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Optimize truncate, round, floor, and ceiling
* libguile/numbers.c (scm_c_truncate): Use ceil (x) instead of -floor (-x). (scm_truncate_number): Implement directly instead of by checking the sign and using scm_floor or scm_ceiling. Use scm_truncate_quotient for fractions. Make extensible, so that new number types implemented in GOOPS will be able to do the job more efficiently, since it is often easier to implement truncate than floor or ceiling. (scm_round_number): Optimize fractions case by using scm_round_quotient. Make extensible, so that new number types implemented in GOOPS will be able to do the job efficiently. (scm_floor, scm_ceiling): Optimize fractions case by using scm_floor_quotient and scm_ceiling_quotient, respectively. * test-suite/tests/numbers.test: Add test cases.
This commit is contained in:
Mark H Weaver
Andy Wingo
parent
8f9da3406b
commit
8b56bcec44
2 changed files with 432 additions and 67 deletions
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@ -8851,7 +8851,8 @@ scm_c_truncate (double x)
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return trunc (x);
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#else
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if (x < 0.0)
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return -floor (-x);
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return ceil (x);
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else
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return floor (x);
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#endif
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}
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@ -8898,19 +8899,25 @@ scm_c_round (double x)
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: result);
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}
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SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0,
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SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0,
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(SCM x),
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"Round the number @var{x} towards zero.")
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#define FUNC_NAME s_scm_truncate_number
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{
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if (scm_is_false (scm_negative_p (x)))
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return scm_floor (x);
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if (SCM_I_INUMP (x) || SCM_BIGP (x))
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return x;
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else if (SCM_REALP (x))
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return scm_from_double (scm_c_truncate (SCM_REAL_VALUE (x)));
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else if (SCM_FRACTIONP (x))
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return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x),
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SCM_FRACTION_DENOMINATOR (x));
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else
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return scm_ceiling (x);
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SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1,
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s_scm_truncate_number);
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}
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#undef FUNC_NAME
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SCM_DEFINE (scm_round_number, "round", 1, 0, 0,
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SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0,
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(SCM x),
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"Round the number @var{x} towards the nearest integer. "
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"When it is exactly halfway between two integers, "
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@ -8921,20 +8928,12 @@ SCM_DEFINE (scm_round_number, "round", 1, 0, 0,
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return x;
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else if (SCM_REALP (x))
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return scm_from_double (scm_c_round (SCM_REAL_VALUE (x)));
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else if (SCM_FRACTIONP (x))
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return scm_round_quotient (SCM_FRACTION_NUMERATOR (x),
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SCM_FRACTION_DENOMINATOR (x));
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else
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{
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/* OPTIMIZE-ME: Fraction case could be done more efficiently by a
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single quotient+remainder division then examining to see which way
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the rounding should go. */
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SCM plus_half = scm_sum (x, exactly_one_half);
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SCM result = scm_floor (plus_half);
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/* Adjust so that the rounding is towards even. */
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if (scm_is_true (scm_num_eq_p (plus_half, result))
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&& scm_is_true (scm_odd_p (result)))
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return scm_difference (result, SCM_INUM1);
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else
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return result;
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}
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SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1,
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s_scm_round_number);
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}
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#undef FUNC_NAME
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@ -8948,22 +8947,8 @@ SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0,
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else if (SCM_REALP (x))
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return scm_from_double (floor (SCM_REAL_VALUE (x)));
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else if (SCM_FRACTIONP (x))
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{
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SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
