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Add 'round-ash', a rounding arithmetic shift operator
* libguile/numbers.c (left_shift_exact_integer, floor_right_shift_exact_integer, round_right_shift_exact_integer): New static functions. (scm_round_ash): New procedure. (scm_ash): Reimplement in terms of 'left_shift_exact_integer' and 'floor_right_shift_exact_integer'. * libguile/numbers.h: Add prototype for scm_round_ash. Rename the second argument of 'scm_ash' from 'cnt' to 'count'. * test-suite/tests/numbers.test (round-ash, ash): Add new unified testing framework for 'ash' and 'round-ash'. Previously, the tests for 'ash' were not very comprehensive; for example, they did not include a single test where the number to be shifted was a bignum. * doc/ref/api-data.texi (Bitwise Operations): Add documentation for 'round-ash'. Improve documentation for `ash'.
This commit is contained in:
Mark H Weaver
parent
a285b18ca8
commit
e08a12b535
4 changed files with 234 additions and 153 deletions
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@ -1686,19 +1686,15 @@ starts from 0 for the least significant bit.
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@end lisp
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@end lisp
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@end deffn
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@end deffn
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@deffn {Scheme Procedure} ash n cnt
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@deffn {Scheme Procedure} ash n count
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@deffnx {C Function} scm_ash (n, cnt)
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@deffnx {C Function} scm_ash (n, count)
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Return @var{n} shifted left by @var{cnt} bits, or shifted right if
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Return @math{floor(@var{n} * 2^@var{count})}.
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@var{cnt} is negative. This is an ``arithmetic'' shift.
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@var{n} and @var{count} must be exact integers.
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This is effectively a multiplication by @m{2^{cnt}, 2^@var{cnt}}, and
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With @var{n} viewed as an infinite-precision twos-complement
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when @var{cnt} is negative it's a division, rounded towards negative
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integer, @code{ash} means a left shift introducing zero bits
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infinity. (Note that this is not the same rounding as @code{quotient}
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when @var{count} is positive, or a right shift dropping bits
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does.)
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when @var{count} is negative. This is an ``arithmetic'' shift.
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With @var{n} viewed as an infinite precision twos complement,
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@code{ash} means a left shift introducing zero bits, or a right shift
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dropping bits.
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@lisp
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@lisp
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(number->string (ash #b1 3) 2) @result{} "1000"
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(number->string (ash #b1 3) 2) @result{} "1000"
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@ -1709,6 +1705,28 @@ dropping bits.
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@end lisp
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@end lisp
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@end deffn
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@end deffn
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@deffn {Scheme Procedure} round-ash n count
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@deffnx {C Function} scm_round_ash (n, count)
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Return @math{round(@var{n} * 2^@var{count})}.
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@var{n} and @var{count} must be exact integers.
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With @var{n} viewed as an infinite-precision twos-complement
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integer, @code{round-ash} means a left shift introducing zero
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bits when @var{count} is positive, or a right shift rounding
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to the nearest integer (with ties going to the nearest even
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integer) when @var{count} is negative. This is a rounded
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``arithmetic'' shift.
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@lisp
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(number->string (round-ash #b1 3) 2) @result{} \"1000\"
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(number->string (round-ash #b1010 -1) 2) @result{} \"101\"
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(number->string (round-ash #b1010 -2) 2) @result{} \"10\"
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(number->string (round-ash #b1011 -2) 2) @result{} \"11\"
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(number->string (round-ash #b1101 -2) 2) @result{} \"11\"
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(number->string (round-ash #b1110 -2) 2) @result{} \"100\"
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@end lisp
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@end deffn
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@deffn {Scheme Procedure} logcount n
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@deffn {Scheme Procedure} logcount n
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@deffnx {C Function} scm_logcount (n)
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@deffnx {C Function} scm_logcount (n)
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Return the number of bits in integer @var{n}. If @var{n} is
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Return the number of bits in integer @var{n}. If @var{n} is
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@ -4791,19 +4791,119 @@ SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0,
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}
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}
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#undef FUNC_NAME
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#undef FUNC_NAME
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/* Efficiently compute (N * 2^COUNT),
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where N is an exact integer, and COUNT > 0. */
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static SCM
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left_shift_exact_integer (SCM n, long count)
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{
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if (SCM_I_INUMP (n))
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{
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scm_t_inum nn = SCM_I_INUM (n);
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/* Left shift of count >= SCM_I_FIXNUM_BIT-1 will always
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overflow a non-zero fixnum. For smaller shifts we check the
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bits going into positions above SCM_I_FIXNUM_BIT-1. If they're
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all 0s for nn>=0, or all 1s for nn<0 then there's no overflow.
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Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". */
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if (nn == 0)
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return n;
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else if (count < SCM_I_FIXNUM_BIT-1 &&
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((scm_t_bits) (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - count)) + 1)
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<= 1))
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return SCM_I_MAKINUM (nn << count);
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else
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{
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SCM result = scm_i_inum2big (nn);
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mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result),
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count);
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return result;
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}
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}
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else if (SCM_BIGP (n))
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{
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SCM result = scm_i_mkbig ();
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mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), count);
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scm_remember_upto_here_1 (n);
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return result;
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}
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else
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scm_syserror ("left_shift_exact_integer");
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}
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/* Efficiently compute floor (N / 2^COUNT),
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where N is an exact integer and COUNT > 0. */
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static SCM
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floor_right_shift_exact_integer (SCM n, long count)
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{
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if (SCM_I_INUMP (n))
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{
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scm_t_inum nn = SCM_I_INUM (n);
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if (count >= SCM_I_FIXNUM_BIT)
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return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM (-1));
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else
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return SCM_I_MAKINUM (SCM_SRS (nn, count));
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}
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else if (SCM_BIGP (n))
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{
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SCM result = scm_i_mkbig ();
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mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n),
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count);
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scm_remember_upto_here_1 (n);
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return scm_i_normbig (result);
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}
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else
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scm_syserror ("floor_right_shift_exact_integer");
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}
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/* Efficiently compute round (N / 2^COUNT),
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where N is an exact integer and COUNT > 0. */
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static SCM
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round_right_shift_exact_integer (SCM n, long count)
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{
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if (SCM_I_INUMP (n))
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{
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if (count >= SCM_I_FIXNUM_BIT)
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return SCM_INUM0;
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else
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{
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scm_t_inum nn = SCM_I_INUM (n);
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scm_t_inum qq = SCM_SRS (nn, count);
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if (0 == (nn & (1L << (count-1))))
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return SCM_I_MAKINUM (qq); /* round down */
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else if (nn & ((1L << (count-1)) - 1))
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return SCM_I_MAKINUM (qq + 1); /* round up */
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else
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return SCM_I_MAKINUM ((~1L) & (qq + 1)); /* round to even */
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}
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}
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else if (SCM_BIGP (n))
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{
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SCM q = scm_i_mkbig ();
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mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), count);
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if (mpz_tstbit (SCM_I_BIG_MPZ (n), count-1)
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&& (mpz_odd_p (SCM_I_BIG_MPZ (q))
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|| (mpz_scan1 (SCM_I_BIG_MPZ (n), 0) < count-1)))
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mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1);
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scm_remember_upto_here_1 (n);
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return scm_i_normbig (q);
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}
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else
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scm_syserror ("round_right_shift_exact_integer");
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}
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SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
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SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
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(SCM n, SCM cnt),
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(SCM n, SCM count),
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"Return @var{n} shifted left by @var{cnt} bits, or shifted right\n"
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"Return @math{floor(@var{n} * 2^@var{count})}.\n"
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"if @var{cnt} is negative. This is an ``arithmetic'' shift.\n"
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"@var{n} and @var{count} must be exact integers.\n"
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"\n"
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"\n"
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"This is effectively a multiplication by 2^@var{cnt}, and when\n"
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"With @var{n} viewed as an infinite-precision twos-complement\n"
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"@var{cnt} is negative it's a division, rounded towards negative\n"
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"integer, @code{ash} means a left shift introducing zero bits\n"
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"infinity. (Note that this is not the same rounding as\n"
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"when @var{count} is positive, or a right shift dropping bits\n"
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"@code{quotient} does.)\n"
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"when @var{count} is negative. This is an ``arithmetic'' shift.\n"
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"\n"
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"With @var{n} viewed as an infinite precision twos complement,\n"
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"@code{ash} means a left shift introducing zero bits, or a right\n"
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"shift dropping bits.\n"
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"\n"
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"\n"
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"@lisp\n"
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"@lisp\n"
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"(number->string (ash #b1 3) 2) @result{} \"1000\"\n"
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"(number->string (ash #b1 3) 2) @result{} \"1000\"\n"
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@ -4814,79 +4914,57 @@ SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
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"@end lisp")
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"@end lisp")
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#define FUNC_NAME s_scm_ash
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#define FUNC_NAME s_scm_ash
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{
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{
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long bits_to_shift;
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if (SCM_I_INUMP (n) || SCM_BIGP (n))
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bits_to_shift = scm_to_long (cnt);
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if (SCM_I_INUMP (n))
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{
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{
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scm_t_inum nn = SCM_I_INUM (n);
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long bits_to_shift = scm_to_long (count);
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if (bits_to_shift > 0)
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if (bits_to_shift > 0)
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{
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return left_shift_exact_integer (n, bits_to_shift);
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/* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always
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else if (SCM_LIKELY (bits_to_shift < 0))
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overflow a non-zero fixnum. For smaller shifts we check the
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return floor_right_shift_exact_integer (n, -bits_to_shift);
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bits going into positions above SCM_I_FIXNUM_BIT-1. If they're
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else
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all 0s for nn>=0, or all 1s for nn<0 then there's no overflow.
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Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 -
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bits_to_shift)". */
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if (nn == 0)
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return n;
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return n;
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if (bits_to_shift < SCM_I_FIXNUM_BIT-1
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&& ((scm_t_bits)
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(SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1)
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<= 1))
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{
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return SCM_I_MAKINUM (nn << bits_to_shift);
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}
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}
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else
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else
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{
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SCM result = scm_i_inum2big (nn);
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mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result),
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bits_to_shift);
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return result;
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}
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}
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else
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{
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bits_to_shift = -bits_to_shift;
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if (bits_to_shift >= SCM_LONG_BIT)
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return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1));
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else
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return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift));
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}
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}
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else if (SCM_BIGP (n))
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{
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SCM result;
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if (bits_to_shift == 0)
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return n;
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result = scm_i_mkbig ();
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if (bits_to_shift >= 0)
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{
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mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n),
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bits_to_shift);
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return result;
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}
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else
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{
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/* GMP doesn't have an fdiv_q_2exp variant returning just a long, so
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we have to allocate a bignum even if the result is going to be a
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fixnum. */
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mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n),
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-bits_to_shift);
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return scm_i_normbig (result);
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}
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}
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else
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{
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SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
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SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
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}
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#undef FUNC_NAME
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SCM_DEFINE (scm_round_ash, "round-ash", 2, 0, 0,
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(SCM n, SCM count),
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"Return @math{round(@var{n} * 2^@var{count})}.\n"
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"@var{n} and @var{count} must be exact integers.\n"
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"\n"
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"With @var{n} viewed as an infinite-precision twos-complement\n"
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"integer, @code{round-ash} means a left shift introducing zero\n"
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"bits when @var{count} is positive, or a right shift rounding\n"
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"to the nearest integer (with ties going to the nearest even\n"
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"integer) when @var{count} is negative. This is a rounded\n"
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"``arithmetic'' shift.\n"
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"\n"
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"@lisp\n"
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"(number->string (round-ash #b1 3) 2) @result{} \"1000\"\n"
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"(number->string (round-ash #b1010 -1) 2) @result{} \"101\"\n"
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"(number->string (round-ash #b1010 -2) 2) @result{} \"10\"\n"
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"(number->string (round-ash #b1011 -2) 2) @result{} \"11\"\n"
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"(number->string (round-ash #b1101 -2) 2) @result{} \"11\"\n"
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"(number->string (round-ash #b1110 -2) 2) @result{} \"100\"\n"
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"@end lisp")
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#define FUNC_NAME s_scm_round_ash
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{
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if (SCM_I_INUMP (n) || SCM_BIGP (n))
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{
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long bits_to_shift = scm_to_long (count);
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if (bits_to_shift > 0)
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return left_shift_exact_integer (n, bits_to_shift);
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else if (SCM_LIKELY (bits_to_shift < 0))
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return round_right_shift_exact_integer (n, -bits_to_shift);
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else
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return n;
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}
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}
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else
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SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
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}
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}
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#undef FUNC_NAME
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#undef FUNC_NAME
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@ -206,7 +206,8 @@ SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
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SCM_API SCM scm_lognot (SCM n);
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SCM_API SCM scm_lognot (SCM n);
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SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
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SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
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SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
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SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
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SCM_API SCM scm_ash (SCM n, SCM cnt);
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SCM_API SCM scm_ash (SCM n, SCM count);
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SCM_API SCM scm_round_ash (SCM n, SCM count);
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SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
|
SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
|
||||||
SCM_API SCM scm_logcount (SCM n);
|
SCM_API SCM scm_logcount (SCM n);
|
||||||
SCM_API SCM scm_integer_length (SCM n);
|
SCM_API SCM scm_integer_length (SCM n);
|
||||||
|
|
|
||||||
|
|
@ -200,71 +200,6 @@
|
||||||
(pass-if "1- fixnum = bignum (64-bit)"
|
(pass-if "1- fixnum = bignum (64-bit)"
|
||||||
(eqv? -2305843009213693953 (1- -2305843009213693952))))
|
(eqv? -2305843009213693953 (1- -2305843009213693952))))
|
||||||
|
|
||||||
;;;
|
|
||||||
;;; ash
