static int sum_tab (mpfr_ptr ret, mpfr_t *tab, unsigned long n, mpfr_rnd_t rnd) { mpfr_ptr *tabtmp; unsigned long i; int inexact; MPFR_TMP_DECL(marker); MPFR_TMP_MARK(marker); tabtmp = (mpfr_ptr *) MPFR_TMP_ALLOC(n * sizeof(mpfr_srcptr)); for (i = 0; i < n; i++) tabtmp[i] = tab[i]; inexact = mpfr_sum (ret, tabtmp, n, rnd); MPFR_TMP_FREE(marker); return inexact; }
int mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) { mpfr_exp_t bx,cx; mpfr_uexp_t d; mpfr_prec_t p, sh, cnt; mp_size_t n; mp_limb_t *ap, *bp, *cp; mp_limb_t limb; int inexact; mp_limb_t bcp,bcp1; /* Cp and C'p+1 */ mp_limb_t bbcp = (mp_limb_t) -1, bbcp1 = (mp_limb_t) -1; /* Cp+1 and C'p+2, gcc claims that they might be used uninitialized. We fill them with invalid values, which should produce a failure if so. See README.dev file. */ 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)); /* Read prec and num of limbs */ p = MPFR_PREC (b); n = MPFR_PREC2LIMBS (p); /* Fast cmp of |b| and |c|*/ bx = MPFR_GET_EXP (b); cx = MPFR_GET_EXP (c); if (MPFR_UNLIKELY(bx == cx)) { mp_size_t k = n - 1; /* Check mantissa since exponent are equals */ bp = MPFR_MANT(b); cp = MPFR_MANT(c); while (k>=0 && MPFR_UNLIKELY(bp[k] == cp[k])) k--; if (MPFR_UNLIKELY(k < 0)) /* b == c ! */ { /* Return exact number 0 */ if (rnd_mode == MPFR_RNDD) MPFR_SET_NEG(a); else MPFR_SET_POS(a); MPFR_SET_ZERO(a); MPFR_RET(0); } else if (bp[k] > cp[k]) goto BGreater; else { MPFR_ASSERTD(bp[k]<cp[k]); goto CGreater; } } else if (MPFR_UNLIKELY(bx < cx)) { /* Swap b and c and set sign */ mpfr_srcptr t; mpfr_exp_t tx; CGreater: MPFR_SET_OPPOSITE_SIGN(a,b); t = b; b = c; c = t; tx = bx; bx = cx; cx = tx; } else { /* b > c */ BGreater: MPFR_SET_SAME_SIGN(a,b); } /* Now b > c */ MPFR_ASSERTD(bx >= cx); d = (mpfr_uexp_t) bx - cx; DEBUG (printf ("New with diff=%lu\n", (unsigned long) d)); if (MPFR_UNLIKELY(d <= 1)) { if (MPFR_LIKELY(d < 1)) { /* <-- b --> <-- c --> : exact sub */ ap = MPFR_MANT(a); mpn_sub_n (ap, MPFR_MANT(b), MPFR_MANT(c), n); /* Normalize */ ExactNormalize: limb = ap[n-1]; if (MPFR_LIKELY(limb)) { /* First limb is not zero. */ count_leading_zeros(cnt, limb); /* cnt could be == 0 <= SubD1Lose */ if (MPFR_LIKELY(cnt)) { mpn_lshift(ap, ap, n, cnt); /* Normalize number */ bx -= cnt; /* Update final expo */ } /* Last limb should be ok */ MPFR_ASSERTD(!(ap[0] & MPFR_LIMB_MASK((unsigned int) (-p) % GMP_NUMB_BITS))); } else { /* First limb is zero */ mp_size_t k = n-1, len; /* Find the first limb not equal to zero. FIXME:It is assume it exists (since |b| > |c| and same prec)*/ do { MPFR_ASSERTD( k > 0 ); limb = ap[--k]; } while (limb == 0); MPFR_ASSERTD(limb != 0); count_leading_zeros(cnt, limb); k++; len = n - k; /* Number of last limb */ MPFR_ASSERTD(k >= 0); if (MPFR_LIKELY(cnt)) mpn_lshift(ap+len, ap, k, cnt); /* Normalize the High Limb*/ else { /* Must use DECR since src and dest may overlap & dest>=src*/ MPN_COPY_DECR(ap+len, ap, k); } MPN_ZERO(ap, len); /* Zeroing the last limbs */ bx -= cnt + len*GMP_NUMB_BITS; /* Update Expo */ /* Last limb should be ok */ MPFR_ASSERTD(!(ap[len]&MPFR_LIMB_MASK((unsigned int) (-p) % GMP_NUMB_BITS))); } /* Check expo underflow */ if (MPFR_UNLIKELY(bx < __gmpfr_emin)) { MPFR_TMP_FREE(marker); /* inexact=0 */ DEBUG( printf("(D==0 Underflow)\n") ); if (rnd_mode == MPFR_RNDN && (bx < __gmpfr_emin - 1 || (/*inexact >= 0 &&*/ mpfr_powerof2_raw (a)))) rnd_mode = MPFR_RNDZ; return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a)); } MPFR_SET_EXP (a, bx); /* No rounding is necessary since the result is exact */ MPFR_ASSERTD(ap[n-1] > ~ap[n-1]); MPFR_TMP_FREE(marker); return 0; } else /* if (d == 1) */ { /* | <-- b --> | <-- c --> */ mp_limb_t c0, mask; mp_size_t k; MPFR_UNSIGNED_MINUS_MODULO(sh, p); /* If we lose at least one bit, compute 2*b-c (Exact) * else compute b-c/2 */ bp = MPFR_MANT(b); cp = MPFR_MANT(c); k = n-1; limb = bp[k] - cp[k]/2; if (limb > MPFR_LIMB_HIGHBIT) { /* We can't lose precision: compute b-c/2 */ /* Shift c in the allocated temporary block */ SubD1NoLose: c0 = cp[0] & (MPFR_LIMB_ONE<<sh); cp = MPFR_TMP_LIMBS_ALLOC (n); mpn_rshift(cp, MPFR_MANT(c), n, 1); if (MPFR_LIKELY(c0 == 0)) { /* Result is exact: no need of rounding! */ ap = MPFR_MANT(a); mpn_sub_n (ap, bp, cp, n); MPFR_SET_EXP(a, bx); /* No expo overflow! */ /* No truncate or normalize is needed */ MPFR_ASSERTD(ap[n-1] > ~ap[n-1]); /* No rounding is necessary since the result is exact */ MPFR_TMP_FREE(marker); return 0; } ap = MPFR_MANT(a); mask = ~MPFR_LIMB_MASK(sh); cp[0] &= mask; /* Delete last bit of c */ mpn_sub_n (ap, bp, cp, n); MPFR_SET_EXP(a, bx); /* No expo overflow! */ MPFR_ASSERTD( !(ap[0] & ~mask) ); /* Check last bits */ /* No normalize is needed */ MPFR_ASSERTD(ap[n-1] > ~ap[n-1]); /* Rounding is necessary since c0 = 1*/ /* Cp =-1 and C'p+1=0 */ bcp = 1; bcp1 = 0; if (MPFR_LIKELY(rnd_mode == MPFR_RNDN)) { /* Even Rule apply: Check Ap-1 */ if (MPFR_LIKELY( (ap[0] & (MPFR_LIMB_ONE<<sh)) == 0) ) goto truncate; else goto sub_one_ulp; } MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a)); if (rnd_mode == MPFR_RNDZ) goto sub_one_ulp; else goto truncate; } else if (MPFR_LIKELY(limb < MPFR_LIMB_HIGHBIT)) { /* We lose at least one bit of prec */ /* Calcul of 2*b-c (Exact) */ /* Shift b in the allocated temporary block */ SubD1Lose: bp = MPFR_TMP_LIMBS_ALLOC (n); mpn_lshift (bp, MPFR_MANT(b), n, 1); ap = MPFR_MANT(a); mpn_sub_n (ap, bp, cp, n); bx--; goto ExactNormalize; } else { /* Case: limb = 100000000000 */ /* Check while b[k] == c'[k] (C' is C shifted by 1) */ /* If b[k]<c'[k] => We lose at least one bit*/ /* If b[k]>c'[k] => We don't lose any bit */ /* If k==-1 => We don't lose any bit AND the result is 100000000000 0000000000 00000000000 */ mp_limb_t carry; do { carry = cp[k]&MPFR_LIMB_ONE; k--; } while (k>=0 && bp[k]==(carry=cp[k]/2+(carry<<(GMP_NUMB_BITS-1)))); if (MPFR_UNLIKELY(k<0)) { /*If carry then (sh==0 and Virtual c'[-1] > Virtual b[-1]) */ if (MPFR_UNLIKELY(carry)) /* carry = cp[0]&MPFR_LIMB_ONE */ { /* FIXME: Can be faster? */ MPFR_ASSERTD(sh == 0); goto SubD1Lose; } /* Result is a power of 2 */ ap = MPFR_MANT (a); MPN_ZERO (ap, n); ap[n-1] = MPFR_LIMB_HIGHBIT; MPFR_SET_EXP (a, bx); /* No expo overflow! */ /* No Normalize is needed*/ /* No Rounding is needed */ MPFR_TMP_FREE (marker); return 0; } /* carry = cp[k]/2+(cp[k-1]&1)<<(GMP_NUMB_BITS-1) = c'[k]*/ else if (bp[k] > carry) goto SubD1NoLose; else { MPFR_ASSERTD(bp[k]<carry); goto SubD1Lose; } } } } else if (MPFR_UNLIKELY(d >= p)) { ap = MPFR_MANT(a); MPFR_UNSIGNED_MINUS_MODULO(sh, p); /* We can't set A before since we use cp for rounding... */ /* Perform rounding: check if a=b or a=b-ulp(b) */ if (MPFR_UNLIKELY(d == p)) { /* cp == -1 and c'p+1 = ? */ bcp = 1; /* We need Cp+1 later for a very improbable case. */ bbcp = (MPFR_MANT(c)[n-1] & (MPFR_LIMB_ONE<<(GMP_NUMB_BITS-2))); /* We need also C'p+1 for an even more unprobable case... */ if (MPFR_LIKELY( bbcp )) bcp1 = 1; else { 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); bcp1 = (k>=0); } else bcp1 = 1; } DEBUG( printf("(D=P) Cp=-1 Cp+1=%d C'p+1=%d \n", bbcp!=0, bcp1!=0) ); bp = MPFR_MANT (b); /* Even if src and dest overlap, it is ok using MPN_COPY */ if (MPFR_LIKELY(rnd_mode == MPFR_RNDN)) { if (MPFR_UNLIKELY( bcp && bcp1==0 )) /* Cp=-1 and C'p+1=0: Even rule Apply! */ /* Check Ap-1 = Bp-1 */ if ((bp[0] & (MPFR_LIMB_ONE<<sh)) == 0) { MPN_COPY(ap, bp, n); goto truncate; } MPN_COPY(ap, bp, n); goto sub_one_ulp; } MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a)); if (rnd_mode == MPFR_RNDZ) { MPN_COPY(ap, bp, n); goto sub_one_ulp; } else { MPN_COPY(ap, bp, n); goto truncate; } } else { /* Cp=0, Cp+1=-1 if d==p+1, C'p+1=-1 */ bcp = 0; bbcp = (d==p+1); bcp1 = 1; DEBUG( printf("(D>P) Cp=%d Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0) ); /* Need to compute C'p+2 if d==p+1 and if rnd_mode=NEAREST (Because of a very improbable case) */ if (MPFR_UNLIKELY(d==p+1 && rnd_mode==MPFR_RNDN)) { 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); bbcp1 = (k>=0); } else bbcp1 = 1; DEBUG( printf("(D>P) C'p+2=%d\n", bbcp1!=0) ); } /* Copy mantissa B in A */ MPN_COPY(ap, MPFR_MANT(b), n); /* Round */ if (MPFR_LIKELY(rnd_mode == MPFR_RNDN)) goto truncate; MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a)); if (rnd_mode == MPFR_RNDZ) goto sub_one_ulp; else /* rnd_mode = AWAY */ goto truncate; } } else { mpfr_uexp_t dm; mp_size_t m; mp_limb_t mask; /* General case: 2 <= d < p */ MPFR_UNSIGNED_MINUS_MODULO(sh, p); cp = MPFR_TMP_LIMBS_ALLOC (n); /* Shift c in temporary allocated place */ 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 >=2 and m == 0: just shift */ MPFR_ASSERTD(dm >= 2); 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)) { /* Try to compute them from C' rather than C (FIXME: Faster?) */ 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 { /* 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 { /*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/ do { kx--; } while (kx>=0 && tp[kx]==0); bcp1 = (kx>=0); } } DEBUG( printf("sh=%lu Cp=%d C'p+1=%d\n", sh, bcp!=0, bcp1!=0) ); /* Check if we can lose a bit, and if so compute Cp+1 and C'p+2 */ bp = MPFR_MANT(b); if (MPFR_UNLIKELY((bp[n-1]-cp[n-1]) <= MPFR_LIMB_HIGHBIT)) { /* We can lose a bit so we precompute Cp+1 and C'p+2 */ /* Test for trivial case: since C'p+1=0, Cp+1=0 and C'p+2 =0 */ if (MPFR_LIKELY(bcp1 == 0)) { bbcp = 0; bbcp1 = 0; } else /* bcp1 != 0 */ { /* We can lose a bit: compute Cp+1 and C'p+2 from mantissa C */ mp_limb_t *tp = MPFR_MANT(c); /* Start from bit x=(p+1)-d in mantissa C */ mpfr_prec_t x = p+1-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); DEBUG (printf ("(pre) x=%lu Kx=%ld Sx=%lu\n", (unsigned long) x, (long) kx, (unsigned long) sx)); bbcp = (tp[kx] & (MPFR_LIMB_ONE<<sx)) ; /* Looks at the last bits of limb kx (If sx=0, does nothing)*/ /* If Cp+1=0, since C'p+1!=0, C'p+2=1 ! */ if (MPFR_LIKELY(bbcp==0 || (tp[kx]&MPFR_LIMB_MASK(sx)))) bbcp1 = 1; else { /*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/ do { kx--; } while (kx>=0 && tp[kx]==0); bbcp1 = (kx>=0); DEBUG (printf ("(Pre) Scan done for %ld\n", (long) kx)); } } /*End of Bcp1 != 0*/ DEBUG( printf("(Pre) Cp+1=%d C'p+2=%d\n", bbcp!=0, bbcp1!=0) ); } /* End of "can lose a bit" */ /* Clean shifted C' */ mask = ~MPFR_LIMB_MASK (sh); cp[0] &= mask; /* Subtract the mantissa c from b in a */ ap = MPFR_MANT(a); mpn_sub_n (ap, bp, cp, n); DEBUG( mpfr_print_mant_binary("Sub= ", ap, p) ); /* Normalize: we lose at max one bit*/ if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0)) { /* High bit is not set and we have to fix it! */ /* Ap >= 010000xxx001 */ mpn_lshift(ap, ap, n, 1); /* Ap >= 100000xxx010 */ if (MPFR_UNLIKELY(bcp!=0)) /* Check if Cp = -1 */ /* Since Cp == -1, we have to substract one more */ { mpn_sub_1(ap, ap, n, MPFR_LIMB_ONE<<sh); MPFR_ASSERTD(MPFR_LIMB_MSB(ap[n-1]) != 0); } /* Ap >= 10000xxx001 */ /* Final exponent -1 since we have shifted the mantissa */ bx--; /* Update bcp and bcp1 */ MPFR_ASSERTN(bbcp != (mp_limb_t) -1); MPFR_ASSERTN(bbcp1 != (mp_limb_t) -1); bcp = bbcp; bcp1 = bbcp1; /* We dont't have anymore a valid Cp+1! But since Ap >= 100000xxx001, the final sub can't unnormalize!*/ } MPFR_ASSERTD( !(ap[0] & ~mask) ); /* Rounding */ if (MPFR_LIKELY(rnd_mode == MPFR_RNDN)) { if (MPFR_LIKELY(bcp==0)) goto truncate; else if ((bcp1) || ((ap[0] & (MPFR_LIMB_ONE<<sh)) != 0)) goto sub_one_ulp; else goto truncate; } /* Update rounding mode */ MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a)); if (rnd_mode == MPFR_RNDZ && (MPFR_LIKELY(bcp || bcp1))) goto sub_one_ulp; goto truncate; } MPFR_RET_NEVER_GO_HERE (); /* Sub one ulp to the result */ sub_one_ulp: mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh); /* Result should be smaller than exact value: inexact=-1 */ inexact = -1; /* Check normalisation */ if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0)) { /* ap was a power of 2, and we lose a bit */ /* Now it is 0111111111111111111[00000 */ mpn_lshift(ap, ap, n, 1); bx--; /* And the lost bit x depends on Cp+1, and Cp */ /* Compute Cp+1 if it isn't already compute (ie d==1) */ /* FIXME: Is this case possible? */ if (MPFR_UNLIKELY(d == 1)) bbcp = 0; DEBUG( printf("(SubOneUlp)Cp=%d, Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0)); /* Compute the last bit (Since we have shifted the mantissa) we need one more bit!*/ MPFR_ASSERTN(bbcp != (mp_limb_t) -1); if ( (rnd_mode == MPFR_RNDZ && bcp==0) || (rnd_mode==MPFR_RNDN && bbcp==0) || (bcp && bcp1==0) ) /*Exact result*/ { ap[0] |= MPFR_LIMB_ONE<<sh; if (rnd_mode == MPFR_RNDN) inexact = 1; DEBUG( printf("(SubOneUlp) Last bit set\n") ); } /* Result could be exact if C'p+1 = 0 and rnd == Zero since we have had one more bit to the result */ /* Fixme: rnd_mode == MPFR_RNDZ needed ? */ if (bcp1==0 && rnd_mode==MPFR_RNDZ) { DEBUG( printf("(SubOneUlp) Exact result\n") ); inexact = 0; } } goto end_of_sub; truncate: /* Check if the result is an exact power of 2: 100000000000 in which cases, we could have to do sub_one_ulp due to some nasty reasons: If Result is a Power of 2: + If rnd = AWAY, | If Cp=-1 and C'p+1 = 0, SubOneUlp and the result is EXACT. If Cp=-1 and C'p+1 =-1, SubOneUlp and the result is above. Otherwise truncate + If rnd = NEAREST, If Cp= 0 and Cp+1 =-1 and C'p+2=-1, SubOneUlp and the result is above If cp=-1 and C'p+1 = 0, SubOneUlp and the result is exact. Otherwise truncate. X bit should always be set if SubOneUlp*/ if (MPFR_UNLIKELY(ap[n-1] == MPFR_LIMB_HIGHBIT)) { mp_size_t k = n-1; do { k--; } while (k>=0 && ap[k]==0); if (MPFR_UNLIKELY(k<0)) { /* It is a power of 2! */ /* Compute Cp+1 if it isn't already compute (ie d==1) */ /* FIXME: Is this case possible? */ if (d == 1) bbcp=0; DEBUG( printf("(Truncate) Cp=%d, Cp+1=%d C'p+1=%d C'p+2=%d\n", \ bcp!=0, bbcp!=0, bcp1!=0, bbcp1!=0) ); MPFR_ASSERTN(bbcp != (mp_limb_t) -1); MPFR_ASSERTN((rnd_mode != MPFR_RNDN) || (bcp != 0) || (bbcp == 0) || (bbcp1 != (mp_limb_t) -1)); if (((rnd_mode != MPFR_RNDZ) && bcp) || ((rnd_mode == MPFR_RNDN) && (bcp == 0) && (bbcp) && (bbcp1))) { DEBUG( printf("(Truncate) Do sub\n") ); mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh); mpn_lshift(ap, ap, n, 1); ap[0] |= MPFR_LIMB_ONE<<sh; bx--; /* FIXME: Explain why it works (or why not)... */ inexact = (bcp1 == 0) ? 0 : (rnd_mode==MPFR_RNDN) ? -1 : 1; goto end_of_sub; } } } /* Calcul of Inexact flag.*/ inexact = MPFR_LIKELY(bcp || bcp1) ? 1 : 0; end_of_sub: /* Update Expo */ /* FIXME: Is this test really useful? If d==0 : Exact case. This is never called. if 1 < d < p : bx=MPFR_EXP(b) or MPFR_EXP(b)-1 > MPFR_EXP(c) > emin if d == 1 : bx=MPFR_EXP(b). If we could lose any bits, the exact normalisation is called. if d >= p : bx=MPFR_EXP(b) >= MPFR_EXP(c) + p > emin After SubOneUlp, we could have one bit less. if 1 < d < p : bx >= MPFR_EXP(b)-2 >= MPFR_EXP(c) > emin if d == 1 : bx >= MPFR_EXP(b)-1 = MPFR_EXP(c) > emin. if d >= p : bx >= MPFR_EXP(b)-1 > emin since p>=2. */ MPFR_ASSERTD( bx >= __gmpfr_emin); /* if (MPFR_UNLIKELY(bx < __gmpfr_emin)) { DEBUG( printf("(Final Underflow)\n") ); if (rnd_mode == MPFR_RNDN && (bx < __gmpfr_emin - 1 || (inexact >= 0 && mpfr_powerof2_raw (a)))) rnd_mode = MPFR_RNDZ; MPFR_TMP_FREE(marker); return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a)); } */ MPFR_SET_EXP (a, bx); MPFR_TMP_FREE(marker); MPFR_RET (inexact * MPFR_INT_SIGN (a)); }
/* agm(x,y) is between x and y, so we don't need to save exponent range */ int mpfr_agm (mpfr_ptr r, mpfr_srcptr op2, mpfr_srcptr op1, mp_rnd_t rnd_mode) { int compare, inexact; mp_size_t s; mp_prec_t p, q; mp_limb_t *up, *vp, *tmpp; mpfr_t u, v, tmp; unsigned long n; /* number of iterations */ unsigned long err = 0; MPFR_ZIV_DECL (loop); MPFR_TMP_DECL(marker); MPFR_LOG_FUNC (("op2[%#R]=%R op1[%#R]=%R rnd=%d", op2,op2,op1,op1,rnd_mode), ("r[%#R]=%R inexact=%d", r, r, inexact)); /* Deal with special values */ if (MPFR_ARE_SINGULAR (op1, op2)) { /* If a or b is NaN, the result is NaN */ if (MPFR_IS_NAN(op1) || MPFR_IS_NAN(op2)) { MPFR_SET_NAN(r); MPFR_RET_NAN; } /* now one of a or b is Inf or 0 */ /* If a and b is +Inf, the result is +Inf. Otherwise if a or b is -Inf or 0, the result is NaN */ else if (MPFR_IS_INF(op1) || MPFR_IS_INF(op2)) { if (MPFR_IS_STRICTPOS(op1) && MPFR_IS_STRICTPOS(op2)) { MPFR_SET_INF(r); MPFR_SET_SAME_SIGN(r, op1); MPFR_RET(0); /* exact */ } else { MPFR_SET_NAN(r); MPFR_RET_NAN; } } else /* a and b are neither NaN nor Inf, and one is zero */ { /* If a or b is 0, the result is +0 since a sqrt is positive */ MPFR_ASSERTD (MPFR_IS_ZERO (op1) || MPFR_IS_ZERO (op2)); MPFR_SET_POS (r); MPFR_SET_ZERO (r); MPFR_RET (0); /* exact */ } } MPFR_CLEAR_FLAGS (r); /* If a or b is negative (excluding -Infinity), the result is NaN */ if (MPFR_UNLIKELY(MPFR_IS_NEG(op1) || MPFR_IS_NEG(op2))) { MPFR_SET_NAN(r); MPFR_RET_NAN; } /* Precision of the following calculus */ q = MPFR_PREC(r); p = q + MPFR_INT_CEIL_LOG2(q) + 15; MPFR_ASSERTD (p >= 7); /* see algorithms.tex */ s = (p - 1) / BITS_PER_MP_LIMB + 1; /* b (op2) and a (op1) are the 2 operands but we want b >= a */ compare = mpfr_cmp (op1, op2); if (MPFR_UNLIKELY( compare == 0 )) { mpfr_set (r, op1, rnd_mode); MPFR_RET (0); /* exact */ } else if (compare > 0) { mpfr_srcptr t = op1; op1 = op2; op2 = t; } /* Now b(=op2) >= a (=op1) */ MPFR_TMP_MARK(marker); /* Main loop */ MPFR_ZIV_INIT (loop, p); for (;;) { mp_prec_t eq; /* Init temporary vars */ MPFR_TMP_INIT (up, u, p, s); MPFR_TMP_INIT (vp, v, p, s); MPFR_TMP_INIT (tmpp, tmp, p, s); /* Calculus of un and vn */ mpfr_mul (u, op1, op2, GMP_RNDN); /* Faster since PREC(op) < PREC(u) */ mpfr_sqrt (u, u, GMP_RNDN); mpfr_add (v, op1, op2, GMP_RNDN); /* add with !=prec is still good*/ mpfr_div_2ui (v, v, 1, GMP_RNDN); n = 1; while (mpfr_cmp2 (u, v, &eq) != 0 && eq <= p - 2) { mpfr_add (tmp, u, v, GMP_RNDN); mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN); /* See proof in algorithms.tex */ if (4*eq > p) { mpfr_t w; /* tmp = U(k) */ mpfr_init2 (w, (p + 1) / 2); mpfr_sub (w, v, u, GMP_RNDN); /* e = V(k-1)-U(k-1) */ mpfr_sqr (w, w, GMP_RNDN); /* e = e^2 */ mpfr_div_2ui (w, w, 4, GMP_RNDN); /* e*= (1/2)^2*1/4 */ mpfr_div (w, w, tmp, GMP_RNDN); /* 1/4*e^2/U(k) */ mpfr_sub (v, tmp, w, GMP_RNDN); err = MPFR_GET_EXP (tmp) - MPFR_GET_EXP (v); /* 0 or 1 */ mpfr_clear (w); break; } mpfr_mul (u, u, v, GMP_RNDN); mpfr_sqrt (u, u, GMP_RNDN); mpfr_swap (v, tmp); n ++; } /* the error on v is bounded by (18n+51) ulps, or twice if there was an exponent loss in the final subtraction */ err += MPFR_INT_CEIL_LOG2(18 * n + 51); /* 18n+51 should not overflow since n is about log(p) */ /* we should have n+2 <= 2^(p/4) [see algorithms.tex] */ if (MPFR_LIKELY (MPFR_INT_CEIL_LOG2(n + 2) <= p / 4 && MPFR_CAN_ROUND (v, p - err, q, rnd_mode))) break; /* Stop the loop */ /* Next iteration */ MPFR_ZIV_NEXT (loop, p); s = (p - 1) / BITS_PER_MP_LIMB + 1; } MPFR_ZIV_FREE (loop); /* Setting of the result */ inexact = mpfr_set (r, v, rnd_mode); /* Let's clean */ MPFR_TMP_FREE(marker); return inexact; /* agm(u,v) can be exact for u, v rational only for u=v. Proof (due to Nicolas Brisebarre): it suffices to consider u=1 and v<1. Then 1/AGM(1,v) = 2F1(1/2,1/2,1;1-v^2), and a theorem due to G.V. Chudnovsky states that for x a non-zero algebraic number with |x|<1, then 2F1(1/2,1/2,1;x) and 2F1(-1/2,1/2,1;x) are algebraically independent over Q. */ }
int mpfr_mul_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mpfr_rnd_t rnd_mode) { mp_limb_t *yp; mp_size_t xn; int cnt, inexact; MPFR_TMP_DECL (marker); if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) { if (MPFR_IS_NAN (x)) { MPFR_SET_NAN (y); MPFR_RET_NAN; } else if (MPFR_IS_INF (x)) { if (u != 0) { MPFR_SET_INF (y); MPFR_SET_SAME_SIGN (y, x); MPFR_RET (0); /* infinity is exact */ } else /* 0 * infinity */ { MPFR_SET_NAN (y); MPFR_RET_NAN; } } else /* x is zero */ { MPFR_ASSERTD (MPFR_IS_ZERO (x)); MPFR_SET_ZERO (y); MPFR_SET_SAME_SIGN (y, x); MPFR_RET (0); /* zero is exact */ } } else if (MPFR_UNLIKELY (u <= 1)) { if (u < 1) { MPFR_SET_ZERO (y); MPFR_SET_SAME_SIGN (y, x); MPFR_RET (0); /* zero is exact */ } else return mpfr_set (y, x, rnd_mode); } else if (MPFR_UNLIKELY (IS_POW2 (u))) return mpfr_mul_2si (y, x, MPFR_INT_CEIL_LOG2 (u), rnd_mode); yp = MPFR_MANT (y); xn = MPFR_LIMB_SIZE (x); MPFR_ASSERTD (xn < MP_SIZE_T_MAX); MPFR_TMP_MARK(marker); yp = MPFR_TMP_LIMBS_ALLOC (xn + 1); MPFR_ASSERTN (u == (mp_limb_t) u); yp[xn] = mpn_mul_1 (yp, MPFR_MANT (x), xn, u); /* x * u is stored in yp[xn], ..., yp[0] */ /* since the case u=1 was treated above, we have u >= 2, thus yp[xn] >= 1 since x was msb-normalized */ MPFR_ASSERTD (yp[xn] != 0); if (MPFR_LIKELY (MPFR_LIMB_MSB (yp[xn]) == 0)) { count_leading_zeros (cnt, yp[xn]); mpn_lshift (yp, yp, xn + 1, cnt); } else { cnt = 0; } /* now yp[xn], ..., yp[0] is msb-normalized too, and has at most PREC(x) + (GMP_NUMB_BITS - cnt) non-zero bits */ MPFR_RNDRAW (inexact, y, yp, (mpfr_prec_t) (xn + 1) * GMP_NUMB_BITS, rnd_mode, MPFR_SIGN (x), cnt -- ); MPFR_TMP_FREE (marker); cnt = GMP_NUMB_BITS - cnt; if (MPFR_UNLIKELY (__gmpfr_emax < MPFR_EMAX_MIN + cnt || MPFR_GET_EXP (x) > __gmpfr_emax - cnt)) return mpfr_overflow (y, rnd_mode, MPFR_SIGN(x)); MPFR_SET_EXP (y, MPFR_GET_EXP (x) + cnt); MPFR_SET_SAME_SIGN (y, x); return inexact; }
/* Don't need to save / restore exponent range: the cache does it */ int mpfr_const_log2_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode) { unsigned long n = MPFR_PREC (x); mpfr_prec_t w; /* working precision */ unsigned long N; mpz_t *T, *P, *Q; mpfr_t t, q; int inexact; int ok = 1; /* ensures that the 1st try will give correct rounding */ unsigned long lgN, i; MPFR_GROUP_DECL(group); MPFR_TMP_DECL(marker); MPFR_ZIV_DECL(loop); MPFR_LOG_FUNC ( ("rnd_mode=%d", rnd_mode), ("x[%Pu]=%.*Rg inex=%d", mpfr_get_prec(x), mpfr_log_prec, x, inexact)); if (n < 1253) w = n + 10; /* ensures correct rounding for the four rounding modes, together with N = w / 3 + 1 (see below). */ else if (n < 2571) w = n + 11; /* idem */ else if (n < 3983) w = n + 12; else if (n < 4854) w = n + 13; else if (n < 26248) w = n + 14; else { w = n + 15; ok = 0; } MPFR_TMP_MARK(marker); MPFR_GROUP_INIT_2(group, w, t, q); MPFR_ZIV_INIT (loop, w); for (;;) { N = w / 3 + 1; /* Warning: do not change that (even increasing N!) without checking correct rounding in the above ranges for n. */ /* the following are needed for error analysis (see algorithms.tex) */ MPFR_ASSERTD(w >= 3 && N >= 2); lgN = MPFR_INT_CEIL_LOG2 (N) + 1; T = (mpz_t *) MPFR_TMP_ALLOC (3 * lgN * sizeof (mpz_t)); P = T + lgN; Q = T + 2*lgN; for (i = 0; i < lgN; i++) { mpz_init (T[i]); mpz_init (P[i]); mpz_init (Q[i]); } S (T, P, Q, 0, N, 0); mpfr_set_z (t, T[0], MPFR_RNDN); mpfr_set_z (q, Q[0], MPFR_RNDN); mpfr_div (t, t, q, MPFR_RNDN); for (i = 0; i < lgN; i++) { mpz_clear (T[i]); mpz_clear (P[i]); mpz_clear (Q[i]); } if (MPFR_LIKELY (ok != 0 || mpfr_can_round (t, w - 2, MPFR_RNDN, rnd_mode, n))) break; MPFR_ZIV_NEXT (loop, w); MPFR_GROUP_REPREC_2(group, w, t, q); } MPFR_ZIV_FREE (loop); inexact = mpfr_set (x, t, rnd_mode); MPFR_GROUP_CLEAR(group); MPFR_TMP_FREE(marker); return inexact; }
int mpfr_sqr (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode) { int cc, inexact; mpfr_exp_t ax; mp_limb_t *tmp; mp_limb_t b1; mpfr_prec_t bq; mp_size_t bn, tn; MPFR_TMP_DECL(marker); MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", b, b, rnd_mode), ("y[%#R]=%R inexact=%d", a, a, inexact)); /* deal with special cases */ if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(b))) { if (MPFR_IS_NAN(b)) { MPFR_SET_NAN(a); MPFR_RET_NAN; } MPFR_SET_POS (a); if (MPFR_IS_INF(b)) MPFR_SET_INF(a); else ( MPFR_ASSERTD(MPFR_IS_ZERO(b)), MPFR_SET_ZERO(a) ); MPFR_RET(0); } ax = 2 * MPFR_GET_EXP (b); bq = MPFR_PREC(b); MPFR_ASSERTD (2 * bq > bq); /* PREC_MAX is /2 so no integer overflow */ bn = MPFR_LIMB_SIZE(b); /* number of limbs of b */ tn = 1 + (2 * bq - 1) / GMP_NUMB_BITS; /* number of limbs of square, 2*bn or 2*bn-1 */ MPFR_TMP_MARK(marker); tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) 2 * bn * BYTES_PER_MP_LIMB); /* Multiplies the mantissa in temporary allocated space */ mpn_sqr_n (tmp, MPFR_MANT(b), bn); b1 = tmp[2 * bn - 1]; /* now tmp[0]..tmp[2*bn-1] contains the product of both mantissa, with tmp[2*bn-1]>=2^(GMP_NUMB_BITS-2) */ b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */ /* if the mantissas of b and c are uniformly distributed in ]1/2, 1], then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */ tmp += 2 * bn - tn; /* +0 or +1 */ if (MPFR_UNLIKELY(b1 == 0)) mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */ cc = mpfr_round_raw (MPFR_MANT (a), tmp, 2 * bq, 0, MPFR_PREC (a), rnd_mode, &inexact); /* cc = 1 ==> result is a power of two */ if (MPFR_UNLIKELY(cc)) MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT; MPFR_TMP_FREE(marker); { mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc); if (MPFR_UNLIKELY( ax2 > __gmpfr_emax)) return mpfr_overflow (a, rnd_mode, MPFR_SIGN_POS); if (MPFR_UNLIKELY( ax2 < __gmpfr_emin)) { /* In the rounding to the nearest mode, if the exponent of the exact result (i.e. before rounding, i.e. without taking cc into account) is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if both arguments are powers of 2), then round to zero. */ if (rnd_mode == MPFR_RNDN && (ax + (mpfr_exp_t) b1 < __gmpfr_emin || mpfr_powerof2_raw (b))) rnd_mode = MPFR_RNDZ; return mpfr_underflow (a, rnd_mode, MPFR_SIGN_POS); } MPFR_SET_EXP (a, ax2); MPFR_SET_POS (a); } MPFR_RET (inexact); }
static int mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) { /* Old implementation */ int sign_product, cc, inexact; mpfr_exp_t ax; mp_limb_t *tmp; mp_limb_t b1; mpfr_prec_t bq, cq; mp_size_t bn, cn, tn, k; MPFR_TMP_DECL(marker); /* deal with special cases */ if (MPFR_ARE_SINGULAR(b,c)) { if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c)) { MPFR_SET_NAN(a); MPFR_RET_NAN; } sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) ); if (MPFR_IS_INF(b)) { if (MPFR_IS_INF(c) || MPFR_NOTZERO(c)) { MPFR_SET_SIGN(a,sign_product); MPFR_SET_INF(a); MPFR_RET(0); /* exact */ } else { MPFR_SET_NAN(a); MPFR_RET_NAN; } } else if (MPFR_IS_INF(c)) { if (MPFR_NOTZERO(b)) { MPFR_SET_SIGN(a, sign_product); MPFR_SET_INF(a); MPFR_RET(0); /* exact */ } else { MPFR_SET_NAN(a); MPFR_RET_NAN; } } else { MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c)); MPFR_SET_SIGN(a, sign_product); MPFR_SET_ZERO(a); MPFR_RET(0); /* 0 * 0 is exact */ } } sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) ); ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c); bq = MPFR_PREC(b); cq = MPFR_PREC(c); MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */ bn = (bq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of b */ cn = (cq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of c */ k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */ tn = (bq + cq + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS; /* <= k, thus no int overflow */ MPFR_ASSERTD(tn <= k); /* Check for no size_t overflow*/ MPFR_ASSERTD((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB); MPFR_TMP_MARK(marker); tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB); /* multiplies two mantissa in temporary allocated space */ b1 = (MPFR_LIKELY(bn >= cn)) ? mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn) : mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn); /* now tmp[0]..tmp[k-1] contains the product of both mantissa, with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */ b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */ /* if the mantissas of b and c are uniformly distributed in ]1/2, 1], then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */ tmp += k - tn; if (MPFR_UNLIKELY(b1 == 0)) mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */ cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq, MPFR_IS_NEG_SIGN(sign_product), MPFR_PREC (a), rnd_mode, &inexact); /* cc = 1 ==> result is a power of two */ if (MPFR_UNLIKELY(cc)) MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT; MPFR_TMP_FREE(marker); { mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc); if (MPFR_UNLIKELY( ax2 > __gmpfr_emax)) return mpfr_overflow (a, rnd_mode, sign_product); if (MPFR_UNLIKELY( ax2 < __gmpfr_emin)) { /* In the rounding to the nearest mode, if the exponent of the exact result (i.e. before rounding, i.e. without taking cc into account) is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if both arguments are powers of 2), then round to zero. */ if (rnd_mode == MPFR_RNDN && (ax + (mpfr_exp_t) b1 < __gmpfr_emin || (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c)))) rnd_mode = MPFR_RNDZ; return mpfr_underflow (a, rnd_mode, sign_product); } MPFR_SET_EXP (a, ax2); MPFR_SET_SIGN(a, sign_product); } MPFR_RET (inexact); }
int mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode) { mp_size_t rsize; /* number of limbs of r (plus 1 if exact limb multiple) */ mp_size_t rrsize; mp_size_t usize; /* number of limbs of u */ mp_size_t tsize; /* number of limbs of the sqrtrem remainder */ mp_size_t k; mp_size_t l; mpfr_limb_ptr rp, rp0; mpfr_limb_ptr up; mpfr_limb_ptr sp; mp_limb_t sticky0; /* truncated part of input */ mp_limb_t sticky1; /* truncated part of rp[0] */ mp_limb_t sticky; int odd_exp; int sh; /* number of extra bits in rp[0] */ int inexact; /* return ternary flag */ mpfr_exp_t expr; MPFR_TMP_DECL(marker); MPFR_LOG_FUNC (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (u), mpfr_log_prec, u, rnd_mode), ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (r), mpfr_log_prec, r, inexact)); if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u))) { if (MPFR_IS_NAN(u)) { MPFR_SET_NAN(r); MPFR_RET_NAN; } else if (MPFR_IS_ZERO(u)) { /* 0+ or 0- */ MPFR_SET_SAME_SIGN(r, u); MPFR_SET_ZERO(r); MPFR_RET(0); /* zero is exact */ } else { MPFR_ASSERTD(MPFR_IS_INF(u)); /* sqrt(-Inf) = NAN */ if (MPFR_IS_NEG(u)) { MPFR_SET_NAN(r); MPFR_RET_NAN; } MPFR_SET_POS(r); MPFR_SET_INF(r); MPFR_RET(0); } } if (MPFR_UNLIKELY(MPFR_IS_NEG(u))) { MPFR_SET_NAN(r); MPFR_RET_NAN; } MPFR_SET_POS(r); MPFR_TMP_MARK (marker); MPFR_UNSIGNED_MINUS_MODULO(sh,MPFR_PREC(r)); if (sh == 0 && rnd_mode == MPFR_RNDN) sh = GMP_NUMB_BITS; /* ugly case */ rsize = MPFR_LIMB_SIZE(r) + (sh == GMP_NUMB_BITS); /* rsize is the number of limbs of r + 1 if exact limb multiple and rounding to nearest, this is the number of wanted limbs for the square root */ rrsize = rsize + rsize; usize = MPFR_LIMB_SIZE(u); /* number of limbs of u */ rp0 = MPFR_MANT(r); rp = (sh < GMP_NUMB_BITS) ? rp0 : MPFR_TMP_LIMBS_ALLOC (rsize); up = MPFR_MANT(u); sticky0 = MPFR_LIMB_ZERO; /* truncated part of input */ sticky1 = MPFR_LIMB_ZERO; /* truncated part of rp[0] */ odd_exp = (unsigned int) MPFR_GET_EXP (u) & 1; inexact = -1; /* return ternary flag */ sp = MPFR_TMP_LIMBS_ALLOC (rrsize); /* copy the most significant limbs of u to {sp, rrsize} */ if (MPFR_LIKELY(usize <= rrsize)) /* in case r and u have the same precision, we have indeed rrsize = 2 * usize */ { k = rrsize - usize; if (MPFR_LIKELY(k)) MPN_ZERO (sp, k); if (odd_exp) { if (MPFR_LIKELY(k)) sp[k - 1] = mpn_rshift (sp + k, up, usize, 1); else sticky0 = mpn_rshift (sp, up, usize, 1); } else MPN_COPY (sp + rrsize - usize, up, usize); } else /* usize > rrsize: truncate the input */ { k = usize - rrsize; if (odd_exp) sticky0 = mpn_rshift (sp, up + k, rrsize, 1); else MPN_COPY (sp, up + k, rrsize); l = k; while (sticky0 == MPFR_LIMB_ZERO && l != 0) sticky0 = up[--l]; } /* sticky0 is non-zero iff the truncated part of the input is non-zero */ /* mpn_rootrem with NULL 2nd argument is faster than mpn_sqrtrem, thus use it if available and if the user asked to use GMP internal functions */ #if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_ROOTREM) tsize = __gmpn_rootrem (rp, NULL, sp, rrsize, 2); #else tsize = mpn_sqrtrem (rp, NULL, sp, rrsize); #endif /* a return value of zero in mpn_sqrtrem indicates a perfect square */ sticky = sticky0 || tsize != 0; /* truncate low bits of rp[0] */ sticky1 = rp[0] & ((sh < GMP_NUMB_BITS) ? MPFR_LIMB_MASK(sh) : ~MPFR_LIMB_ZERO); rp[0] -= sticky1; sticky = sticky || sticky1; expr = (MPFR_GET_EXP(u) + odd_exp) / 2; /* exact */ if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD || sticky == MPFR_LIMB_ZERO) { inexact = (sticky == MPFR_LIMB_ZERO) ? 0 : -1; goto truncate; } else if (rnd_mode == MPFR_RNDN) { /* if sh < GMP_NUMB_BITS, the round bit is bit (sh-1) of sticky1 and the sticky bit is formed by the low sh-1 bits from sticky1, together with the sqrtrem remainder and sticky0. */ if (sh < GMP_NUMB_BITS) { if (sticky1 & (MPFR_LIMB_ONE << (sh - 1))) { /* round bit is set */ if (sticky1 == (MPFR_LIMB_ONE << (sh - 1)) && tsize == 0 && sticky0 == 0) goto even_rule; else goto add_one_ulp; } else /* round bit is zero */ goto truncate; /* with the default inexact=-1 */ } else /* sh = GMP_NUMB_BITS: the round bit is the most significant bit of rp[0], and the remaining GMP_NUMB_BITS-1 bits contribute to the sticky bit */ { if (sticky1 & MPFR_LIMB_HIGHBIT) { /* round bit is set */ if (sticky1 == MPFR_LIMB_HIGHBIT && tsize == 0 && sticky0 == 0) goto even_rule; else goto add_one_ulp; } else /* round bit is zero */ goto truncate; /* with the default inexact=-1 */ } } else /* rnd_mode=GMP_RDNU, necessarily sticky <> 0, thus add 1 ulp */ goto add_one_ulp; even_rule: /* has to set inexact */ if (sh < GMP_NUMB_BITS) inexact = (rp[0] & (MPFR_LIMB_ONE << sh)) ? 1 : -1; else inexact = (rp[1] & MPFR_LIMB_ONE) ? 1 : -1; if (inexact == -1) goto truncate; /* else go through add_one_ulp */ add_one_ulp: inexact = 1; /* always here */ if (sh == GMP_NUMB_BITS) { rp ++; rsize --; sh = 0; } if (mpn_add_1 (rp0, rp, rsize, MPFR_LIMB_ONE << sh)) { expr ++; rp[rsize - 1] = MPFR_LIMB_HIGHBIT; } goto end; truncate: /* inexact = 0 or -1 */ if (sh == GMP_NUMB_BITS) MPN_COPY (rp0, rp + 1, rsize - 1); end: MPFR_ASSERTN (expr >= MPFR_EMIN_MIN && expr <= MPFR_EMAX_MAX); MPFR_EXP (r) = expr; MPFR_TMP_FREE(marker); return mpfr_check_range (r, inexact, rnd_mode); }
/* 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)); }
/* Compute the first 2^m terms from the hypergeometric series with x = p / 2^r */ static int GENERIC (mpfr_ptr y, mpz_srcptr p, long r, int m) { unsigned long n,i,k,j,l; int is_p_one; mpz_t* P,*S; #ifdef A mpz_t *T; #endif mpz_t* ptoj; #ifdef R_IS_RATIONAL mpz_t* qtoj; mpfr_t tmp; #endif mp_exp_t diff, expo; mp_prec_t precy = MPFR_PREC(y); MPFR_TMP_DECL(marker); MPFR_TMP_MARK(marker); MPFR_CLEAR_FLAGS(y); n = 1UL << m; P = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); S = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); ptoj = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); /* ptoj[i] = mantissa^(2^i) */ #ifdef A T = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); #endif #ifdef R_IS_RATIONAL qtoj = (mpz_t*) MPFR_TMP_ALLOC ((m+1) * sizeof(mpz_t)); #endif for (i = 0 ; i <= m ; i++) { mpz_init (P[i]); mpz_init (S[i]); mpz_init (ptoj[i]); #ifdef R_IS_RATIONAL mpz_init (qtoj[i]); #endif #ifdef A mpz_init (T[i]); #endif } mpz_set (ptoj[0], p); #ifdef C # if C2 != 1 mpz_mul_ui (ptoj[0], ptoj[0], C2); # endif #endif is_p_one = mpz_cmp_ui(ptoj[0], 1) == 0; #ifdef A # ifdef B mpz_set_ui (T[0], A1 * B1); # else mpz_set_ui (T[0], A1); # endif #endif if (!is_p_one) for (i = 1 ; i < m ; i++) mpz_mul (ptoj[i], ptoj[i-1], ptoj[i-1]); #ifdef R_IS_RATIONAL mpz_set_si (qtoj[0], r); for (i = 1 ; i <= m ; i++) mpz_mul(qtoj[i], qtoj[i-1], qtoj[i-1]); #endif mpz_set_ui (P[0], 1); mpz_set_ui (S[0], 1); k = 0; for (i = 1 ; i < n ; i++) { k++; #ifdef A # ifdef B mpz_set_ui (T[k], (A1 + A2*i)*(B1+B2*i)); # else mpz_set_ui (T[k], A1 + A2*i); # endif #endif #ifdef C # ifdef NO_FACTORIAL mpz_set_ui (P[k], (C1 + C2 * (i-1))); mpz_set_ui (S[k], 1); # else mpz_set_ui (P[k], (i+1) * (C1 + C2 * (i-1))); mpz_set_ui (S[k], i+1); # endif #else # ifdef NO_FACTORIAL mpz_set_ui (P[k], 1); # else mpz_set_ui (P[k], i+1); # endif mpz_set (S[k], P[k]); #endif for (j = i+1, l = 0 ; (j & 1) == 0 ; l++, j>>=1, k--) { if (!is_p_one) mpz_mul (S[k], S[k], ptoj[l]); #ifdef A # ifdef B # if (A2*B2) != 1 mpz_mul_ui (P[k], P[k], A2*B2); # endif # else # if A2 != 1 mpz_mul_ui (P[k], P[k], A2); # endif #endif mpz_mul (S[k], S[k], T[k-1]); #endif mpz_mul (S[k-1], S[k-1], P[k]); #ifdef R_IS_RATIONAL mpz_mul (S[k-1], S[k-1], qtoj[l]); #else mpz_mul_2exp (S[k-1], S[k-1], r*(1<<l)); #endif mpz_add (S[k-1], S[k-1], S[k]); mpz_mul (P[k-1], P[k-1], P[k]); #ifdef A mpz_mul (T[k-1], T[k-1], T[k]); #endif } } diff = mpz_sizeinbase(S[0],2) - 2*precy; expo = diff; if (diff >= 0) mpz_div_2exp(S[0],S[0],diff); else mpz_mul_2exp(S[0],S[0],-diff); diff = mpz_sizeinbase(P[0],2) - precy; expo -= diff; if (diff >=0) mpz_div_2exp(P[0],P[0],diff); else mpz_mul_2exp(P[0],P[0],-diff); mpz_tdiv_q(S[0], S[0], P[0]); mpfr_set_z(y, S[0], GMP_RNDD); MPFR_SET_EXP (y, MPFR_GET_EXP (y) + expo); #ifdef R_IS_RATIONAL /* exact division */ mpz_div_ui (qtoj[m], qtoj[m], r); mpfr_init2 (tmp, MPFR_PREC(y)); mpfr_set_z (tmp, qtoj[m] , GMP_RNDD); mpfr_div (y, y, tmp, GMP_RNDD); mpfr_clear (tmp); #else mpfr_div_2ui(y, y, r*(i-1), GMP_RNDN); #endif for (i = 0 ; i <= m ; i++) { mpz_clear (P[i]); mpz_clear (S[i]); mpz_clear (ptoj[i]); #ifdef R_IS_RATIONAL mpz_clear (qtoj[i]); #endif #ifdef A mpz_clear (T[i]); #endif } MPFR_TMP_FREE (marker); return 0; }
int mpfr_set_f (mpfr_ptr y, mpf_srcptr x, mpfr_rnd_t rnd_mode) { mp_limb_t *my, *mx, *tmp; unsigned long cnt, sx, sy; int inexact, carry = 0; MPFR_TMP_DECL(marker); sx = ABS(SIZ(x)); /* number of limbs of the mantissa of x */ if (sx == 0) /* x is zero */ { MPFR_SET_ZERO(y); MPFR_SET_POS(y); return 0; /* 0 is exact */ } if (SIZ(x) * MPFR_FROM_SIGN_TO_INT(MPFR_SIGN(y)) < 0) MPFR_CHANGE_SIGN (y); sy = MPFR_LIMB_SIZE (y); my = MPFR_MANT(y); mx = PTR(x); count_leading_zeros(cnt, mx[sx - 1]); if (sy <= sx) /* we may have to round even when sy = sx */ { unsigned long xprec = sx * GMP_NUMB_BITS; MPFR_TMP_MARK(marker); tmp = MPFR_TMP_LIMBS_ALLOC (sx); if (cnt) mpn_lshift (tmp, mx, sx, cnt); else /* FIXME: we may avoid the copy here, and directly call mpfr_round_raw on mx instead of tmp */ MPN_COPY (tmp, mx, sx); carry = mpfr_round_raw (my, tmp, xprec, (SIZ(x) < 0), MPFR_PREC(y), rnd_mode, &inexact); if (MPFR_UNLIKELY(carry)) /* result is a power of two */ my[sy - 1] = MPFR_LIMB_HIGHBIT; MPFR_TMP_FREE(marker); } else { if (cnt) mpn_lshift (my + sy - sx, mx, sx, cnt); else MPN_COPY (my + sy - sx, mx, sx); MPN_ZERO(my, sy - sx); /* no rounding necessary, since y has a larger mantissa */ inexact = 0; } /* warning: EXP(x) * GMP_NUMB_BITS may exceed the maximal exponent */ if (EXP(x) > 1 + (__gmpfr_emax - 1) / GMP_NUMB_BITS) { /* EXP(x) >= 2 + floor((__gmpfr_emax-1)/GMP_NUMB_BITS) EXP(x) >= 2 + (__gmpfr_emax - GMP_NUMB_BITS) / GMP_NUMB_BITS >= 1 + __gmpfr_emax / GMP_NUMB_BITS EXP(x) * GMP_NUMB_BITS >= __gmpfr_emax + GMP_NUMB_BITS Since 0 <= cnt <= GMP_NUMB_BITS-1, and 0 <= carry <= 1, we have then EXP(x) * GMP_NUMB_BITS - cnt + carry > __gmpfr_emax */ return mpfr_overflow (y, rnd_mode, MPFR_SIGN (y)); } else { /* Do not use MPFR_SET_EXP as the exponent may be out of range. */ MPFR_EXP (y) = EXP (x) * GMP_NUMB_BITS - (mpfr_exp_t) cnt + carry; } return mpfr_check_range (y, inexact, rnd_mode); }