC */ |
---|
2088 | if (((pe[0] & 0xf) != 0) || (pe[1] != 0) |
---|
2089 | || (pe[2] != 0) || (pe[3] != 0)) |
---|
2090 | { |
---|
2091 | enan (y, NBITS); |
---|
2092 | return; |
---|
2093 | } |
---|
2094 | #endif /* !IBMPC */ |
---|
2095 | #endif /* NANS */ |
---|
2096 | eclear (y); |
---|
2097 | einfin (y, ldp); |
---|
2098 | if (yy[0]) |
---|
2099 | eneg (y); |
---|
2100 | return; |
---|
2101 | } |
---|
2102 | #endif |
---|
2103 | r >>= 4; |
---|
2104 | /* If zero exponent, then the significand is denormalized. |
---|
2105 | * So, take back the understood high significand bit. */ |
---|
2106 | if (r == 0) |
---|
2107 | { |
---|
2108 | denorm = 1; |
---|
2109 | yy[M] &= ~0x10; |
---|
2110 | } |
---|
2111 | r += EXONE - 01777; |
---|
2112 | yy[E] = r; |
---|
2113 | p = &yy[M + 1]; |
---|
2114 | #ifdef IBMPC |
---|
2115 | *p++ = *(--e); |
---|
2116 | *p++ = *(--e); |
---|
2117 | *p++ = *(--e); |
---|
2118 | #else /* !IBMPC */ |
---|
2119 | ++e; |
---|
2120 | *p++ = *e++; |
---|
2121 | *p++ = *e++; |
---|
2122 | *p++ = *e++; |
---|
2123 | #endif /* !IBMPC */ |
---|
2124 | (void) eshift (yy, -5); |
---|
2125 | if (denorm) |
---|
2126 | { /* if zero exponent, then normalize the significand */ |
---|
2127 | if ((k = enormlz (yy)) > NBITS) |
---|
2128 | ecleazs (yy); |
---|
2129 | else |
---|
2130 | yy[E] -= (unsigned short) (k - 1); |
---|
2131 | } |
---|
2132 | emovo (yy, y, ldp); |
---|
2133 | #endif /* !DEC */ |
---|
2134 | } |
---|
2135 | |
---|
2136 | /* |
---|
2137 | ; e type to IEEE double precision |
---|
2138 | ; double d; |
---|
2139 | ; unsigned short x[NE]; |
---|
2140 | ; etoe53( x, &d ); |
---|
2141 | */ |
---|
2142 | |
---|
2143 | #ifdef DEC |
---|
2144 | |
---|
2145 | static void |
---|
2146 | etoe53 (x, e) |
---|
2147 | unsigned short *x, *e; |
---|
2148 | { |
---|
2149 | etodec (x, e); /* see etodec.c */ |
---|
2150 | } |
---|
2151 | |
---|
2152 | static void |
---|
2153 | toe53 (x, y) |
---|
2154 | unsigned short *x, *y; |
---|
2155 | { |
---|
2156 | todec (x, y); |
---|
2157 | } |
---|
2158 | |
---|
2159 | #else |
---|
2160 | |
---|
2161 | static void |
---|
2162 | toe53 (short unsigned int *x, short unsigned int *y) |
---|
2163 | { |
---|
2164 | unsigned short i; |
---|
2165 | unsigned short *p; |
---|
2166 | |
---|
2167 | |
---|
2168 | #ifdef NANS |
---|
2169 | if (eiisnan (x)) |
---|
2170 | { |
---|
2171 | enan (y, 53); |
---|
2172 | return; |
---|
2173 | } |
---|
2174 | #endif |
---|
2175 | p = &x[0]; |
---|
2176 | #ifdef IBMPC |
---|
2177 | y += 3; |
---|
2178 | #endif |
---|
2179 | #ifdef DEC |
---|
2180 | y += 3; |
---|
2181 | #endif |
---|
2182 | *y = 0; /* output high order */ |
---|
2183 | if (*p++) |
---|
2184 | *y = 0x8000; /* output sign bit */ |
---|
2185 | |
---|
2186 | i = *p++; |
---|
2187 | if (i >= (unsigned int) 2047) |
---|
2188 | { /* Saturate at largest number less than infinity. */ |
---|
2189 | #ifdef USE_INFINITY |
---|
2190 | *y |= 0x7ff0; |
---|
2191 | #ifdef IBMPC |
---|
2192 | *(--y) = 0; |
---|
2193 | *(--y) = 0; |
---|
2194 | *(--y) = 0; |
---|
2195 | #else /* !IBMPC */ |
---|
2196 | ++y; |
---|
2197 | *y++ = 0; |
---|
2198 | *y++ = 0; |
---|
2199 | *y++ = 0; |
---|
2200 | #endif /* IBMPC */ |
---|
2201 | #else /* !USE_INFINITY */ |
---|
2202 | *y |= (unsigned short) 0x7fef; |
---|
2203 | #ifdef IBMPC |
---|
2204 | *(--y) = 0xffff; |
---|
2205 | *(--y) = 0xffff; |
---|
2206 | *(--y) = 0xffff; |
---|
2207 | #else /* !IBMPC */ |
---|
2208 | ++y; |
---|
2209 | *y++ = 0xffff; |
---|
2210 | *y++ = 0xffff; |
---|
2211 | *y++ = 0xffff; |
---|
2212 | #endif |
---|
2213 | #endif /* !USE_INFINITY */ |
---|
2214 | return; |
---|
2215 | } |
---|
2216 | if (i == 0) |
---|
2217 | { |
---|
2218 | (void) eshift (x, 4); |
---|
2219 | } |
---|
2220 | else |
---|
2221 | { |
---|
2222 | i <<= 4; |
---|
2223 | (void) eshift (x, 5); |
---|
2224 | } |
---|
2225 | i |= *p++ & (unsigned short) 0x0f; /* *p = xi[M] */ |
---|
2226 | *y |= (unsigned short) i; /* high order output already has sign bit set */ |
---|
2227 | #ifdef IBMPC |
---|
2228 | *(--y) = *p++; |
---|
2229 | *(--y) = *p++; |
---|
2230 | *(--y) = *p; |
---|
2231 | #else /* !IBMPC */ |
---|
2232 | ++y; |
---|
2233 | *y++ = *p++; |
---|
2234 | *y++ = *p++; |
---|
2235 | *y++ = *p++; |
---|
2236 | #endif /* !IBMPC */ |
---|
2237 | } |
---|
2238 | |
---|
2239 | #endif /* not DEC */ |
---|
2240 | #endif /* LDBL_MANT_DIG == 53 */ |
---|
2241 | |
---|
2242 | #if LDBL_MANT_DIG == 24 |
---|
2243 | /* |
---|
2244 | ; Convert IEEE single precision to e type |
---|
2245 | ; float d; |
---|
2246 | ; unsigned short x[N+2]; |
---|
2247 | ; dtox( &d, x ); |
---|
2248 | */ |
---|
2249 | void |
---|
2250 | e24toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) |
---|
2251 | { |
---|
2252 | register unsigned short r; |
---|
2253 | register unsigned short *p, *e; |
---|
2254 | unsigned short yy[NI]; |
---|
2255 | int denorm, k; |
---|
2256 | |
---|
2257 | e = pe; |
---|
2258 | denorm = 0; /* flag if denormalized number */ |
---|
2259 | ecleaz (yy); |
---|
2260 | #ifdef IBMPC |
---|
2261 | e += 1; |
---|
2262 | #endif |
---|
2263 | #ifdef DEC |
---|
2264 | e += 1; |
---|
2265 | #endif |
---|
2266 | r = *e; |
---|
2267 | yy[0] = 0; |
---|
2268 | if (r & 0x8000) |
---|
2269 | yy[0] = 0xffff; |
---|
2270 | yy[M] = (r & 0x7f) | 0200; |
---|
2271 | r &= ~0x807f; /* strip sign and 7 significand bits */ |
---|
2272 | #ifdef USE_INFINITY |
---|
2273 | if (r == 0x7f80) |
---|
2274 | { |
---|
2275 | #ifdef NANS |
---|
2276 | #ifdef MIEEE |
---|
2277 | if (((pe[0] & 0x7f) != 0) || (pe[1] != 0)) |
---|
2278 | { |
---|
2279 | enan (y, NBITS); |
---|
2280 | return; |
---|
2281 | } |
---|
2282 | #else /* !MIEEE */ |
---|
2283 | if (((pe[1] & 0x7f) != 0) || (pe[0] != 0)) |
---|
2284 | { |
---|
2285 | enan (y, NBITS); |
---|
2286 | return; |
---|
2287 | } |
---|
2288 | #endif /* !MIEEE */ |
---|
2289 | #endif /* NANS */ |
---|
2290 | eclear (y); |
---|
2291 | einfin (y, ldp); |
---|
2292 | if (yy[0]) |
---|
2293 | eneg (y); |
---|
2294 | return; |
---|
2295 | } |
---|
2296 | #endif |
---|
2297 | r >>= 7; |
---|
2298 | /* If zero exponent, then the significand is denormalized. |
---|
2299 | * So, take back the understood high significand bit. */ |
---|
2300 | if (r == 0) |
---|
2301 | { |
---|
2302 | denorm = 1; |
---|
2303 | yy[M] &= ~0200; |
---|
2304 | } |
---|
2305 | r += EXONE - 0177; |
---|
2306 | yy[E] = r; |
---|
2307 | p = &yy[M + 1]; |
---|
2308 | #ifdef IBMPC |
---|
2309 | *p++ = *(--e); |
---|
2310 | #endif |
---|
2311 | #ifdef DEC |
---|
2312 | *p++ = *(--e); |
---|
2313 | #endif |
---|
2314 | #ifdef MIEEE |
---|
2315 | ++e; |
---|
2316 | *p++ = *e++; |
---|
2317 | #endif |
---|
2318 | (void) eshift (yy, -8); |
---|
2319 | if (denorm) |
---|
2320 | { /* if zero exponent, then normalize the significand */ |
---|
2321 | if ((k = enormlz (yy)) > NBITS) |
---|
2322 | ecleazs (yy); |
---|
2323 | else |
---|
2324 | yy[E] -= (unsigned short) (k - 1); |
---|
2325 | } |
---|
2326 | emovo (yy, y, ldp); |
