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1 /* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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2
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3 This file is part of GCC.
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4
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5 GCC is free software; you can redistribute it and/or modify it under
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6 the terms of the GNU General Public License as published by the Free
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7 Software Foundation; either version 3, or (at your option) any later
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8 version.
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9
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10 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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11 WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 for more details.
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14
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15 Under Section 7 of GPL version 3, you are granted additional
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16 permissions described in the GCC Runtime Library Exception, version
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17 3.1, as published by the Free Software Foundation.
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18
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19 You should have received a copy of the GNU General Public License and
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20 a copy of the GCC Runtime Library Exception along with this program;
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21 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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22 <http://www.gnu.org/licenses/>. */
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23
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24 #include "bid_internal.h"
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25
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26 /*****************************************************************************
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27 * BID64 nextup
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28 ****************************************************************************/
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29
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30 #if DECIMAL_CALL_BY_REFERENCE
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31 void
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32 bid64_nextup (UINT64 * pres,
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33 UINT64 *
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34 px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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35 UINT64 x = *px;
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36 #else
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37 UINT64
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38 bid64_nextup (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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39 _EXC_INFO_PARAM) {
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40 #endif
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41
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42 UINT64 res;
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43 UINT64 x_sign;
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44 UINT64 x_exp;
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45 BID_UI64DOUBLE tmp1;
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46 int x_nr_bits;
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47 int q1, ind;
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48 UINT64 C1; // C1 represents x_signif (UINT64)
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49
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50 // check for NaNs and infinities
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51 if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
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52 if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
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53 x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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54 else
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55 x = x & 0xfe03ffffffffffffull; // clear G6-G12
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56 if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
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57 // set invalid flag
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58 *pfpsf |= INVALID_EXCEPTION;
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59 // return quiet (SNaN)
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60 res = x & 0xfdffffffffffffffull;
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61 } else { // QNaN
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62 res = x;
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63 }
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64 BID_RETURN (res);
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65 } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
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66 if (!(x & 0x8000000000000000ull)) { // x is +inf
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67 res = 0x7800000000000000ull;
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68 } else { // x is -inf
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69 res = 0xf7fb86f26fc0ffffull; // -MAXFP = -999...99 * 10^emax
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70 }
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71 BID_RETURN (res);
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72 }
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73 // unpack the argument
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74 x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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75 // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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76 if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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77 x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
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78 C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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79 if (C1 > 9999999999999999ull) { // non-canonical
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80 x_exp = 0;
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81 C1 = 0;
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82 }
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83 } else {
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84 x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
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85 C1 = x & MASK_BINARY_SIG1;
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86 }
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87
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88 // check for zeros (possibly from non-canonical values)
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89 if (C1 == 0x0ull) {
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90 // x is 0
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91 res = 0x0000000000000001ull; // MINFP = 1 * 10^emin
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92 } else { // x is not special and is not zero
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93 if (x == 0x77fb86f26fc0ffffull) {
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94 // x = +MAXFP = 999...99 * 10^emax
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95 res = 0x7800000000000000ull; // +inf
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96 } else if (x == 0x8000000000000001ull) {
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97 // x = -MINFP = 1...99 * 10^emin
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98 res = 0x8000000000000000ull; // -0
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99 } else { // -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
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100 // can add/subtract 1 ulp to the significand
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101
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102 // Note: we could check here if x >= 10^16 to speed up the case q1 =16
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103 // q1 = nr. of decimal digits in x (1 <= q1 <= 54)
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104 // determine first the nr. of bits in x
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105 if (C1 >= MASK_BINARY_OR2) { // x >= 2^53
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106 // split the 64-bit value in two 32-bit halves to avoid rounding errors
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107 if (C1 >= 0x0000000100000000ull) { // x >= 2^32
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108 tmp1.d = (double) (C1 >> 32); // exact conversion
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109 x_nr_bits =
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110 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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111 } else { // x < 2^32
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112 tmp1.d = (double) C1; // exact conversion
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113 x_nr_bits =
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114 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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115 }
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116 } else { // if x < 2^53
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117 tmp1.d = (double) C1; // exact conversion
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118 x_nr_bits =
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119 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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120 }
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121 q1 = nr_digits[x_nr_bits - 1].digits;
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122 if (q1 == 0) {
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123 q1 = nr_digits[x_nr_bits - 1].digits1;
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124 if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
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125 q1++;
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126 }
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127 // if q1 < P16 then pad the significand with zeros
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128 if (q1 < P16) {
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129 if (x_exp > (UINT64) (P16 - q1)) {
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130 ind = P16 - q1; // 1 <= ind <= P16 - 1
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131 // pad with P16 - q1 zeros, until exponent = emin
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132 // C1 = C1 * 10^ind
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133 C1 = C1 * ten2k64[ind];
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134 x_exp = x_exp - ind;
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135 } else { // pad with zeros until the exponent reaches emin
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136 ind = x_exp;
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137 C1 = C1 * ten2k64[ind];
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138 x_exp = EXP_MIN;
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139 }
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140 }
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141 if (!x_sign) { // x > 0
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142 // add 1 ulp (add 1 to the significand)
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143 C1++;
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144 if (C1 == 0x002386f26fc10000ull) { // if C1 = 10^16
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145 C1 = 0x00038d7ea4c68000ull; // C1 = 10^15
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146 x_exp++;
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147 }
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148 // Ok, because MAXFP = 999...99 * 10^emax was caught already
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149 } else { // x < 0
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150 // subtract 1 ulp (subtract 1 from the significand)
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151 C1--;
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152 if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) { // if C1 = 10^15 - 1
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153 C1 = 0x002386f26fc0ffffull; // C1 = 10^16 - 1
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154 x_exp--;
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155 }
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156 }
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157 // assemble the result
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158 // if significand has 54 bits
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159 if (C1 & MASK_BINARY_OR2) {
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160 res =
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161 x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 &
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162 MASK_BINARY_SIG2);
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163 } else { // significand fits in 53 bits
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164 res = x_sign | (x_exp << 53) | C1;
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165 }
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166 } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
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167 } // end x is not special and is not zero
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168 BID_RETURN (res);
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169 }
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170
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171 /*****************************************************************************
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172 * BID64 nextdown
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173 ****************************************************************************/
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174
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175 #if DECIMAL_CALL_BY_REFERENCE
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176 void
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177 bid64_nextdown (UINT64 * pres,
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178 UINT64 *
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179 px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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180 UINT64 x = *px;
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181 #else
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182 UINT64
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183 bid64_nextdown (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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184 _EXC_INFO_PARAM) {
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185 #endif
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186
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187 UINT64 res;
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188 UINT64 x_sign;
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189 UINT64 x_exp;
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190 BID_UI64DOUBLE tmp1;
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191 int x_nr_bits;
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192 int q1, ind;
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193 UINT64 C1; // C1 represents x_signif (UINT64)
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194
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195 // check for NaNs and infinities
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196 if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
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197 if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
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198 x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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199 else
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200 x = x & 0xfe03ffffffffffffull; // clear G6-G12
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201 if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
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202 // set invalid flag
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203 *pfpsf |= INVALID_EXCEPTION;
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204 // return quiet (SNaN)
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205 res = x & 0xfdffffffffffffffull;
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206 } else { // QNaN
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207 res = x;
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208 }
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209 BID_RETURN (res);
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210 } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
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211 if (x & 0x8000000000000000ull) { // x is -inf
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212 res = 0xf800000000000000ull;
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213 } else { // x is +inf
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214 res = 0x77fb86f26fc0ffffull; // +MAXFP = +999...99 * 10^emax
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215 }
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216 BID_RETURN (res);
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217 }
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218 // unpack the argument
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219 x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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220 // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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221 if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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222 x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
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223 C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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224 if (C1 > 9999999999999999ull) { // non-canonical
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225 x_exp = 0;
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226 C1 = 0;
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227 }
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228 } else {
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229 x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
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230 C1 = x & MASK_BINARY_SIG1;
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231 }
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232
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233 // check for zeros (possibly from non-canonical values)
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234 if (C1 == 0x0ull) {
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235 // x is 0
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236 res = 0x8000000000000001ull; // -MINFP = -1 * 10^emin
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237 } else { // x is not special and is not zero
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238 if (x == 0xf7fb86f26fc0ffffull) {
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239 // x = -MAXFP = -999...99 * 10^emax
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240 res = 0xf800000000000000ull; // -inf
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241 } else if (x == 0x0000000000000001ull) {
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242 // x = +MINFP = 1...99 * 10^emin
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243 res = 0x0000000000000000ull; // -0
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244 } else { // -MAXFP + 1ulp <= x <= -MINFP OR MINFP + 1 ulp <= x <= MAXFP
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245 // can add/subtract 1 ulp to the significand
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246
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247 // Note: we could check here if x >= 10^16 to speed up the case q1 =16
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248 // q1 = nr. of decimal digits in x (1 <= q1 <= 16)
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249 // determine first the nr. of bits in x
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250 if (C1 >= 0x0020000000000000ull) { // x >= 2^53
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251 // split the 64-bit value in two 32-bit halves to avoid
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252 // rounding errors
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253 if (C1 >= 0x0000000100000000ull) { // x >= 2^32
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254 tmp1.d = (double) (C1 >> 32); // exact conversion
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255 x_nr_bits =
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256 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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257 } else { // x < 2^32
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258 tmp1.d = (double) C1; // exact conversion
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259 x_nr_bits =
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260 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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261 }
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262 } else { // if x < 2^53
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263 tmp1.d = (double) C1; // exact conversion
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264 x_nr_bits =
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265 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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266 }
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267 q1 = nr_digits[x_nr_bits - 1].digits;
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268 if (q1 == 0) {
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269 q1 = nr_digits[x_nr_bits - 1].digits1;
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270 if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
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271 q1++;
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272 }
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273 // if q1 < P16 then pad the significand with zeros
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274 if (q1 < P16) {
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275 if (x_exp > (UINT64) (P16 - q1)) {
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276 ind = P16 - q1; // 1 <= ind <= P16 - 1
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277 // pad with P16 - q1 zeros, until exponent = emin
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278 // C1 = C1 * 10^ind
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279 C1 = C1 * ten2k64[ind];
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280 x_exp = x_exp - ind;
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281 } else { // pad with zeros until the exponent reaches emin
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282 ind = x_exp;
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283 C1 = C1 * ten2k64[ind];
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284 x_exp = EXP_MIN;
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285 }
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286 }
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287 if (x_sign) { // x < 0
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288 // add 1 ulp (add 1 to the significand)
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289 C1++;
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290 if (C1 == 0x002386f26fc10000ull) { // if C1 = 10^16
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291 C1 = 0x00038d7ea4c68000ull; // C1 = 10^15
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292 x_exp++;
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293 // Ok, because -MAXFP = -999...99 * 10^emax was caught already
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294 }
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295 } else { // x > 0
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296 // subtract 1 ulp (subtract 1 from the significand)
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297 C1--;
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298 if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) { // if C1 = 10^15 - 1
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299 C1 = 0x002386f26fc0ffffull; // C1 = 10^16 - 1
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300 x_exp--;
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301 }
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302 }
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303 // assemble the result
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304 // if significand has 54 bits
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305 if (C1 & MASK_BINARY_OR2) {
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306 res =
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307 x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 &
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308 MASK_BINARY_SIG2);
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309 } else { // significand fits in 53 bits
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310 res = x_sign | (x_exp << 53) | C1;
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311 }
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312 } // end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
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313 } // end x is not special and is not zero
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314 BID_RETURN (res);
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315 }
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316
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317 /*****************************************************************************
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318 * BID64 nextafter
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319 ****************************************************************************/
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320
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321 #if DECIMAL_CALL_BY_REFERENCE
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322 void
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323 bid64_nextafter (UINT64 * pres, UINT64 * px,
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324 UINT64 *
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325 py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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326 UINT64 x = *px;
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327 UINT64 y = *py;
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328 #else
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329 UINT64
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330 bid64_nextafter (UINT64 x,
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331 UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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332 _EXC_INFO_PARAM) {
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333 #endif
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334
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335 UINT64 res;
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336 UINT64 tmp1, tmp2;
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337 FPSC tmp_fpsf = 0; // dummy fpsf for calls to comparison functions
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338 int res1, res2;
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339
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340 // check for NaNs or infinities
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341 if (((x & MASK_SPECIAL) == MASK_SPECIAL) ||
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342 ((y & MASK_SPECIAL) == MASK_SPECIAL)) {
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343 // x is NaN or infinity or y is NaN or infinity
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344
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345 if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
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346 if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
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347 x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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348 else
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349 x = x & 0xfe03ffffffffffffull; // clear G6-G12
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350 if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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351 // set invalid flag
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352 *pfpsf |= INVALID_EXCEPTION;
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353 // return quiet (x)
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354 res = x & 0xfdffffffffffffffull;
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355 } else { // x is QNaN
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356 if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
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357 // set invalid flag
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358 *pfpsf |= INVALID_EXCEPTION;
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359 }
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360 // return x
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361 res = x;
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362 }
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363 BID_RETURN (res);
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364 } else if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
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365 if ((y & 0x0003ffffffffffffull) > 999999999999999ull)
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366 y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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367 else
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368 y = y & 0xfe03ffffffffffffull; // clear G6-G12
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369 if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
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370 // set invalid flag
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371 *pfpsf |= INVALID_EXCEPTION;
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372 // return quiet (y)
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373 res = y & 0xfdffffffffffffffull;
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374 } else { // y is QNaN
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375 // return y
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376 res = y;
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377 }
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378 BID_RETURN (res);
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379 } else { // at least one is infinity
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380 if ((x & MASK_ANY_INF) == MASK_INF) { // x = inf
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381 x = x & (MASK_SIGN | MASK_INF);
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382 }
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383 if ((y & MASK_ANY_INF) == MASK_INF) { // y = inf
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384 y = y & (MASK_SIGN | MASK_INF);
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385 }
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386 }
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387 }
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388 // neither x nor y is NaN
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389
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390 // if not infinity, check for non-canonical values x (treated as zero)
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391 if ((x & MASK_ANY_INF) != MASK_INF) { // x != inf
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392 // unpack x
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393 if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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394 // if the steering bits are 11 (condition will be 0), then
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395 // the exponent is G[0:w+1]
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396 if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
|
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397 9999999999999999ull) {
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|
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398 // non-canonical
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|
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399 x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
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400 }
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401 } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) x is unch.
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402 ; // canonical
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403 }
|
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404 }
|
|
|
405 // no need to check for non-canonical y
|
|
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406
|
|
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407 // neither x nor y is NaN
|
|
|
408 tmp_fpsf = *pfpsf; // save fpsf
|
|
|
409 #if DECIMAL_CALL_BY_REFERENCE
|
|
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410 bid64_quiet_equal (&res1, px,
|
|
|
411 py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
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|
|
412 bid64_quiet_greater (&res2, px,
|
|
|
413 py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
414 #else
|
|
|
415 res1 =
|
|
|
416 bid64_quiet_equal (x,
|
|
|
417 y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
418 res2 =
|
|
|
419 bid64_quiet_greater (x,
|
|
|
420 y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
421 #endif
|
|
|
422 *pfpsf = tmp_fpsf; // restore fpsf
|
|
|
423 if (res1) { // x = y
|
|
|
424 // return x with the sign of y
|
|
|
425 res = (y & 0x8000000000000000ull) | (x & 0x7fffffffffffffffull);
|
|
|
426 } else if (res2) { // x > y
|
|
|
427 #if DECIMAL_CALL_BY_REFERENCE
|
|
|
428 bid64_nextdown (&res,
|
|
|
429 px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
430 #else
|
|
|
431 res =
|
|
|
432 bid64_nextdown (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
433 #endif
|
|
|
434 } else { // x < y
|
|
|
435 #if DECIMAL_CALL_BY_REFERENCE
|
|
|
436 bid64_nextup (&res, px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
437 #else
|
|
|
438 res = bid64_nextup (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
|
439 #endif
|
|
|
440 }
|
|
|
441 // if the operand x is finite but the result is infinite, signal
|
|
|
442 // overflow and inexact
|
|
|
443 if (((x & MASK_INF) != MASK_INF) && ((res & MASK_INF) == MASK_INF)) {
|
|
|
444 // set the inexact flag
|
|
|
445 *pfpsf |= INEXACT_EXCEPTION;
|
|
|
446 // set the overflow flag
|
|
|
447 *pfpsf |= OVERFLOW_EXCEPTION;
|
|
|
448 }
|
|
|
449 // if the result is in (-10^emin, 10^emin), and is different from the
|
|
|
450 // operand x, signal underflow and inexact
|
|
|
451 tmp1 = 0x00038d7ea4c68000ull; // +100...0[16] * 10^emin
|
|
|
452 tmp2 = res & 0x7fffffffffffffffull;
|
|
|
453 tmp_fpsf = *pfpsf; // save fpsf
|
|
|
454 #if DECIMAL_CALL_BY_REFERENCE
|
|
|
455 bid64_quiet_greater (&res1, &tmp1,
|
|
|
456 &tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
|
457 _EXC_INFO_ARG);
|
|
|
458 bid64_quiet_not_equal (&res2, &x,
|
|
|
459 &res _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
|
460 _EXC_INFO_ARG);
|
|
|
461 #else
|
|
|
462 res1 =
|
|
|
463 bid64_quiet_greater (tmp1,
|
|
|
464 tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
|
465 _EXC_INFO_ARG);
|
|
|
466 res2 =
|
|
|
467 bid64_quiet_not_equal (x,
|
|
|
468 res _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
|
469 _EXC_INFO_ARG);
|
|
|
470 #endif
|
|
|
471 *pfpsf = tmp_fpsf; // restore fpsf
|
|
|
472 if (res1 && res2) {
|
|
|
473 // if (bid64_quiet_greater (tmp1, tmp2, &tmp_fpsf) &&
|
|
|
474 // bid64_quiet_not_equal (x, res, &tmp_fpsf)) {
|
|
|
475 // set the inexact flag
|
|
|
476 *pfpsf |= INEXACT_EXCEPTION;
|
|
|
477 // set the underflow flag
|
|
|
478 *pfpsf |= UNDERFLOW_EXCEPTION;
|
|
|
479 }
|
|
|
480 BID_RETURN (res);
|
|
|
481 }
|
