/* mpfr_urandom (rop, state, rnd_mode) -- Generate a uniform pseudorandom real number between 0 and 1 (exclusive) and round it to the precision of rop according to the given rounding mode. Copyright 2000-2004, 2006-2017 Free Software Foundation, Inc. Contributed by the AriC and Caramba projects, INRIA. This file is part of the GNU MPFR Library. The GNU MPFR 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 3 of the License, or (at your option) any later version. The GNU MPFR 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 MPFR Library; see the file COPYING.LESSER. If not, see http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ #define MPFR_NEED_LONGLONG_H #include "mpfr-impl.h" /* generate one random bit */ static int random_rounding_bit (gmp_randstate_t rstate) { mp_limb_t r; mpfr_rand_raw (&r, rstate, 1); return r & MPFR_LIMB_ONE; } /* NOTE: The current behavior is to consider "underflow before rounding" (the significand does not need to be drawn), while the rule in MPFR is "underflow after rounding". This is unfixable in this 3.1 branch without changing the behavior of the PRNG (thus breaking the ABI). */ /* The mpfr_urandom() function is implemented in the following way for the generic case. 1. One determines the exponent exp: 0 with probability 1/2, -1 with probability 1/4, -2 with probability 1/8, etc. 2. One draws a 1-ulp interval ]a,b[ containing the exact result (the interval can be regarded as open since it has the same measure as the closed interval). 3. Rounding is done. For the directed rounding modes, the rounded value is uniquely determined. For rounding to nearest, ]a,m[ and ]m,b[, where m = (a+b)/2, have the same measure, so that one gets a or b with equal probabilities. Note: Only low-level functions are used (except just before a "return"), so that we do not need MPFR_SAVE_EXPO_*. */ int mpfr_urandom (mpfr_ptr rop, gmp_randstate_t rstate, mpfr_rnd_t rnd_mode) { mpfr_limb_ptr rp; mpfr_prec_t nbits; mp_size_t nlimbs; mp_size_t n; mpfr_exp_t exp; int cnt; int inex; rp = MPFR_MANT (rop); nbits = MPFR_PREC (rop); MPFR_SET_POS (rop); if (MPFR_UNLIKELY (__gmpfr_emin > 0)) { /* The minimum positive representable number 2^(emin-1) is >= 1, so that we need to round to +0 or 2^(emin-1). For the directed rounding modes, the rounded value is uniquely determined. For rounding to nearest: if emin = 1, one has probability 1/2 for each; otherwise (i.e. if emin > 1), the rounded value is 0. */ __gmpfr_flags |= MPFR_FLAGS_UNDERFLOW; if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA || (__gmpfr_emin == 1 && rnd_mode == MPFR_RNDN && random_rounding_bit (rstate))) { mpfr_set_ui_2exp (rop, 1, __gmpfr_emin - 1, rnd_mode); MPFR_RET (+1); } else { MPFR_SET_ZERO (rop); MPFR_RET (-1); } } exp = 0; MPFR_ASSERTD (exp >= __gmpfr_emin); /* Step 1 (exponent). */ #define DRAW_BITS 8 /* we draw DRAW_BITS at a time */ cnt = DRAW_BITS; MPFR_ASSERTN(DRAW_BITS <= GMP_NUMB_BITS); while (cnt == DRAW_BITS) { /* generate DRAW_BITS in rp[0] */ mpfr_rand_raw (rp, rstate, DRAW_BITS); if (MPFR_UNLIKELY (rp[0] == 0)) cnt = DRAW_BITS; else { count_leading_zeros (cnt, rp[0]); cnt -= GMP_NUMB_BITS - DRAW_BITS; } exp -= cnt; /* no integer overflow */ if (MPFR_UNLIKELY (exp < __gmpfr_emin)) { /* To get here, we have been drawing more than -emin zeros in a row, then return 0 or the smallest representable positive number. The rounding-to-nearest mode is subtle: We need to round to the smallest representable positive number iff the exponent is emin - 1. This condition can be satisfied only if the current emin is emin - 1. In this case, if cnt != DRAW_BITS, this in the final emin, so that the condition is satisfied. But if cnt == DRAW_BITS, we need to draw an additional bit to determine whether emin == emin - 1 or emin < emin - 1 (with equal probabilities); the reason is that we return just below instead of doing more iterations in the "while" loop to find the final value of emin. */ __gmpfr_flags |= MPFR_FLAGS_UNDERFLOW; if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA || (rnd_mode == MPFR_RNDN && exp == __gmpfr_emin - 1 && (cnt != DRAW_BITS || random_rounding_bit (rstate)))) { mpfr_set_ui_2exp (rop, 1, __gmpfr_emin - 1, rnd_mode); MPFR_RET (+1); } else { MPFR_SET_ZERO (rop); MPFR_RET (-1); } } MPFR_ASSERTD (exp >= __gmpfr_emin); } MPFR_ASSERTD (exp >= __gmpfr_emin); MPFR_EXP (rop) = exp; /* Warning: may be larger than emax */ /* Step 2 (significand): we need generate only nbits-1 bits, since the most significant bit is 1. */ mpfr_rand_raw (rp, rstate, nbits - 1); nlimbs = MPFR_LIMB_SIZE (rop); n = nlimbs * GMP_NUMB_BITS - nbits; if (MPFR_LIKELY (n != 0)) /* this will put the low bits to zero */ mpn_lshift (rp, rp, nlimbs, n); rp[nlimbs - 1] |= MPFR_LIMB_HIGHBIT; /* Rounding */ if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA || (rnd_mode == MPFR_RNDN && random_rounding_bit (rstate))) { if (MPFR_UNLIKELY (exp > __gmpfr_emax)) mpfr_set_inf (rop, +1); /* overflow */ else mpfr_nextabove (rop); inex = +1; /* There is an overflow in the first case and possibly in the second case. If this occurs, the flag will be set by mpfr_check_range. */ } else inex = -1; return mpfr_check_range (rop, inex, rnd_mode); }