---|
2327 | } |
---|
2328 | |
---|
2329 | static void |
---|
2330 | toe24 (short unsigned int *x, short unsigned int *y) |
---|
2331 | { |
---|
2332 | unsigned short i; |
---|
2333 | unsigned short *p; |
---|
2334 | |
---|
2335 | #ifdef NANS |
---|
2336 | if (eiisnan (x)) |
---|
2337 | { |
---|
2338 | enan (y, 24); |
---|
2339 | return; |
---|
2340 | } |
---|
2341 | #endif |
---|
2342 | p = &x[0]; |
---|
2343 | #ifdef IBMPC |
---|
2344 | y += 1; |
---|
2345 | #endif |
---|
2346 | #ifdef DEC |
---|
2347 | y += 1; |
---|
2348 | #endif |
---|
2349 | *y = 0; /* output high order */ |
---|
2350 | if (*p++) |
---|
2351 | *y = 0x8000; /* output sign bit */ |
---|
2352 | |
---|
2353 | i = *p++; |
---|
2354 | if (i >= 255) |
---|
2355 | { /* Saturate at largest number less than infinity. */ |
---|
2356 | #ifdef USE_INFINITY |
---|
2357 | *y |= (unsigned short) 0x7f80; |
---|
2358 | #ifdef IBMPC |
---|
2359 | *(--y) = 0; |
---|
2360 | #endif |
---|
2361 | #ifdef DEC |
---|
2362 | *(--y) = 0; |
---|
2363 | #endif |
---|
2364 | #ifdef MIEEE |
---|
2365 | ++y; |
---|
2366 | *y = 0; |
---|
2367 | #endif |
---|
2368 | #else /* !USE_INFINITY */ |
---|
2369 | *y |= (unsigned short) 0x7f7f; |
---|
2370 | #ifdef IBMPC |
---|
2371 | *(--y) = 0xffff; |
---|
2372 | #endif |
---|
2373 | #ifdef DEC |
---|
2374 | *(--y) = 0xffff; |
---|
2375 | #endif |
---|
2376 | #ifdef MIEEE |
---|
2377 | ++y; |
---|
2378 | *y = 0xffff; |
---|
2379 | #endif |
---|
2380 | #endif /* !USE_INFINITY */ |
---|
2381 | return; |
---|
2382 | } |
---|
2383 | if (i == 0) |
---|
2384 | { |
---|
2385 | (void) eshift (x, 7); |
---|
2386 | } |
---|
2387 | else |
---|
2388 | { |
---|
2389 | i <<= 7; |
---|
2390 | (void) eshift (x, 8); |
---|
2391 | } |
---|
2392 | i |= *p++ & (unsigned short) 0x7f; /* *p = xi[M] */ |
---|
2393 | *y |= i; /* high order output already has sign bit set */ |
---|
2394 | #ifdef IBMPC |
---|
2395 | *(--y) = *p; |
---|
2396 | #endif |
---|
2397 | #ifdef DEC |
---|
2398 | *(--y) = *p; |
---|
2399 | #endif |
---|
2400 | #ifdef MIEEE |
---|
2401 | ++y; |
---|
2402 | *y = *p; |
---|
2403 | #endif |
---|
2404 | } |
---|
2405 | #endif /* LDBL_MANT_DIG == 24 */ |
---|
2406 | |
---|
2407 | /* Compare two e type numbers. |
---|
2408 | * |
---|
2409 | * unsigned short a[NE], b[NE]; |
---|
2410 | * ecmp( a, b ); |
---|
2411 | * |
---|
2412 | * returns +1 if a > b |
---|
2413 | * 0 if a == b |
---|
2414 | * -1 if a < b |
---|
2415 | * -2 if either a or b is a NaN. |
---|
2416 | */ |
---|
2417 | static int |
---|
2418 | ecmp (const short unsigned int *a, const short unsigned int *b) |
---|
2419 | { |
---|
2420 | unsigned short ai[NI], bi[NI]; |
---|
2421 | register unsigned short *p, *q; |
---|
2422 | register int i; |
---|
2423 | int msign; |
---|
2424 | |
---|
2425 | #ifdef NANS |
---|
2426 | if (eisnan (a) || eisnan (b)) |
---|
2427 | return (-2); |
---|
2428 | #endif |
---|
2429 | emovi (a, ai); |
---|
2430 | p = ai; |
---|
2431 | emovi (b, bi); |
---|
2432 | q = bi; |
---|
2433 | |
---|
2434 | if (*p != *q) |
---|
2435 | { /* the signs are different */ |
---|
2436 | /* -0 equals + 0 */ |
---|
2437 | for (i = 1; i < NI - 1; i++) |
---|
2438 | { |
---|
2439 | if (ai[i] != 0) |
---|
2440 | goto nzro; |
---|
2441 | if (bi[i] != 0) |
---|
2442 | goto nzro; |
---|
2443 | } |
---|
2444 | return (0); |
---|
2445 | nzro: |
---|
2446 | if (*p == 0) |
---|
2447 | return (1); |
---|
2448 | else |
---|
2449 | return (-1); |
---|
2450 | } |
---|
2451 | /* both are the same sign */ |
---|
2452 | if (*p == 0) |
---|
2453 | msign = 1; |
---|
2454 | else |
---|
2455 | msign = -1; |
---|
2456 | i = NI - 1; |
---|
2457 | do |
---|
2458 | { |
---|
2459 | if (*p++ != *q++) |
---|
2460 | { |
---|
2461 | goto diff; |
---|
2462 | } |
---|
2463 | } |
---|
2464 | while (--i > 0); |
---|
2465 | |
---|
2466 | return (0); /* equality */ |
---|
2467 | |
---|
2468 | |
---|
2469 | |
---|
2470 | diff: |
---|
2471 | |
---|
2472 | if (*(--p) > *(--q)) |
---|
2473 | return (msign); /* p is bigger */ |
---|
2474 | else |
---|
2475 | return (-msign); /* p is littler */ |
---|
2476 | } |
---|
2477 | |
---|
2478 | |
---|
2479 | /* |
---|
2480 | ; Shift significand |
---|
2481 | ; |
---|
2482 | ; Shifts significand area up or down by the number of bits |
---|
2483 | ; given by the variable sc. |
---|
2484 | */ |
---|
2485 | static int |
---|
2486 | eshift (short unsigned int *x, int sc) |
---|
2487 | { |
---|
2488 | unsigned short lost; |
---|
2489 | unsigned short *p; |
---|
2490 | |
---|
2491 | if (sc == 0) |
---|
2492 | return (0); |
---|
2493 | |
---|
2494 | lost = 0; |
---|
2495 | p = x + NI - 1; |
---|
2496 | |
---|
2497 | if (sc < 0) |
---|
2498 | { |
---|
2499 | sc = -sc; |
---|
2500 | while (sc >= 16) |
---|
2501 | { |
---|
2502 | lost |= *p; /* remember lost bits */ |
---|
2503 | eshdn6 (x); |
---|
2504 | sc -= 16; |
---|
2505 | } |
---|
2506 | |
---|
2507 | while (sc >= 8) |
---|
2508 | { |
---|
2509 | lost |= *p & 0xff; |
---|
2510 | eshdn8 (x); |
---|
2511 | sc -= 8; |
---|
2512 | } |
---|
2513 | |
---|
2514 | while (sc > 0) |
---|
2515 | { |
---|
2516 | lost |= *p & 1; |
---|
2517 | eshdn1 (x); |
---|
2518 | sc -= 1; |
---|
2519 | } |
---|
2520 | } |
---|
2521 | else |
---|
2522 | { |
---|
2523 | while (sc >= 16) |
---|
2524 | { |
---|
2525 | eshup6 (x); |
---|
2526 | sc -= 16; |
---|
2527 | } |
---|
2528 | |
---|
2529 | while (sc >= 8) |
---|
2530 | { |
---|
2531 | eshup8 (x); |
---|
2532 | sc -= 8; |
---|
2533 | } |
---|
2534 | |
---|
2535 | while (sc > 0) |
---|
2536 | { |
---|
2537 | eshup1 (x); |
---|
2538 | sc -= 1; |
---|
2539 | } |
---|
2540 | } |
---|
2541 | if (lost) |
---|
2542 | lost = 1; |
---|
2543 | return ((int) lost); |
---|
2544 | } |
---|
2545 | |
---|
2546 | |
---|
2547 | |
---|
2548 | /* |
---|
2549 | ; normalize |
---|
2550 | ; |
---|
2551 | ; Shift normalizes the significand area pointed to by argument |
---|
2552 | ; shift count (up = positive) is returned. |
---|
2553 | */ |
---|
2554 | static int |
---|
2555 | enormlz (short unsigned int *x) |
---|
2556 | { |
---|
2557 | register unsigned short *p; |
---|
2558 | int sc; |
---|
2559 | |
---|
2560 | sc = 0; |
---|
2561 | p = &x[M]; |
---|
2562 | if (*p != 0) |
---|
2563 | goto normdn; |
---|
2564 | ++p; |
---|
2565 | if (*p & 0x8000) |
---|
2566 | return (0); /* already normalized */ |
---|
2567 | while (*p == 0) |
---|
2568 | { |
---|
2569 | eshup6 (x); |
---|
2570 | sc += 16; |
---|
2571 | /* With guard word, there are NBITS+16 bits available. |
---|
2572 | * return true if all are zero. |
---|
2573 | */ |
---|
2574 | if (sc > NBITS) |
---|
2575 | return (sc); |
---|
2576 | } |
---|
2577 | /* see if high byte is zero */ |
---|
2578 | while ((*p & 0xff00) == 0) |
---|
2579 | { |
---|
2580 | eshup8 (x); |
---|
2581 | sc += 8; |
---|
2582 | } |
---|
2583 | /* now shift 1 bit at a time */ |
---|
2584 | while ((*p & 0x8000) == 0) |
---|
2585 | { |
---|
2586 | eshup1 (x); |
---|
2587 | sc += 1; |
---|
2588 | if (sc > (NBITS + 16)) |