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return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x),
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SCM_FRACTION_DENOMINATOR (x));
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if (scm_is_false (scm_negative_p (x)))
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{
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/* For positive x, rounding towards zero is correct. */
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return q;
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}
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else
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{
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/* For negative x, we need to return q-1 unless x is an
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integer. But fractions are never integer, per our
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assumptions. */
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return scm_difference (q, SCM_INUM1);
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}
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}
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else
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SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor);
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}
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@ -8979,22 +8964,8 @@ SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0,
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else if (SCM_REALP (x))
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return scm_from_double (ceil (SCM_REAL_VALUE (x)));
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else if (SCM_FRACTIONP (x))
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{
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SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
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return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x),
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SCM_FRACTION_DENOMINATOR (x));
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if (scm_is_false (scm_positive_p (x)))
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{
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/* For negative x, rounding towards zero is correct. */
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return q;
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}
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else
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{
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/* For positive x, we need to return q+1 unless x is an
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integer. But fractions are never integer, per our
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assumptions. */
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return scm_sum (q, SCM_INUM1);
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}
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}
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else
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SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling);
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}
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@ -3306,6 +3306,284 @@
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(pass-if "(/ 25+125i 4+3i)"
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(= (/ 25+125i 4+3i) 19.0+17.0i))))
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;;;
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;;; floor
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;;;
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(with-test-prefix "floor"
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(pass-if (= 1 (floor 1.75)))
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(pass-if (= 1 (floor 1.5)))
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(pass-if (= 1 (floor 1.25)))
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(pass-if (= 0 (floor 0.75)))
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(pass-if (= 0 (floor 0.5)))
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(pass-if (= 0 (floor 0.0)))
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(pass-if (= -1 (floor -0.5)))
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(pass-if (= -2 (floor -1.25)))
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(pass-if (= -2 (floor -1.5)))
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(with-test-prefix "inum"
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(pass-if "0"
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(and (= 0 (floor 0))
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(exact? (floor 0))))
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(pass-if "1"
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(and (= 1 (floor 1))
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(exact? (floor 1))))
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(pass-if "-1"
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(and (= -1 (floor -1))
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(exact? (floor -1)))))
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(with-test-prefix "bignum"
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(let ((x (1+ most-positive-fixnum)))
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(pass-if "(1+ most-positive-fixnum)"
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(and (= x (floor x))
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(exact? (floor x)))))
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(let ((x (1- most-negative-fixnum)))
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(pass-if "(1- most-negative-fixnum)"
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(and (= x (floor x))
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(exact? (floor x))))))
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(with-test-prefix "frac"
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(define (=exact x y)
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(and (= x y)
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(exact? y)))
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(pass-if (=exact -3 (floor -7/3)))
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(pass-if (=exact -2 (floor -5/3)))
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(pass-if (=exact -2 (floor -4/3)))
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(pass-if (=exact -1 (floor -2/3)))
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(pass-if (=exact -1 (floor -1/3)))
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(pass-if (=exact 0 (floor 1/3)))
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(pass-if (=exact 0 (floor 2/3)))
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(pass-if (=exact 1 (floor 4/3)))
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(pass-if (=exact 1 (floor 5/3)))
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(pass-if (=exact 2 (floor 7/3)))
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(pass-if (=exact -3 (floor -17/6)))
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(pass-if (=exact -3 (floor -16/6)))
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(pass-if (=exact -3 (floor -15/6)))
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(pass-if (=exact -3 (floor -14/6)))
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(pass-if (=exact -3 (floor -13/6)))
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(pass-if (=exact -2 (floor -11/6)))
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(pass-if (=exact -2 (floor -10/6)))
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(pass-if (=exact -2 (floor -9/6)))
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(pass-if (=exact -2 (floor -8/6)))
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(pass-if (=exact -2 (floor -7/6)))
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(pass-if (=exact -1 (floor -5/6)))
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(pass-if (=exact -1 (floor -4/6)))
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(pass-if (=exact -1 (floor -3/6)))
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(pass-if (=exact -1 (floor -2/6)))
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(pass-if (=exact -1 (floor -1/6)))
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(pass-if (=exact 0 (floor 1/6)))
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(pass-if (=exact 0 (floor 2/6)))
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(pass-if (=exact 0 (floor 3/6)))
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(pass-if (=exact 0 (floor 4/6)))
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(pass-if (=exact 0 (floor 5/6)))
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(pass-if (=exact 1 (floor 7/6)))
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(pass-if (=exact 1 (floor 8/6)))
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(pass-if (=exact 1 (floor 9/6)))
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(pass-if (=exact 1 (floor 10/6)))
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(pass-if (=exact 1 (floor 11/6)))
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(pass-if (=exact 2 (floor 13/6)))
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(pass-if (=exact 2 (floor 14/6)))
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(pass-if (=exact 2 (floor 15/6)))
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(pass-if (=exact 2 (floor 16/6)))
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(pass-if (=exact 2 (floor 17/6))))
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(with-test-prefix "real"
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(pass-if "0.0"
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(and (= 0.0 (floor 0.0))
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(inexact? (floor 0.0))))
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(pass-if "1.0"
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(and (= 1.0 (floor 1.0))
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(inexact? (floor 1.0))))
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(pass-if "-1.0"
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(and (= -1.0 (floor -1.0))
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(inexact? (floor -1.0))))
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(pass-if "-3.1"
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(and (= -4.0 (floor -3.1))
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(inexact? (floor -3.1))))
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(pass-if "3.1"
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(and (= 3.0 (floor 3.1))
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(inexact? (floor 3.1))))
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(pass-if "3.9"
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(and (= 3.0 (floor 3.9))
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(inexact? (floor 3.9))))
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(pass-if "-3.9"
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(and (= -4.0 (floor -3.9))
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(inexact? (floor -3.9))))
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(pass-if "1.5"
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(and (= 1.0 (floor 1.5))
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(inexact? (floor 1.5))))
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(pass-if "2.5"
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(and (= 2.0 (floor 2.5))
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(inexact? (floor 2.5))))
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(pass-if "3.5"
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(and (= 3.0 (floor 3.5))
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(inexact? (floor 3.5))))
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(pass-if "-1.5"
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(and (= -2.0 (floor -1.5))
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(inexact? (floor -1.5))))
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(pass-if "-2.5"
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(and (= -3.0 (floor -2.5))
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(inexact? (floor -2.5))))
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(pass-if "-3.5"
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(and (= -4.0 (floor -3.5))
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(inexact? (floor -3.5))))))
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;;;
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;;; ceiling
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;;;
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(with-test-prefix "ceiling"
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(pass-if (= 2 (ceiling 1.75)))
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(pass-if (= 2 (ceiling 1.5)))
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(pass-if (= 2 (ceiling 1.25)))
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(pass-if (= 1 (ceiling 0.75)))
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(pass-if (= 1 (ceiling 0.5)))
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(pass-if (= 0 (ceiling 0.0)))
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(pass-if (= 0 (ceiling -0.5)))
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(pass-if (= -1 (ceiling -1.25)))
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(pass-if (= -1 (ceiling -1.5)))
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(with-test-prefix "inum"
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(pass-if "0"
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(and (= 0 (ceiling 0))
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(exact? (ceiling 0))))
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(pass-if "1"
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(and (= 1 (ceiling 1))
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(exact? (ceiling 1))))
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(pass-if "-1"
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(and (= -1 (ceiling -1))
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(exact? (ceiling -1)))))
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(with-test-prefix "bignum"
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(let ((x (1+ most-positive-fixnum)))
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(pass-if "(1+ most-positive-fixnum)"
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(and (= x (ceiling x))
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(exact? (ceiling x)))))
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(let ((x (1- most-negative-fixnum)))
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(pass-if "(1- most-negative-fixnum)"
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(and (= x (ceiling x))
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(exact? (ceiling x))))))
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(with-test-prefix "frac"
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(define (=exact x y)
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(and (= x y)
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(exact? y)))
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(pass-if (=exact -2 (ceiling -7/3)))
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(pass-if (=exact -1 (ceiling -5/3)))
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(pass-if (=exact -1 (ceiling -4/3)))
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(pass-if (=exact 0 (ceiling -2/3)))
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(pass-if (=exact 0 (ceiling -1/3)))
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(pass-if (=exact 1 (ceiling 1/3)))
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(pass-if (=exact 1 (ceiling 2/3)))
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(pass-if (=exact 2 (ceiling 4/3)))
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(pass-if (=exact 2 (ceiling 5/3)))
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(pass-if (=exact 3 (ceiling 7/3)))
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(pass-if (=exact -2 (ceiling -17/6)))
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(pass-if (=exact -2 (ceiling -16/6)))
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(pass-if (=exact -2 (ceiling -15/6)))
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(pass-if (=exact -2 (ceiling -14/6)))
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(pass-if (=exact -2 (ceiling -13/6)))
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(pass-if (=exact -1 (ceiling -11/6)))
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(pass-if (=exact -1 (ceiling -10/6)))
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(pass-if (=exact -1 (ceiling -9/6)))
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(pass-if (=exact -1 (ceiling -8/6)))
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(pass-if (=exact -1 (ceiling -7/6)))
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(pass-if (=exact 0 (ceiling -5/6)))
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(pass-if (=exact 0 (ceiling -4/6)))
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(pass-if (=exact 0 (ceiling -3/6)))
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(pass-if (=exact 0 (ceiling -2/6)))
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(pass-if (=exact 0 (ceiling -1/6)))
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(pass-if (=exact 1 (ceiling 1/6)))
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(pass-if (=exact 1 (ceiling 2/6)))
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(pass-if (=exact 1 (ceiling 3/6)))
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(pass-if (=exact 1 (ceiling 4/6)))
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(pass-if (=exact 1 (ceiling 5/6)))
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(pass-if (=exact 2 (ceiling 7/6)))
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(pass-if (=exact 2 (ceiling 8/6)))
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(pass-if (=exact 2 (ceiling 9/6)))
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(pass-if (=exact 2 (ceiling 10/6)))
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(pass-if (=exact 2 (ceiling 11/6)))
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(pass-if (=exact 3 (ceiling 13/6)))
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(pass-if (=exact 3 (ceiling 14/6)))
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(pass-if (=exact 3 (ceiling 15/6)))
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(pass-if (=exact 3 (ceiling 16/6)))
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(pass-if (=exact 3 (ceiling 17/6))))
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(with-test-prefix "real"
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(pass-if "0.0"
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(and (= 0.0 (ceiling 0.0))
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(inexact? (ceiling 0.0))))
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(pass-if "1.0"
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(and (= 1.0 (ceiling 1.0))
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(inexact? (ceiling 1.0))))
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(pass-if "-1.0"
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(and (= -1.0 (ceiling -1.0))
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(inexact? (ceiling -1.0))))
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(pass-if "-3.1"
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(and (= -3.0 (ceiling -3.1))
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(inexact? (ceiling -3.1))))
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(pass-if "3.1"
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(and (= 4.0 (ceiling 3.1))
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(inexact? (ceiling 3.1))))
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(pass-if "3.9"
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(and (= 4.0 (ceiling 3.9))
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(inexact? (ceiling 3.9))))
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(pass-if "-3.9"
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(and (= -3.0 (ceiling -3.9))
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(inexact? (ceiling -3.9))))
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(pass-if "1.5"
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(and (= 2.0 (ceiling 1.5))
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(inexact? (ceiling 1.5))))
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(pass-if "2.5"
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(and (= 3.0 (ceiling 2.5))
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(inexact? (ceiling 2.5))))
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(pass-if "3.5"
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(and (= 4.0 (ceiling 3.5))
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(inexact? (ceiling 3.5))))
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(pass-if "-1.5"
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(and (= -1.0 (ceiling -1.5))
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(inexact? (ceiling -1.5))))
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(pass-if "-2.5"
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(and (= -2.0 (ceiling -2.5))
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(inexact? (ceiling -2.5))))
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(pass-if "-3.5"
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(and (= -3.0 (ceiling -3.5))
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(inexact? (ceiling -3.5))))))
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;;;
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;;; truncate
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;;;
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@ -3319,7 +3597,131 @@
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(pass-if (= 0 (truncate 0.0)))
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(pass-if (= 0 (truncate -0.5)))
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(pass-if (= -1 (truncate -1.25)))
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(pass-if (= -1 (truncate -1.5))))
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(pass-if (= -1 (truncate -1.5)))
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(with-test-prefix "inum"
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(pass-if "0"
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(and (= 0 (truncate 0))
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(exact? (truncate 0))))
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|
||||
(pass-if "1"
|
||||
(and (= 1 (truncate 1))
|
||||
(exact? (truncate 1))))
|
||||
|
||||
(pass-if "-1"
|
||||
(and (= -1 (truncate -1))
|
||||
(exact? (truncate -1)))))
|
||||
|
||||
(with-test-prefix "bignum"
|
||||
(let ((x (1+ most-positive-fixnum)))
|
||||
(pass-if "(1+ most-positive-fixnum)"
|
||||
(and (= x (truncate x))
|
||||
(exact? (truncate x)))))
|
||||
|
||||
(let ((x (1- most-negative-fixnum)))
|
||||
(pass-if "(1- most-negative-fixnum)"
|
||||
(and (= x (truncate x))
|
||||
(exact? (truncate x))))))
|
||||
|
||||
(with-test-prefix "frac"
|
||||
(define (=exact x y)
|
||||
(and (= x y)
|
||||
(exact? y)))
|
||||
|
||||
(pass-if (=exact -2 (truncate -7/3)))
|
||||
(pass-if (=exact -1 (truncate -5/3)))
|
||||
(pass-if (=exact -1 (truncate -4/3)))
|
||||
(pass-if (=exact 0 (truncate -2/3)))
|
||||
(pass-if (=exact 0 (truncate -1/3)))
|
||||
(pass-if (=exact 0 (truncate 1/3)))
|
||||
(pass-if (=exact 0 (truncate 2/3)))
|
||||
(pass-if (=exact 1 (truncate 4/3)))
|
||||
(pass-if (=exact 1 (truncate 5/3)))
|
||||
(pass-if (=exact 2 (truncate 7/3)))
|
||||
|
||||
(pass-if (=exact -2 (truncate -17/6)))
|
||||
(pass-if (=exact -2 (truncate -16/6)))
|
||||
(pass-if (=exact -2 (truncate -15/6)))
|
||||
(pass-if (=exact -2 (truncate -14/6)))
|
||||
(pass-if (=exact -2 (truncate -13/6)))
|
||||
(pass-if (=exact -1 (truncate -11/6)))
|
||||
(pass-if (=exact -1 (truncate -10/6)))
|
||||
(pass-if (=exact -1 (truncate -9/6)))
|
||||
(pass-if (=exact -1 (truncate -8/6)))
|
||||
(pass-if (=exact -1 (truncate -7/6)))
|
||||
(pass-if (=exact 0 (truncate -5/6)))
|
||||
(pass-if (=exact 0 (truncate -4/6)))
|
||||
(pass-if (=exact 0 (truncate -3/6)))
|
||||
(pass-if (=exact 0 (truncate -2/6)))
|
||||
(pass-if (=exact 0 (truncate -1/6)))
|
||||
(pass-if (=exact 0 (truncate 1/6)))
|
||||
(pass-if (=exact 0 (truncate 2/6)))
|
||||
(pass-if (=exact 0 (truncate 3/6)))
|
||||
(pass-if (=exact 0 (truncate 4/6)))
|
||||
(pass-if (=exact 0 (truncate 5/6)))
|
||||
(pass-if (=exact 1 (truncate 7/6)))
|
||||
(pass-if (=exact 1 (truncate 8/6)))
|
||||
(pass-if (=exact 1 (truncate 9/6)))
|
||||
(pass-if (=exact 1 (truncate 10/6)))
|
||||
(pass-if (=exact 1 (truncate 11/6)))
|
||||
(pass-if (=exact 2 (truncate 13/6)))
|
||||
(pass-if (=exact 2 (truncate 14/6)))
|
||||
(pass-if (=exact 2 (truncate 15/6)))
|
||||
(pass-if (=exact 2 (truncate 16/6)))
|
||||
(pass-if (=exact 2 (truncate 17/6))))
|
||||
|
||||
(with-test-prefix "real"
|
||||
(pass-if "0.0"
|
||||
(and (= 0.0 (truncate 0.0))
|
||||
(inexact? (truncate 0.0))))
|
||||
|
||||
(pass-if "1.0"
|
||||
(and (= 1.0 (truncate 1.0))
|
||||
(inexact? (truncate 1.0))))
|
||||
|
||||
(pass-if "-1.0"
|
||||
(and (= -1.0 (truncate -1.0))
|
||||
(inexact? (truncate -1.0))))
|
||||
|
||||
(pass-if "-3.1"
|
||||
(and (= -3.0 (truncate -3.1))
|
||||
(inexact? (truncate -3.1))))
|
||||
|
||||
(pass-if "3.1"
|
||||
(and (= 3.0 (truncate 3.1))
|
||||
(inexact? (truncate 3.1))))
|
||||
|
||||
(pass-if "3.9"
|
||||
(and (= 3.0 (truncate 3.9))
|
||||
(inexact? (truncate 3.9))))
|
||||
|
||||
(pass-if "-3.9"
|
||||
(and (= -3.0 (truncate -3.9))
|
||||
(inexact? (truncate -3.9))))
|
||||
|
||||
(pass-if "1.5"
|
||||
(and (= 1.0 (truncate 1.5))
|
||||
(inexact? (truncate 1.5))))
|
||||
|
||||
(pass-if "2.5"
|
||||
(and (= 2.0 (truncate 2.5))
|
||||
(inexact? (truncate 2.5))))
|
||||
|
||||
(pass-if "3.5"
|
||||
(and (= 3.0 (truncate 3.5))
|
||||
(inexact? (truncate 3.5))))
|
||||
|
||||
(pass-if "-1.5"
|
||||
(and (= -1.0 (truncate -1.5))
|
||||
(inexact? (truncate -1.5))))
|
||||
|
||||
(pass-if "-2.5"
|
||||
(and (= -2.0 (truncate -2.5))
|
||||
(inexact? (truncate -2.5))))
|
||||
|
||||
(pass-if "-3.5"
|
||||
(and (= -3.0 (truncate -3.5))
|
||||
(inexact? (truncate -3.5))))))
|
||||
|
||||
;;;
|
||||
;;; round
|
||||
|
|
@ -3567,14 +3969,6 @@
|
|||
(let ((big (ash 1 4096)))
|
||||
(= 1.0 (exact->inexact (/ (1+ big) big))))))
|
||||
|
||||
;;;
|
||||
;;; floor
|
||||
;;;
|
||||
|
||||
;;;
|
||||
;;; ceiling
|
||||
;;;
|
||||
|
||||
;;;
|
||||
;;; expt
|
||||
;;;
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue