ieee754dp ieee754dp_logb(ieee754dp x) { COMPXDP; CLEARCX; EXPLODEXDP; switch (xc) { case IEEE754_CLASS_SNAN: return ieee754dp_nanxcpt(x, "logb", x); case IEEE754_CLASS_QNAN: return x; case IEEE754_CLASS_INF: return ieee754dp_inf(0); case IEEE754_CLASS_ZERO: return ieee754dp_inf(1); case IEEE754_CLASS_DNORM: DPDNORMX; break; case IEEE754_CLASS_NORM: break; } return ieee754dp_fint(xe); }
ieee754dp ieee754dp_fsp(ieee754sp x) { COMPXSP; EXPLODEXSP; CLEARCX; FLUSHXSP; switch (xc) { case IEEE754_CLASS_SNAN: SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_nanxcpt(ieee754dp_indef(), "fsp"); case IEEE754_CLASS_QNAN: return ieee754dp_nanxcpt(builddp(xs, DP_EMAX + 1 + DP_EBIAS, ((u64) xm << (DP_MBITS - SP_MBITS))), "fsp", x); case IEEE754_CLASS_INF: return ieee754dp_inf(xs); case IEEE754_CLASS_ZERO: return ieee754dp_zero(xs); case IEEE754_CLASS_DNORM: /* normalize */ while ((xm >> SP_MBITS) == 0) { xm <<= 1; xe--; } break; case IEEE754_CLASS_NORM: break; } /* CAN'T possibly overflow,underflow, or need rounding */ /* drop the hidden bit */ xm &= ~SP_HIDDEN_BIT; return builddp(xs, xe + DP_EBIAS, (u64) xm << (DP_MBITS - SP_MBITS)); }
ieee754dp ieee754dp_fsp(ieee754sp x) { COMPXSP; EXPLODEXSP; CLEARCX; FLUSHXSP; switch (xc) { case IEEE754_CLASS_SNAN: SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_nanxcpt(ieee754dp_indef(), "fsp"); case IEEE754_CLASS_QNAN: return ieee754dp_nanxcpt(builddp(xs, DP_EMAX + 1 + DP_EBIAS, ((u64) xm << (DP_MBITS - SP_MBITS))), "fsp", x); case IEEE754_CLASS_INF: return ieee754dp_inf(xs); case IEEE754_CLASS_ZERO: return ieee754dp_zero(xs); case IEEE754_CLASS_DNORM: while ((xm >> SP_MBITS) == 0) { xm <<= 1; xe--; } break; case IEEE754_CLASS_NORM: break; } xm &= ~SP_HIDDEN_BIT; return builddp(xs, xe + DP_EBIAS, (u64) xm << (DP_MBITS - SP_MBITS)); }
ieee754dp ieee754dp_abs(ieee754dp x) { COMPXDP; EXPLODEXDP; CLEARCX; FLUSHXDP; /* Clear sign ALWAYS, irrespective of NaN */ DPSIGN(x) = 0; if (xc == IEEE754_CLASS_SNAN) { return ieee754dp_nanxcpt(ieee754dp_indef(), "abs"); } return x; }
union ieee754dp ieee754dp_fsp(union ieee754sp x) { COMPXSP; EXPLODEXSP; ieee754_clearcx(); FLUSHXSP; switch (xc) { case IEEE754_CLASS_SNAN: return ieee754dp_nanxcpt(ieee754dp_nan_fsp(xs, xm)); case IEEE754_CLASS_QNAN: return ieee754dp_nan_fsp(xs, xm); case IEEE754_CLASS_INF: return ieee754dp_inf(xs); case IEEE754_CLASS_ZERO: return ieee754dp_zero(xs); case IEEE754_CLASS_DNORM: /* normalize */ while ((xm >> SP_FBITS) == 0) { xm <<= 1; xe--; } break; case IEEE754_CLASS_NORM: break; } /* * Can't possibly overflow,underflow, or need rounding */ /* drop the hidden bit */ xm &= ~SP_HIDDEN_BIT; return builddp(xs, xe + DP_EBIAS, (u64) xm << (DP_FBITS - SP_FBITS)); }
ieee754dp ieee754dp_abs(ieee754dp x) { COMPXDP; EXPLODEXDP; CLEARCX; FLUSHXDP; DPSIGN(x) = 0; if (xc == IEEE754_CLASS_SNAN) { SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_nanxcpt(ieee754dp_indef(), "abs"); } return x; }
ieee754dp ieee754dp_neg(ieee754dp x) { COMPXDP; EXPLODEXDP; CLEARCX; FLUSHXDP; DPSIGN(x) ^= 1; if (xc == IEEE754_CLASS_SNAN) { ieee754dp y = ieee754dp_indef(); SETCX(IEEE754_INVALID_OPERATION); DPSIGN(y) = DPSIGN(x); return ieee754dp_nanxcpt(y, "neg"); } return x; }
ieee754dp ieee754dp_scalb(ieee754dp x, int n) { COMPXDP; CLEARCX; EXPLODEXDP; switch (xc) { case IEEE754_CLASS_SNAN: return ieee754dp_nanxcpt(x, "scalb", x, n); case IEEE754_CLASS_QNAN: case IEEE754_CLASS_INF: case IEEE754_CLASS_ZERO: return x; case IEEE754_CLASS_DNORM: DPDNORMX; break; case IEEE754_CLASS_NORM: break; } DPNORMRET2(xs, xe + n, xm << 3, "scalb", x, n); }
ieee754dp ieee754dp_neg(ieee754dp x) { COMPXDP; EXPLODEXDP; CLEARCX; FLUSHXDP; /* * Invert the sign ALWAYS to prevent an endless recursion on * pow() in libc. */ /* quick fix up */ DPSIGN(x) ^= 1; if (xc == IEEE754_CLASS_SNAN) { ieee754dp y = ieee754dp_indef(); SETCX(IEEE754_INVALID_OPERATION); DPSIGN(y) = DPSIGN(x); return ieee754dp_nanxcpt(y, "neg"); } return x; }
ieee754dp ieee754dp_div(ieee754dp x, ieee754dp y) { COMPXDP; COMPYDP; EXPLODEXDP; EXPLODEYDP; CLEARCX; FLUSHXDP; FLUSHYDP; switch (CLPAIR(xc, yc)) { case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF): SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_nanxcpt(ieee754dp_indef(), "div", x, y); case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN): return y; case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF): return x; /* Infinity handling */ case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF): SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_xcpt(ieee754dp_indef(), "div", x, y); case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF): return ieee754dp_zero(xs ^ ys); case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM): return ieee754dp_inf(xs ^ ys); /* Zero handling */ case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO): SETCX(IEEE754_INVALID_OPERATION); return ieee754dp_xcpt(ieee754dp_indef(), "div", x, y); case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO): SETCX(IEEE754_ZERO_DIVIDE); return ieee754dp_xcpt(ieee754dp_inf(xs ^ ys), "div", x, y); case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM): return ieee754dp_zero(xs == ys ? 0 : 1); case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM): DPDNORMX; case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM): DPDNORMY; break; case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM): DPDNORMX; break; case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM): break; } assert(xm & DP_HIDDEN_BIT); assert(ym & DP_HIDDEN_BIT); /* provide rounding space */ xm <<= 3; ym <<= 3; { /* now the dirty work */ u64 rm = 0; int re = xe - ye; u64 bm; for (bm = DP_MBIT(DP_MBITS + 2); bm; bm >>= 1) { if (xm >= ym) { xm -= ym; rm |= bm; if (xm == 0) break; } xm <<= 1; } rm <<= 1; if (xm) rm |= 1; /* have remainder, set sticky */ assert(rm); /* normalise rm to rounding precision ? */ while ((rm >> (DP_MBITS + 3)) == 0) { rm <<= 1; re--; } DPNORMRET2(xs == ys ? 0 : 1, re, rm, "div", x, y); } }
union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y) { COMPXDP; COMPYDP; EXPLODEXDP; EXPLODEYDP; FLUSHXDP; FLUSHYDP; ieee754_clearcx(); switch (CLPAIR(xc, yc)) { case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN): return ieee754dp_nanxcpt(y); case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF): return ieee754dp_nanxcpt(x); /* * Quiet NaN handling */ /* * The case of both inputs quiet NaNs */ case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN): return x; /* * The cases of exactly one input quiet NaN (numbers * are here preferred as returned values to NaNs) */ case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN): return x; case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF): return y; /* * Infinity and zero handling */ case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO): return xs ? y : x; case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM): return ys ? x : y; case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO): return ieee754dp_zero(xs & ys); case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM): DPDNORMX; case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM): DPDNORMY; break; case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM): DPDNORMX; } /* Finally get to do some computation */ assert(xm & DP_HIDDEN_BIT); assert(ym & DP_HIDDEN_BIT); /* Compare signs */ if (xs > ys) return y; else if (xs < ys) return x; /* Signs of inputs are equal, let's compare exponents */ if (xs == 0) { /* Inputs are both positive */ if (xe > ye) return x; else if (xe < ye) return y; } else { /* Inputs are both negative */ if (xe > ye) return y; else if (xe < ye) return x; } /* Signs and exponents of inputs are equal, let's compare mantissas */ if (xs == 0) { /* Inputs are both positive, with equal signs and exponents */ if (xm <= ym) return y; return x; } /* Inputs are both negative, with equal signs and exponents */ if (xm <= ym) return x; return y; }
union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y) { COMPXDP; COMPYDP; EXPLODEXDP; EXPLODEYDP; FLUSHXDP; FLUSHYDP; ieee754_clearcx(); switch (CLPAIR(xc, yc)) { case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN): return ieee754dp_nanxcpt(y); case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF): return ieee754dp_nanxcpt(x); /* numbers are preferred to NaNs */ case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN): return x; case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF): return y; /* * Infinity and zero handling */ case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO): return xs ? y : x; case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM): case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM): return ys ? x : y; case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO): if (xs == ys) return x; return ieee754dp_zero(1); case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM): DPDNORMX; case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM): DPDNORMY; break; case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM): DPDNORMX; } /* Finally get to do some computation */ assert(xm & DP_HIDDEN_BIT); assert(ym & DP_HIDDEN_BIT); /* Compare signs */ if (xs > ys) return y; else if (xs < ys) return x; /* Compare exponent */ if (xe > ye) return x; else if (xe < ye) return y; /* Compare mantissa */ if (xm <= ym) return y; return x; }