1 | #include <stdint.h>
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2 | #include <float.h>
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3 | #include <math.h>
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4 | #include "atomic.h"
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5 |
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6 | #define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i
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7 | #define ZEROINFNAN (0x7ff-0x3ff-52-1)
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8 |
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9 | struct num { uint64_t m; int e; int sign; };
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10 |
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11 | static struct num normalize(double x)
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12 | {
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13 | uint64_t ix = ASUINT64(x);
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14 | int e = ix>>52;
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15 | int sign = e & 0x800;
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16 | e &= 0x7ff;
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17 | if (!e) {
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18 | ix = ASUINT64(x*0x1p63);
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19 | e = ix>>52 & 0x7ff;
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20 | e = e ? e-63 : 0x800;
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21 | }
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22 | ix &= (1ull<<52)-1;
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23 | ix |= 1ull<<52;
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24 | ix <<= 1;
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25 | e -= 0x3ff + 52 + 1;
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26 | return (struct num){ix,e,sign};
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27 | }
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28 |
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29 | static void mul(uint64_t *hi, uint64_t *lo, uint64_t x, uint64_t y)
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30 | {
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31 | uint64_t t1,t2,t3;
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32 | uint64_t xlo = (uint32_t)x, xhi = x>>32;
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33 | uint64_t ylo = (uint32_t)y, yhi = y>>32;
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34 |
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35 | t1 = xlo*ylo;
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36 | t2 = xlo*yhi + xhi*ylo;
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37 | t3 = xhi*yhi;
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38 | *lo = t1 + (t2<<32);
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39 | *hi = t3 + (t2>>32) + (t1 > *lo);
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40 | }
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41 |
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42 | double fma(double x, double y, double z)
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43 | {
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44 | #pragma STDC FENV_ACCESS ON
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45 |
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46 | /* normalize so top 10bits and last bit are 0 */
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47 | struct num nx, ny, nz;
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48 | nx = normalize(x);
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49 | ny = normalize(y);
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50 | nz = normalize(z);
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51 |
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52 | if (nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN)
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53 | return x*y + z;
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54 | if (nz.e >= ZEROINFNAN) {
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55 | if (nz.e > ZEROINFNAN) /* z==0 */
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56 | return x*y + z;
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57 | return z;
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58 | }
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59 |
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60 | /* mul: r = x*y */
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61 | uint64_t rhi, rlo, zhi, zlo;
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62 | mul(&rhi, &rlo, nx.m, ny.m);
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63 | /* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
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64 |
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65 | /* align exponents */
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66 | int e = nx.e + ny.e;
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67 | int d = nz.e - e;
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68 | /* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
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69 | if (d > 0) {
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70 | if (d < 64) {
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71 | zlo = nz.m<<d;
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72 | zhi = nz.m>>64-d;
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73 | } else {
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74 | zlo = 0;
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75 | zhi = nz.m;
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76 | e = nz.e - 64;
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77 | d -= 64;
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78 | if (d == 0) {
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79 | } else if (d < 64) {
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80 | rlo = rhi<<64-d | rlo>>d | !!(rlo<<64-d);
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81 | rhi = rhi>>d;
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82 | } else {
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83 | rlo = 1;
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84 | rhi = 0;
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85 | }
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86 | }
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87 | } else {
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88 | zhi = 0;
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89 | d = -d;
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90 | if (d == 0) {
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91 | zlo = nz.m;
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92 | } else if (d < 64) {
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93 | zlo = nz.m>>d | !!(nz.m<<64-d);
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94 | } else {
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95 | zlo = 1;
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96 | }
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97 | }
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98 |
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99 | /* add */
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100 | int sign = nx.sign^ny.sign;
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101 | int samesign = !(sign^nz.sign);
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102 | int nonzero = 1;
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103 | if (samesign) {
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104 | /* r += z */
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105 | rlo += zlo;
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106 | rhi += zhi + (rlo < zlo);
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107 | } else {
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108 | /* r -= z */
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109 | uint64_t t = rlo;
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110 | rlo -= zlo;
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111 | rhi = rhi - zhi - (t < rlo);
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112 | if (rhi>>63) {
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113 | rlo = -rlo;
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114 | rhi = -rhi-!!rlo;
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115 | sign = !sign;
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116 | }
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117 | nonzero = !!rhi;
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118 | }
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119 |
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120 | /* set rhi to top 63bit of the result (last bit is sticky) */
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121 | if (nonzero) {
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122 | e += 64;
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123 | d = a_clz_64(rhi)-1;
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124 | /* note: d > 0 */
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125 | rhi = rhi<<d | rlo>>64-d | !!(rlo<<d);
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126 | } else if (rlo) {
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127 | d = a_clz_64(rlo)-1;
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128 | if (d < 0)
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129 | rhi = rlo>>1 | (rlo&1);
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130 | else
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131 | rhi = rlo<<d;
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132 | } else {
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133 | /* exact +-0 */
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134 | return x*y + z;
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135 | }
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136 | e -= d;
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137 |
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138 | /* convert to double */
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139 | int64_t i = rhi; /* i is in [1<<62,(1<<63)-1] */
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140 | if (sign)
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141 | i = -i;
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142 | double r = i; /* |r| is in [0x1p62,0x1p63] */
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143 |
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144 | if (e < -1022-62) {
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145 | /* result is subnormal before rounding */
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146 | if (e == -1022-63) {
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147 | double c = 0x1p63;
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148 | if (sign)
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149 | c = -c;
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150 | if (r == c) {
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151 | /* min normal after rounding, underflow depends
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152 | on arch behaviour which can be imitated by
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153 | a double to float conversion */
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154 | float fltmin = 0x0.ffffff8p-63*FLT_MIN * r;
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155 | return DBL_MIN/FLT_MIN * fltmin;
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156 | }
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157 | /* one bit is lost when scaled, add another top bit to
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158 | only round once at conversion if it is inexact */
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159 | if (rhi << 53) {
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160 | i = rhi>>1 | (rhi&1) | 1ull<<62;
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161 | if (sign)
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162 | i = -i;
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163 | r = i;
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164 | r = 2*r - c; /* remove top bit */
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165 |
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166 | /* raise underflow portably, such that it
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167 | cannot be optimized away */
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168 | {
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169 | double_t tiny = DBL_MIN/FLT_MIN * r;
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170 | r += (double)(tiny*tiny) * (r-r);
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171 | }
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172 | }
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173 | } else {
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174 | /* only round once when scaled */
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175 | d = 10;
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176 | i = ( rhi>>d | !!(rhi<<64-d) ) << d;
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177 | if (sign)
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178 | i = -i;
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179 | r = i;
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180 | }
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181 | }
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182 | return scalbn(r, e);
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183 | }
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