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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 | // SPDX-License-Identifier: GPL-2.0-only /* IEEE754 floating point arithmetic * double precision: common utilities */ /* * MIPS floating point support * Copyright (C) 1994-2000 Algorithmics Ltd. */ #include <linux/compiler.h> #include "ieee754dp.h" int ieee754dp_class(union ieee754dp x) { COMPXDP; EXPLODEXDP; return xc; } static inline int ieee754dp_isnan(union ieee754dp x) { return ieee754_class_nan(ieee754dp_class(x)); } static inline int ieee754dp_issnan(union ieee754dp x) { int qbit; assert(ieee754dp_isnan(x)); qbit = (DPMANT(x) & DP_MBIT(DP_FBITS - 1)) == DP_MBIT(DP_FBITS - 1); return ieee754_csr.nan2008 ^ qbit; } /* * Raise the Invalid Operation IEEE 754 exception * and convert the signaling NaN supplied to a quiet NaN. */ union ieee754dp __cold ieee754dp_nanxcpt(union ieee754dp r) { assert(ieee754dp_issnan(r)); ieee754_setcx(IEEE754_INVALID_OPERATION); if (ieee754_csr.nan2008) { DPMANT(r) |= DP_MBIT(DP_FBITS - 1); } else { DPMANT(r) &= ~DP_MBIT(DP_FBITS - 1); if (!ieee754dp_isnan(r)) DPMANT(r) |= DP_MBIT(DP_FBITS - 2); } return r; } static u64 ieee754dp_get_rounding(int sn, u64 xm) { /* inexact must round of 3 bits */ if (xm & (DP_MBIT(3) - 1)) { switch (ieee754_csr.rm) { case FPU_CSR_RZ: break; case FPU_CSR_RN: xm += 0x3 + ((xm >> 3) & 1); /* xm += (xm&0x8)?0x4:0x3 */ break; case FPU_CSR_RU: /* toward +Infinity */ if (!sn) /* ?? */ xm += 0x8; break; case FPU_CSR_RD: /* toward -Infinity */ if (sn) /* ?? */ xm += 0x8; break; } } return xm; } /* generate a normal/denormal number with over,under handling * sn is sign * xe is an unbiased exponent * xm is 3bit extended precision value. */ union ieee754dp ieee754dp_format(int sn, int xe, u64 xm) { assert(xm); /* we don't gen exact zeros (probably should) */ assert((xm >> (DP_FBITS + 1 + 3)) == 0); /* no excess */ assert(xm & (DP_HIDDEN_BIT << 3)); if (xe < DP_EMIN) { /* strip lower bits */ int es = DP_EMIN - xe; if (ieee754_csr.nod) { ieee754_setcx(IEEE754_UNDERFLOW); ieee754_setcx(IEEE754_INEXACT); switch(ieee754_csr.rm) { case FPU_CSR_RN: case FPU_CSR_RZ: return ieee754dp_zero(sn); case FPU_CSR_RU: /* toward +Infinity */ if (sn == 0) return ieee754dp_min(0); else return ieee754dp_zero(1); case FPU_CSR_RD: /* toward -Infinity */ if (sn == 0) return ieee754dp_zero(0); else return ieee754dp_min(1); } } if (xe == DP_EMIN - 1 && ieee754dp_get_rounding(sn, xm) >> (DP_FBITS + 1 + 3)) { /* Not tiny after rounding */ ieee754_setcx(IEEE754_INEXACT); xm = ieee754dp_get_rounding(sn, xm); xm >>= 1; /* Clear grs bits */ xm &= ~(DP_MBIT(3) - 1); xe++; } else { /* sticky right shift es bits */ xm = XDPSRS(xm, es); xe += es; assert((xm & (DP_HIDDEN_BIT << 3)) == 0); assert(xe == DP_EMIN); } } if (xm & (DP_MBIT(3) - 1)) { ieee754_setcx(IEEE754_INEXACT); if ((xm & (DP_HIDDEN_BIT << 3)) == 0) { ieee754_setcx(IEEE754_UNDERFLOW); } /* inexact must round of 3 bits */ xm = ieee754dp_get_rounding(sn, xm); /* adjust exponent for rounding add overflowing */ if (xm >> (DP_FBITS + 3 + 1)) { /* add causes mantissa overflow */ xm >>= 1; xe++; } } /* strip grs bits */ xm >>= 3; assert((xm >> (DP_FBITS + 1)) == 0); /* no excess */ assert(xe >= DP_EMIN); if (xe > DP_EMAX) { ieee754_setcx(IEEE754_OVERFLOW); ieee754_setcx(IEEE754_INEXACT); /* -O can be table indexed by (rm,sn) */ switch (ieee754_csr.rm) { case FPU_CSR_RN: return ieee754dp_inf(sn); case FPU_CSR_RZ: return ieee754dp_max(sn); case FPU_CSR_RU: /* toward +Infinity */ if (sn == 0) return ieee754dp_inf(0); else return ieee754dp_max(1); case FPU_CSR_RD: /* toward -Infinity */ if (sn == 0) return ieee754dp_max(0); else return ieee754dp_inf(1); } } /* gen norm/denorm/zero */ if ((xm & DP_HIDDEN_BIT) == 0) { /* we underflow (tiny/zero) */ assert(xe == DP_EMIN); if (ieee754_csr.mx & IEEE754_UNDERFLOW) ieee754_setcx(IEEE754_UNDERFLOW); return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm); } else { assert((xm >> (DP_FBITS + 1)) == 0); /* no excess */ assert(xm & DP_HIDDEN_BIT); return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT); } } |