MPFR_COLD_FUNCTION_ATTR int mpfr_overflow (mpfr_ptr x, mpfr_rnd_t rnd_mode, int sign) { int inex; MPFR_LOG_FUNC (("x[%Pu]=%.*Rg rnd=%d sign=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode, sign), ("x[%Pu]=%.*Rg", mpfr_get_prec (x), mpfr_log_prec, x)); MPFR_ASSERT_SIGN (sign); if (MPFR_IS_LIKE_RNDZ(rnd_mode, sign < 0)) { mpfr_setmax (x, __gmpfr_emax); inex = -1; } else { MPFR_SET_INF(x); inex = 1; } MPFR_SET_SIGN(x, sign); __gmpfr_flags |= MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW; return sign > 0 ? inex : -inex; }
int mpfr_overflow (mpfr_ptr x, mpfr_rnd_t rnd_mode, int sign) { int inex; MPFR_ASSERT_SIGN(sign); if (MPFR_IS_LIKE_RNDZ(rnd_mode, sign < 0)) { mpfr_setmax (x, __gmpfr_emax); inex = -1; } else { MPFR_SET_INF(x); inex = 1; } MPFR_SET_SIGN(x,sign); __gmpfr_flags |= MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW; return sign > 0 ? inex : -inex; }
int mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) { /****** Declaration ******/ mpfr_t x; int inexact; MPFR_SAVE_EXPO_DECL (expo); MPFR_LOG_FUNC (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode), ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, inexact)); /* Special value checking */ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt))) { if (MPFR_IS_NAN (xt)) { MPFR_SET_NAN (y); MPFR_RET_NAN; } else if (MPFR_IS_INF (xt)) { /* tanh(inf) = 1 && tanh(-inf) = -1 */ return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode); } else /* tanh (0) = 0 and xt is zero */ { MPFR_ASSERTD (MPFR_IS_ZERO(xt)); MPFR_SET_ZERO (y); MPFR_SET_SAME_SIGN (y, xt); MPFR_RET (0); } } /* tanh(x) = x - x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */ MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 0, rnd_mode, {}); MPFR_TMP_INIT_ABS (x, xt); MPFR_SAVE_EXPO_MARK (expo); /* General case */ { /* Declaration of the intermediary variable */ mpfr_t t, te; mpfr_exp_t d; /* Declaration of the size variable */ mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */ mpfr_prec_t Nt; /* working precision */ long int err; /* error */ int sign = MPFR_SIGN (xt); MPFR_ZIV_DECL (loop); MPFR_GROUP_DECL (group); /* First check for BIG overflow of exp(2*x): For x > 0, exp(2*x) > 2^(2*x) If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) { /* initialise of intermediary variables since 'set_one' label assumes the variables have been initialize */ MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te); goto set_one; } /* Compute the precision of intermediary variable */ /* The optimal number of bits: see algorithms.tex */ Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4; /* if x is small, there will be a cancellation in exp(2x)-1 */ if (MPFR_GET_EXP (x) < 0) Nt += -MPFR_GET_EXP (x); /* initialise of intermediary variable */ MPFR_GROUP_INIT_2 (group, Nt, t, te); MPFR_ZIV_INIT (loop, Nt); for (;;) { /* tanh = (exp(2x)-1)/(exp(2x)+1) */ mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */ /* since x > 0, we can only have an overflow */ mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */ if (MPFR_UNLIKELY (MPFR_IS_INF (te))) { set_one: inexact = MPFR_FROM_SIGN_TO_INT (sign); mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign); if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign))) { inexact = -inexact; mpfr_nexttozero (y); } break; } d = MPFR_GET_EXP (te); /* For Error calculation */ mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1*/ mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1*/ d = d - MPFR_GET_EXP (te); mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/ /* Calculation of the error */ d = MAX(3, d + 1); err = Nt - (d + 1); if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) { inexact = mpfr_set4 (y, t, rnd_mode, sign); break; } /* if t=1, we still can round since |sinh(x)| < 1 */ if (MPFR_GET_EXP (t) == 1) goto set_one; /* Actualisation of the precision */ MPFR_ZIV_NEXT (loop, Nt); MPFR_GROUP_REPREC_2 (group, Nt, t, te); } MPFR_ZIV_FREE (loop); MPFR_GROUP_CLEAR (group); } MPFR_SAVE_EXPO_FREE (expo); inexact = mpfr_check_range (y, inexact, rnd_mode); return inexact; }
int mpfr_round_raw_generic( #if flag == 0 mp_limb_t *yp, #endif const mp_limb_t *xp, mpfr_prec_t xprec, int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode #if use_inexp != 0 , int *inexp #endif ) { mp_size_t xsize, nw; mp_limb_t himask, lomask, sb; int rw; #if flag == 0 int carry; #endif #if use_inexp == 0 int *inexp; #endif if (use_inexp) MPFR_ASSERTD(inexp != ((int*) 0)); MPFR_ASSERTD(neg == 0 || neg == 1); if (flag && !use_inexp && (xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg))) return 0; xsize = MPFR_PREC2LIMBS (xprec); nw = yprec / GMP_NUMB_BITS; rw = yprec & (GMP_NUMB_BITS - 1); if (MPFR_UNLIKELY(xprec <= yprec)) { /* No rounding is necessary. */ /* if yp=xp, maybe an overlap: MPN_COPY_DECR is OK when src <= dst */ if (MPFR_LIKELY(rw)) nw++; MPFR_ASSERTD(nw >= 1); MPFR_ASSERTD(nw >= xsize); if (use_inexp) *inexp = 0; #if flag == 0 MPN_COPY_DECR(yp + (nw - xsize), xp, xsize); MPN_ZERO(yp, nw - xsize); #endif return 0; } if (use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg)) { mp_size_t k = xsize - nw - 1; if (MPFR_LIKELY(rw)) { nw++; lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw); himask = ~lomask; } else { lomask = MPFR_LIMB_MAX; himask = MPFR_LIMB_MAX; } MPFR_ASSERTD(k >= 0); sb = xp[k] & lomask; /* First non-significant bits */ /* Rounding to nearest? */ if (MPFR_LIKELY (rnd_mode == MPFR_RNDN || rnd_mode == MPFR_RNDNA)) { /* Rounding to nearest */ mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw); if ((sb & rbmask) == 0) /* rounding bit = 0 ? */ goto rnd_RNDZ; /* yes, behave like rounding toward zero */ /* Rounding to nearest with rounding bit = 1 */ if (MPFR_UNLIKELY (rnd_mode == MPFR_RNDNA)) /* FIXME: *inexp is not set. First, add a testcase that triggers the bug (at least with a sanitizer). */ goto rnd_RNDN_add_one_ulp; /* like rounding away from zero */ sb &= ~rbmask; /* first bits after the rounding bit */ while (MPFR_UNLIKELY(sb == 0) && k > 0) sb = xp[--k]; if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */ { /* sb == 0 && rnd_mode == MPFR_RNDN */ sb = xp[xsize - nw] & (himask ^ (himask << 1)); if (sb == 0) { if (use_inexp) *inexp = 2*MPFR_EVEN_INEX*neg-MPFR_EVEN_INEX; /* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX */ /* since neg = 0 or 1 and sb = 0 */ #if flag == 0 MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; #endif return 0; /* sb != 0 && rnd_mode != MPFR_RNDZ */ } else { /* sb != 0 && rnd_mode == MPFR_RNDN */ if (use_inexp) *inexp = MPFR_EVEN_INEX-2*MPFR_EVEN_INEX*neg; /* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX */ /* since neg = 0 or 1 and sb != 0 */ goto rnd_RNDN_add_one_ulp; } } else /* sb != 0 && rnd_mode == MPFR_RNDN */ { if (use_inexp) *inexp = 1-2*neg; /* neg == 0 ? 1 : -1 */ rnd_RNDN_add_one_ulp: #if flag == 1 return 1; /* sb != 0 && rnd_mode != MPFR_RNDZ */ #else carry = mpn_add_1 (yp, xp + xsize - nw, nw, rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw) : MPFR_LIMB_ONE); yp[0] &= himask; return carry; #endif } } /* Rounding toward zero? */ else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg)) { /* rnd_mode == MPFR_RNDZ */ rnd_RNDZ: while (MPFR_UNLIKELY(sb == 0) && k > 0) sb = xp[--k]; if (use_inexp) /* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */ /* ((neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1 */ *inexp = MPFR_UNLIKELY(sb == 0) ? 0 : (2*neg-1); #if flag == 0 MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; #endif return 0; /* sb != 0 && rnd_mode != MPFR_RNDZ */ } else { /* Rounding away from zero */ while (MPFR_UNLIKELY(sb == 0) && k > 0) sb = xp[--k]; if (MPFR_UNLIKELY(sb == 0)) { /* sb = 0 && rnd_mode != MPFR_RNDZ */ if (use_inexp) /* ((neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1 */ *inexp = 0; #if flag == 0 MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; #endif return 0; } else { /* sb != 0 && rnd_mode != MPFR_RNDZ */ if (use_inexp) *inexp = 1-2*neg; /* neg == 0 ? 1 : -1 */ #if flag == 1 return 1; #else carry = mpn_add_1(yp, xp + xsize - nw, nw, rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw) : 1); yp[0] &= himask; return carry; #endif } } } else { /* Rounding toward zero / no inexact flag */ #if flag == 0 if (MPFR_LIKELY(rw)) { nw++; himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw); } else himask = MPFR_LIMB_MAX; MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; #endif return 0; } }
/* compute sign(b) * (|b| + |c|) Returns 0 iff result is exact, a negative value when the result is less than the exact value, a positive value otherwise. */ int mpfr_add1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) { mpfr_uexp_t d; mpfr_prec_t p; unsigned int sh; mp_size_t n; mp_limb_t *ap, *cp; mpfr_exp_t bx; mp_limb_t limb; int inexact; MPFR_TMP_DECL(marker); MPFR_TMP_MARK(marker); MPFR_ASSERTD(MPFR_PREC(a) == MPFR_PREC(b) && MPFR_PREC(b) == MPFR_PREC(c)); MPFR_ASSERTD(MPFR_IS_PURE_FP(b)); MPFR_ASSERTD(MPFR_IS_PURE_FP(c)); MPFR_ASSERTD(MPFR_GET_EXP(b) >= MPFR_GET_EXP(c)); /* Read prec and num of limbs */ p = MPFR_PREC(b); n = MPFR_PREC2LIMBS (p); MPFR_UNSIGNED_MINUS_MODULO(sh, p); bx = MPFR_GET_EXP(b); d = (mpfr_uexp_t) (bx - MPFR_GET_EXP(c)); DEBUG (printf ("New add1sp with diff=%lu\n", (unsigned long) d)); if (MPFR_UNLIKELY(d == 0)) { /* d==0 */ DEBUG( mpfr_print_mant_binary("C= ", MPFR_MANT(c), p) ); DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) ); bx++; /* exp + 1 */ ap = MPFR_MANT(a); limb = mpn_add_n(ap, MPFR_MANT(b), MPFR_MANT(c), n); DEBUG( mpfr_print_mant_binary("A= ", ap, p) ); MPFR_ASSERTD(limb != 0); /* There must be a carry */ limb = ap[0]; /* Get LSB (In fact, LSW) */ mpn_rshift(ap, ap, n, 1); /* Shift mantissa A */ ap[n-1] |= MPFR_LIMB_HIGHBIT; /* Set MSB */ ap[0] &= ~MPFR_LIMB_MASK(sh); /* Clear LSB bit */ if (MPFR_LIKELY((limb&(MPFR_LIMB_ONE<<sh)) == 0)) /* Check exact case */ { inexact = 0; goto set_exponent; } /* Zero: Truncate Nearest: Even Rule => truncate or add 1 Away: Add 1 */ if (MPFR_LIKELY(rnd_mode==MPFR_RNDN)) { if (MPFR_LIKELY((ap[0]&(MPFR_LIMB_ONE<<sh))==0)) { inexact = -1; goto set_exponent; } else goto add_one_ulp; } MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(b)); if (rnd_mode==MPFR_RNDZ) { inexact = -1; goto set_exponent; } else goto add_one_ulp; } else if (MPFR_UNLIKELY (d >= p)) { if (MPFR_LIKELY (d > p)) { /* d > p : Copy B in A */ /* Away: Add 1 Nearest: Trunc Zero: Trunc */ if (MPFR_LIKELY (rnd_mode==MPFR_RNDN || MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (b)))) { copy_set_exponent: ap = MPFR_MANT (a); MPN_COPY (ap, MPFR_MANT(b), n); inexact = -1; goto set_exponent; } else { copy_add_one_ulp: ap = MPFR_MANT(a); MPN_COPY (ap, MPFR_MANT(b), n); goto add_one_ulp; } } else { /* d==p : Copy B in A */ /* Away: Add 1 Nearest: Even Rule if C is a power of 2, else Add 1 Zero: Trunc */ if (MPFR_LIKELY(rnd_mode==MPFR_RNDN)) { /* Check if C was a power of 2 */ cp = MPFR_MANT(c); if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT)) { mp_size_t k = n-1; do { k--; } while (k>=0 && cp[k]==0); if (MPFR_UNLIKELY(k<0)) /* Power of 2: Even rule */ if ((MPFR_MANT (b)[0]&(MPFR_LIMB_ONE<<sh))==0) goto copy_set_exponent; } /* Not a Power of 2 */ goto copy_add_one_ulp; } else if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (b))) goto copy_set_exponent; else goto copy_add_one_ulp; } } else { mp_limb_t mask; mp_limb_t bcp, bcp1; /* Cp and C'p+1 */ /* General case: 1 <= d < p */ cp = MPFR_TMP_LIMBS_ALLOC (n); /* Shift c in temporary allocated place */ { mpfr_uexp_t dm; mp_size_t m; dm = d % GMP_NUMB_BITS; m = d / GMP_NUMB_BITS; if (MPFR_UNLIKELY(dm == 0)) { /* dm = 0 and m > 0: Just copy */ MPFR_ASSERTD(m!=0); MPN_COPY(cp, MPFR_MANT(c)+m, n-m); MPN_ZERO(cp+n-m, m); } else if (MPFR_LIKELY(m == 0)) { /* dm >=1 and m == 0: just shift */ MPFR_ASSERTD(dm >= 1); mpn_rshift(cp, MPFR_MANT(c), n, dm); } else { /* dm > 0 and m > 0: shift and zero */ mpn_rshift(cp, MPFR_MANT(c)+m, n-m, dm); MPN_ZERO(cp+n-m, m); } } DEBUG( mpfr_print_mant_binary("Before", MPFR_MANT(c), p) ); DEBUG( mpfr_print_mant_binary("B= ", MPFR_MANT(b), p) ); DEBUG( mpfr_print_mant_binary("After ", cp, p) ); /* Compute bcp=Cp and bcp1=C'p+1 */ if (MPFR_LIKELY (sh > 0)) { /* Try to compute them from C' rather than C */ bcp = (cp[0] & (MPFR_LIMB_ONE<<(sh-1))) ; if (MPFR_LIKELY(cp[0]&MPFR_LIMB_MASK(sh-1))) bcp1 = 1; else { /* We can't compute C'p+1 from C'. Compute it from C */ /* Start from bit x=p-d+sh in mantissa C (+sh since we have already looked sh bits in C'!) */ mpfr_prec_t x = p-d+sh-1; if (MPFR_LIKELY(x>p)) /* We are already looked at all the bits of c, so C'p+1 = 0*/ bcp1 = 0; else { mp_limb_t *tp = MPFR_MANT(c); mp_size_t kx = n-1 - (x / GMP_NUMB_BITS); mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS); DEBUG (printf ("(First) x=%lu Kx=%ld Sx=%lu\n", (unsigned long) x, (long) kx, (unsigned long) sx)); /* Looks at the last bits of limb kx (if sx=0 does nothing)*/ if (tp[kx] & MPFR_LIMB_MASK(sx)) bcp1 = 1; else { /*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/ do { kx--; } while (kx>=0 && tp[kx]==0); bcp1 = (kx >= 0); } } } } else /* sh == 0 */ { /* Compute Cp and C'p+1 from C with sh=0 */ mp_limb_t *tp = MPFR_MANT(c); /* Start from bit x=p-d in mantissa C */ mpfr_prec_t x = p-d; mp_size_t kx = n-1 - (x / GMP_NUMB_BITS); mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS); MPFR_ASSERTD(p >= d); bcp = tp[kx] & (MPFR_LIMB_ONE<<sx); /* Looks at the last bits of limb kx (If sx=0, does nothing)*/ if (tp[kx]&MPFR_LIMB_MASK(sx)) bcp1 = 1; else { do { kx--; } while (kx>=0 && tp[kx]==0); bcp1 = (kx>=0); } } DEBUG (printf("sh=%u Cp=%lu C'p+1=%lu\n", sh, (unsigned long) bcp, (unsigned long) bcp1)); /* Clean shifted C' */ mask = ~MPFR_LIMB_MASK(sh); cp[0] &= mask; /* Add the mantissa c from b in a */ ap = MPFR_MANT(a); limb = mpn_add_n (ap, MPFR_MANT(b), cp, n); DEBUG( mpfr_print_mant_binary("Add= ", ap, p) ); /* Check for overflow */ if (MPFR_UNLIKELY (limb)) { limb = ap[0] & (MPFR_LIMB_ONE<<sh); /* Get LSB */ mpn_rshift (ap, ap, n, 1); /* Shift mantissa*/ bx++; /* Fix exponent */ ap[n-1] |= MPFR_LIMB_HIGHBIT; /* Set MSB */ ap[0] &= mask; /* Clear LSB bit */ bcp1 |= bcp; /* Recompute C'p+1 */ bcp = limb; /* Recompute Cp */ DEBUG (printf ("(Overflow) Cp=%lu C'p+1=%lu\n", (unsigned long) bcp, (unsigned long) bcp1)); DEBUG (mpfr_print_mant_binary ("Add= ", ap, p)); } /* Round: Zero: Truncate but could be exact. Away: Add 1 if Cp or C'p+1 !=0 Nearest: Truncate but could be exact if Cp==0 Add 1 if C'p+1 !=0, Even rule else */ if (MPFR_LIKELY(rnd_mode == MPFR_RNDN)) { if (MPFR_LIKELY(bcp == 0)) { inexact = MPFR_LIKELY(bcp1) ? -1 : 0; goto set_exponent; } else if (MPFR_UNLIKELY(bcp1==0) && (ap[0]&(MPFR_LIMB_ONE<<sh))==0) { inexact = -1; goto set_exponent; } else goto add_one_ulp; } MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(b)); if (rnd_mode == MPFR_RNDZ) { inexact = MPFR_LIKELY(bcp || bcp1) ? -1 : 0; goto set_exponent; } else { if (MPFR_UNLIKELY(bcp==0 && bcp1==0)) { inexact = 0; goto set_exponent; } else goto add_one_ulp; } } MPFR_ASSERTN(0); add_one_ulp: /* add one unit in last place to a */ DEBUG( printf("AddOneUlp\n") ); if (MPFR_UNLIKELY( mpn_add_1(ap, ap, n, MPFR_LIMB_ONE<<sh) )) { /* Case 100000x0 = 0x1111x1 + 1*/ DEBUG( printf("Pow of 2\n") ); bx++; ap[n-1] = MPFR_LIMB_HIGHBIT; } inexact = 1; set_exponent: if (MPFR_UNLIKELY(bx > __gmpfr_emax)) /* Check for overflow */ { DEBUG( printf("Overflow\n") ); MPFR_TMP_FREE(marker); MPFR_SET_SAME_SIGN(a,b); return mpfr_overflow(a, rnd_mode, MPFR_SIGN(a)); } MPFR_SET_EXP (a, bx); MPFR_SET_SAME_SIGN(a,b); MPFR_TMP_FREE(marker); MPFR_RET (inexact * MPFR_INT_SIGN (a)); }
static void test_generic (mpfr_prec_t p0, mpfr_prec_t p1, unsigned int nmax) { mpfr_prec_t prec, xprec, yprec; mpfr_t x, y, z, t, w; #if defined(TWO_ARGS_ALL) mpfr_t u; #endif #if defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) double d; #endif #if defined(ULONG_ARG1) || defined(ULONG_ARG2) unsigned long i; #endif mpfr_rnd_t rnd; int inexact, compare, compare2; unsigned int n; unsigned long ctrt = 0, ctrn = 0; int test_of = 1, test_uf = 1; mpfr_exp_t old_emin, old_emax; old_emin = mpfr_get_emin (); old_emax = mpfr_get_emax (); mpfr_inits2 (MPFR_PREC_MIN, x, y, z, t, w, (mpfr_ptr) 0); #if defined(TWO_ARGS_ALL) mpfr_init2 (u, MPFR_PREC_MIN); #endif /* generic test */ for (prec = p0; prec <= p1; prec++) { mpfr_set_prec (z, prec); mpfr_set_prec (t, prec); yprec = prec + 10; mpfr_set_prec (y, yprec); mpfr_set_prec (w, yprec); /* Note: in precision p1, we test 4 special cases. */ for (n = 0; n < (prec == p1 ? nmax + 4 : nmax); n++) { int infinite_input = 0; unsigned int flags; mpfr_exp_t oemin, oemax; xprec = prec; if (randlimb () & 1) { xprec *= (double) randlimb () / MP_LIMB_T_MAX; if (xprec < MPFR_PREC_MIN) xprec = MPFR_PREC_MIN; } mpfr_set_prec (x, xprec); #if defined(TWO_ARGS) mpfr_set_prec (u, xprec); #elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_set_prec (u, IEEE_DBL_MANT_DIG); #elif defined(ULONG_ARG1) || defined(ULONG_ARG2) mpfr_set_prec (u, sizeof (unsigned long) * CHAR_BIT); #endif if (n > 3 || prec < p1) { #if defined(RAND_FUNCTION) RAND_FUNCTION (x); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) RAND_FUNCTION (u); #endif #else /* ! defined(RAND_FUNCTION) */ tests_default_random (x, TEST_RANDOM_POS, TEST_RANDOM_EMIN, TEST_RANDOM_EMAX, TEST_RANDOM_ALWAYS_SCALE); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) tests_default_random (u, TEST_RANDOM_POS2, TEST_RANDOM_EMIN, TEST_RANDOM_EMAX, TEST_RANDOM_ALWAYS_SCALE); #endif #endif /* ! defined(RAND_FUNCTION) */ } else { /* Special cases tested in precision p1 if n <= 3. They are useful really in the extended exponent range. */ #if (defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2)) && defined(MPFR_ERRDIVZERO) goto next_n; #endif set_emin (MPFR_EMIN_MIN); set_emax (MPFR_EMAX_MAX); if (n <= 1) { mpfr_set_si (x, n == 0 ? 1 : -1, MPFR_RNDN); mpfr_set_exp (x, mpfr_get_emin ()); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, MPFR_RNDN); mpfr_set_exp (u, mpfr_get_emin ()); #endif } else /* 2 <= n <= 3 */ { if (getenv ("MPFR_CHECK_MAX") == NULL) goto next_n; mpfr_set_si (x, n == 0 ? 1 : -1, MPFR_RNDN); mpfr_setmax (x, REDUCE_EMAX); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, MPFR_RNDN); mpfr_setmax (u, mpfr_get_emax ()); #endif } } #if defined(ULONG_ARG1) || defined(ULONG_ARG2) i = randlimb (); inexact = mpfr_set_ui (u, i, MPFR_RNDN); MPFR_ASSERTN (inexact == 0); #endif /* Exponent range for the test. */ oemin = mpfr_get_emin (); oemax = mpfr_get_emax (); rnd = RND_RAND (); mpfr_clear_flags (); #ifdef DEBUG_TGENERIC TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (y)); #endif #if defined(TWO_ARGS) compare = TEST_FUNCTION (y, x, u, rnd); #elif defined(DOUBLE_ARG1) d = mpfr_get_d (u, rnd); compare = TEST_FUNCTION (y, d, x, rnd); /* d can be infinite due to overflow in mpfr_get_d */ infinite_input |= DOUBLE_ISINF (d); #elif defined(DOUBLE_ARG2) d = mpfr_get_d (u, rnd); compare = TEST_FUNCTION (y, x, d, rnd); /* d can be infinite due to overflow in mpfr_get_d */ infinite_input |= DOUBLE_ISINF (d); #elif defined(ULONG_ARG1) compare = TEST_FUNCTION (y, i, x, rnd); #elif defined(ULONG_ARG2) compare = TEST_FUNCTION (y, x, i, rnd); #else compare = TEST_FUNCTION (y, x, rnd); #endif flags = __gmpfr_flags; if (mpfr_get_emin () != oemin || mpfr_get_emax () != oemax) { printf ("tgeneric: the exponent range has been modified" " by the tested function!\n"); exit (1); } TGENERIC_CHECK ("bad inexact flag", (compare != 0) ^ (mpfr_inexflag_p () == 0)); ctrt++; /* Tests in a reduced exponent range. */ { unsigned int oldflags = flags; mpfr_exp_t e, emin, emax; /* Determine the smallest exponent range containing the exponents of the mpfr_t inputs (x, and u if TWO_ARGS) and output (y). */ emin = MPFR_EMAX_MAX; emax = MPFR_EMIN_MIN; if (MPFR_IS_PURE_FP (x)) { e = MPFR_GET_EXP (x); if (e < emin) emin = e; if (e > emax) emax = e; } #if defined(TWO_ARGS) if (MPFR_IS_PURE_FP (u)) { e = MPFR_GET_EXP (u); if (e < emin) emin = e; if (e > emax) emax = e; } #endif if (MPFR_IS_PURE_FP (y)) { e = MPFR_GET_EXP (y); if (test_of && e - 1 >= emax) { unsigned int ex_flags; mpfr_set_emax (e - 1); mpfr_clear_flags (); #if defined(TWO_ARGS) inexact = TEST_FUNCTION (w, x, u, rnd); #elif defined(DOUBLE_ARG1) inexact = TEST_FUNCTION (w, d, x, rnd); #elif defined(DOUBLE_ARG2) inexact = TEST_FUNCTION (w, x, d, rnd); #elif defined(ULONG_ARG1) inexact = TEST_FUNCTION (w, i, x, rnd); #elif defined(ULONG_ARG2) inexact = TEST_FUNCTION (w, x, i, rnd); #else inexact = TEST_FUNCTION (w, x, rnd); #endif flags = __gmpfr_flags; mpfr_set_emax (oemax); ex_flags = MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT; if (flags != ex_flags) { printf ("tgeneric: error for " MAKE_STR(TEST_FUNCTION) ", reduced exponent range [%" MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC "d] (overflow test) on:\n", (mpfr_eexp_t) oemin, (mpfr_eexp_t) e - 1); printf ("x = "); mpfr_dump (x); #if defined(TWO_ARGS_ALL) printf ("u = "); mpfr_dump (u); #endif printf ("yprec = %u, rnd_mode = %s\n", (unsigned int) yprec, mpfr_print_rnd_mode (rnd)); printf ("Expected flags ="); flags_out (ex_flags); printf (" got flags ="); flags_out (flags); printf ("inex = %d, w = ", inexact); mpfr_dump (w); exit (1); } test_of = 0; /* Overflow is tested only once. */ } if (test_uf && e + 1 <= emin) { unsigned int ex_flags; mpfr_set_emin (e + 1); mpfr_clear_flags (); #if defined(TWO_ARGS) inexact = TEST_FUNCTION (w, x, u, rnd); #elif defined(DOUBLE_ARG1) inexact = TEST_FUNCTION (w, d, x, rnd); #elif defined(DOUBLE_ARG2) inexact = TEST_FUNCTION (w, x, d, rnd); #elif defined(ULONG_ARG1) inexact = TEST_FUNCTION (w, i, x, rnd); #elif defined(ULONG_ARG2) inexact = TEST_FUNCTION (w, x, i, rnd); #else inexact = TEST_FUNCTION (w, x, rnd); #endif flags = __gmpfr_flags; mpfr_set_emin (oemin); ex_flags = MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT; if (flags != ex_flags) { printf ("tgeneric: error for " MAKE_STR(TEST_FUNCTION) ", reduced exponent range [%" MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC "d] (underflow test) on:\n", (mpfr_eexp_t) e + 1, (mpfr_eexp_t) oemax); printf ("x = "); mpfr_dump (x); #if defined(TWO_ARGS_ALL) printf ("u = "); mpfr_dump (u); #endif printf ("yprec = %u, rnd_mode = %s\n", (unsigned int) yprec, mpfr_print_rnd_mode (rnd)); printf ("Expected flags ="); flags_out (ex_flags); printf (" got flags ="); flags_out (flags); printf ("inex = %d, w = ", inexact); mpfr_dump (w); exit (1); } test_uf = 0; /* Underflow is tested only once. */ } if (e < emin) emin = e; if (e > emax) emax = e; } if (emin > emax) emin = emax; /* case where all values are singular */ /* Consistency test in a reduced exponent range. Doing it for the first 10 samples and for prec == p1 (which has some special cases) should be sufficient. */ if (ctrt <= 10 || prec == p1) { mpfr_set_emin (emin); mpfr_set_emax (emax); #ifdef DEBUG_TGENERIC /* Useful information in case of assertion failure. */ printf ("tgeneric: reduced exponent range [%" MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC "d]\n", (mpfr_eexp_t) emin, (mpfr_eexp_t) emax); #endif mpfr_clear_flags (); #if defined(TWO_ARGS) inexact = TEST_FUNCTION (w, x, u, rnd); #elif defined(DOUBLE_ARG1) inexact = TEST_FUNCTION (w, d, x, rnd); #elif defined(DOUBLE_ARG2) inexact = TEST_FUNCTION (w, x, d, rnd); #elif defined(ULONG_ARG1) inexact = TEST_FUNCTION (w, i, x, rnd); #elif defined(ULONG_ARG2) inexact = TEST_FUNCTION (w, x, i, rnd); #else inexact = TEST_FUNCTION (w, x, rnd); #endif flags = __gmpfr_flags; mpfr_set_emin (oemin); mpfr_set_emax (oemax); if (! (SAME_VAL (w, y) && SAME_SIGN (inexact, compare) && flags == oldflags)) { printf ("tgeneric: error for " MAKE_STR(TEST_FUNCTION) ", reduced exponent range [%" MPFR_EXP_FSPEC "d,%" MPFR_EXP_FSPEC "d] on:\n", (mpfr_eexp_t) emin, (mpfr_eexp_t) emax); printf ("x = "); mpfr_dump (x); #if defined(TWO_ARGS_ALL) printf ("u = "); mpfr_dump (u); #endif printf ("yprec = %u, rnd_mode = %s\n", (unsigned int) yprec, mpfr_print_rnd_mode (rnd)); printf ("Expected:\n y = "); mpfr_dump (y); printf (" inex = %d, flags =", compare); flags_out (oldflags); printf ("Got:\n w = "); mpfr_dump (w); printf (" inex = %d, flags =", inexact); flags_out (flags); exit (1); } } __gmpfr_flags = oldflags; /* restore the flags */ } if (MPFR_IS_SINGULAR (y)) { if (MPFR_IS_NAN (y) || mpfr_nanflag_p ()) TGENERIC_CHECK ("bad NaN flag", MPFR_IS_NAN (y) && mpfr_nanflag_p ()); else if (MPFR_IS_INF (y)) { TGENERIC_CHECK ("bad overflow flag", (compare != 0) ^ (mpfr_overflow_p () == 0)); TGENERIC_CHECK ("bad divide-by-zero flag", (compare == 0 && !infinite_input) ^ (mpfr_divby0_p () == 0)); } else if (MPFR_IS_ZERO (y)) TGENERIC_CHECK ("bad underflow flag", (compare != 0) ^ (mpfr_underflow_p () == 0)); } else if (mpfr_divby0_p ()) { TGENERIC_CHECK ("both overflow and divide-by-zero", ! mpfr_overflow_p ()); TGENERIC_CHECK ("both underflow and divide-by-zero", ! mpfr_underflow_p ()); TGENERIC_CHECK ("bad compare value (divide-by-zero)", compare == 0); } else if (mpfr_overflow_p ()) { TGENERIC_CHECK ("both underflow and overflow", ! mpfr_underflow_p ()); TGENERIC_CHECK ("bad compare value (overflow)", compare != 0); mpfr_nexttoinf (y); TGENERIC_CHECK ("should have been max MPFR number (overflow)", MPFR_IS_INF (y)); } else if (mpfr_underflow_p ()) { TGENERIC_CHECK ("bad compare value (underflow)", compare != 0); mpfr_nexttozero (y); TGENERIC_CHECK ("should have been min MPFR number (underflow)", MPFR_IS_ZERO (y)); } else if (mpfr_can_round (y, yprec, rnd, rnd, prec)) { ctrn++; mpfr_set (t, y, rnd); /* Risk of failures are known when some flags are already set before the function call. Do not set the erange flag, as it will remain set after the function call and no checks are performed in such a case (see the mpfr_erangeflag_p test below). */ if (randlimb () & 1) __gmpfr_flags = MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE; #ifdef DEBUG_TGENERIC TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (z)); #endif /* Let's increase the precision of the inputs in a random way. In most cases, this doesn't make any difference, but for the mpfr_fmod bug fixed in r6230, this triggers the bug. */ mpfr_prec_round (x, mpfr_get_prec (x) + (randlimb () & 15), MPFR_RNDN); #if defined(TWO_ARGS) mpfr_prec_round (u, mpfr_get_prec (u) + (randlimb () & 15), MPFR_RNDN); inexact = TEST_FUNCTION (z, x, u, rnd); #elif defined(DOUBLE_ARG1) inexact = TEST_FUNCTION (z, d, x, rnd); #elif defined(DOUBLE_ARG2) inexact = TEST_FUNCTION (z, x, d, rnd); #elif defined(ULONG_ARG1) inexact = TEST_FUNCTION (z, i, x, rnd); #elif defined(ULONG_ARG2) inexact = TEST_FUNCTION (z, x, i, rnd); #else inexact = TEST_FUNCTION (z, x, rnd); #endif if (mpfr_erangeflag_p ()) goto next_n; if (! mpfr_equal_p (t, z)) { printf ("tgeneric: results differ for " MAKE_STR(TEST_FUNCTION) " on\n x = "); mpfr_dump (x); #if defined(TWO_ARGS_ALL) printf (" u = "); mpfr_dump (u); #endif printf (" prec = %u, rnd_mode = %s\n", (unsigned int) prec, mpfr_print_rnd_mode (rnd)); printf ("Got "); mpfr_dump (z); printf ("Expected "); mpfr_dump (t); printf ("Approx "); mpfr_dump (y); exit (1); } compare2 = mpfr_cmp (t, y); /* if rounding to nearest, cannot know the sign of t - f(x) because of composed rounding: y = o(f(x)) and t = o(y) */ if (compare * compare2 >= 0) compare = compare + compare2; else compare = inexact; /* cannot determine sign(t-f(x)) */ if (! SAME_SIGN (inexact, compare)) { printf ("Wrong inexact flag for rnd=%s: expected %d, got %d" "\n", mpfr_print_rnd_mode (rnd), compare, inexact); printf ("x = "); mpfr_dump (x); #if defined(TWO_ARGS_ALL) printf ("u = "); mpfr_dump (u); #endif printf ("y = "); mpfr_dump (y); printf ("t = "); mpfr_dump (t); exit (1); } } else if (getenv ("MPFR_SUSPICIOUS_OVERFLOW") != NULL) { /* For developers only! */ MPFR_ASSERTN (MPFR_IS_PURE_FP (y)); mpfr_nexttoinf (y); if (MPFR_IS_INF (y) && MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y)) && !mpfr_overflow_p () && TGENERIC_SO_TEST) { printf ("Possible bug! |y| is the maximum finite number " "and has been obtained when\nrounding toward zero" " (%s). Thus there is a very probable overflow,\n" "but the overflow flag is not set!\n", mpfr_print_rnd_mode (rnd)); printf ("x = "); mpfr_dump (x); #if defined(TWO_ARGS_ALL) printf ("u = "); mpfr_dump (u); #endif exit (1); } } next_n: /* In case the exponent range has been changed by tests_default_random() or for special values... */ mpfr_set_emin (old_emin); mpfr_set_emax (old_emax); } } #ifndef TGENERIC_NOWARNING if (3 * ctrn < 2 * ctrt) printf ("Warning! Too few normal cases in generic tests (%lu / %lu)\n", ctrn, ctrt); #endif mpfr_clears (x, y, z, t, w, (mpfr_ptr) 0); #if defined(TWO_ARGS_ALL) mpfr_clear (u); #endif }
static void test_generic (mp_prec_t p0, mp_prec_t p1, unsigned int N) { mp_prec_t prec, xprec, yprec; mpfr_t x, y, z, t; #ifdef TWO_ARGS mpfr_t u; #elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_t u; double d; #endif mp_rnd_t rnd; int inexact, compare, compare2; unsigned int n; unsigned long ctrt = 0, ctrn = 0; mp_exp_t old_emin, old_emax; old_emin = mpfr_get_emin (); old_emax = mpfr_get_emax (); mpfr_init (x); mpfr_init (y); mpfr_init (z); mpfr_init (t); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_init (u); #endif /* generic test */ for (prec = p0; prec <= p1; prec++) { mpfr_set_prec (z, prec); mpfr_set_prec (t, prec); yprec = prec + 10; mpfr_set_prec (y, yprec); /* Note: in precision p1, we test 4 special cases. */ for (n = 0; n < (prec == p1 ? N + 4 : N); n++) { xprec = prec; if (randlimb () & 1) { xprec *= (double) randlimb () / MP_LIMB_T_MAX; if (xprec < MPFR_PREC_MIN) xprec = MPFR_PREC_MIN; } mpfr_set_prec (x, xprec); #ifdef TWO_ARGS mpfr_set_prec (u, xprec); #elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_set_prec (u, IEEE_DBL_MANT_DIG); #endif if (n > 3 || prec < p1) { #if defined(RAND_FUNCTION) RAND_FUNCTION (x); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) RAND_FUNCTION (u); #endif #else tests_default_random (x, TEST_RANDOM_POS, TEST_RANDOM_EMIN, TEST_RANDOM_EMAX); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) tests_default_random (u, TEST_RANDOM_POS2, TEST_RANDOM_EMIN, TEST_RANDOM_EMAX); #endif #endif } else { /* Special cases tested in precision p1 if n <= 3. They are useful really in the extended exponent range. */ set_emin (MPFR_EMIN_MIN); set_emax (MPFR_EMAX_MAX); if (n <= 1) { mpfr_set_si (x, n == 0 ? 1 : -1, GMP_RNDN); mpfr_set_exp (x, mpfr_get_emin ()); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, GMP_RNDN); mpfr_set_exp (u, mpfr_get_emin ()); #endif } else /* 2 <= n <= 3 */ { if (getenv ("MPFR_CHECK_MAX") == NULL) goto next_n; mpfr_set_si (x, n == 0 ? 1 : -1, GMP_RNDN); mpfr_setmax (x, REDUCE_EMAX); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_set_si (u, randlimb () % 2 == 0 ? 1 : -1, GMP_RNDN); mpfr_setmax (u, mpfr_get_emax ()); #endif } } rnd = RND_RAND (); mpfr_clear_flags (); #ifdef DEBUG_TGENERIC TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (y)); #endif #if defined(TWO_ARGS) compare = TEST_FUNCTION (y, x, u, rnd); #elif defined(DOUBLE_ARG1) d = mpfr_get_d (u, rnd); compare = TEST_FUNCTION (y, d, x, rnd); #elif defined(DOUBLE_ARG2) d = mpfr_get_d (u, rnd); compare = TEST_FUNCTION (y, x, d, rnd); #else compare = TEST_FUNCTION (y, x, rnd); #endif TGENERIC_CHECK ("Bad inexact flag", (compare != 0) ^ (mpfr_inexflag_p () == 0)); ctrt++; if (MPFR_IS_SINGULAR (y)) { if (MPFR_IS_NAN (y) || mpfr_nanflag_p ()) TGENERIC_CHECK ("Bad NaN flag", MPFR_IS_NAN (y) && mpfr_nanflag_p ()); else if (MPFR_IS_INF (y)) TGENERIC_CHECK ("Bad overflow flag", (compare != 0) ^ (mpfr_overflow_p () == 0)); else if (MPFR_IS_ZERO (y)) TGENERIC_CHECK ("Bad underflow flag", (compare != 0) ^ (mpfr_underflow_p () == 0)); } else if (mpfr_overflow_p ()) { TGENERIC_CHECK ("Bad compare value (overflow)", compare != 0); mpfr_nexttoinf (y); TGENERIC_CHECK ("Should have been max MPFR number", MPFR_IS_INF (y)); } else if (mpfr_underflow_p ()) { TGENERIC_CHECK ("Bad compare value (underflow)", compare != 0); mpfr_nexttozero (y); TGENERIC_CHECK ("Should have been min MPFR number", MPFR_IS_ZERO (y)); } else if (mpfr_can_round (y, yprec, rnd, rnd, prec)) { ctrn++; mpfr_set (t, y, rnd); /* Risk of failures are known when some flags are already set before the function call. Do not set the erange flag, as it will remain set after the function call and no checks are performed in such a case (see the mpfr_erangeflag_p test below). */ if (randlimb () & 1) __gmpfr_flags = MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE; #ifdef DEBUG_TGENERIC TGENERIC_INFO (TEST_FUNCTION, MPFR_PREC (z)); #endif /* Let's increase the precision of the inputs in a random way. In most cases, this doesn't make any difference, but this triggers the mpfr_fmod bug fixed in r6235. */ mpfr_prec_round (x, mpfr_get_prec (x) + (randlimb () & 15), GMP_RNDN); #if defined(TWO_ARGS) mpfr_prec_round (u, mpfr_get_prec (u) + (randlimb () & 15), GMP_RNDN); inexact = TEST_FUNCTION (z, x, u, rnd); #elif defined(DOUBLE_ARG1) inexact = TEST_FUNCTION (z, d, x, rnd); #elif defined(DOUBLE_ARG2) inexact = TEST_FUNCTION (z, x, d, rnd); #else inexact = TEST_FUNCTION (z, x, rnd); #endif if (mpfr_erangeflag_p ()) goto next_n; if (mpfr_nan_p (z) || mpfr_cmp (t, z) != 0) { printf ("results differ for x="); mpfr_out_str (stdout, 2, xprec, x, GMP_RNDN); #ifdef TWO_ARGS printf ("\nu="); mpfr_out_str (stdout, 2, xprec, u, GMP_RNDN); #elif defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) printf ("\nu="); mpfr_out_str (stdout, 2, IEEE_DBL_MANT_DIG, u, GMP_RNDN); #endif printf (" prec=%u rnd_mode=%s\n", (unsigned) prec, mpfr_print_rnd_mode (rnd)); printf ("got "); mpfr_out_str (stdout, 2, prec, z, GMP_RNDN); puts (""); printf ("expected "); mpfr_out_str (stdout, 2, prec, t, GMP_RNDN); puts (""); printf ("approx "); mpfr_print_binary (y); puts (""); exit (1); } compare2 = mpfr_cmp (t, y); /* if rounding to nearest, cannot know the sign of t - f(x) because of composed rounding: y = o(f(x)) and t = o(y) */ if (compare * compare2 >= 0) compare = compare + compare2; else compare = inexact; /* cannot determine sign(t-f(x)) */ if (((inexact == 0) && (compare != 0)) || ((inexact > 0) && (compare <= 0)) || ((inexact < 0) && (compare >= 0))) { printf ("Wrong inexact flag for rnd=%s: expected %d, got %d" "\n", mpfr_print_rnd_mode (rnd), compare, inexact); printf ("x="); mpfr_print_binary (x); puts (""); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) printf ("u="); mpfr_print_binary (u); puts (""); #endif printf ("y="); mpfr_print_binary (y); puts (""); printf ("t="); mpfr_print_binary (t); puts (""); exit (1); } } else if (getenv ("MPFR_SUSPICIOUS_OVERFLOW") != NULL) { /* For developers only! */ MPFR_ASSERTN (MPFR_IS_PURE_FP (y)); mpfr_nexttoinf (y); if (MPFR_IS_INF (y) && MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y)) && !mpfr_overflow_p ()) { printf ("Possible bug! |y| is the maximum finite number " "and has been obtained when\nrounding toward zero" " (%s). Thus there is a very probable overflow,\n" "but the overflow flag is not set!\n", mpfr_print_rnd_mode (rnd)); printf ("x="); mpfr_print_binary (x); puts (""); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) printf ("u="); mpfr_print_binary (u); puts (""); #endif exit (1); } } next_n: /* In case the exponent range has been changed by tests_default_random() or for special values... */ mpfr_set_emin (old_emin); mpfr_set_emax (old_emax); } } #ifndef TGENERIC_NOWARNING if (3 * ctrn < 2 * ctrt) printf ("Warning! Too few normal cases in generic tests (%lu / %lu)\n", ctrn, ctrt); #endif mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (t); #if defined(TWO_ARGS) || defined(DOUBLE_ARG1) || defined(DOUBLE_ARG2) mpfr_clear (u); #endif }
int mpfr_round_raw_generic( #if flag == 0 mp_limb_t *yp, #endif const mp_limb_t *xp, mpfr_prec_t xprec, int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode #if use_inexp != 0 , int *inexp #endif ) { mp_size_t xsize, nw; mp_limb_t himask, lomask, sb; int rw; #if flag == 0 int carry; #endif #if use_inexp == 0 int *inexp; #endif if (use_inexp) MPFR_ASSERTD(inexp != ((int*) 0)); MPFR_ASSERTD(neg == 0 || neg == 1); if (flag && !use_inexp && (xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg))) return 0; xsize = (xprec-1)/GMP_NUMB_BITS + 1; nw = yprec / GMP_NUMB_BITS; rw = yprec & (GMP_NUMB_BITS - 1); if (MPFR_UNLIKELY(xprec <= yprec)) { /* No rounding is necessary. */ /* if yp=xp, maybe an overlap: MPN_COPY_DECR is ok when src <= dst */ if (MPFR_LIKELY(rw)) nw++; MPFR_ASSERTD(nw >= 1); MPFR_ASSERTD(nw >= xsize); if (use_inexp) *inexp = 0; #if flag == 0 MPN_COPY_DECR(yp + (nw - xsize), xp, xsize); MPN_ZERO(yp, nw - xsize); #endif return 0; } if (use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg)) { mp_size_t k = xsize - nw - 1; if (MPFR_LIKELY(rw)) { nw++; lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw); himask = ~lomask; } else { lomask = ~(mp_limb_t) 0; himask = ~(mp_limb_t) 0; } MPFR_ASSERTD(k >= 0); sb = xp[k] & lomask; /* First non-significant bits */ /* Rounding to nearest ? */ if (MPFR_LIKELY( rnd_mode == MPFR_RNDN) ) { /* Rounding to nearest */ mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw); if (sb & rbmask) /* rounding bit */ sb &= ~rbmask; /* it is 1, clear it */ else { /* Rounding bit is 0, behave like rounding to 0 */ goto rnd_RNDZ; } while (MPFR_UNLIKELY(sb == 0) && k > 0) sb = xp[--k]; /* rounding to nearest, with rounding bit = 1 */ if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */ { /* sb == 0 && rnd_mode == MPFR_RNDN */ sb = xp[xsize - nw] & (himask ^ (himask << 1)); if (sb == 0) { if (use_inexp) *inexp = 2*MPFR_EVEN_INEX*neg-MPFR_EVEN_INEX; /* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX;*/ /* Since neg = 0 or 1 and sb=0*/ #if flag == 1 return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ */; #else MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; return 0; #endif } else { /* sb != 0 && rnd_mode == MPFR_RNDN */ if (use_inexp) *inexp = MPFR_EVEN_INEX-2*MPFR_EVEN_INEX*neg; /*((neg!=0)^(sb!=0))? MPFR_EVEN_INEX : -MPFR_EVEN_INEX; */ /*Since neg= 0 or 1 and sb != 0 */ goto rnd_RNDN_add_one_ulp; } } else /* sb != 0 && rnd_mode == MPFR_RNDN*/ { if (use_inexp) /* *inexp = (neg == 0) ? 1 : -1; but since neg = 0 or 1 */ *inexp = 1-2*neg; rnd_RNDN_add_one_ulp: #if flag == 1 return 1; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/ #else carry = mpn_add_1 (yp, xp + xsize - nw, nw, rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw) : MPFR_LIMB_ONE); yp[0] &= himask; return carry; #endif } } /* Rounding to Zero ? */ else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg)) { /* rnd_mode == MPFR_RNDZ */ rnd_RNDZ: while (MPFR_UNLIKELY(sb == 0) && k > 0) sb = xp[--k]; if (use_inexp) /* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */ /* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/ *inexp = MPFR_UNLIKELY(sb == 0) ? 0 : (2*neg-1); #if flag == 1 return 0; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/ #else MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; return 0; #endif } else { /* rnd_mode = Away */ while (MPFR_UNLIKELY(sb == 0) && k > 0) sb = xp[--k]; if (MPFR_UNLIKELY(sb == 0)) { /* sb = 0 && rnd_mode != MPFR_RNDZ */ if (use_inexp) /* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/ *inexp = 0; #if flag == 1 return 0; #else MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; return 0; #endif } else { /* sb != 0 && rnd_mode != MPFR_RNDZ */ if (use_inexp) /* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/ *inexp = 1-2*neg; #if flag == 1 return 1; #else carry = mpn_add_1(yp, xp + xsize - nw, nw, rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw) : 1); yp[0] &= himask; return carry; #endif } } } else { /* Roundind mode = Zero / No inexact flag */ #if flag == 1 return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ*/; #else if (MPFR_LIKELY(rw)) { nw++; himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw); } else himask = ~(mp_limb_t) 0; MPN_COPY_INCR(yp, xp + xsize - nw, nw); yp[0] &= himask; return 0; #endif } }