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Implement centered-divide with new integer lib
* libguile/integers.c (scm_integer_centered_divide_ii) (scm_integer_centered_divide_iz, scm_integer_centered_divide_zi) (scm_integer_centered_divide_zz): New internal functions. (integer_centered_divide_zz): New helper. * libguile/integers.h: Declare internal functions. * libguile/numbers.c (scm_centered_divide): Use the new functions. (scm_i_bigint_centered_divide): Remove unused helper.
This commit is contained in:
Andy Wingo
parent
99b046d58b
commit
ccb78fc7b1
3 changed files with 151 additions and 143 deletions
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@ -1231,3 +1231,136 @@ scm_integer_centered_remainder_zz (SCM x, SCM y)
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{
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return integer_centered_remainder_zz (scm_bignum (x), scm_bignum (y));
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}
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static void
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integer_centered_divide_zz (struct scm_bignum *x, struct scm_bignum *y,
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SCM *qp, SCM *rp)
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{
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mpz_t q, r, min_r, zx, zy;
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mpz_init (q);
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mpz_init (r);
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mpz_init (min_r);
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alias_bignum_to_mpz (x, zx);
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alias_bignum_to_mpz (y, zy);
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/* Note that x might be small enough to fit into a fixnum, so we must
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not let it escape into the wild */
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/* min_r will eventually become -abs(y/2) */
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mpz_tdiv_q_2exp (min_r, zy, 1);
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/* Arrange for rr to initially be non-positive, because that
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simplifies the test to see if it is within the needed bounds. */
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if (mpz_sgn (zy) > 0)
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{
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mpz_cdiv_qr (q, r, zx, zy);
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mpz_neg (min_r, min_r);
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if (mpz_cmp (r, min_r) < 0)
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{
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mpz_sub_ui (q, q, 1);
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mpz_add (r, r, zy);
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}
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}
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else
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{
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mpz_fdiv_qr (q, r, zx, zy);
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if (mpz_cmp (r, min_r) < 0)
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{
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mpz_add_ui (q, q, 1);
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mpz_sub (r, r, zy);
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}
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}
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scm_remember_upto_here_2 (x, y);
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mpz_clear (min_r);
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*qp = take_mpz (q);
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*rp = take_mpz (r);
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}
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void
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scm_integer_centered_divide_ii (scm_t_inum x, scm_t_inum y, SCM *qp, SCM *rp)
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{
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if (y == 0)
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scm_num_overflow ("centered-divide");
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scm_t_inum q = x / y;
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scm_t_inum r = x % y;
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if (x > 0)
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{
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if (y > 0)
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{
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if (r >= (y + 1) / 2)
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{ q++; r -= y; }
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}
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else
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{
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if (r >= (1 - y) / 2)
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{ q--; r += y; }
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}
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}
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else
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{
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if (y > 0)
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{
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if (r < -y / 2)
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{ q--; r += y; }
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}
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else
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{
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if (r < y / 2)
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{ q++; r -= y; }
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}
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}
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*qp = long_to_scm (q);
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*rp = SCM_I_MAKINUM (r);
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}
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void
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scm_integer_centered_divide_iz (scm_t_inum x, SCM y, SCM *qp, SCM *rp)
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{
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integer_centered_divide_zz (long_to_bignum (x), scm_bignum (y), qp, rp);
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}
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void
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scm_integer_centered_divide_zi (SCM x, scm_t_inum y, SCM *qp, SCM *rp)
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{
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if (y == 0)
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scm_num_overflow ("centered-divide");
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mpz_t q, zx;
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mpz_init (q);
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alias_bignum_to_mpz (scm_bignum (x), zx);
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scm_t_inum r;
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/* Arrange for r to initially be non-positive, because that
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simplifies the test to see if it is within the needed bounds. */
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if (y > 0)
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{
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r = - mpz_cdiv_q_ui (q, zx, y);
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if (r < -y / 2)
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{
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mpz_sub_ui (q, q, 1);
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r += y;
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}
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}
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else
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{
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r = - mpz_cdiv_q_ui (q, zx, -y);
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mpz_neg (q, q);
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if (r < y / 2)
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{
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mpz_add_ui (q, q, 1);
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r -= y;
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}
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}
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scm_remember_upto_here_1 (x);
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*qp = take_mpz (q);
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*rp = SCM_I_MAKINUM (r);
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}
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void
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scm_integer_centered_divide_zz (SCM x, SCM y, SCM *qp, SCM *rp)
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{
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integer_centered_divide_zz (scm_bignum (x), scm_bignum (y), qp, rp);
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}
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@ -96,6 +96,15 @@ SCM_INTERNAL SCM scm_integer_centered_remainder_iz (scm_t_inum x, SCM y);
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SCM_INTERNAL SCM scm_integer_centered_remainder_zi (SCM x, scm_t_inum y);
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SCM_INTERNAL SCM scm_integer_centered_remainder_zz (SCM x, SCM y);
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SCM_INTERNAL void scm_integer_centered_divide_ii (scm_t_inum x, scm_t_inum y,
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SCM *qp, SCM *rp);
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SCM_INTERNAL void scm_integer_centered_divide_iz (scm_t_inum x, SCM y,
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SCM *qp, SCM *rp);
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SCM_INTERNAL void scm_integer_centered_divide_zi (SCM x, scm_t_inum y,
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SCM *qp, SCM *rp);
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SCM_INTERNAL void scm_integer_centered_divide_zz (SCM x, SCM y,
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SCM *qp, SCM *rp);
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#endif /* SCM_INTEGERS_H */
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@ -2320,7 +2320,6 @@ scm_i_exact_rational_centered_remainder (SCM x, SCM y)
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static void scm_i_inexact_centered_divide (double x, double y,
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SCM *qp, SCM *rp);
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static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp);
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static void scm_i_exact_rational_centered_divide (SCM x, SCM y,
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SCM *qp, SCM *rp);
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@ -2352,57 +2351,15 @@ SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0,
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void
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scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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{
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if (SCM_LIKELY (SCM_I_INUMP (x)))
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if (SCM_I_INUMP (x))
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{
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scm_t_inum xx = SCM_I_INUM (x);
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if (SCM_LIKELY (SCM_I_INUMP (y)))
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{
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scm_t_inum yy = SCM_I_INUM (y);
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if (SCM_UNLIKELY (yy == 0))
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scm_num_overflow (s_scm_centered_divide);
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else
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{
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scm_t_inum qq = xx / yy;
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scm_t_inum rr = xx % yy;
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if (SCM_LIKELY (xx > 0))
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{
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if (SCM_LIKELY (yy > 0))
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{
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if (rr >= (yy + 1) / 2)
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{ qq++; rr -= yy; }
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}
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else
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{
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if (rr >= (1 - yy) / 2)
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{ qq--; rr += yy; }
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}
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}
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else
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{
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if (SCM_LIKELY (yy > 0))
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{
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if (rr < -yy / 2)
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{ qq--; rr += yy; }
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}
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else
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{
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if (rr < yy / 2)
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{ qq++; rr -= yy; }
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}
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}
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if (SCM_LIKELY (SCM_FIXABLE (qq)))
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*qp = SCM_I_MAKINUM (qq);
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else
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*qp = scm_i_inum2big (qq);
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*rp = SCM_I_MAKINUM (rr);
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}
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}
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if (SCM_I_INUMP (y))
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scm_integer_centered_divide_ii (SCM_I_INUM (x), SCM_I_INUM (y), qp, rp);
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else if (SCM_BIGP (y))
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/* Pass a denormalized bignum version of x (even though it
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can fit in a fixnum) to scm_i_bigint_centered_divide */
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scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp);
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scm_integer_centered_divide_iz (SCM_I_INUM (x), y, qp, rp);
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else if (SCM_REALP (y))
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scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp);
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scm_i_inexact_centered_divide (SCM_I_INUM (x), SCM_REAL_VALUE (y),
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qp, rp);
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else if (SCM_FRACTIONP (y))
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scm_i_exact_rational_centered_divide (x, y, qp, rp);
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else
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@ -2411,49 +2368,10 @@ scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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}
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else if (SCM_BIGP (x))
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{
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if (SCM_LIKELY (SCM_I_INUMP (y)))
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{
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scm_t_inum yy = SCM_I_INUM (y);
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if (SCM_UNLIKELY (yy == 0))
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scm_num_overflow (s_scm_centered_divide);
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else
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{
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SCM q = scm_i_mkbig ();
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scm_t_inum rr;
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/* Arrange for rr to initially be non-positive,
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because that simplifies the test to see
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if it is within the needed bounds. */
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if (yy > 0)
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{
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rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q),
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SCM_I_BIG_MPZ (x), yy);
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scm_remember_upto_here_1 (x);
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if (rr < -yy / 2)
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{
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mpz_sub_ui (SCM_I_BIG_MPZ (q),
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SCM_I_BIG_MPZ (q), 1);
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rr += yy;
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}
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}
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else
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{
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rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q),
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SCM_I_BIG_MPZ (x), -yy);
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scm_remember_upto_here_1 (x);
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mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q));
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if (rr < yy / 2)
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{
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mpz_add_ui (SCM_I_BIG_MPZ (q),
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SCM_I_BIG_MPZ (q), 1);
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rr -= yy;
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}
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}
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*qp = scm_i_normbig (q);
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*rp = SCM_I_MAKINUM (rr);
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}
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}
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if (SCM_I_INUMP (y))
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scm_integer_centered_divide_zi (x, SCM_I_INUM (y), qp, rp);
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else if (SCM_BIGP (y))
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scm_i_bigint_centered_divide (x, y, qp, rp);
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scm_integer_centered_divide_zz (x, y, qp, rp);
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else if (SCM_REALP (y))
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scm_i_inexact_centered_divide (scm_i_big2dbl (x), SCM_REAL_VALUE (y),
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qp, rp);
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@ -2507,58 +2425,6 @@ scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp)
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*rp = scm_i_from_double (r);
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}
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/* Assumes that both x and y are bigints, though
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x might be able to fit into a fixnum. */
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static void
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scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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{
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SCM q, r, min_r;
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/* Note that x might be small enough to fit into a
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fixnum, so we must not let it escape into the wild */
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q = scm_i_mkbig ();
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r = scm_i_mkbig ();
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/* min_r will eventually become -abs(y/2) */
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min_r = scm_i_mkbig ();
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mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r),
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SCM_I_BIG_MPZ (y), 1);
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/* Arrange for rr to initially be non-positive,
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because that simplifies the test to see
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if it is within the needed bounds. */
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if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0)
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{
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mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r),
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SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
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mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r));
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if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0)
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{
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mpz_sub_ui (SCM_I_BIG_MPZ (q),
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SCM_I_BIG_MPZ (q), 1);
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mpz_add (SCM_I_BIG_MPZ (r),
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SCM_I_BIG_MPZ (r),
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SCM_I_BIG_MPZ (y));
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}
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}
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else
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{
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mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r),
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SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
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if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0)
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{
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mpz_add_ui (SCM_I_BIG_MPZ (q),
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SCM_I_BIG_MPZ (q), 1);
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mpz_sub (SCM_I_BIG_MPZ (r),
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SCM_I_BIG_MPZ (r),
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SCM_I_BIG_MPZ (y));
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}
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}
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scm_remember_upto_here_2 (x, y);
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*qp = scm_i_normbig (q);
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*rp = scm_i_normbig (r);
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}
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static void
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scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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{
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