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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 /*****************************************************************************
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25 * BID64 fma
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26 *****************************************************************************
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27 *
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28 * Algorithm description:
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29 *
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30 * if multiplication is guranteed exact (short coefficients)
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31 * call the unpacked arg. equivalent of bid64_add(x*y, z)
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32 * else
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33 * get full coefficient_x*coefficient_y product
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34 * call subroutine to perform addition of 64-bit argument
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35 * to 128-bit product
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36 *
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37 ****************************************************************************/
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38
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39 #include "bid_inline_add.h"
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40
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41 #if DECIMAL_CALL_BY_REFERENCE
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42 extern void bid64_mul (UINT64 * pres, UINT64 * px,
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43 UINT64 *
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44 py _RND_MODE_PARAM _EXC_FLAGS_PARAM
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45 _EXC_MASKS_PARAM _EXC_INFO_PARAM);
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46 #else
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47
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48 extern UINT64 bid64_mul (UINT64 x,
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49 UINT64 y _RND_MODE_PARAM
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50 _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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51 _EXC_INFO_PARAM);
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52 #endif
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53
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54 #if DECIMAL_CALL_BY_REFERENCE
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55
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56 void
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57 bid64_fma (UINT64 * pres, UINT64 * px, UINT64 * py,
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58 UINT64 *
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59 pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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60 _EXC_INFO_PARAM) {
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61 UINT64 x, y, z;
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62 #else
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63
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64 UINT64
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65 bid64_fma (UINT64 x, UINT64 y,
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66 UINT64 z _RND_MODE_PARAM _EXC_FLAGS_PARAM
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67 _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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68 #endif
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69 UINT128 P, PU, CT, CZ;
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70 UINT64 sign_x, sign_y, coefficient_x, coefficient_y, sign_z,
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71 coefficient_z;
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72 UINT64 C64, remainder_y, res;
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73 UINT64 CYh, CY0L, T, valid_x, valid_y, valid_z;
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74 int_double tempx, tempy;
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75 int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy,
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76 bin_expon_product, rmode;
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77 int digits_p, bp, final_exponent, exponent_z, digits_z, ez, ey,
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78 scale_z, uf_status;
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79
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80 #if DECIMAL_CALL_BY_REFERENCE
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81 #if !DECIMAL_GLOBAL_ROUNDING
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82 _IDEC_round rnd_mode = *prnd_mode;
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83 #endif
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84 x = *px;
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85 y = *py;
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86 z = *pz;
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87 #endif
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88
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89 valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
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90 valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
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91 valid_z = unpack_BID64 (&sign_z, &exponent_z, &coefficient_z, z);
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92
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93 // unpack arguments, check for NaN, Infinity, or 0
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94 if (!valid_x || !valid_y || !valid_z) {
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95
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96 if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
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97 // if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y)
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98 // check first for non-canonical NaN payload
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99 y = y & 0xfe03ffffffffffffull; // clear G6-G12
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100 if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
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101 y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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102 }
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103 if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
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104 // set invalid flag
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105 *pfpsf |= INVALID_EXCEPTION;
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106 // return quiet (y)
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107 res = y & 0xfdffffffffffffffull;
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108 } else { // y is QNaN
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109 // return y
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110 res = y;
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111 // if z = SNaN or x = SNaN signal invalid exception
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112 if ((z & MASK_SNAN) == MASK_SNAN
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113 || (x & MASK_SNAN) == MASK_SNAN) {
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114 // set invalid flag
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115 *pfpsf |= INVALID_EXCEPTION;
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116 }
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117 }
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118 BID_RETURN (res)
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119 } else if ((z & MASK_NAN) == MASK_NAN) { // z is NAN
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120 // if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z)
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121 // check first for non-canonical NaN payload
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122 z = z & 0xfe03ffffffffffffull; // clear G6-G12
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123 if ((z & 0x0003ffffffffffffull) > 999999999999999ull) {
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124 z = z & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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125 }
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126 if ((z & MASK_SNAN) == MASK_SNAN) { // z is SNAN
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127 // set invalid flag
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128 *pfpsf |= INVALID_EXCEPTION;
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129 // return quiet (z)
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130 res = z & 0xfdffffffffffffffull;
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131 } else { // z is QNaN
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132 // return z
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133 res = z;
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134 // if x = SNaN signal invalid exception
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135 if ((x & MASK_SNAN) == MASK_SNAN) {
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136 // set invalid flag
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137 *pfpsf |= INVALID_EXCEPTION;
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138 }
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139 }
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140 BID_RETURN (res)
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141 } else if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
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142 // if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x)
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143 // check first for non-canonical NaN payload
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144 x = x & 0xfe03ffffffffffffull; // clear G6-G12
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145 if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
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146 x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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147 }
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148 if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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149 // set invalid flag
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150 *pfpsf |= INVALID_EXCEPTION;
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151 // return quiet (x)
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152 res = x & 0xfdffffffffffffffull;
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153 } else { // x is QNaN
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154 // return x
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155 res = x; // clear out G[6]-G[16]
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156 }
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157 BID_RETURN (res)
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158 }
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159
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160 if (!valid_x) {
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161 // x is Inf. or 0
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162
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163 // x is Infinity?
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164 if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
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165 // check if y is 0
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166 if (!coefficient_y) {
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167 // y==0, return NaN
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168 #ifdef SET_STATUS_FLAGS
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169 if ((z & 0x7e00000000000000ull) != 0x7c00000000000000ull)
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170 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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171 #endif
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172 BID_RETURN (0x7c00000000000000ull);
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173 }
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174 // test if z is Inf of oposite sign
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175 if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull)
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176 && (((x ^ y) ^ z) & 0x8000000000000000ull)) {
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177 // return NaN
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178 #ifdef SET_STATUS_FLAGS
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179 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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180 #endif
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181 BID_RETURN (0x7c00000000000000ull);
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182 }
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183 // otherwise return +/-Inf
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184 BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
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185 0x7800000000000000ull);
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186 }
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187 // x is 0
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188 if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)
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189 && ((z & 0x7800000000000000ull) != 0x7800000000000000ull)) {
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190
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191 if (coefficient_z) {
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192 exponent_y = exponent_x - DECIMAL_EXPONENT_BIAS + exponent_y;
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193
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194 sign_z = z & 0x8000000000000000ull;
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195
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196 if (exponent_y >= exponent_z)
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197 BID_RETURN (z);
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198 res =
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199 add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z,
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200 &rnd_mode, pfpsf);
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201 BID_RETURN (res);
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202 }
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203 }
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204 }
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205 if (!valid_y) {
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206 // y is Inf. or 0
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207
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208 // y is Infinity?
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209 if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
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210 // check if x is 0
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211 if (!coefficient_x) {
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212 // y==0, return NaN
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213 #ifdef SET_STATUS_FLAGS
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214 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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215 #endif
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216 BID_RETURN (0x7c00000000000000ull);
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217 }
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218 // test if z is Inf of oposite sign
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219 if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull)
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220 && (((x ^ y) ^ z) & 0x8000000000000000ull)) {
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221 #ifdef SET_STATUS_FLAGS
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222 __set_status_flags (pfpsf, INVALID_EXCEPTION);
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223 #endif
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224 // return NaN
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225 BID_RETURN (0x7c00000000000000ull);
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226 }
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227 // otherwise return +/-Inf
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228 BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
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229 0x7800000000000000ull);
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230 }
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231 // y is 0
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232 if (((z & 0x7800000000000000ull) != 0x7800000000000000ull)) {
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233
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234 if (coefficient_z) {
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235 exponent_y += exponent_x - DECIMAL_EXPONENT_BIAS;
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236
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237 sign_z = z & 0x8000000000000000ull;
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238
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239 if (exponent_y >= exponent_z)
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240 BID_RETURN (z);
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241 res =
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242 add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z,
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243 &rnd_mode, pfpsf);
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244 BID_RETURN (res);
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245 }
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246 }
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247 }
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248
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249 if (!valid_z) {
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250 // y is Inf. or 0
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251
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252 // test if y is NaN/Inf
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253 if ((z & 0x7800000000000000ull) == 0x7800000000000000ull) {
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254 BID_RETURN (coefficient_z & QUIET_MASK64);
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255 }
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256 // z is 0, return x*y
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257 if ((!coefficient_x) || (!coefficient_y)) {
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258 //0+/-0
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259 exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS;
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260 if (exponent_x > DECIMAL_MAX_EXPON_64)
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261 exponent_x = DECIMAL_MAX_EXPON_64;
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262 else if (exponent_x < 0)
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263 exponent_x = 0;
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264 if (exponent_x <= exponent_z)
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265 res = ((UINT64) exponent_x) << 53;