---|
2589 | { |
---|
2590 | mtherr ("enormlz", UNDERFLOW); |
---|
2591 | return (sc); |
---|
2592 | } |
---|
2593 | } |
---|
2594 | return (sc); |
---|
2595 | |
---|
2596 | /* Normalize by shifting down out of the high guard word |
---|
2597 | of the significand */ |
---|
2598 | normdn: |
---|
2599 | |
---|
2600 | if (*p & 0xff00) |
---|
2601 | { |
---|
2602 | eshdn8 (x); |
---|
2603 | sc -= 8; |
---|
2604 | } |
---|
2605 | while (*p != 0) |
---|
2606 | { |
---|
2607 | eshdn1 (x); |
---|
2608 | sc -= 1; |
---|
2609 | |
---|
2610 | if (sc < -NBITS) |
---|
2611 | { |
---|
2612 | mtherr ("enormlz", OVERFLOW); |
---|
2613 | return (sc); |
---|
2614 | } |
---|
2615 | } |
---|
2616 | return (sc); |
---|
2617 | } |
---|
2618 | |
---|
2619 | |
---|
2620 | |
---|
2621 | |
---|
2622 | /* Convert e type number to decimal format ASCII string. |
---|
2623 | * The constants are for 64 bit precision. |
---|
2624 | */ |
---|
2625 | |
---|
2626 | #define NTEN 12 |
---|
2627 | #define MAXP 4096 |
---|
2628 | |
---|
2629 | #if NE == 10 |
---|
2630 | static const unsigned short etens[NTEN + 1][NE] = { |
---|
2631 | {0x6576, 0x4a92, 0x804a, 0x153f, |
---|
2632 | 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */ |
---|
2633 | {0x6a32, 0xce52, 0x329a, 0x28ce, |
---|
2634 | 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */ |
---|
2635 | {0x526c, 0x50ce, 0xf18b, 0x3d28, |
---|
2636 | 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,}, |
---|
2637 | {0x9c66, 0x58f8, 0xbc50, 0x5c54, |
---|
2638 | 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,}, |
---|
2639 | {0x851e, 0xeab7, 0x98fe, 0x901b, |
---|
2640 | 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,}, |
---|
2641 | {0x0235, 0x0137, 0x36b1, 0x336c, |
---|
2642 | 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,}, |
---|
2643 | {0x50f8, 0x25fb, 0xc76b, 0x6b71, |
---|
2644 | 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,}, |
---|
2645 | {0x0000, 0x0000, 0x0000, 0x0000, |
---|
2646 | 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,}, |
---|
2647 | {0x0000, 0x0000, 0x0000, 0x0000, |
---|
2648 | 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,}, |
---|
2649 | {0x0000, 0x0000, 0x0000, 0x0000, |
---|
2650 | 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,}, |
---|
2651 | {0x0000, 0x0000, 0x0000, 0x0000, |
---|
2652 | 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,}, |
---|
2653 | {0x0000, 0x0000, 0x0000, 0x0000, |
---|
2654 | 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,}, |
---|
2655 | {0x0000, 0x0000, 0x0000, 0x0000, |
---|
2656 | 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */ |
---|
2657 | }; |
---|
2658 | |
---|
2659 | static const unsigned short emtens[NTEN + 1][NE] = { |
---|
2660 | {0x2030, 0xcffc, 0xa1c3, 0x8123, |
---|
2661 | 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */ |
---|
2662 | {0x8264, 0xd2cb, 0xf2ea, 0x12d4, |
---|
2663 | 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */ |
---|
2664 | {0xf53f, 0xf698, 0x6bd3, 0x0158, |
---|
2665 | 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,}, |
---|
2666 | {0xe731, 0x04d4, 0xe3f2, 0xd332, |
---|
2667 | 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,}, |
---|
2668 | {0xa23e, 0x5308, 0xfefb, 0x1155, |
---|
2669 | 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,}, |
---|
2670 | {0xe26d, 0xdbde, 0xd05d, 0xb3f6, |
---|
2671 | 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,}, |
---|
2672 | {0x2a20, 0x6224, 0x47b3, 0x98d7, |
---|
2673 | 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,}, |
---|
2674 | {0x0b5b, 0x4af2, 0xa581, 0x18ed, |
---|
2675 | 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,}, |
---|
2676 | {0xbf71, 0xa9b3, 0x7989, 0xbe68, |
---|
2677 | 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,}, |
---|
2678 | {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b, |
---|
2679 | 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,}, |
---|
2680 | {0xc155, 0xa4a8, 0x404e, 0x6113, |
---|
2681 | 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,}, |
---|
2682 | {0xd70a, 0x70a3, 0x0a3d, 0xa3d7, |
---|
2683 | 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,}, |
---|
2684 | {0xcccd, 0xcccc, 0xcccc, 0xcccc, |
---|
2685 | 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */ |
---|
2686 | }; |
---|
2687 | #else |
---|
2688 | static const unsigned short etens[NTEN + 1][NE] = { |
---|
2689 | {0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */ |
---|
2690 | {0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */ |
---|
2691 | {0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,}, |
---|
2692 | {0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,}, |
---|
2693 | {0xddbc, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,}, |
---|
2694 | {0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,}, |
---|
2695 | {0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,}, |
---|
2696 | {0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,}, |
---|
2697 | {0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,}, |
---|
2698 | {0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,}, |
---|
2699 | {0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,}, |
---|
2700 | {0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,}, |
---|
2701 | {0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */ |
---|
2702 | }; |
---|
2703 | |
---|
2704 | static const unsigned short emtens[NTEN + 1][NE] = { |
---|
2705 | {0x2de4, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */ |
---|
2706 | {0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */ |
---|
2707 | {0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,}, |
---|
2708 | {0x7133, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,}, |
---|
2709 | {0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,}, |
---|
2710 | {0xac7d, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,}, |
---|
2711 | {0x3f24, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,}, |
---|
2712 | {0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,}, |
---|
2713 | {0x4c2f, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,}, |
---|
2714 | {0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,}, |
---|
2715 | {0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,}, |
---|
2716 | {0x3d71, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,}, |
---|
2717 | {0xcccd, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */ |
---|
2718 | }; |
---|
2719 | #endif |
---|
2720 | |
---|
2721 | |
---|
2722 | |
---|
2723 | /* ASCII string outputs for unix */ |
---|
2724 | |
---|
2725 | |
---|
2726 | #if 0 |
---|
2727 | void |
---|
2728 | _IO_ldtostr (x, string, ndigs, flags, fmt) |
---|
2729 | long double *x; |
---|
2730 | char *string; |
---|
2731 | int ndigs; |
---|
2732 | int flags; |
---|
2733 | char fmt; |
---|
2734 | { |
---|
2735 | unsigned short w[NI]; |
---|
2736 | char *t, *u; |
---|
2737 | LDPARMS rnd; |
---|
2738 | LDPARMS *ldp = &rnd; |
---|
2739 | |
---|
2740 | rnd.rlast = -1; |
---|
2741 | rnd.rndprc = NBITS; |
---|
2742 | |
---|
2743 | if (sizeof (long double) == 16) |
---|
2744 | e113toe ((unsigned short *) x, w, ldp); |
---|
2745 | else |
---|
2746 | e64toe ((unsigned short *) x, w, ldp); |
---|
2747 | |
---|
2748 | etoasc (w, string, ndigs, -1, ldp); |
---|
2749 | if (ndigs == 0 && flags == 0) |
---|
2750 | { |
---|
2751 | /* Delete the decimal point unless alternate format. */ |
---|
2752 | t = string; |
---|
2753 | while (*t != '.') |
---|
2754 | ++t; |
---|
2755 | u = t + 1; |
---|
2756 | while (*t != '\0') |
---|
2757 | *t++ = *u++; |
---|
2758 | } |
---|
2759 | if (*string == ' ') |
---|
2760 | { |
---|
2761 | t = string; |
---|
2762 | u = t + 1; |
---|
2763 | while (*t != '\0') |
---|
2764 | *t++ = *u++; |
---|
2765 | } |
---|
2766 | if (fmt == 'E') |
---|
2767 | { |
---|
2768 | t = string; |
---|
2769 | while (*t != 'e') |
---|
2770 | ++t; |
---|
2771 | *t = 'E'; |
---|
2772 | } |
---|
2773 | } |
---|
2774 | |
---|
2775 | #endif |
---|
2776 | |
---|
2777 | /* This routine will not return more than NDEC+1 digits. */ |
---|
2778 | |
---|
2779 | char * |
---|
2780 | _ldtoa_r (struct _reent *ptr, long double d, int mode, int ndigits, |
---|
2781 | int *decpt, int *sign, char **rve) |
---|
2782 | { |
---|
2783 | unsigned short e[NI]; |
---|
2784 | char *s, *p; |
---|
2785 | int i, j, k; |
---|
2786 | int orig_ndigits; |
---|
2787 | LDPARMS rnd; |
---|
2788 | LDPARMS *ldp = &rnd; |
---|
2789 | char *outstr; |
---|
2790 | char outbuf[NDEC + MAX_EXP_DIGITS + 10]; |
---|
2791 | union uconv du; |
---|
2792 | du.d = d; |
---|
2793 | |
---|
2794 | orig_ndigits = ndigits; |
---|
2795 | rnd.rlast = -1; |
---|
2796 | rnd.rndprc = NBITS; |
---|
2797 | |
---|
2798 | _REENT_CHECK_MP (ptr); |
---|
2799 | |
---|
2800 | /* reentrancy addition to use mprec storage pool */ |
---|
2801 | if (_REENT_MP_RESULT (ptr)) |
---|
2802 | { |
---|
2803 | _REENT_MP_RESULT (ptr)->_k = _REENT_MP_RESULT_K (ptr); |
---|
2804 | _REENT_MP_RESULT (ptr)->_maxwds = 1 << _REENT_MP_RESULT_K (ptr); |
---|
2805 | Bfree (ptr, _REENT_MP_RESULT (ptr)); |
---|
2806 | _REENT_MP_RESULT (ptr) = 0; |
---|
2807 | } |
---|
2808 | |
---|
2809 | #if LDBL_MANT_DIG == 24 |
---|
2810 | e24toe (&du.pe, e, ldp); |
---|
2811 | #elif LDBL_MANT_DIG == 53 |
---|
2812 | e53toe (&du.pe, e, ldp); |
---|
2813 | #elif LDBL_MANT_DIG == 64 |
---|
2814 | e64toe (&du.pe, e, ldp); |
---|
2815 | #else |
---|
2816 | e113toe (&du.pe, e, ldp); |
---|
2817 | #endif |
---|
2818 | |
---|
2819 | if (eisneg (e)) |
---|
2820 | *sign = 1; |
---|
2821 | else |
---|
2822 | *sign = 0; |
---|
2823 | /* Mode 3 is "f" format. */ |
---|
2824 | if (mode != 3) |
---|
2825 | ndigits -= 1; |
---|
2826 | /* Mode 0 is for %.999 format, which is supposed to give a |
---|
2827 | minimum length string that will convert back to the same binary value. |
---|
2828 | For now, just ask for 20 digits which is enough but sometimes too many. */ |
---|
2829 | if (mode == 0) |
---|
2830 | ndigits = 20; |
---|
2831 | |
---|
2832 | /* This sanity limit must agree with the corresponding one in etoasc, to |
---|
2833 | keep straight the returned value of outexpon. */ |
---|
2834 | if (ndigits > NDEC) |
---|
2835 | ndigits = NDEC; |
---|
2836 | |
---|
2837 | etoasc (e, outbuf, ndigits, mode, ldp); |
---|
2838 | s = outbuf; |
---|
2839 | if (eisinf (e) || eisnan (e)) |
---|
2840 | { |
---|
2841 | *decpt = 9999; |
---|
2842 | goto stripspaces; |
---|
2843 | } |
---|
2844 | *decpt = ldp->outexpon + 1; |
---|
2845 | |
---|
2846 | /* Transform the string returned by etoasc into what the caller wants. */ |
---|
2847 | |
---|
2848 | /* Look for decimal point and delete it from the string. */ |
---|
2849 | s = outbuf; |
---|
2850 | while (*s != '\0') |
---|
2851 | { |
---|
2852 | if (*s == '.') |
---|
2853 | goto yesdecpt; |
---|
2854 | ++s; |
---|
2855 | } |
---|
2856 | goto nodecpt; |
---|
2857 | |
---|
2858 | yesdecpt: |
---|
2859 | |
---|
2860 | /* Delete the decimal point. */ |
---|
2861 | while (*s != '\0') |
---|
2862 | { |
---|
2863 | *s = *(s + 1); |
---|
2864 | ++s; |
---|
2865 | } |
---|
2866 | |
---|
2867 | nodecpt: |
---|
2868 | |
---|
2869 | /* Back up over the exponent field. */ |
---|
2870 | while (*s != 'E' && s > outbuf) |
---|
2871 | --s; |
---|
2872 | *s = '\0'; |
---|
2873 | |
---|
2874 | stripspaces: |
---|
2875 | |
---|
2876 | /* Strip leading spaces and sign. */ |
---|
2877 | p = outbuf; |
---|
2878 | while (*p == ' ' || *p == '-') |
---|
2879 | ++p; |
---|
2880 | |
---|
2881 | /* Find new end of string. */ |
---|
2882 | s = outbuf; |
---|
2883 | while ((*s++ = *p++) != '\0') |
---|
2884 | ; |
---|
2885 | --s; |
---|
2886 | |
---|
2887 | /* Strip trailing zeros. */ |
---|
2888 | if (mode == 2) |
---|
2889 | k = 1; |
---|
2890 | else if (ndigits > ldp->outexpon) |
---|
2891 | k = ndigits; |
---|
2892 | else |
---|
2893 | k = ldp->outexpon; |
---|
2894 | |
---|
2895 | while (*(s - 1) == '0' && ((s - outbuf) > k)) |
---|
2896 | *(--s) = '\0'; |
---|
2897 | |
---|
2898 | /* In f format, flush small off-scale values to zero. |
---|
2899 | Rounding has been taken care of by etoasc. */ |
---|
2900 | if (mode == 3 && ((ndigits + ldp->outexpon) < 0)) |
---|
2901 | { |
---|
2902 | s = outbuf; |
---|
2903 | *s = '\0'; |
---|
2904 | *decpt = 0; |
---|
2905 | } |
---|
2906 | |
---|
2907 | /* reentrancy addition to use mprec storage pool */ |
---|
2908 | /* we want to have enough space to hold the formatted result */ |
---|
2909 | |
---|
2910 | if (mode == 3) /* f format, account for sign + dec digits + decpt + frac */ |
---|
2911 | i = *decpt + orig_ndigits + 3; |
---|
2912 | else /* account for sign + max precision digs + E + exp sign + exponent */ |
---|
2913 | i = orig_ndigits + MAX_EXP_DIGITS + 4; |
---|
2914 | |
---|
2915 | j = sizeof (__ULong); |
---|
2916 | for (_REENT_MP_RESULT_K (ptr) = 0; |
---|
2917 | sizeof (_Bigint) - sizeof (__ULong) + j <= i; j <<= 1) |
---|
2918 | _REENT_MP_RESULT_K (ptr)++; |
---|
2919 | _REENT_MP_RESULT (ptr) = Balloc (ptr, _REENT_MP_RESULT_K (ptr)); |
---|
2920 | |
---|
2921 | /* Copy from internal temporary buffer to permanent buffer. */ |
---|
2922 | outstr = (char *) _REENT_MP_RESULT (ptr); |
---|
2923 | strcpy (outstr, outbuf); |
---|
2924 | |
---|
2925 | if (rve) |
---|
2926 | *rve = outstr + (s - outbuf); |
---|
2927 | |
---|
2928 | return outstr; |
---|
2929 | } |
---|
2930 | |
---|
2931 | /* Routine used to tell if long double is NaN or Infinity or regular number. |
---|
2932 | Returns: 0 = regular number |
---|
2933 | 1 = Nan |
---|
2934 | 2 = Infinity |
---|
2935 | */ |
---|
2936 | int |
---|
2937 | _ldcheck (long double *d) |
---|
2938 | { |
---|
2939 | unsigned short e[NI]; |
---|
2940 | LDPARMS rnd; |
---|
2941 | LDPARMS *ldp = &rnd; |
---|
2942 | |
---|
2943 | union uconv du; |
---|
2944 | |
---|
2945 | rnd.rlast = -1; |
---|
2946 | rnd.rndprc = NBITS; |
---|
2947 | du.d = *d; |
---|
2948 | #if LDBL_MANT_DIG == 24 |
---|
2949 | e24toe (&du.pe, e, ldp); |
---|
2950 | #elif LDBL_MANT_DIG == 53 |
---|
2951 | e53toe (&du.pe, e, ldp); |
---|
2952 | #elif LDBL_MANT_DIG == 64 |
---|
2953 | e64toe (&du.pe, e, ldp); |
---|
2954 | #else |
---|
2955 | e113toe (&du.pe, e, ldp); |
---|
2956 | #endif |
---|
2957 | |
---|
2958 | if ((e[NE - 1] & 0x7fff) == 0x7fff) |
---|
2959 | { |
---|
2960 | #ifdef NANS |
---|
2961 | if (eisnan (e)) |
---|
2962 | return (1); |
---|
2963 | #endif |
---|
2964 | return (2); |
---|
2965 | } |
---|
2966 | else |
---|
2967 | return (0); |
---|
2968 | } /* _ldcheck */ |
---|
2969 | |
---|
2970 | static void |
---|
2971 | etoasc (short unsigned int *x, char *string, int ndigits, int outformat, |
---|
2972 | LDPARMS * ldp) |
---|
2973 | { |
---|
2974 | long digit; |
---|
2975 | unsigned short y[NI], t[NI], u[NI], w[NI]; |
---|
2976 | const unsigned short *p, *r, *ten; |
---|
2977 | unsigned short sign; |
---|
2978 | int i, j, k, expon, rndsav, ndigs; |
---|
2979 | char *s, *ss; |
---|
2980 | unsigned short m; |
---|
2981 | unsigned short *equot = ldp->equot; |
---|
2982 | |
---|
2983 | ndigs = ndigits; |
---|
2984 | rndsav = ldp->rndprc; |
---|
2985 | #ifdef NANS |
---|
2986 | if (eisnan (x)) |
---|
2987 | { |
---|
2988 | sprintf (string, " NaN "); |
---|
2989 | expon = 9999; |
---|
2990 | goto bxit; |
---|
2991 | } |
---|
2992 | #endif |
---|
2993 | ldp->rndprc = NBITS; /* set to full precision */ |
---|
2994 | emov (x, y); /* retain external format */ |
---|
2995 | if (y[NE - 1] & 0x8000) |
---|
2996 | { |
---|
2997 | sign = 0xffff; |
---|
2998 | y[NE - 1] &= 0x7fff; |
---|
2999 | } |
---|
3000 | else |
---|
3001 | { |
---|
3002 | sign = 0; |
---|
3003 | } |
---|
3004 | expon = 0; |
---|
3005 | ten = &etens[NTEN][0]; |
---|
3006 | emov (eone, t); |
---|
3007 | /* Test for zero exponent */ |
---|
3008 | if (y[NE - 1] == 0) |
---|
3009 | { |
---|
3010 | for (k = 0; k < NE - 1; k++) |
---|
3011 | { |
---|
3012 | if (y[k] != 0) |
---|
3013 | goto tnzro; /* denormalized number */ |
---|
3014 | } |
---|
3015 | goto isone; /* legal all zeros */ |
---|
3016 | } |
---|
3017 | tnzro: |
---|
3018 | |
---|
3019 | /* Test for infinity. |
---|
3020 | */ |
---|
3021 | if (y[NE - 1] == 0x7fff) |
---|
3022 | { |
---|
3023 | if (sign) |
---|
3024 | sprintf (string, " -Infinity "); |
---|
3025 | else |
---|
3026 | sprintf (string, " Infinity "); |
---|
3027 | expon = 9999; |
---|
3028 | goto bxit; |
---|
3029 | } |
---|
3030 | |
---|
3031 | /* Test for exponent nonzero but significand denormalized. |
---|
3032 | * This is an error condition. |
---|
3033 | */ |
---|
3034 | if ((y[NE - 1] != 0) && ((y[NE - 2] & 0x8000) == 0)) |
---|
3035 | { |
---|
3036 | mtherr ("etoasc", DOMAIN); |
---|
3037 | sprintf (string, "NaN"); |
---|
3038 | expon = 9999; |
---|
3039 | goto bxit; |
---|
3040 | } |
---|
3041 | |
---|
3042 | /* Compare to 1.0 */ |
---|
3043 | i = ecmp (eone, y); |
---|
3044 | if (i == 0) |
---|
3045 | goto isone; |
---|
3046 | |
---|
3047 | if (i < 0) |
---|
3048 | { /* Number is greater than 1 */ |
---|
3049 | /* Convert significand to an integer and strip trailing decimal zeros. */ |
---|
3050 | emov (y, u); |
---|
3051 | u[NE - 1] = EXONE + NBITS - 1; |
---|
3052 | |
---|
3053 | p = &etens[NTEN - 4][0]; |
---|
3054 | m = 16; |
---|
3055 | do |
---|
3056 | { |
---|
3057 | ediv (p, u, t, ldp); |
---|
3058 | efloor (t, w, ldp); |
---|
3059 | for (j = 0; j < NE - 1; j++) |
---|
3060 | { |
---|
3061 | if (t[j] != w[j]) |
---|
3062 | goto noint; |
---|
3063 | } |
---|
3064 | emov (t, u); |
---|
3065 | expon += (int) m; |
---|
3066 | noint: |
---|
3067 | p += NE; |
---|
3068 | m >>= 1; |
---|
3069 | } |
---|
3070 | while (m != 0); |
---|
3071 | |
---|
3072 | /* Rescale from integer significand */ |
---|
3073 | u[NE - 1] += y[NE - 1] - (unsigned int) (EXONE + NBITS - 1); |
---|
3074 | emov (u, y); |
---|
3075 | /* Find power of 10 */ |
---|
3076 | emov (eone, t); |
---|
3077 | m = MAXP; |
---|
3078 | p = &etens[0][0]; |
---|
3079 | while (ecmp (ten, u) <= 0) |
---|
3080 | { |
---|
3081 | if (ecmp (p, u) <= 0) |
---|
3082 | { |
---|
3083 | ediv (p, u, u, ldp); |
---|
3084 | emul (p, t, t, ldp); |
---|
3085 | expon += (int) m; |
---|
3086 | } |
---|
3087 | m >>= 1; |
---|
3088 | if (m == 0) |
---|
3089 | break; |
---|
3090 | p += NE; |
---|
3091 | } |
---|
3092 | } |
---|
3093 | else |
---|
3094 | { /* Number is less than 1.0 */ |
---|
3095 | /* Pad significand with trailing decimal zeros. */ |
---|
3096 | if (y[NE - 1] == 0) |
---|
3097 | { |
---|
3098 | while ((y[NE - 2] & 0x8000) == 0) |
---|
3099 | { |
---|
3100 | emul (ten, y, y, ldp); |
---|
3101 | expon -= 1; |
---|
3102 | } |
---|
3103 | } |
---|
3104 | else |
---|
3105 | { |
---|
3106 | emovi (y, w); |
---|
3107 | for (i = 0; i < NDEC + 1; i++) |
---|
3108 | { |
---|
3109 | if ((w[NI - 1] & 0x7) != 0) |
---|
3110 | break; |
---|
3111 | /* multiply by 10 */ |
---|
3112 | emovz (w, u); |
---|
3113 | eshdn1 (u); |
---|
3114 | eshdn1 (u); |
---|
3115 | eaddm (w, u); |
---|
3116 | u[1] += 3; |
---|
3117 | while (u[2] != 0) |
---|
3118 | { |
---|
3119 | eshdn1 (u); |
---|
3120 | u[1] += 1; |
---|
3121 | } |
---|
3122 | if (u[NI - 1] != 0) |
---|
3123 | break; |
---|
3124 | if (eone[NE - 1] <= u[1]) |
---|
3125 | break; |
---|
3126 | emovz (u, w); |
---|
3127 | expon -= 1; |
---|
3128 | } |
---|
3129 | emovo (w, y, ldp); |
---|
3130 | } |
---|
3131 | k = -MAXP; |
---|
3132 | p = &emtens[0][0]; |
---|
3133 | r = &etens[0][0]; |
---|
3134 | emov (y, w); |
---|
3135 | emov (eone, t); |
---|
3136 | while (ecmp (eone, w) > 0) |
---|
3137 | { |
---|
3138 | if (ecmp (p, w) >= 0) |
---|
3139 | { |
---|
3140 | emul (r, w, w, ldp); |
---|
3141 | emul (r, t, t, ldp); |
---|
3142 | expon += k; |
---|
3143 | } |
---|
3144 | k /= 2; |
---|
3145 | if (k == 0) |
---|
3146 | break; |
---|
3147 | p += NE; |
---|
3148 | r += NE; |
---|
3149 | } |
---|
3150 | ediv (t, eone, t, ldp); |
---|
3151 | } |
---|
3152 | isone: |
---|
3153 | /* Find the first (leading) digit. */ |
---|
3154 | emovi (t, w); |
---|
3155 | emovz (w, t); |
---|
3156 | emovi (y, w); |
---|
3157 | emovz (w, y); |
---|
3158 | eiremain (t, y, ldp); |
---|
3159 | digit = equot[NI - 1]; |
---|
3160 | while ((digit == 0) && (ecmp (y, ezero) != 0)) |
---|
3161 | { |
---|
3162 | eshup1 (y); |
---|
3163 | emovz (y, u); |
---|
3164 | eshup1 (u); |
---|
3165 | eshup1 (u); |
---|
3166 | eaddm (u, y); |
---|
3167 | eiremain (t, y, ldp); |
---|
3168 | digit = equot[NI - 1]; |
---|
3169 | expon -= 1; |
---|
3170 | } |
---|
3171 | s = string; |
---|
3172 | if (sign) |
---|
3173 | *s++ = '-'; |
---|
3174 | else |
---|
3175 | *s++ = ' '; |
---|
3176 | /* Examine number of digits requested by caller. */ |
---|
3177 | if (outformat == 3) |
---|
3178 | ndigs += expon; |
---|
3179 | /* |
---|
3180 | else if( ndigs < 0 ) |
---|
3181 | ndigs = 0; |
---|
3182 | */ |
---|
3183 | if (ndigs > NDEC) |
---|
3184 | ndigs = NDEC; |
---|
3185 | if (digit == 10) |
---|
3186 | { |
---|
3187 | *s++ = '1'; |
---|
3188 | *s++ = '.'; |
---|
3189 | if (ndigs > 0) |
---|
3190 | { |
---|
3191 | *s++ = '0'; |
---|
3192 | ndigs -= 1; |
---|
3193 | } |
---|
3194 | expon += 1; |
---|
3195 | if (ndigs < 0) |
---|
3196 | { |
---|
3197 | ss = s; |
---|
3198 | goto doexp; |
---|
3199 | } |
---|
3200 | } |
---|
3201 | else |
---|
3202 | { |
---|
3203 | *s++ = (char) digit + '0'; |
---|
3204 | *s++ = '.'; |
---|
3205 | } |
---|
3206 | /* Generate digits after the decimal point. */ |
---|
3207 | for (k = 0; k <= ndigs; k++) |
---|
3208 | { |
---|
3209 | /* multiply current number by 10, without normalizing */ |
---|
3210 | eshup1 (y); |
---|
3211 | emovz (y, u); |
---|
3212 | eshup1 (u); |
---|
3213 | eshup1 (u); |
---|
3214 | eaddm (u, y); |
---|
3215 | eiremain (t, y, ldp); |
---|
3216 | *s++ = (char) equot[NI - 1] + '0'; |
---|
3217 | } |
---|
3218 | digit = equot[NI - 1]; |
---|
3219 | --s; |
---|
3220 | ss = s; |
---|
3221 | /* round off the ASCII string */ |
---|
3222 | if (digit > 4) |
---|
3223 | { |
---|
3224 | /* Test for critical rounding case in ASCII output. */ |
---|
3225 | if (digit == 5) |
---|
3226 | { |
---|
3227 | emovo (y, t, ldp); |
---|
3228 | if (ecmp (t, ezero) != 0) |
---|
3229 | goto roun; /* round to nearest */ |
---|
3230 | if (ndigs < 0 || (*(s - 1 - (*(s - 1) == '.')) & 1) == 0) |
---|
3231 | goto doexp; /* round to even */ |
---|
3232 | } |
---|
3233 | /* Round up and propagate carry-outs */ |
---|
3234 | roun: |
---|
3235 | --s; |
---|
3236 | k = *s & 0x7f; |
---|
3237 | /* Carry out to most significant digit? */ |
---|
3238 | if (ndigs < 0) |
---|
3239 | { |
---|
3240 | /* This will print like "1E-6". */ |
---|
3241 | *s = '1'; |
---|
3242 | expon += 1; |
---|
3243 | goto doexp; |
---|
3244 | } |
---|
3245 | else if (k == '.') |
---|
3246 | { |
---|
3247 | --s; |
---|
3248 | k = *s; |
---|
3249 | k += 1; |
---|
3250 | *s = (char) k; |
---|
3251 | /* Most significant digit carries to 10? */ |
---|
3252 | if (k > '9') |
---|
3253 | { |
---|
3254 | expon += 1; |
---|
3255 | *s = '1'; |
---|
3256 | } |
---|
3257 | goto doexp; |
---|
3258 | } |
---|
3259 | /* Round up and carry out from less significant digits */ |
---|
3260 | k += 1; |
---|
3261 | *s = (char) k; |
---|
3262 | if (k > '9') |
---|
3263 | { |
---|
3264 | *s = '0'; |
---|
3265 | goto roun; |
---|
3266 | } |
---|
3267 | } |
---|
3268 | doexp: |
---|
3269 | #ifdef __GO32__ |
---|
3270 | if (expon >= 0) |
---|
3271 | sprintf (ss, "e+%02d", expon); |
---|
3272 | else |
---|
3273 | sprintf (ss, "e-%02d", -expon); |
---|
3274 | #else |
---|
3275 | sprintf (ss, "E%d", expon); |
---|
3276 | #endif |
---|
3277 | bxit: |
---|
3278 | ldp->rndprc = rndsav; |
---|
3279 | ldp->outexpon = expon; |
---|
3280 | } |
---|
3281 | |
---|
3282 | |
---|
3283 | #if 0 /* Broken, unusable implementation of strtold */ |
---|
3284 | |
---|
3285 | /* |
---|
3286 | ; ASCTOQ |
---|
3287 | ; ASCTOQ.MAC LATEST REV: 11 JAN 84 |
---|
3288 | ; SLM, 3 JAN 78 |
---|
3289 | ; |
---|
3290 | ; Convert ASCII string to quadruple precision floating point |
---|
3291 | ; |
---|
3292 | ; Numeric input is free field decimal number |
---|
3293 | ; with max of 15 digits with or without |
---|
3294 | ; decimal point entered as ASCII from teletype. |
---|
3295 | ; Entering E after the number followed by a second |
---|
3296 | ; number causes the second number to be interpreted |
---|
3297 | ; as a power of 10 to be multiplied by the first number |
---|
3298 | ; (i.e., "scientific" notation). |
---|
3299 | ; |
---|
3300 | ; Usage: |
---|
3301 | ; asctoq( string, q ); |
---|
3302 | */ |
---|
3303 | |
---|
3304 | long double |
---|
3305 | _strtold (char *s, char **se) |
---|
3306 | { |
---|
3307 | union uconv x; |
---|
3308 | LDPARMS rnd; |
---|
3309 | LDPARMS *ldp = &rnd; |
---|
3310 | int lenldstr; |
---|
3311 | |
---|
3312 | rnd.rlast = -1; |
---|
3313 | rnd.rndprc = NBITS; |
---|
3314 | |
---|
3315 | lenldstr = asctoeg (s, &x.pe, LDBL_MANT_DIG, ldp); |
---|
3316 | if (se) |
---|
3317 | *se = s + lenldstr; |
---|
3318 | return x.d; |
---|
3319 | } |
---|
3320 | |
---|
3321 | #define REASONABLE_LEN 200 |
---|
3322 | |
---|
3323 | static int |
---|
3324 | asctoeg (char *ss, short unsigned int *y, int oprec, LDPARMS * ldp) |
---|
3325 | { |
---|
3326 | unsigned short yy[NI], xt[NI], tt[NI]; |
---|
3327 | int esign, decflg, sgnflg, nexp, exp, prec, lost; |
---|
3328 | int k, trail, c, rndsav; |
---|
3329 | long lexp; |
---|
3330 | unsigned short nsign; |
---|
3331 | const unsigned short *p; |
---|
3332 | char *sp, *s, *lstr; |
---|
3333 | int lenldstr; |
---|
3334 | int mflag = 0; |
---|
3335 | char tmpstr[REASONABLE_LEN]; |
---|
3336 | |
---|
3337 | /* Copy the input string. */ |
---|
3338 | c = strlen (ss) + 2; |
---|
3339 | if (c <= REASONABLE_LEN) |
---|
3340 | lstr = tmpstr; |
---|
3341 | else |
---|
3342 | { |
---|
3343 | lstr = (char *) calloc (c, 1); |
---|
3344 | mflag = 1; |
---|
3345 | } |
---|
3346 | s = ss; |
---|
3347 | lenldstr = 0; |
---|
3348 | while (*s == ' ') /* skip leading spaces */ |
---|
3349 | { |
---|
3350 | ++s; |
---|
3351 | ++lenldstr; |
---|
3352 | } |
---|
3353 | sp = lstr; |
---|
3354 | for (k = 0; k < c; k++) |
---|
3355 | { |
---|
3356 | if ((*sp++ = *s++) == '\0') |
---|
3357 | break; |
---|
3358 | } |
---|
3359 | *sp = '\0'; |
---|
3360 | s = lstr; |
---|
3361 | |
---|
3362 | rndsav = ldp->rndprc; |
---|
3363 | ldp->rndprc = NBITS; /* Set to full precision */ |
---|
3364 | lost = 0; |
---|
3365 | nsign = 0; |
---|
3366 | decflg = 0; |
---|
3367 | sgnflg = 0; |
---|
3368 | nexp = 0; |
---|
3369 | exp = 0; |
---|
3370 | prec = 0; |
---|
3371 | ecleaz (yy); |
---|
3372 | trail = 0; |
---|
3373 | |
---|
3374 | nxtcom: |
---|
3375 | k = *s - '0'; |
---|
3376 | if ((k >= 0) && (k <= 9)) |
---|
3377 | { |
---|
3378 | /* Ignore leading zeros */ |
---|
3379 | if ((prec == 0) && (decflg == 0) && (k == 0)) |
---|
3380 | goto donchr; |
---|
3381 | /* Identify and strip trailing zeros after the decimal point. */ |
---|
3382 | if ((trail == 0) && (decflg != 0)) |
---|
3383 | { |
---|
3384 | sp = s; |
---|
3385 | while ((*sp >= '0') && (*sp <= '9')) |
---|
3386 | ++sp; |
---|
3387 | /* Check for syntax error */ |
---|
3388 | c = *sp & 0x7f; |
---|
3389 | if ((c != 'e') && (c != 'E') && (c != '\0') |
---|
3390 | && (c != '\n') && (c != '\r') && (c != ' ') && (c != ',')) |
---|
3391 | goto error; |
---|
3392 | --sp; |
---|
3393 | while (*sp == '0') |
---|
3394 | *sp-- = 'z'; |
---|
3395 | trail = 1; |
---|
3396 | if (*s == 'z') |
---|
3397 | goto donchr; |
---|
3398 | } |
---|
3399 | /* If enough digits were given to more than fill up the yy register, |
---|
3400 | * continuing until overflow into the high guard word yy[2] |
---|
3401 | * guarantees that there will be a roundoff bit at the top |
---|
3402 | * of the low guard word after normalization. |
---|
3403 | */ |
---|
3404 | if (yy[2] == 0) |
---|
3405 | { |
---|
3406 | if (decflg) |
---|
3407 | nexp += 1; /* count digits after decimal point */ |
---|