|
|
||||||
;;;
|
|
||||||
|
|
||||||
(with-test-prefix "ash"
|
|
||||||
|
|
||||||
(pass-if "documented?"
|
|
||||||
(documented? ash))
|
|
||||||
|
|
||||||
(pass-if (eqv? 0 (ash 0 0)))
|
|
||||||
(pass-if (eqv? 0 (ash 0 1)))
|
|
||||||
(pass-if (eqv? 0 (ash 0 1000)))
|
|
||||||
(pass-if (eqv? 0 (ash 0 -1)))
|
|
||||||
(pass-if (eqv? 0 (ash 0 -1000)))
|
|
||||||
|
|
||||||
(pass-if (eqv? 1 (ash 1 0)))
|
|
||||||
(pass-if (eqv? 2 (ash 1 1)))
|
|
||||||
(pass-if (eqv? 340282366920938463463374607431768211456 (ash 1 128)))
|
|
||||||
(pass-if (eqv? 0 (ash 1 -1)))
|
|
||||||
(pass-if (eqv? 0 (ash 1 -1000)))
|
|
||||||
|
|
||||||
(pass-if (eqv? -1 (ash -1 0)))
|
|
||||||
(pass-if (eqv? -2 (ash -1 1)))
|
|
||||||
(pass-if (eqv? -340282366920938463463374607431768211456 (ash -1 128)))
|
|
||||||
(pass-if (eqv? -1 (ash -1 -1)))
|
|
||||||
(pass-if (eqv? -1 (ash -1 -1000)))
|
|
||||||
|
|
||||||
(pass-if (eqv? -3 (ash -3 0)))
|
|
||||||
(pass-if (eqv? -6 (ash -3 1)))
|
|
||||||
(pass-if (eqv? -1020847100762815390390123822295304634368 (ash -3 128)))
|
|
||||||
(pass-if (eqv? -2 (ash -3 -1)))
|
|
||||||
(pass-if (eqv? -1 (ash -3 -1000)))
|
|
||||||
|
|
||||||
(pass-if (eqv? -6 (ash -23 -2)))
|
|
||||||
|
|
||||||
(pass-if (eqv? most-positive-fixnum (ash most-positive-fixnum 0)))
|
|
||||||
(pass-if (eqv? (* 2 most-positive-fixnum) (ash most-positive-fixnum 1)))
|
|
||||||
(pass-if (eqv? (* 4 most-positive-fixnum) (ash most-positive-fixnum 2)))
|
|
||||||
(pass-if
|
|
||||||
(eqv? (* most-positive-fixnum 340282366920938463463374607431768211456)
|
|
||||||
(ash most-positive-fixnum 128)))
|
|
||||||
(pass-if (eqv? (quotient most-positive-fixnum 2)
|
|
||||||
(ash most-positive-fixnum -1)))
|
|
||||||
(pass-if (eqv? 0 (ash most-positive-fixnum -1000)))
|
|
||||||
|
|
||||||
(let ((mpf4 (quotient most-positive-fixnum 4)))
|
|
||||||
(pass-if (eqv? (* 2 mpf4) (ash mpf4 1)))
|
|
||||||
(pass-if (eqv? (* 4 mpf4) (ash mpf4 2)))
|
|
||||||
(pass-if (eqv? (* 8 mpf4) (ash mpf4 3))))
|
|
||||||
|
|
||||||
(pass-if (eqv? most-negative-fixnum (ash most-negative-fixnum 0)))
|
|
||||||
(pass-if (eqv? (* 2 most-negative-fixnum) (ash most-negative-fixnum 1)))
|
|
||||||
(pass-if (eqv? (* 4 most-negative-fixnum) (ash most-negative-fixnum 2)))
|
|
||||||
(pass-if
|
|
||||||
(eqv? (* most-negative-fixnum 340282366920938463463374607431768211456)
|
|
||||||
(ash most-negative-fixnum 128)))
|
|
||||||
(pass-if (eqv? (quotient-floor most-negative-fixnum 2)
|
|
||||||
(ash most-negative-fixnum -1)))
|
|
||||||
(pass-if (eqv? -1 (ash most-negative-fixnum -1000)))
|
|
||||||
|
|
||||||
(let ((mnf4 (quotient-floor most-negative-fixnum 4)))
|
|
||||||
(pass-if (eqv? (* 2 mnf4) (ash mnf4 1)))
|
|
||||||
(pass-if (eqv? (* 4 mnf4) (ash mnf4 2)))
|
|
||||||
(pass-if (eqv? (* 8 mnf4) (ash mnf4 3)))))
|
|
||||||
|
|
||||||
;;;
|
;;;
|
||||||
;;; exact?
|
;;; exact?
|
||||||
;;;
|
;;;
|
||||||
|
|
@ -4914,3 +4849,52 @@
|
||||||
round-quotient
|
round-quotient
|
||||||
round-remainder
|
round-remainder
|
||||||
valid-round-answer?)))
|
valid-round-answer?)))
|
||||||
|
|
||||||
|
;;;
|
||||||
|
;;; ash
|
||||||
|
;;; round-ash
|
||||||
|
;;;
|
||||||
|
|
||||||
|
(let ()
|
||||||
|
(define (test-ash-variant name ash-variant round-variant)
|
||||||
|
(with-test-prefix name
|
||||||
|
(define (test n count)
|
||||||
|
(pass-if (list n count)
|
||||||
|
(eqv? (ash-variant n count)
|
||||||
|
(round-variant (* n (expt 2 count))))))
|
||||||
|
|
||||||
|
(pass-if "documented?"
|
||||||
|
(documented? ash-variant))
|
||||||
|
|
||||||
|
(for-each (lambda (n)
|
||||||
|
(for-each (lambda (count) (test n count))
|
||||||
|
'(-1000 -3 -2 -1 0 1 2 3 1000)))
|
||||||
|
(list 0 1 3 23 -1 -3 -23
|
||||||
|
fixnum-max
|
||||||
|
(1+ fixnum-max)
|
||||||
|
(1- fixnum-max)
|
||||||
|
(* fixnum-max 4)
|
||||||
|
(quotient fixnum-max 4)
|
||||||
|
fixnum-min
|
||||||
|
(1+ fixnum-min)
|
||||||
|
(1- fixnum-min)
|
||||||
|
(* fixnum-min 4)
|
||||||
|
(quotient fixnum-min 4)))
|
||||||
|
|
||||||
|
(do ((count -2 (1- count))
|
||||||
|
(vals '(1 3 5 7 9 11)
|
||||||
|
(map (lambda (n) (* 2 n)) vals)))
|
||||||
|
((> (car vals) (* 2 fixnum-max)) 'done)
|
||||||
|
(for-each (lambda (n)
|
||||||
|
(test n count)
|
||||||
|
(test (- n) count))
|
||||||
|
vals))
|
||||||
|
|
||||||
|
;; Test rounding
|
||||||
|
(for-each (lambda (base)
|
||||||
|
(for-each (lambda (offset) (test (+ base offset) -3))
|
||||||
|
'(#b11001 #b11100 #b11101 #b10001 #b10100 #b10101)))
|
||||||
|
(list 0 64 -64 (* 64 fixnum-max) (* 64 fixnum-min)))))
|
||||||
|
|
||||||
|
(test-ash-variant 'ash ash floor)
|
||||||
|
(test-ash-variant 'round-ash round-ash round))
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue