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Optimize division operators handling of fractions
* libguile/numbers.c: (scm_euclidean_quotient, scm_euclidean_remainder, scm_euclidean_divide, scm_centered_quotient, scm_centered_remainder, scm_centered_divide): Optimize case where both arguments are exact and at least one is a fraction, by reducing to a subproblem involving only integers, and then adjusting the resulting remainder as needed.
This commit is contained in:
Mark H Weaver
Andy Wingo
parent
5fbf680be9
commit
03ddd15bae
1 changed files with 83 additions and 137 deletions
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@ -1093,7 +1093,7 @@ two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos,
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}
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static SCM scm_i_inexact_euclidean_quotient (double x, double y);
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static SCM scm_i_slow_exact_euclidean_quotient (SCM x, SCM y);
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static SCM scm_i_exact_rational_euclidean_quotient (SCM x, SCM y);
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SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0,
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(SCM x, SCM y),
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@ -1148,7 +1148,7 @@ SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0,
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else if (SCM_REALP (y))
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return scm_i_inexact_euclidean_quotient (xx, SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_euclidean_quotient (x, y);
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return scm_i_exact_rational_euclidean_quotient (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2,
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s_scm_euclidean_quotient);
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@ -1194,7 +1194,7 @@ SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0,
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return scm_i_inexact_euclidean_quotient
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(scm_i_big2dbl (x), SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_euclidean_quotient (x, y);
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return scm_i_exact_rational_euclidean_quotient (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2,
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s_scm_euclidean_quotient);
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@ -1214,8 +1214,11 @@ SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0,
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if (SCM_REALP (y))
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return scm_i_inexact_euclidean_quotient
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(scm_i_fraction2double (x), SCM_REAL_VALUE (y));
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else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))
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return scm_i_exact_rational_euclidean_quotient (x, y);
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else
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return scm_i_slow_exact_euclidean_quotient (x, y);
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2,
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s_scm_euclidean_quotient);
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}
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else
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1,
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@ -1236,28 +1239,16 @@ scm_i_inexact_euclidean_quotient (double x, double y)
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return scm_nan ();
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}
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/* Compute exact euclidean_quotient the slow way.
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We use this only if both arguments are exact,
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and at least one of them is a fraction */
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static SCM
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scm_i_slow_exact_euclidean_quotient (SCM x, SCM y)
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scm_i_exact_rational_euclidean_quotient (SCM x, SCM y)
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{
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if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)))
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1,
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s_scm_euclidean_quotient);
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else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)))
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2,
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s_scm_euclidean_quotient);
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else if (scm_is_true (scm_positive_p (y)))
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return scm_floor (scm_divide (x, y));
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else if (scm_is_true (scm_negative_p (y)))
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return scm_ceiling (scm_divide (x, y));
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else
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scm_num_overflow (s_scm_euclidean_quotient);
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return scm_euclidean_quotient
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(scm_product (scm_numerator (x), scm_denominator (y)),
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scm_product (scm_numerator (y), scm_denominator (x)));
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}
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static SCM scm_i_inexact_euclidean_remainder (double x, double y);
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static SCM scm_i_slow_exact_euclidean_remainder (SCM x, SCM y);
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static SCM scm_i_exact_rational_euclidean_remainder (SCM x, SCM y);
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SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0,
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(SCM x, SCM y),
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@ -1317,7 +1308,7 @@ SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0,
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else if (SCM_REALP (y))
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return scm_i_inexact_euclidean_remainder (xx, SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_euclidean_remainder (x, y);
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return scm_i_exact_rational_euclidean_remainder (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2,
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s_scm_euclidean_remainder);
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@ -1352,7 +1343,7 @@ SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0,
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return scm_i_inexact_euclidean_remainder
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(scm_i_big2dbl (x), SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_euclidean_remainder (x, y);
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return scm_i_exact_rational_euclidean_remainder (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2,
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s_scm_euclidean_remainder);
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@ -1372,8 +1363,11 @@ SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0,
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if (SCM_REALP (y))
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return scm_i_inexact_euclidean_remainder
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(scm_i_fraction2double (x), SCM_REAL_VALUE (y));
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else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))
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return scm_i_exact_rational_euclidean_remainder (x, y);
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else
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return scm_i_slow_exact_euclidean_remainder (x, y);
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2,
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s_scm_euclidean_remainder);
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}
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else
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1,
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@ -1406,33 +1400,21 @@ scm_i_inexact_euclidean_remainder (double x, double y)
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return scm_from_double (x - q * y);
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}
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/* Compute exact euclidean_remainder the slow way.
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We use this only if both arguments are exact,
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and at least one of them is a fraction */
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static SCM
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scm_i_slow_exact_euclidean_remainder (SCM x, SCM y)
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scm_i_exact_rational_euclidean_remainder (SCM x, SCM y)
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{
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SCM q;
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if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)))
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1,
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s_scm_euclidean_remainder);
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else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)))
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SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2,
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s_scm_euclidean_remainder);
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else if (scm_is_true (scm_positive_p (y)))
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q = scm_floor (scm_divide (x, y));
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else if (scm_is_true (scm_negative_p (y)))
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q = scm_ceiling (scm_divide (x, y));
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else
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scm_num_overflow (s_scm_euclidean_remainder);
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return scm_difference (x, scm_product (y, q));
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SCM xd = scm_denominator (x);
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SCM yd = scm_denominator (y);
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SCM r1 = scm_euclidean_remainder (scm_product (scm_numerator (x), yd),
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scm_product (scm_numerator (y), xd));
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return scm_divide (r1, scm_product (xd, yd));
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}
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static void scm_i_inexact_euclidean_divide (double x, double y,
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SCM *qp, SCM *rp);
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static void scm_i_slow_exact_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp);
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static void scm_i_exact_rational_euclidean_divide (SCM x, SCM y,
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SCM *qp, SCM *rp);
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SCM_PRIMITIVE_GENERIC (scm_i_euclidean_divide, "euclidean/", 2, 0, 0,
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(SCM x, SCM y),
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@ -1518,7 +1500,7 @@ scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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else if (SCM_REALP (y))
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return scm_i_inexact_euclidean_divide (xx, SCM_REAL_VALUE (y), qp, rp);
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_euclidean_divide (x, y, qp, rp);
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return scm_i_exact_rational_euclidean_divide (x, y, qp, rp);
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else
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return two_valued_wta_dispatch_2
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(g_scm_euclidean_divide, x, y, SCM_ARG2,
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@ -1569,7 +1551,7 @@ scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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return scm_i_inexact_euclidean_divide
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(scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp);
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_euclidean_divide (x, y, qp, rp);
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return scm_i_exact_rational_euclidean_divide (x, y, qp, rp);
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else
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return two_valued_wta_dispatch_2
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(g_scm_euclidean_divide, x, y, SCM_ARG2,
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@ -1591,8 +1573,12 @@ scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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if (SCM_REALP (y))
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return scm_i_inexact_euclidean_divide
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(scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp);
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else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))
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return scm_i_exact_rational_euclidean_divide (x, y, qp, rp);
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else
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return scm_i_slow_exact_euclidean_divide (x, y, qp, rp);
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return two_valued_wta_dispatch_2
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(g_scm_euclidean_divide, x, y, SCM_ARG2,
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s_scm_euclidean_divide, qp, rp);
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}
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else
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return two_valued_wta_dispatch_2 (g_scm_euclidean_divide, x, y, SCM_ARG1,
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@ -1617,33 +1603,22 @@ scm_i_inexact_euclidean_divide (double x, double y, SCM *qp, SCM *rp)
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*rp = scm_from_double (r);
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}
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/* Compute exact euclidean quotient and remainder the slow way.
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We use this only if both arguments are exact,
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and at least one of them is a fraction */
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static void
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scm_i_slow_exact_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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scm_i_exact_rational_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp)
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{
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SCM q;
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SCM r1;
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SCM xd = scm_denominator (x);
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SCM yd = scm_denominator (y);
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if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)))
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return two_valued_wta_dispatch_2 (g_scm_euclidean_divide, x, y, SCM_ARG1,
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s_scm_euclidean_divide, qp, rp);
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else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)))
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return two_valued_wta_dispatch_2 (g_scm_euclidean_divide, x, y, SCM_ARG2,
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s_scm_euclidean_divide, qp, rp);
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else if (scm_is_true (scm_positive_p (y)))
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q = scm_floor (scm_divide (x, y));
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else if (scm_is_true (scm_negative_p (y)))
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q = scm_ceiling (scm_divide (x, y));
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else
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scm_num_overflow (s_scm_euclidean_divide);
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*qp = q;
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*rp = scm_difference (x, scm_product (q, y));
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scm_euclidean_divide (scm_product (scm_numerator (x), yd),
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scm_product (scm_numerator (y), xd),
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qp, &r1);
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*rp = scm_divide (r1, scm_product (xd, yd));
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}
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static SCM scm_i_inexact_centered_quotient (double x, double y);
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static SCM scm_i_bigint_centered_quotient (SCM x, SCM y);
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static SCM scm_i_slow_exact_centered_quotient (SCM x, SCM y);
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static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y);
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SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0,
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(SCM x, SCM y),
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@ -1713,7 +1688,7 @@ SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0,
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else if (SCM_REALP (y))
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return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_centered_quotient (x, y);
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return scm_i_exact_rational_centered_quotient (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2,
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s_scm_centered_quotient);
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@ -1762,7 +1737,7 @@ SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0,
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return scm_i_inexact_centered_quotient
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(scm_i_big2dbl (x), SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_centered_quotient (x, y);
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return scm_i_exact_rational_centered_quotient (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2,
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s_scm_centered_quotient);
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@ -1782,8 +1757,11 @@ SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0,
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if (SCM_REALP (y))
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return scm_i_inexact_centered_quotient
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(scm_i_fraction2double (x), SCM_REAL_VALUE (y));
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else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))
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return scm_i_exact_rational_centered_quotient (x, y);
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else
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return scm_i_slow_exact_centered_quotient (x, y);
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SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2,
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s_scm_centered_quotient);
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}
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else
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SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1,
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@ -1847,31 +1825,17 @@ scm_i_bigint_centered_quotient (SCM x, SCM y)
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return scm_i_normbig (q);
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}
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/* Compute exact centered quotient the slow way.
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We use this only if both arguments are exact,
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and at least one of them is a fraction */
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static SCM
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scm_i_slow_exact_centered_quotient (SCM x, SCM y)
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scm_i_exact_rational_centered_quotient (SCM x, SCM y)
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{
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if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)))
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SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1,
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s_scm_centered_quotient);
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else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)))
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SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2,
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s_scm_centered_quotient);
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else if (scm_is_true (scm_positive_p (y)))
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return scm_floor (scm_sum (scm_divide (x, y),
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exactly_one_half));
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else if (scm_is_true (scm_negative_p (y)))
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return scm_ceiling (scm_difference (scm_divide (x, y),
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exactly_one_half));
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else
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scm_num_overflow (s_scm_centered_quotient);
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return scm_centered_quotient
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(scm_product (scm_numerator (x), scm_denominator (y)),
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scm_product (scm_numerator (y), scm_denominator (x)));
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}
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static SCM scm_i_inexact_centered_remainder (double x, double y);
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static SCM scm_i_bigint_centered_remainder (SCM x, SCM y);
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static SCM scm_i_slow_exact_centered_remainder (SCM x, SCM y);
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static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y);
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SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0,
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(SCM x, SCM y),
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@ -1938,7 +1902,7 @@ SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0,
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else if (SCM_REALP (y))
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return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y));
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else if (SCM_FRACTIONP (y))
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return scm_i_slow_exact_centered_remainder (x, y);
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return scm_i_exact_rational_centered_remainder (x, y);
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else
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SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2,
|
||||
s_scm_centered_remainder);
|
||||
|
|
@ -1979,7 +1943,7 @@ SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0,
|
|||
return scm_i_inexact_centered_remainder
|
||||
(scm_i_big2dbl (x), SCM_REAL_VALUE (y));
|
||||
else if (SCM_FRACTIONP (y))
|
||||
return scm_i_slow_exact_centered_remainder (x, y);
|
||||
return scm_i_exact_rational_centered_remainder (x, y);
|
||||
else
|
||||
SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2,
|
||||
s_scm_centered_remainder);
|
||||
|
|
@ -1999,8 +1963,11 @@ SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0,
|
|||
if (SCM_REALP (y))
|
||||
return scm_i_inexact_centered_remainder
|
||||
(scm_i_fraction2double (x), SCM_REAL_VALUE (y));
|
||||
else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))
|
||||
return scm_i_exact_rational_centered_remainder (x, y);
|
||||
else
|
||||
return scm_i_slow_exact_centered_remainder (x, y);
|
||||
SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2,
|
||||
s_scm_centered_remainder);
|
||||
}
|
||||
else
|
||||
SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1,
|
||||
|
|
@ -2073,34 +2040,22 @@ scm_i_bigint_centered_remainder (SCM x, SCM y)
|
|||
return scm_i_normbig (r);
|
||||
}
|
||||
|
||||
/* Compute exact centered_remainder the slow way.
|
||||
We use this only if both arguments are exact,
|
||||
and at least one of them is a fraction */
|
||||
static SCM
|
||||
scm_i_slow_exact_centered_remainder (SCM x, SCM y)
|
||||
scm_i_exact_rational_centered_remainder (SCM x, SCM y)
|
||||
{
|
||||
SCM q;
|
||||
|
||||
if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)))
|
||||
SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1,
|
||||
s_scm_centered_remainder);
|
||||
else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)))
|
||||
SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2,
|
||||
s_scm_centered_remainder);
|
||||
else if (scm_is_true (scm_positive_p (y)))
|
||||
q = scm_floor (scm_sum (scm_divide (x, y), exactly_one_half));
|
||||
else if (scm_is_true (scm_negative_p (y)))
|
||||
q = scm_ceiling (scm_difference (scm_divide (x, y), exactly_one_half));
|
||||
else
|
||||
scm_num_overflow (s_scm_centered_remainder);
|
||||
return scm_difference (x, scm_product (y, q));
|
||||
SCM xd = scm_denominator (x);
|
||||
SCM yd = scm_denominator (y);
|
||||
SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd),
|
||||
scm_product (scm_numerator (y), xd));
|
||||
return scm_divide (r1, scm_product (xd, yd));
|
||||
}
|
||||
|
||||
|
||||
static void scm_i_inexact_centered_divide (double x, double y,
|
||||
SCM *qp, SCM *rp);
|
||||
static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp);
|
||||
static void scm_i_slow_exact_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp);
|
||||
static void scm_i_exact_rational_centered_divide (SCM x, SCM y,
|
||||
SCM *qp, SCM *rp);
|
||||
|
||||
SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0,
|
||||
(SCM x, SCM y),
|
||||
|
|
@ -2185,7 +2140,7 @@ scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
|||
else if (SCM_REALP (y))
|
||||
return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp);
|
||||
else if (SCM_FRACTIONP (y))
|
||||
return scm_i_slow_exact_centered_divide (x, y, qp, rp);
|
||||
return scm_i_exact_rational_centered_divide (x, y, qp, rp);
|
||||
else
|
||||
return two_valued_wta_dispatch_2
|
||||
(g_scm_centered_divide, x, y, SCM_ARG2,
|
||||
|
|
@ -2241,7 +2196,7 @@ scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
|||
return scm_i_inexact_centered_divide
|
||||
(scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp);
|
||||
else if (SCM_FRACTIONP (y))
|
||||
return scm_i_slow_exact_centered_divide (x, y, qp, rp);
|
||||
return scm_i_exact_rational_centered_divide (x, y, qp, rp);
|
||||
else
|
||||
return two_valued_wta_dispatch_2
|
||||
(g_scm_centered_divide, x, y, SCM_ARG2,
|
||||
|
|
@ -2253,7 +2208,7 @@ scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
|||
SCM_BIGP (y) || SCM_FRACTIONP (y))
|
||||
return scm_i_inexact_centered_divide
|
||||
(SCM_REAL_VALUE (x), scm_to_double (y), qp, rp);
|
||||
else
|
||||
else
|
||||
return two_valued_wta_dispatch_2
|
||||
(g_scm_centered_divide, x, y, SCM_ARG2,
|
||||
s_scm_centered_divide, qp, rp);
|
||||
|
|
@ -2263,8 +2218,12 @@ scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
|||
if (SCM_REALP (y))
|
||||
return scm_i_inexact_centered_divide
|
||||
(scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp);
|
||||
else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))
|
||||
return scm_i_exact_rational_centered_divide (x, y, qp, rp);
|
||||
else
|
||||
return scm_i_slow_exact_centered_divide (x, y, qp, rp);
|
||||
return two_valued_wta_dispatch_2
|
||||
(g_scm_centered_divide, x, y, SCM_ARG2,
|
||||
s_scm_centered_divide, qp, rp);
|
||||
}
|
||||
else
|
||||
return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1,
|
||||
|
|
@ -2341,30 +2300,17 @@ scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
|||
*rp = scm_i_normbig (r);
|
||||
}
|
||||
|
||||
/* Compute exact centered quotient and remainder the slow way.
|
||||
We use this only if both arguments are exact,
|
||||
and at least one of them is a fraction */
|
||||
static void
|
||||
scm_i_slow_exact_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
||||
scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp)
|
||||
{
|
||||
SCM q;
|
||||
SCM r1;
|
||||
SCM xd = scm_denominator (x);
|
||||
SCM yd = scm_denominator (y);
|
||||
|
||||
if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)))
|
||||
return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1,
|
||||
s_scm_centered_divide, qp, rp);
|
||||
else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)))
|
||||
return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG2,
|
||||
s_scm_centered_divide, qp, rp);
|
||||
else if (scm_is_true (scm_positive_p (y)))
|
||||
q = scm_floor (scm_sum (scm_divide (x, y),
|
||||
exactly_one_half));
|
||||
else if (scm_is_true (scm_negative_p (y)))
|
||||
q = scm_ceiling (scm_difference (scm_divide (x, y),
|
||||
exactly_one_half));
|
||||
else
|
||||
scm_num_overflow (s_scm_centered_divide);
|
||||
*qp = q;
|
||||
*rp = scm_difference (x, scm_product (q, y));
|
||||
scm_centered_divide (scm_product (scm_numerator (x), yd),
|
||||
scm_product (scm_numerator (y), xd),
|
||||
qp, &r1);
|
||||
*rp = scm_divide (r1, scm_product (xd, yd));
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue