/* s_nextafterl.c -- long double version of s_nextafter.c. * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: $"; #endif /* IEEE functions * nextafterl(x,y) * return the next machine floating-point number of x in the * direction toward y. * Special cases: */ #include #include #include #include #include long double __nextafterl(long double x, long double y) { int64_t hx, hy, ihx, ihy, lx; double xhi, xlo, yhi; ldbl_unpack (x, &xhi, &xlo); EXTRACT_WORDS64 (hx, xhi); EXTRACT_WORDS64 (lx, xlo); yhi = ldbl_high (y); EXTRACT_WORDS64 (hy, yhi); ihx = hx&0x7fffffffffffffffLL; /* |hx| */ ihy = hy&0x7fffffffffffffffLL; /* |hy| */ if((ihx>0x7ff0000000000000LL) || /* x is nan */ (ihy>0x7ff0000000000000LL)) /* y is nan */ return x+y; /* signal the nan */ if(x==y) return y; /* x=y, return y */ if(ihx == 0) { /* x == 0 */ long double u; /* return +-minsubnormal */ hy = (hy & 0x8000000000000000ULL) | 1; INSERT_WORDS64 (yhi, hy); x = yhi; u = math_opt_barrier (x); u = u * u; math_force_eval (u); /* raise underflow flag */ return x; } long double u; if(x > y) { /* x > y, x -= ulp */ /* This isn't the largest magnitude correctly rounded long double as you can see from the lowest mantissa bit being zero. It is however the largest magnitude long double with a 106 bit mantissa, and nextafterl is insane with variable precision. So to make nextafterl sane we assume 106 bit precision. */ if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL)) { u = x+x; /* overflow, return -inf */ math_force_eval (u); __set_errno (ERANGE); return y; } if (hx >= 0x7ff0000000000000LL) { u = 0x1.fffffffffffff7ffffffffffff8p+1023L; return u; } if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */ u = math_opt_barrier (x); x -= LDBL_TRUE_MIN; if (ihx < 0x0360000000000000LL || (hx > 0 && lx <= 0) || (hx < 0 && lx > 1)) { u = u * u; math_force_eval (u); /* raise underflow flag */ __set_errno (ERANGE); } return x; } /* If the high double is an exact power of two and the low double is the opposite sign, then 1ulp is one less than what we might determine from the high double. Similarly if X is an exact power of two, and positive, because making it a little smaller will result in the exponent decreasing by one and normalisation of the mantissa. */ if ((hx & 0x000fffffffffffffLL) == 0 && ((lx != 0 && (hx ^ lx) < 0) || (lx == 0 && hx >= 0))) ihx -= 1LL << 52; if (ihx < (106LL << 52)) { /* ulp will denormal */ INSERT_WORDS64 (yhi, ihx & (0x7ffLL<<52)); u = yhi * 0x1p-105; } else { INSERT_WORDS64 (yhi, (ihx & (0x7ffLL<<52))-(105LL<<52)); u = yhi; } return x - u; } else { /* x < y, x += ulp */ if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL)) { u = x+x; /* overflow, return +inf */ math_force_eval (u); __set_errno (ERANGE); return y; } if ((uint64_t) hx >= 0xfff0000000000000ULL) { u = -0x1.fffffffffffff7ffffffffffff8p+1023L; return u; } if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */ u = math_opt_barrier (x); x += LDBL_TRUE_MIN; if (ihx < 0x0360000000000000LL || (hx > 0 && lx < 0 && lx != 0x8000000000000001LL) || (hx < 0 && lx >= 0)) { u = u * u; math_force_eval (u); /* raise underflow flag */ __set_errno (ERANGE); } if (x == 0.0L) /* handle negative LDBL_TRUE_MIN case */ x = -0.0L; return x; } /* If the high double is an exact power of two and the low double is the opposite sign, then 1ulp is one less than what we might determine from the high double. Similarly if X is an exact power of two, and negative, because making it a little larger will result in the exponent decreasing by one and normalisation of the mantissa. */ if ((hx & 0x000fffffffffffffLL) == 0 && ((lx != 0 && (hx ^ lx) < 0) || (lx == 0 && hx < 0))) ihx -= 1LL << 52; if (ihx < (106LL << 52)) { /* ulp will denormal */ INSERT_WORDS64 (yhi, ihx & (0x7ffLL<<52)); u = yhi * 0x1p-105; } else { INSERT_WORDS64 (yhi, (ihx & (0x7ffLL<<52))-(105LL<<52)); u = yhi; } return x + u; } } strong_alias (__nextafterl, __nexttowardl) long_double_symbol (libm, __nextafterl, nextafterl); long_double_symbol (libm, __nexttowardl, nexttowardl);