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266 else
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267 res = ((UINT64) exponent_z) << 53;
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268 if ((sign_x ^ sign_y) == sign_z)
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269 res |= sign_z;
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270 #ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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271 #ifndef IEEE_ROUND_NEAREST
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272 else if (rnd_mode == ROUNDING_DOWN)
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273 res |= 0x8000000000000000ull;
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274 #endif
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275 #endif
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276 BID_RETURN (res);
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277 }
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278 }
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279 }
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280
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281 /* get binary coefficients of x and y */
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282
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283 //--- get number of bits in the coefficients of x and y ---
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284 // version 2 (original)
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285 tempx.d = (double) coefficient_x;
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286 bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52);
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287
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288 tempy.d = (double) coefficient_y;
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289 bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52);
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290
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291 // magnitude estimate for coefficient_x*coefficient_y is
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292 // 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx)
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293 bin_expon_product = bin_expon_cx + bin_expon_cy;
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294
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295 // check if coefficient_x*coefficient_y<2^(10*k+3)
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296 // equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1
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297 if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) {
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298 // easy multiply
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299 C64 = coefficient_x * coefficient_y;
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300 final_exponent = exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS;
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301 if ((final_exponent > 0) || (!coefficient_z)) {
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302 res =
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303 get_add64 (sign_x ^ sign_y,
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304 final_exponent, C64, sign_z, exponent_z, coefficient_z, rnd_mode, pfpsf);
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305 BID_RETURN (res);
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306 } else {
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307 P.w[0] = C64;
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308 P.w[1] = 0;
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309 extra_digits = 0;
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310 }
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311 } else {
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312 if (!coefficient_z) {
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313 #if DECIMAL_CALL_BY_REFERENCE
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314 bid64_mul (&res, px,
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315 py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
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316 _EXC_INFO_ARG);
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317 #else
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318 res =
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319 bid64_mul (x,
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320 y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
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321 _EXC_INFO_ARG);
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322 #endif
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323 BID_RETURN (res);
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324 }
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325 // get 128-bit product: coefficient_x*coefficient_y
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326 __mul_64x64_to_128 (P, coefficient_x, coefficient_y);
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327
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328 // tighten binary range of P: leading bit is 2^bp
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329 // unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1
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330 bin_expon_product -= 2 * BINARY_EXPONENT_BIAS;
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331 __tight_bin_range_128 (bp, P, bin_expon_product);
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332
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333 // get number of decimal digits in the product
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334 digits_p = estimate_decimal_digits[bp];
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335 if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P)))
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336 digits_p++; // if power10_table_128[digits_p] <= P
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337
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338 // determine number of decimal digits to be rounded out
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339 extra_digits = digits_p - MAX_FORMAT_DIGITS;
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340 final_exponent =
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341 exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS;
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342 }
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343
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344 if (((unsigned) final_exponent) >= 3 * 256) {
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345 if (final_exponent < 0) {
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346 //--- get number of bits in the coefficients of z ---
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347 tempx.d = (double) coefficient_z;
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348 bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
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349 // get number of decimal digits in the coeff_x
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350 digits_z = estimate_decimal_digits[bin_expon_cx];
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351 if (coefficient_z >= power10_table_128[digits_z].w[0])
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352 digits_z++;
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353 // underflow
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354 if ((final_exponent + 16 < 0)
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355 || (exponent_z + digits_z > 33 + final_exponent)) {
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356 res =
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357 BID_normalize (sign_z, exponent_z, coefficient_z,
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358 sign_x ^ sign_y, 1, rnd_mode, pfpsf);
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359 BID_RETURN (res);
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360 }
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361
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362 ez = exponent_z + digits_z - 16;
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363 if (ez < 0)
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364 ez = 0;
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365 scale_z = exponent_z - ez;
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366 coefficient_z *= power10_table_128[scale_z].w[0];
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367 ey = final_exponent - extra_digits;
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368 extra_digits = ez - ey;
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369 if (extra_digits > 33) {
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370 res =
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371 BID_normalize (sign_z, exponent_z, coefficient_z,
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372 sign_x ^ sign_y, 1, rnd_mode, pfpsf);
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373 BID_RETURN (res);
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374 }
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375 //else // extra_digits<=32
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376
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377 if (extra_digits > 17) {
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378 CYh = __truncate (P, 16);
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379 // get remainder
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380 T = power10_table_128[16].w[0];
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381 __mul_64x64_to_64 (CY0L, CYh, T);
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382 remainder_y = P.w[0] - CY0L;
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383
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384 extra_digits -= 16;
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385 P.w[0] = CYh;
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386 P.w[1] = 0;
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387 } else
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388 remainder_y = 0;
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389
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390 // align coeff_x, CYh
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391 __mul_64x64_to_128 (CZ, coefficient_z,
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392 power10_table_128[extra_digits].w[0]);
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393
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394 if (sign_z == (sign_y ^ sign_x)) {
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395 __add_128_128 (CT, CZ, P);
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396 if (__unsigned_compare_ge_128
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397 (CT, power10_table_128[16 + extra_digits])) {
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398 extra_digits++;
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399 ez++;
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400 }
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401 } else {
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402 if (remainder_y && (__unsigned_compare_ge_128 (CZ, P))) {
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403 P.w[0]++;
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404 if (!P.w[0])
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405 P.w[1]++;
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406 }
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407 __sub_128_128 (CT, CZ, P);
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408 if (((SINT64) CT.w[1]) < 0) {
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409 sign_z = sign_y ^ sign_x;
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410 CT.w[0] = 0 - CT.w[0];
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411 CT.w[1] = 0 - CT.w[1];
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412 if (CT.w[0])
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413 CT.w[1]--;
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414 } else if(!(CT.w[1]|CT.w[0]))
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415 sign_z = (rnd_mode!=ROUNDING_DOWN)? 0: 0x8000000000000000ull;
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416 if (ez
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417 &&
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418 (__unsigned_compare_gt_128
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419 (power10_table_128[15 + extra_digits], CT))) {
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420 extra_digits--;
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421 ez--;
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422 }
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423 }
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424
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425 #ifdef SET_STATUS_FLAGS
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426 uf_status = 0;
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427 if ((!ez)
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428 &&
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429 __unsigned_compare_gt_128 (power10_table_128
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430 [extra_digits + 15], CT)) {
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431 rmode = rnd_mode;
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432 if (sign_z && (unsigned) (rmode - 1) < 2)
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|
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433 rmode = 3 - rmode;
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|
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434 //__add_128_64(PU, CT, round_const_table[rmode][extra_digits]);
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|
|
435 PU = power10_table_128[extra_digits + 15];
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|
|
436 PU.w[0]--;
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|
|
437 if (__unsigned_compare_gt_128 (PU, CT)
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|
|
438 || (rmode == ROUNDING_DOWN)
|
|
|
439 || (rmode == ROUNDING_TO_ZERO))
|
|
|
440 uf_status = UNDERFLOW_EXCEPTION;
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|
|
441 else if (extra_digits < 2) {
|
|
|
442 if ((rmode == ROUNDING_UP)) {
|
|
|
443 if (!extra_digits)
|
|
|
444 uf_status = UNDERFLOW_EXCEPTION;
|
|
|
445 else {
|
|
|
446 if (remainder_y && (sign_z != (sign_y ^ sign_x)))
|
|
|
447 remainder_y = power10_table_128[16].w[0] - remainder_y;
|
|
|
448
|
|
|
449 if (power10_table_128[15].w[0] > remainder_y)
|
|
|
450 uf_status = UNDERFLOW_EXCEPTION;
|
|
|
451 }
|
|
|
452 } else // RN or RN_away
|
|
|
453 {
|
|
|
454 if (remainder_y && (sign_z != (sign_y ^ sign_x)))
|
|
|
455 remainder_y = power10_table_128[16].w[0] - remainder_y;
|
|
|
456
|
|
|
457 if (!extra_digits) {
|
|
|
458 remainder_y += round_const_table[rmode][15];
|
|
|
459 if (remainder_y < power10_table_128[16].w[0])
|
|
|
460 uf_status = UNDERFLOW_EXCEPTION;
|
|
|
461 } else {
|
|
|
462 if (remainder_y < round_const_table[rmode][16])
|
|
|
463 uf_status = UNDERFLOW_EXCEPTION;
|
|
|
464 }
|
|
|
465 }
|
|
|
466 //__set_status_flags (pfpsf, uf_status);
|
|
|
467 }
|
|
|
468 }
|
|
|
469 #endif
|
|
|
470 res =
|
|
|
471 __bid_full_round64_remainder (sign_z, ez - extra_digits, CT,
|
|
|
472 extra_digits, remainder_y,
|
|
|
473 rnd_mode, pfpsf, uf_status);
|
|
|
474 BID_RETURN (res);
|
|
|
475
|
|
|
476 } else {
|
|
|
477 if ((sign_z == (sign_x ^ sign_y))
|
|
|
478 || (final_exponent > 3 * 256 + 15)) {
|
|
|
479 res =
|
|
|
480 fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent,
|
|
|
481 1000000000000000ull, rnd_mode,
|
|
|
482 pfpsf);
|
|
|
483 BID_RETURN (res);
|
|
|
484 }
|
|
|
485 }
|
|
|
486 }
|
|
|
487
|
|
|
488
|
|
|
489 if (extra_digits > 0) {
|
|
|
490 res =
|
|
|
491 get_add128 (sign_z, exponent_z, coefficient_z, sign_x ^ sign_y,
|
|
|
492 final_exponent, P, extra_digits, rnd_mode, pfpsf);
|
|
|
493 BID_RETURN (res);
|
|
|
494 }
|
|
|
495 // go to convert_format and exit
|
|
|
496 else {
|
|
|
497 C64 = __low_64 (P);
|
|
|
498
|
|
|
499 res =
|
|
|
500 get_add64 (sign_x ^ sign_y,
|
|
|
501 exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64,
|
|
|
502 sign_z, exponent_z, coefficient_z,
|
|
|
503 rnd_mode, pfpsf);
|
|
|
504 BID_RETURN (res);
|
|
|
505 }
|
|
|
506 }
|
