/* mpn_get_d -- limbs to double conversion. THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN FUTURE GNU MP RELEASES. Copyright 2003, 2004 Free Software Foundation, Inc. This file is part of the GNU MP Library. The GNU MP Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU MP Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU MP Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ #include "mpir.h" #include "gmp-impl.h" #include "longlong.h" #define CONST_1024 (1024) #define CONST_NEG_1023 (-1023) #define CONST_NEG_1022_SUB_53 (-1022 - 53) /* Return the value {ptr,size}*2^exp, and negative if sign<0. Must have size>=1, and a non-zero high limb ptr[size-1]. {ptr,size} is truncated towards zero. This is consistent with other gmp conversions, like mpz_set_f or mpz_set_q, and is easy to implement and test. In the past conversions had attempted (imperfectly) to let the hardware float rounding mode take effect, but that gets tricky since multiple roundings need to be avoided, or taken into account, and denorms mean the effective precision of the mantissa is not constant. (For reference, mpz_get_d on IEEE systems was ok, except it operated on the absolute value. mpf_get_d and mpq_get_d suffered from multiple roundings and from not always using enough bits to get the rounding right.) It's felt that GMP is not primarily concerned with hardware floats, and really isn't enhanced by getting involved with hardware rounding modes (which could even be some weird unknown style), so something unambiguous and straightforward is best. The IEEE code below is the usual case, it knows either a 32-bit or 64-bit limb and is done with shifts and masks. The 64-bit case in particular should come out nice and compact. The generic code works one bit at a time, which will be quite slow, but should support any binary-based "double" and be safe against any rounding mode. Note in particular it works on IEEE systems too. Traps: Hardware traps for overflow to infinity, underflow to zero, or unsupported denorms may or may not be taken. The IEEE code works bitwise and so probably won't trigger them, the generic code works by float operations and so probably will. This difference might be thought less than ideal, but again its felt straightforward code is better than trying to get intimate with hardware exceptions (of perhaps unknown nature). Not done: mpz_get_d in the past handled size==1 with a cast limb->double. This might still be worthwhile there (for up to the mantissa many bits), but for mpn_get_d here, the cost of applying "exp" to the resulting exponent would probably use up any benefit a cast may have over bit twiddling. Also, if the exponent is pushed into denorm range then bit twiddling is the only option, to ensure the desired truncation is obtained. Other: For reference, note that HPPA 8000, 8200, 8500 and 8600 trap FCNV,UDW,DBL to the kernel for values >= 2^63. This makes it slow, and worse the Linux kernel (what versions?) apparently uses untested code in its trap handling routines, and gets the sign wrong. We don't use such a limb to double cast, neither in the IEEE or generic code. */ double mpn_get_d (mp_srcptr ptr, mp_size_t size, mp_size_t sign, long exp) { ASSERT (size >= 0); ASSERT_MPN (ptr, size); ASSERT (size == 0 || ptr[size-1] != 0); if (size == 0) return 0.0; /* Adjust exp to a radix point just above {ptr,size}, guarding against overflow. After this exp can of course be reduced to anywhere within the {ptr,size} region without underflow. */ if (UNLIKELY ((gmp_ui) (GMP_NUMB_BITS * size) > (gmp_ui) (LONG_MAX - exp))) { goto ieee_infinity; /* generic */ exp = LONG_MAX; } else { exp += GMP_NUMB_BITS * size; } #define ONE_LIMB (GMP_LIMB_BITS == 64 && 2*GMP_NUMB_BITS >= 53) #define TWO_LIMBS (GMP_LIMB_BITS == 32 && 3*GMP_NUMB_BITS >= 53) if (ONE_LIMB || TWO_LIMBS) { union ieee_double_extract u; mp_limb_t m0, m1, m2, rmask; int lshift, rshift; m0 = ptr[size-1]; /* high limb */ m1 = (size >= 2 ? ptr[size-2] : 0); /* second highest limb */ count_leading_zeros (lshift, m0); /* relative to just under high non-zero bit */ exp -= (lshift - GMP_NAIL_BITS) + 1; if (ONE_LIMB) { /* lshift to have high of m0 non-zero, and collapse nails */ rshift = GMP_LIMB_BITS - lshift; m1 <<= GMP_NAIL_BITS; rmask = GMP_NAIL_BITS == 0 && lshift == 0 ? 0 : MP_LIMB_T_MAX; m0 = (m0 << lshift) | ((m1 >> rshift) & rmask); /* rshift back to have bit 53 of m0 the high non-zero */ m0 >>= 11; } else /* TWO_LIMBS */ { m2 = (size >= 3 ? ptr[size-3] : 0); /* third highest limb */ /* collapse nails from m1 and m2 */ #if GMP_NAIL_BITS != 0 m1 = (m1 << GMP_NAIL_BITS) | (m2 >> (GMP_NUMB_BITS-GMP_NAIL_BITS)); m2 <<= 2*GMP_NAIL_BITS; #endif /* lshift to have high of m0:m1 non-zero, collapse nails from m0 */ rshift = GMP_LIMB_BITS - lshift; rmask = (GMP_NAIL_BITS == 0 && lshift == 0 ? 0 : MP_LIMB_T_MAX); m0 = (m0 << lshift) | ((m1 >> rshift) & rmask); m1 = (m1 << lshift) | ((m2 >> rshift) & rmask); /* rshift back to have bit 53 of m0:m1 the high non-zero */ m1 = (m1 >> 11) | (m0 << (GMP_LIMB_BITS-11)); m0 >>= 11; } if (UNLIKELY (exp >= CONST_1024)) { /* overflow, return infinity */ ieee_infinity: m0 = 0; m1 = 0; exp = 1024; } else if (UNLIKELY (exp <= CONST_NEG_1023)) { if (LIKELY (exp <= CONST_NEG_1022_SUB_53)) return 0.0; /* denorm underflows to zero */ rshift = -1022 - exp; ASSERT (rshift > 0 && rshift < 53); if (ONE_LIMB) { m0 >>= rshift; } else /* TWO_LIMBS */ { if (rshift >= 32) { m1 = m0; m0 = 0; rshift -= 32; } lshift = GMP_LIMB_BITS - rshift; m1 = (m1 >> rshift) | (rshift == 0 ? 0 : m0 << lshift); m0 >>= rshift; } exp = -1023; } if (ONE_LIMB) { #if GMP_LIMB_BITS > 32 /* avoid compiler warning about big shift */ u.s.manh = m0 >> 32; #endif u.s.manl = m0; } else /* TWO_LIMBS */ { u.s.manh = m0; u.s.manl = m1; } u.s.exp = exp + 1023; u.s.sig = (sign < 0); return u.d; } else { /* Non-IEEE or strange limb size, do something generic. */ mp_size_t i; mp_limb_t limb, bit; int shift; double base, factor, prev_factor, d, new_d, diff; /* "limb" is "ptr[i]" the limb being examined, "bit" is a mask for the bit being examined, initially the highest non-zero bit. */ i = size-1; limb = ptr[i]; count_leading_zeros (shift, limb); bit = GMP_LIMB_HIGHBIT >> shift; /* relative to just under high non-zero bit */ exp -= (shift - GMP_NAIL_BITS) + 1; /* Power up "factor" to 2^exp, being the value of the "bit" in "limb" being examined. */ base = (exp >= 0 ? 2.0 : 0.5); exp = ABS (exp); factor = 1.0; for (;;) { if (exp & 1) { prev_factor = factor; factor *= base; if (factor == 0.0) return 0.0; /* underflow */ if (factor == prev_factor) { d = factor; /* overflow, apparent infinity */ goto generic_done; } } exp >>= 1; if (exp == 0) break; base *= base; } /* Add a "factor" for each non-zero bit, working from high to low. Stop if any rounding occurs, hence implementing a truncation. Note no attention is paid to DBL_MANT_DIG, since the effective number of bits in the mantissa isn't constant when in denorm range. We also encountered an ARM system with apparently somewhat doubtful software floats where DBL_MANT_DIG claimed 53 bits but only 32 actually worked. */ d = factor; /* high bit */ for (;;) { factor *= 0.5; /* next bit */ bit >>= 1; if (bit == 0) { /* next limb, if any */ i--; if (i < 0) break; limb = ptr[i]; bit = GMP_NUMB_HIGHBIT; } if (bit & limb) { new_d = d + factor; diff = new_d - d; if (diff != factor) break; /* rounding occured, stop now */ d = new_d; } } generic_done: return (sign >= 0 ? d : -d); } }