3408 | eshup1 (yy); /* multiply current number by 10 */ |
---|
3409 | emovz (yy, xt); |
---|
3410 | eshup1 (xt); |
---|
3411 | eshup1 (xt); |
---|
3412 | eaddm (xt, yy); |
---|
3413 | ecleaz (xt); |
---|
3414 | xt[NI - 2] = (unsigned short) k; |
---|
3415 | eaddm (xt, yy); |
---|
3416 | } |
---|
3417 | else |
---|
3418 | { |
---|
3419 | /* Mark any lost non-zero digit. */ |
---|
3420 | lost |= k; |
---|
3421 | /* Count lost digits before the decimal point. */ |
---|
3422 | if (decflg == 0) |
---|
3423 | nexp -= 1; |
---|
3424 | } |
---|
3425 | prec += 1; |
---|
3426 | goto donchr; |
---|
3427 | } |
---|
3428 | |
---|
3429 | switch (*s) |
---|
3430 | { |
---|
3431 | case 'z': |
---|
3432 | break; |
---|
3433 | case 'E': |
---|
3434 | case 'e': |
---|
3435 | goto expnt; |
---|
3436 | case '.': /* decimal point */ |
---|
3437 | if (decflg) |
---|
3438 | goto error; |
---|
3439 | ++decflg; |
---|
3440 | break; |
---|
3441 | case '-': |
---|
3442 | nsign = 0xffff; |
---|
3443 | if (sgnflg) |
---|
3444 | goto error; |
---|
3445 | ++sgnflg; |
---|
3446 | break; |
---|
3447 | case '+': |
---|
3448 | if (sgnflg) |
---|
3449 | goto error; |
---|
3450 | ++sgnflg; |
---|
3451 | break; |
---|
3452 | case ',': |
---|
3453 | case ' ': |
---|
3454 | case '\0': |
---|
3455 | case '\n': |
---|
3456 | case '\r': |
---|
3457 | goto daldone; |
---|
3458 | case 'i': |
---|
3459 | case 'I': |
---|
3460 | goto infinite; |
---|
3461 | default: |
---|
3462 | error: |
---|
3463 | #ifdef NANS |
---|
3464 | enan (yy, NI * 16); |
---|
3465 | #else |
---|
3466 | mtherr ("asctoe", DOMAIN); |
---|
3467 | ecleaz (yy); |
---|
3468 | #endif |
---|
3469 | goto aexit; |
---|
3470 | } |
---|
3471 | donchr: |
---|
3472 | ++s; |
---|
3473 | goto nxtcom; |
---|
3474 | |
---|
3475 | /* Exponent interpretation */ |
---|
3476 | expnt: |
---|
3477 | |
---|
3478 | esign = 1; |
---|
3479 | exp = 0; |
---|
3480 | ++s; |
---|
3481 | /* check for + or - */ |
---|
3482 | if (*s == '-') |
---|
3483 | { |
---|
3484 | esign = -1; |
---|
3485 | ++s; |
---|
3486 | } |
---|
3487 | if (*s == '+') |
---|
3488 | ++s; |
---|
3489 | while ((*s >= '0') && (*s <= '9')) |
---|
3490 | { |
---|
3491 | exp *= 10; |
---|
3492 | exp += *s++ - '0'; |
---|
3493 | if (exp > 4977) |
---|
3494 | { |
---|
3495 | if (esign < 0) |
---|
3496 | goto zero; |
---|
3497 | else |
---|
3498 | goto infinite; |
---|
3499 | } |
---|
3500 | } |
---|
3501 | if (esign < 0) |
---|
3502 | exp = -exp; |
---|
3503 | if (exp > 4932) |
---|
3504 | { |
---|
3505 | infinite: |
---|
3506 | ecleaz (yy); |
---|
3507 | yy[E] = 0x7fff; /* infinity */ |
---|
3508 | goto aexit; |
---|
3509 | } |
---|
3510 | if (exp < -4977) |
---|
3511 | { |
---|
3512 | zero: |
---|
3513 | ecleaz (yy); |
---|
3514 | goto aexit; |
---|
3515 | } |
---|
3516 | |
---|
3517 | daldone: |
---|
3518 | nexp = exp - nexp; |
---|
3519 | /* Pad trailing zeros to minimize power of 10, per IEEE spec. */ |
---|
3520 | while ((nexp > 0) && (yy[2] == 0)) |
---|
3521 | { |
---|
3522 | emovz (yy, xt); |
---|
3523 | eshup1 (xt); |
---|
3524 | eshup1 (xt); |
---|
3525 | eaddm (yy, xt); |
---|
3526 | eshup1 (xt); |
---|
3527 | if (xt[2] != 0) |
---|
3528 | break; |
---|
3529 | nexp -= 1; |
---|
3530 | emovz (xt, yy); |
---|
3531 | } |
---|
3532 | if ((k = enormlz (yy)) > NBITS) |
---|
3533 | { |
---|
3534 | ecleaz (yy); |
---|
3535 | goto aexit; |
---|
3536 | } |
---|
3537 | lexp = (EXONE - 1 + NBITS) - k; |
---|
3538 | emdnorm (yy, lost, 0, lexp, 64, ldp); |
---|
3539 | /* convert to external format */ |
---|
3540 | |
---|
3541 | |
---|
3542 | /* Multiply by 10**nexp. If precision is 64 bits, |
---|
3543 | * the maximum relative error incurred in forming 10**n |
---|
3544 | * for 0 <= n <= 324 is 8.2e-20, at 10**180. |
---|
3545 | * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947. |
---|
3546 | * For 0 >= n >= -999, it is -1.55e-19 at 10**-435. |
---|
3547 | */ |
---|
3548 | lexp = yy[E]; |
---|
3549 | if (nexp == 0) |
---|
3550 | { |
---|
3551 | k = 0; |
---|
3552 | goto expdon; |
---|
3553 | } |
---|
3554 | esign = 1; |
---|
3555 | if (nexp < 0) |
---|
3556 | { |
---|
3557 | nexp = -nexp; |
---|
3558 | esign = -1; |
---|
3559 | if (nexp > 4096) |
---|
3560 | { /* Punt. Can't handle this without 2 divides. */ |
---|
3561 | emovi (etens[0], tt); |
---|
3562 | lexp -= tt[E]; |
---|
3563 | k = edivm (tt, yy, ldp); |
---|
3564 | lexp += EXONE; |
---|
3565 | nexp -= 4096; |
---|
3566 | } |
---|
3567 | } |
---|
3568 | p = &etens[NTEN][0]; |
---|
3569 | emov (eone, xt); |
---|
3570 | exp = 1; |
---|
3571 | do |
---|
3572 | { |
---|
3573 | if (exp & nexp) |
---|
3574 | emul (p, xt, xt, ldp); |
---|
3575 | p -= NE; |
---|
3576 | exp = exp + exp; |
---|
3577 | } |
---|
3578 | while (exp <= MAXP); |
---|
3579 | |
---|
3580 | emovi (xt, tt); |
---|
3581 | if (esign < 0) |
---|
3582 | { |
---|
3583 | lexp -= tt[E]; |
---|
3584 | k = edivm (tt, yy, ldp); |
---|
3585 | lexp += EXONE; |
---|
3586 | } |
---|
3587 | else |
---|
3588 | { |
---|
3589 | lexp += tt[E]; |
---|
3590 | k = emulm (tt, yy, ldp); |
---|
3591 | lexp -= EXONE - 1; |
---|
3592 | } |
---|
3593 | |
---|
3594 | expdon: |
---|
3595 | |
---|
3596 | /* Round and convert directly to the destination type */ |
---|
3597 | if (oprec == 53) |
---|
3598 | lexp -= EXONE - 0x3ff; |
---|
3599 | else if (oprec == 24) |
---|
3600 | lexp -= EXONE - 0177; |
---|
3601 | #ifdef DEC |
---|
3602 | else if (oprec == 56) |
---|
3603 | lexp -= EXONE - 0201; |
---|
3604 | #endif |
---|
3605 | ldp->rndprc = oprec; |
---|
3606 | emdnorm (yy, k, 0, lexp, 64, ldp); |
---|
3607 | |
---|
3608 | aexit: |
---|
3609 | |
---|
3610 | ldp->rndprc = rndsav; |
---|
3611 | yy[0] = nsign; |
---|
3612 | switch (oprec) |
---|
3613 | { |
---|
3614 | #ifdef DEC |
---|
3615 | case 56: |
---|
3616 | todec (yy, y); /* see etodec.c */ |
---|
3617 | break; |
---|
3618 | #endif |
---|
3619 | #if LDBL_MANT_DIG == 53 |
---|
3620 | case 53: |
---|
3621 | toe53 (yy, y); |
---|
3622 | break; |
---|
3623 | #elif LDBL_MANT_DIG == 24 |
---|
3624 | case 24: |
---|
3625 | toe24 (yy, y); |
---|
3626 | break; |
---|
3627 | #elif LDBL_MANT_DIG == 64 |
---|
3628 | case 64: |
---|
3629 | toe64 (yy, y); |
---|
3630 | break; |
---|
3631 | #elif LDBL_MANT_DIG == 113 |
---|
3632 | case 113: |
---|
3633 | toe113 (yy, y); |
---|
3634 | break; |
---|
3635 | #else |
---|
3636 | case NBITS: |
---|
3637 | emovo (yy, y, ldp); |
---|
3638 | break; |
---|
3639 | #endif |
---|
3640 | } |
---|
3641 | lenldstr += s - lstr; |
---|
3642 | if (mflag) |
---|
3643 | free (lstr); |
---|
3644 | return lenldstr; |
---|
3645 | } |
---|
3646 | |
---|
3647 | #endif |
---|
3648 | |
---|
3649 | /* y = largest integer not greater than x |
---|
3650 | * (truncated toward minus infinity) |
---|
3651 | * |
---|
3652 | * unsigned short x[NE], y[NE] |
---|
3653 | * LDPARMS *ldp |
---|
3654 | * |
---|
3655 | * efloor( x, y, ldp ); |
---|
3656 | */ |
---|
3657 | static const unsigned short bmask[] = { |
---|
3658 | 0xffff, |
---|
3659 | 0xfffe, |
---|
3660 | 0xfffc, |
---|
3661 | 0xfff8, |
---|
3662 | 0xfff0, |
---|
3663 | 0xffe0, |
---|
3664 | 0xffc0, |
---|
3665 | 0xff80, |
---|
3666 | 0xff00, |
---|
3667 | 0xfe00, |
---|
3668 | 0xfc00, |
---|
3669 | 0xf800, |
---|
3670 | 0xf000, |
---|
3671 | 0xe000, |
---|
3672 | 0xc000, |
---|
3673 | 0x8000, |
---|
3674 | 0x0000, |
---|
3675 | }; |
---|
3676 | |
---|
3677 | static void |
---|
3678 | efloor (short unsigned int *x, short unsigned int *y, LDPARMS * ldp) |
---|
3679 | { |
---|
3680 | register unsigned short *p; |
---|
3681 | int e, expon, i; |
---|
3682 | unsigned short f[NE]; |
---|
3683 | |
---|
3684 | emov (x, f); /* leave in external format */ |
---|
3685 | expon = (int) f[NE - 1]; |
---|
3686 | e = (expon & 0x7fff) - (EXONE - 1); |
---|
3687 | if (e <= 0) |
---|
3688 | { |
---|
3689 | eclear (y); |
---|
3690 | goto isitneg; |
---|
3691 | } |
---|
3692 | /* number of bits to clear out */ |
---|
3693 | e = NBITS - e; |
---|
3694 | emov (f, y); |
---|
3695 | if (e <= 0) |
---|
3696 | return; |
---|
3697 | |
---|
3698 | p = &y[0]; |
---|
3699 | while (e >= 16) |
---|
3700 | { |
---|
3701 | *p++ = 0; |
---|
3702 | e -= 16; |
---|
3703 | } |
---|
3704 | /* clear the remaining bits */ |
---|
3705 | *p &= bmask[e]; |
---|
3706 | /* truncate negatives toward minus infinity */ |
---|
3707 | isitneg: |
---|
3708 | |
---|
3709 | if ((unsigned short) expon & (unsigned short) 0x8000) |
---|
3710 | { |
---|
3711 | for (i = 0; i < NE - 1; i++) |
---|
3712 | { |
---|
3713 | if (f[i] != y[i]) |
---|
3714 | { |
---|
3715 | esub (eone, y, y, ldp); |
---|
3716 | break; |
---|
3717 | } |
---|
3718 | } |
---|
3719 | } |
---|
3720 | } |
---|
3721 | |
---|
3722 | |
---|
3723 | |
---|
3724 | static void |
---|
3725 | eiremain (short unsigned int *den, short unsigned int *num, LDPARMS * ldp) |
---|
3726 | { |
---|
3727 | long ld, ln; |
---|
3728 | unsigned short j; |
---|
3729 | unsigned short *equot = ldp->equot; |
---|
3730 | |
---|
3731 | ld = den[E]; |
---|
3732 | ld -= enormlz (den); |
---|
3733 | ln = num[E]; |
---|
3734 | ln -= enormlz (num); |
---|
3735 | ecleaz (equot); |
---|
3736 | while (ln >= ld) |
---|
3737 | { |
---|
3738 | if (ecmpm (den, num) <= 0) |
---|
3739 | { |
---|
3740 | esubm (den, num); |
---|
3741 | j = 1; |
---|
3742 | } |
---|
3743 | else |
---|
3744 | { |
---|
3745 | j = 0; |
---|
3746 | } |
---|
3747 | eshup1 (equot); |
---|
3748 | equot[NI - 1] |= j; |
---|
3749 | eshup1 (num); |
---|
3750 | ln -= 1; |
---|
3751 | } |
---|
3752 | emdnorm (num, 0, 0, ln, 0, ldp); |
---|
3753 | } |
---|
3754 | |
---|
3755 | /* NaN bit patterns |
---|
3756 | */ |
---|
3757 | #ifdef MIEEE |
---|
3758 | #if !defined(__mips) |
---|
3759 | static const unsigned short nan113[8] = { |
---|
3760 | 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff |
---|
3761 | }; |
---|
3762 | |
---|
3763 | static const unsigned short nan64[6] = { |
---|
3764 | 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff |
---|
3765 | }; |
---|
3766 | static const unsigned short nan53[4] = { 0x7fff, 0xffff, 0xffff, 0xffff }; |
---|
3767 | static const unsigned short nan24[2] = { 0x7fff, 0xffff }; |
---|
3768 | #elif defined(__mips_nan2008) /* __mips */ |
---|
3769 | static const unsigned short nan113[8] = { 0x7fff, 0x8000, 0, 0, 0, 0, 0, 0 }; |
---|
3770 | static const unsigned short nan64[6] = { 0x7fff, 0xc000, 0, 0, 0, 0 }; |
---|
3771 | static const unsigned short nan53[4] = { 0x7ff8, 0, 0, 0 }; |
---|
3772 | static const unsigned short nan24[2] = { 0x7fc0, 0 }; |
---|
3773 | #else /* __mips && !__mips_nan2008 */ |
---|
3774 | static const unsigned short nan113[8] = { |
---|
3775 | 0x7fff, 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff |
---|
3776 | }; |
---|
3777 | |
---|
3778 | static const unsigned short nan64[6] = { |
---|
3779 | 0x7fff, 0xbfff, 0xffff, 0xffff, 0xffff, 0xffff |
---|
3780 | }; |
---|
3781 | static const unsigned short nan53[4] = { 0x7ff7, 0xffff, 0xffff, 0xffff }; |
---|
3782 | static const unsigned short nan24[2] = { 0x7fbf, 0xffff }; |
---|
3783 | #endif /* __mips && !__mips_nan2008 */ |
---|
3784 | #else /* !MIEEE */ |
---|
3785 | #if !defined(__mips) || defined(__mips_nan2008) |
---|
3786 | static const unsigned short nan113[8] = { 0, 0, 0, 0, 0, 0, 0x8000, 0x7fff }; |
---|
3787 | static const unsigned short nan64[6] = { 0, 0, 0, 0, 0xc000, 0x7fff }; |
---|
3788 | static const unsigned short nan53[4] = { 0, 0, 0, 0x7ff8 }; |
---|
3789 | static const unsigned short nan24[2] = { 0, 0x7fc0 }; |
---|
3790 | #else /* __mips && !__mips_nan2008 */ |
---|
3791 | static const unsigned short nan113[8] = { |
---|
3792 | 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff, 0x7fff |
---|
3793 | }; |
---|
3794 | |
---|
3795 | static const unsigned short nan64[6] = { |
---|
3796 | 0xffff, 0xffff, 0xffff, 0xffff, 0xbfff, 0x7fff |
---|
3797 | }; |
---|
3798 | static const unsigned short nan53[4] = { 0xffff, 0xffff, 0xffff, 0x7ff7 }; |
---|
3799 | static const unsigned short nan24[2] = { 0xffff, 0x7fbf }; |
---|
3800 | #endif /* __mips && !__mips_nan2008 */ |
---|
3801 | #endif /* !MIEEE */ |
---|
3802 | |
---|
3803 | |
---|
3804 | static void |
---|
3805 | enan (short unsigned int *nan, int size) |
---|
3806 | { |
---|
3807 | int i, n; |
---|
3808 | const unsigned short *p; |
---|
3809 | |
---|
3810 | switch (size) |
---|
3811 | { |
---|
3812 | #ifndef DEC |
---|
3813 | case 113: |
---|
3814 | n = 8; |
---|
3815 | p = nan113; |
---|
3816 | break; |
---|
3817 | |
---|
3818 | case 64: |
---|
3819 | n = 6; |
---|
3820 | p = nan64; |
---|
3821 | break; |
---|
3822 | |
---|
3823 | case 53: |
---|
3824 | n = 4; |
---|
3825 | p = nan53; |
---|
3826 | break; |
---|
3827 | |
---|
3828 | case 24: |
---|
3829 | n = 2; |
---|
3830 | p = nan24; |
---|
3831 | break; |
---|
3832 | |
---|
3833 | case NBITS: |
---|
3834 | #if !defined(__mips) || defined(__mips_nan2008) |
---|
3835 | for (i = 0; i < NE - 2; i++) |
---|
3836 | *nan++ = 0; |
---|
3837 | *nan++ = 0xc000; |
---|
3838 | #else /* __mips && !__mips_nan2008 */ |
---|
3839 | for (i = 0; i < NE - 2; i++) |
---|
3840 | *nan++ = 0xffff; |
---|
3841 | *nan++ = 0xbfff; |
---|
3842 | #endif /* __mips && !__mips_nan2008 */ |
---|
3843 | *nan++ = 0x7fff; |
---|
3844 | return; |
---|
3845 | |
---|
3846 | case NI * 16: |
---|
3847 | *nan++ = 0; |
---|
3848 | *nan++ = 0x7fff; |
---|
3849 | *nan++ = 0; |
---|
3850 | #if !defined(__mips) || defined(__mips_nan2008) |
---|
3851 | *nan++ = 0xc000; |
---|
3852 | for (i = 4; i < NI - 1; i++) |
---|
3853 | *nan++ = 0; |
---|
3854 | #else /* __mips && !__mips_nan2008 */ |
---|
3855 | *nan++ = 0xbfff; |
---|
3856 | for (i = 4; i < NI - 1; i++) |
---|
3857 | *nan++ = 0xffff; |
---|
3858 | #endif /* __mips && !__mips_nan2008 */ |
---|
3859 | *nan++ = 0; |
---|
3860 | return; |
---|
3861 | #endif |
---|
3862 | default: |
---|
3863 | mtherr ("enan", DOMAIN); |
---|
3864 | return; |
---|
3865 | } |
---|
3866 | for (i = 0; i < n; i++) |
---|
3867 | *nan++ = *p++; |
---|
3868 | } |
---|