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+ GMP Itemized Development Tasks
+ </h1>
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+
+<font size=-1>
+<pre>
+Copyright 2000, 2001, 2002, 2003, 2004, 2006, 2008, 2009 Free Software
+Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published
+by the Free Software Foundation; either version 3 of the License, or (at
+your option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library. If not, see http://www.gnu.org/licenses/.
+</pre>
+</font>
+
+<hr>
+<!-- NB. timestamp updated automatically by emacs -->
+ This file current as of 1 May 2009. An up-to-date version is available at
+ <a href="http://gmplib.org/tasks.html">http://gmplib.org/tasks.html</a>.
+ Please send comments about this page to gmp-devel<font>@</font>gmplib.org.
+
+<p> These are itemized GMP development tasks. Not all the tasks
+ listed here are suitable for volunteers, but many of them are.
+ Please see the <a href="projects.html">projects file</a> for more
+ sizeable projects.
+
+<p> CAUTION: This file needs updating. Many of the tasks here have
+either already been taken care of, or have become irrelevant.
+
+<h4>Correctness and Completeness</h4>
+<ul>
+<li> <code>_LONG_LONG_LIMB</code> in gmp.h is not namespace clean. Reported
+ by Patrick Pelissier.
+ <br>
+ We sort of mentioned <code>_LONG_LONG_LIMB</code> in past releases, so
+ need to be careful about changing it. It used to be a define
+ applications had to set for long long limb systems, but that in
+ particular is no longer relevant now that it's established automatically.
+<li> The various reuse.c tests need to force reallocation by calling
+ <code>_mpz_realloc</code> with a small (1 limb) size.
+<li> One reuse case is missing from mpX/tests/reuse.c:
+ <code>mpz_XXX(a,a,a)</code>.
+<li> When printing <code>mpf_t</code> numbers with exponents >2^53 on
+ machines with 64-bit <code>mp_exp_t</code>, the precision of
+ <code>__mp_bases[base].chars_per_bit_exactly</code> is insufficient and
+ <code>mpf_get_str</code> aborts. Detect and compensate. Alternately,
+ think seriously about using some sort of fixed-point integer value.
+ Avoiding unnecessary floating point is probably a good thing in general,
+ and it might be faster on some CPUs.
+<li> Make the string reading functions allow the `0x' prefix when the base is
+ explicitly 16. They currently only allow that prefix when the base is
+ unspecified (zero).
+<li> <code>mpf_eq</code> is not always correct, when one operand is
+ 1000000000... and the other operand is 0111111111..., i.e., extremely
+ close. There is a special case in <code>mpf_sub</code> for this
+ situation; put similar code in <code>mpf_eq</code>. [In progress.]
+<li> <code>mpf_eq</code> doesn't implement what gmp.texi specifies. It should
+ not use just whole limbs, but partial limbs. [In progress.]
+<li> <code>mpf_set_str</code> doesn't validate it's exponent, for instance
+ garbage 123.456eX789X is accepted (and an exponent 0 used), and overflow
+ of a <code>long</code> is not detected.
+<li> <code>mpf_add</code> doesn't check for a carry from truncated portions of
+ the inputs, and in that respect doesn't implement the "infinite precision
+ followed by truncate" specified in the manual.
+<li> Windows DLLs: tests/mpz/reuse.c and tests/mpf/reuse.c initialize global
+ variables with pointers to <code>mpz_add</code> etc, which doesn't work
+ when those routines are coming from a DLL (because they're effectively
+ function pointer global variables themselves). Need to rearrange perhaps
+ to a set of calls to a test function rather than iterating over an array.
+<li> <code>mpz_pow_ui</code>: Detect when the result would be more memory than
+ a <code>size_t</code> can represent and raise some suitable exception,
+ probably an alloc call asking for <code>SIZE_T_MAX</code>, and if that
+ somehow succeeds then an <code>abort</code>. Various size overflows of
+ this kind are not handled gracefully, probably resulting in segvs.
+ <br>
+ In <code>mpz_n_pow_ui</code>, detect when the count of low zero bits
+ exceeds an <code>unsigned long</code>. There's a (small) chance of this
+ happening but still having enough memory to represent the value.
+ Reported by Winfried Dreckmann in for instance <code>mpz_ui_pow_ui (x,
+ 4UL, 1431655766UL)</code>.
+<li> <code>mpf</code>: Detect exponent overflow and raise some exception.
+ It'd be nice to allow the full <code>mp_exp_t</code> range since that's
+ how it's been in the past, but maybe dropping one bit would make it
+ easier to test if e1+e2 goes out of bounds.
+</ul>
+
+
+
+<h4>Machine Independent Optimization</h4>
+<ul>
+<li> <code>mpf_cmp</code>: For better cache locality, don't test for low zero
+ limbs until the high limbs fail to give an ordering. Reduce code size by
+ turning the three <code>mpn_cmp</code>'s into a single loop stopping when
+ the end of one operand is reached (and then looking for a non-zero in the
+ rest of the other).
+<li> <code>mpf_mul_2exp</code>, <code>mpf_div_2exp</code>: The use of
+ <code>mpn_lshift</code> for any size<=prec means repeated
+ <code>mul_2exp</code> and <code>div_2exp</code> calls accumulate low zero
+ limbs until size==prec+1 is reached. Those zeros will slow down
+ subsequent operations, especially if the value is otherwise only small.
+ If low bits of the low limb are zero, use <code>mpn_rshift</code> so as
+ to not increase the size.
+<li> <code>mpn_dc_sqrtrem</code>: Don't use <code>mpn_addmul_1</code> with
+ multiplier==2, instead either <code>mpn_addlsh1_n</code> when available,
+ or <code>mpn_lshift</code>+<code>mpn_add_n</code> if not.
+<li> <code>mpn_dc_sqrtrem</code>, <code>mpn_sqrtrem2</code>: Don't use
+ <code>mpn_add_1</code> and <code>mpn_sub_1</code> for 1 limb operations,
+ instead <code>ADDC_LIMB</code> and <code>SUBC_LIMB</code>.
+<li> <code>mpn_sqrtrem2</code>: Use plain variables for <code>sp[0]</code> and
+ <code>rp[0]</code> calculations, so the compiler needn't worry about
+ aliasing between <code>sp</code> and <code>rp</code>.
+<li> <code>mpn_sqrtrem</code>: Some work can be saved in the last step when
+ the remainder is not required, as noted in Paul's paper.
+<li> <code>mpq_add</code>, <code>mpq_add</code>: The division "op1.den / gcd"
+ is done twice, where of course only once is necessary. Reported by Larry
+ Lambe.
+<li> <code>mpq_add</code>, <code>mpq_sub</code>: The gcd fits a single limb
+ with high probability and in this case <code>modlimb_invert</code> could
+ be used to calculate the inverse just once for the two exact divisions
+ "op1.den / gcd" and "op2.den / gcd", rather than letting
+ <code>mpn_divexact_1</code> do it each time. This would require a new
+ <code>mpn_preinv_divexact_1</code> interface. Not sure if it'd be worth
+ the trouble.
+<li> <code>mpq_add</code>, <code>mpq_sub</code>: The use of
+ <code>mpz_mul(x,y,x)</code> causes temp allocation or copying in
+ <code>mpz_mul</code> which can probably be avoided. A rewrite using
+ <code>mpn</code> might be best.
+<li> <code>mpn_gcdext</code>: Don't test <code>count_leading_zeros</code> for
+ zero, instead check the high bit of the operand and avoid invoking
+ <code>count_leading_zeros</code>. This is an optimization on all
+ machines, and significant on machines with slow
+ <code>count_leading_zeros</code>, though it's possible an already
+ normalized operand might not be encountered very often.
+<li> Rewrite <code>umul_ppmm</code> to use floating-point for generating the
+ most significant limb (if <code>BITS_PER_MP_LIMB</code> <= 52 bits).
+ (Peter Montgomery has some ideas on this subject.)
+<li> Improve the default <code>umul_ppmm</code> code in longlong.h: Add partial
+ products with fewer operations.
+<li> Consider inlining <code>mpz_set_ui</code>. This would be both small and
+ fast, especially for compile-time constants, but would make application
+ binaries depend on having 1 limb allocated to an <code>mpz_t</code>,
+ preventing the "lazy" allocation scheme below.
+<li> Consider inlining <code>mpz_[cft]div_ui</code> and maybe
+ <code>mpz_[cft]div_r_ui</code>. A <code>__gmp_divide_by_zero</code>
+ would be needed for the divide by zero test, unless that could be left to
+ <code>mpn_mod_1</code> (not sure currently whether all the risc chips
+ provoke the right exception there if using mul-by-inverse).
+<li> Consider inlining: <code>mpz_fits_s*_p</code>. The setups for
+ <code>LONG_MAX</code> etc would need to go into gmp.h, and on Cray it
+ might, unfortunately, be necessary to forcibly include <limits.h>
+ since there's no apparent way to get <code>SHRT_MAX</code> with an
+ expression (since <code>short</code> and <code>unsigned short</code> can
+ be different sizes).
+<li> <code>mpz_powm</code> and <code>mpz_powm_ui</code> aren't very
+ fast on one or two limb moduli, due to a lot of function call
+ overheads. These could perhaps be handled as special cases.
+<li> <code>mpz_powm</code> and <code>mpz_powm_ui</code> want better
+ algorithm selection, and the latter should use REDC. Both could
+ change to use an <code>mpn_powm</code> and <code>mpn_redc</code>.
+<li> <code>mpz_powm</code> REDC should do multiplications by <code>g[]</code>
+ using the division method when they're small, since the REDC form of a
+ small multiplier is normally a full size product. Probably would need a
+ new tuned parameter to say what size multiplier is "small", as a function
+ of the size of the modulus.
+<li> <code>mpz_powm</code> REDC should handle even moduli if possible. Maybe
+ this would mean for m=n*2^k doing mod n using REDC and an auxiliary
+ calculation mod 2^k, then putting them together at the end.
+<li> <code>mpn_gcd</code> might be able to be sped up on small to
+ moderate sizes by improving <code>find_a</code>, possibly just by
+ providing an alternate implementation for CPUs with slowish
+ <code>count_leading_zeros</code>.
+<li> Toom3 could use a low to high cache localized evaluate and interpolate.
+ The necessary <code>mpn_divexact_by3c</code> exists.
+<li> <code>mpf_set_str</code> produces low zero limbs when a string has a
+ fraction but is exactly representable, eg. 0.5 in decimal. These could be
+ stripped to save work in later operations.
+<li> <code>mpz_and</code>, <code>mpz_ior</code> and <code>mpz_xor</code> should
+ use <code>mpn_and_n</code> etc for the benefit of the small number of
+ targets with native versions of those routines. Need to be careful not to
+ pass size==0. Is some code sharing possible between the <code>mpz</code>
+ routines?
+<li> <code>mpf_add</code>: Don't do a copy to avoid overlapping operands
+ unless it's really necessary (currently only sizes are tested, not
+ whether r really is u or v).
+<li> <code>mpf_add</code>: Under the check for v having no effect on the
+ result, perhaps test for r==u and do nothing in that case, rather than
+ currently it looks like an <code>MPN_COPY_INCR</code> will be done to
+ reduce prec+1 limbs to prec.
+<li> <code>mpf_div_ui</code>: Instead of padding with low zeros, call
+ <code>mpn_divrem_1</code> asking for fractional quotient limbs.
+<li> <code>mpf_div_ui</code>: Eliminate <code>TMP_ALLOC</code>. When r!=u
+ there's no overlap and the division can be called on those operands.
+ When r==u and is prec+1 limbs, then it's an in-place division. If r==u
+ and not prec+1 limbs, then move the available limbs up to prec+1 and do
+ an in-place there.
+<li> <code>mpf_div_ui</code>: Whether the high quotient limb is zero can be
+ determined by testing the dividend for high<divisor. When non-zero, the
+ divison can be done on prec dividend limbs instead of prec+1. The result
+ size is also known before the division, so that can be a tail call (once
+ the <code>TMP_ALLOC</code> is eliminated).
+<li> <code>mpn_divrem_2</code> could usefully accept unnormalized divisors and
+ shift the dividend on-the-fly, since this should cost nothing on
+ superscalar processors and avoid the need for temporary copying in
+ <code>mpn_tdiv_qr</code>.
+<li> <code>mpf_sqrt</code>: If r!=u, and if u doesn't need to be padded with
+ zeros, then there's no need for the tp temporary.
+<li> <code>mpq_cmp_ui</code> could form the <code>num1*den2</code> and
+ <code>num2*den1</code> products limb-by-limb from high to low and look at
+ each step for values differing by more than the possible carry bit from
+ the uncalculated portion.
+<li> <code>mpq_cmp</code> could do the same high-to-low progressive multiply
+ and compare. The benefits of karatsuba and higher multiplication
+ algorithms are lost, but if it's assumed only a few high limbs will be
+ needed to determine an order then that's fine.
+<li> <code>mpn_add_1</code>, <code>mpn_sub_1</code>, <code>mpn_add</code>,
+ <code>mpn_sub</code>: Internally use <code>__GMPN_ADD_1</code> etc
+ instead of the functions, so they get inlined on all compilers, not just
+ gcc and others with <code>inline</code> recognised in gmp.h.
+ <code>__GMPN_ADD_1</code> etc are meant mostly to support application
+ inline <code>mpn_add_1</code> etc and if they don't come out good for
+ internal uses then special forms can be introduced, for instance many
+ internal uses are in-place. Sometimes a block of code is executed based
+ on the carry-out, rather than using it arithmetically, and those places
+ might want to do their own loops entirely.
+<li> <code>__gmp_extract_double</code> on 64-bit systems could use just one
+ bitfield for the mantissa extraction, not two, when endianness permits.
+ Might depend on the compiler allowing <code>long long</code> bit fields
+ when that's the only actual 64-bit type.
+<li> tal-notreent.c could keep a block of memory permanently allocated.
+ Currently the last nested <code>TMP_FREE</code> releases all memory, so
+ there's an allocate and free every time a top-level function using
+ <code>TMP</code> is called. Would need
+ <code>mp_set_memory_functions</code> to tell tal-notreent.c to release
+ any cached memory when changing allocation functions though.
+<li> <code>__gmp_tmp_alloc</code> from tal-notreent.c could be partially
+ inlined. If the current chunk has enough room then a couple of pointers
+ can be updated. Only if more space is required then a call to some sort
+ of <code>__gmp_tmp_increase</code> would be needed. The requirement that
+ <code>TMP_ALLOC</code> is an expression might make the implementation a
+ bit ugly and/or a bit sub-optimal.
+<pre>
+#define TMP_ALLOC(n)
+ ((ROUND_UP(n) > current->end - current->point ?
+ __gmp_tmp_increase (ROUND_UP (n)) : 0),
+ current->point += ROUND_UP (n),
+ current->point - ROUND_UP (n))
+</pre>
+<li> <code>__mp_bases</code> has a lot of data for bases which are pretty much
+ never used. Perhaps the table should just go up to base 16, and have
+ code to generate data above that, if and when required. Naturally this
+ assumes the code would be smaller than the data saved.
+<li> <code>__mp_bases</code> field <code>big_base_inverted</code> is only used
+ if <code>USE_PREINV_DIVREM_1</code> is true, and could be omitted
+ otherwise, to save space.
+<li> <code>mpz_get_str</code>, <code>mtox</code>: For power-of-2 bases, which
+ are of course fast, it seems a little silly to make a second pass over
+ the <code>mpn_get_str</code> output to convert to ASCII. Perhaps combine
+ that with the bit extractions.
+<li> <code>mpz_gcdext</code>: If the caller requests only the S cofactor (of
+ A), and A<B, then the code ends up generating the cofactor T (of B) and
+ deriving S from that. Perhaps it'd be possible to arrange to get S in
+ the first place by calling <code>mpn_gcdext</code> with A+B,B. This
+ might only be an advantage if A and B are about the same size.
+<li> <code>mpz_n_pow_ui</code> does a good job with small bases and stripping
+ powers of 2, but it's perhaps a bit too complicated for what it gains.
+ The simpler <code>mpn_pow_1</code> is a little faster on small exponents.
+ (Note some of the ugliness in <code>mpz_n_pow_ui</code> is due to
+ supporting <code>mpn_mul_2</code>.)
+ <br>
+ Perhaps the stripping of 2s in <code>mpz_n_pow_ui</code> should be
+ confined to single limb operands for simplicity and since that's where
+ the greatest gain would be.
+ <br>
+ Ideally <code>mpn_pow_1</code> and <code>mpz_n_pow_ui</code> would be
+ merged. The reason <code>mpz_n_pow_ui</code> writes to an
+ <code>mpz_t</code> is that its callers leave it to make a good estimate
+ of the result size. Callers of <code>mpn_pow_1</code> already know the
+ size by separate means (<code>mp_bases</code>).
+<li> <code>mpz_invert</code> should call <code>mpn_gcdext</code> directly.
+</ul>
+
+
+<h4>Machine Dependent Optimization</h4>
+<ul>
+<li> <code>invert_limb</code> on various processors might benefit from the
+ little Newton iteration done for alpha and ia64.
+<li> Alpha 21264: <code>mpn_addlsh1_n</code> could be implemented with
+ <code>mpn_addmul_1</code>, since that code at 3.5 is a touch faster than
+ a separate <code>lshift</code> and <code>add_n</code> at
+ 1.75+2.125=3.875. Or very likely some specific <code>addlsh1_n</code>
+ code could beat both.
+<li> Alpha 21264: Improve feed-in code for <code>mpn_mul_1</code>,
+ <code>mpn_addmul_1</code>, and <code>mpn_submul_1</code>.
+<li> Alpha 21164: Rewrite <code>mpn_mul_1</code>, <code>mpn_addmul_1</code>,
+ and <code>mpn_submul_1</code> for the 21164. This should use both integer
+ multiplies and floating-point multiplies. For the floating-point
+ operations, the single-limb multiplier should be split into three 21-bit
+ chunks, or perhaps even better in four 16-bit chunks. Probably possible
+ to reach 9 cycles/limb.
+<li> Alpha: GCC 3.4 will introduce <code>__builtin_ctzl</code>,
+ <code>__builtin_clzl</code> and <code>__builtin_popcountl</code> using
+ the corresponding CIX <code>ct</code> instructions, and
+ <code>__builtin_alpha_cmpbge</code>. These should give GCC more
+ information about sheduling etc than the <code>asm</code> blocks
+ currently used in longlong.h and gmp-impl.h.
+<li> Alpha Unicos: Apparently there's no <code>alloca</code> on this system,
+ making <code>configure</code> choose the slower
+ <code>malloc-reentrant</code> allocation method. Is there a better way?
+ Maybe variable-length arrays per notes below.
+<li> Alpha Unicos 21164, 21264: <code>.align</code> is not used since it pads
+ with garbage. Does the code get the intended slotting required for the
+ claimed speeds? <code>.align</code> at the start of a function would
+ presumably be safe no matter how it pads.
+<li> ARM V5: <code>count_leading_zeros</code> can use the <code>clz</code>
+ instruction. For GCC 3.4 and up, do this via <code>__builtin_clzl</code>
+ since then gcc knows it's "predicable".
+<li> Itanium: GCC 3.4 introduces <code>__builtin_popcount</code> which can be
+ used instead of an <code>asm</code> block. The builtin should give gcc
+ more opportunities for scheduling, bundling and predication.
+ <code>__builtin_ctz</code> similarly (it just uses popcount as per
+ current longlong.h).
+<li> UltraSPARC/64: Optimize <code>mpn_mul_1</code>, <code>mpn_addmul_1</code>,
+ for s2 < 2^32 (or perhaps for any zero 16-bit s2 chunk). Not sure how
+ much this can improve the speed, though, since the symmetry that we rely
+ on is lost. Perhaps we can just gain cycles when s2 < 2^16, or more
+ accurately, when two 16-bit s2 chunks which are 16 bits apart are zero.
+<li> UltraSPARC/64: Write native <code>mpn_submul_1</code>, analogous to
+ <code>mpn_addmul_1</code>.
+<li> UltraSPARC/64: Write <code>umul_ppmm</code>. Using four
+ "<code>mulx</code>"s either with an asm block or via the generic C code is
+ about 90 cycles. Try using fp operations, and also try using karatsuba
+ for just three "<code>mulx</code>"s.
+<li> UltraSPARC/32: Rewrite <code>mpn_lshift</code>, <code>mpn_rshift</code>.
+ Will give 2 cycles/limb. Trivial modifications of mpn/sparc64 should do.
+<li> UltraSPARC/32: Write special mpn_Xmul_1 loops for s2 < 2^16.
+<li> UltraSPARC/32: Use <code>mulx</code> for <code>umul_ppmm</code> if
+ possible (see commented out code in longlong.h). This is unlikely to
+ save more than a couple of cycles, so perhaps isn't worth bothering with.
+<li> UltraSPARC/32: On Solaris gcc doesn't give us <code>__sparc_v9__</code>
+ or anything to indicate V9 support when -mcpu=v9 is selected. See
+ gcc/config/sol2-sld-64.h. Will need to pass something through from
+ ./configure to select the right code in longlong.h. (Currently nothing
+ is lost because <code>mulx</code> for multiplying is commented out.)
+<li> UltraSPARC/32: <code>mpn_divexact_1</code> and
+ <code>mpn_modexact_1c_odd</code> can use a 64-bit inverse and take
+ 64-bits at a time from the dividend, as per the 32-bit divisor case in
+ mpn/sparc64/mode1o.c. This must be done in assembler, since the full
+ 64-bit registers (<code>%gN</code>) are not available from C.
+<li> UltraSPARC/32: <code>mpn_divexact_by3c</code> can work 64-bits at a time
+ using <code>mulx</code>, in assembler. This would be the same as for
+ sparc64.
+<li> UltraSPARC: <code>modlimb_invert</code> might save a few cycles from
+ masking down to just the useful bits at each point in the calculation,
+ since <code>mulx</code> speed depends on the highest bit set. Either
+ explicit masks or small types like <code>short</code> and
+ <code>int</code> ought to work.
+<li> Sparc64 HAL R1 <code>popc</code>: This chip reputedly implements
+ <code>popc</code> properly (see gcc sparc.md). Would need to recognise
+ it as <code>sparchalr1</code> or something in configure / config.sub /
+ config.guess. <code>popc_limb</code> in gmp-impl.h could use this (per
+ commented out code). <code>count_trailing_zeros</code> could use it too.
+<li> PA64: Improve <code>mpn_addmul_1</code>, <code>mpn_submul_1</code>, and
+ <code>mpn_mul_1</code>. The current code runs at 11 cycles/limb. It
+ should be possible to saturate the cache, which will happen at 8
+ cycles/limb (7.5 for mpn_mul_1). Write special loops for s2 < 2^32;
+ it should be possible to make them run at about 5 cycles/limb.
+<li> PPC601: See which of the power or powerpc32 code runs better. Currently
+ the powerpc32 is used, but only because it's the default for
+ <code>powerpc*</code>.
+<li> PPC630: Rewrite <code>mpn_addmul_1</code>, <code>mpn_submul_1</code>, and
+ <code>mpn_mul_1</code>. Use both integer and floating-point operations,
+ possibly two floating-point and one integer limb per loop. Split operands
+ into four 16-bit chunks for fast fp operations. Should easily reach 9
+ cycles/limb (using one int + one fp), but perhaps even 7 cycles/limb
+ (using one int + two fp).
+<li> PPC630: <code>mpn_rshift</code> could do the same sort of unrolled loop
+ as <code>mpn_lshift</code>. Some judicious use of m4 might let the two
+ share source code, or with a register to control the loop direction
+ perhaps even share object code.
+<li> Implement <code>mpn_mul_basecase</code> and <code>mpn_sqr_basecase</code>
+ for important machines. Helping the generic sqr_basecase.c with an
+ <code>mpn_sqr_diagonal</code> might be enough for some of the RISCs.
+<li> POWER2/POWER2SC: Schedule <code>mpn_lshift</code>/<code>mpn_rshift</code>.
+ Will bring time from 1.75 to 1.25 cycles/limb.
+<li> X86: Optimize non-MMX <code>mpn_lshift</code> for shifts by 1. (See
+ Pentium code.)
+<li> X86: Good authority has it that in the past an inline <code>rep
+ movs</code> would upset GCC register allocation for the whole function.
+ Is this still true in GCC 3? It uses <code>rep movs</code> itself for
+ <code>__builtin_memcpy</code>. Examine the code for some simple and
+ complex functions to find out. Inlining <code>rep movs</code> would be
+ desirable, it'd be both smaller and faster.
+<li> Pentium P54: <code>mpn_lshift</code> and <code>mpn_rshift</code> can come
+ down from 6.0 c/l to 5.5 or 5.375 by paying attention to pairing after
+ <code>shrdl</code> and <code>shldl</code>, see mpn/x86/pentium/README.
+<li> Pentium P55 MMX: <code>mpn_lshift</code> and <code>mpn_rshift</code>
+ might benefit from some destination prefetching.
+<li> PentiumPro: <code>mpn_divrem_1</code> might be able to use a
+ mul-by-inverse, hoping for maybe 30 c/l.
+<li> K7: <code>mpn_lshift</code> and <code>mpn_rshift</code> might be able to
+ do something branch-free for unaligned startups, and shaving one insn
+ from the loop with alternative indexing might save a cycle.
+<li> PPC32: Try using fewer registers in the current <code>mpn_lshift</code>.
+ The pipeline is now extremely deep, perhaps unnecessarily deep.
+<li> Fujitsu VPP: Vectorize main functions, perhaps in assembly language.
+<li> Fujitsu VPP: Write <code>mpn_mul_basecase</code> and
+ <code>mpn_sqr_basecase</code>. This should use a "vertical multiplication
+ method", to avoid carry propagation. splitting one of the operands in
+ 11-bit chunks.
+<li> Pentium: <code>mpn_lshift</code> by 31 should use the special rshift
+ by 1 code, and vice versa <code>mpn_rshift</code> by 31 should use the
+ special lshift by 1. This would be best as a jump across to the other
+ routine, could let both live in lshift.asm and omit rshift.asm on finding
+ <code>mpn_rshift</code> already provided.
+<li> Cray T3E: Experiment with optimization options. In particular,
+ -hpipeline3 seems promising. We should at least up -O to -O2 or -O3.
+<li> Cray: <code>mpn_com_n</code> and <code>mpn_and_n</code> etc very probably
+ wants a pragma like <code>MPN_COPY_INCR</code>.
+<li> Cray vector systems: <code>mpn_lshift</code>, <code>mpn_rshift</code>,
+ <code>mpn_popcount</code> and <code>mpn_hamdist</code> are nice and small
+ and could be inlined to avoid function calls.
+<li> Cray: Variable length arrays seem to be faster than the tal-notreent.c
+ scheme. Not sure why, maybe they merely give the compiler more
+ information about aliasing (or the lack thereof). Would like to modify
+ <code>TMP_ALLOC</code> to use them, or introduce a new scheme. Memory
+ blocks wanted unconditionally are easy enough, those wanted only
+ sometimes are a problem. Perhaps a special size calculation to ask for a
+ dummy length 1 when unwanted, or perhaps an inlined subroutine
+ duplicating code under each conditional. Don't really want to turn
+ everything into a dog's dinner just because Cray don't offer an
+ <code>alloca</code>.
+<li> Cray: <code>mpn_get_str</code> on power-of-2 bases ought to vectorize.
+ Does it? <code>bits_per_digit</code> and the inner loop over bits in a
+ limb might prevent it. Perhaps special cases for binary, octal and hex
+ would be worthwhile (very possibly for all processors too).
+<li> S390: <code>BSWAP_LIMB_FETCH</code> looks like it could be done with
+ <code>lrvg</code>, as per glibc sysdeps/s390/s390-64/bits/byteswap.h.
+ This is only for 64-bit mode or something is it, since 32-bit mode has
+ other code? Also, is it worth using for <code>BSWAP_LIMB</code> too, or
+ would that mean a store and re-fetch? Presumably that's what comes out
+ in glibc.
+<li> Improve <code>count_leading_zeros</code> for 64-bit machines:
+ <pre>
+ if ((x >> 32) == 0) { x <<= 32; cnt += 32; }
+ if ((x >> 48) == 0) { x <<= 16; cnt += 16; }
+ ... </pre>
+<li> IRIX 6 MIPSpro compiler has an <code>__inline</code> which could perhaps
+ be used in <code>__GMP_EXTERN_INLINE</code>. What would be the right way
+ to identify suitable versions of that compiler?
+<li> IRIX <code>cc</code> is rumoured to have an <code>_int_mult_upper</code>
+ (in <code><intrinsics.h></code> like Cray), but it didn't seem to
+ exist on some IRIX 6.5 systems tried. If it does actually exist
+ somewhere it would very likely be an improvement over a function call to
+ umul.asm.
+<li> <code>mpn_get_str</code> final divisions by the base with
+ <code>udiv_qrnd_unnorm</code> could use some sort of multiply-by-inverse
+ on suitable machines. This ends up happening for decimal by presenting
+ the compiler with a run-time constant, but the same for other bases would
+ be good. Perhaps use could be made of the fact base<256.
+<li> <code>mpn_umul_ppmm</code>, <code>mpn_udiv_qrnnd</code>: Return a
+ structure like <code>div_t</code> to avoid going through memory, in
+ particular helping RISCs that don't do store-to-load forwarding. Clearly
+ this is only possible if the ABI returns a structure of two
+ <code>mp_limb_t</code>s in registers.
+ <br>
+ On PowerPC, structures are returned in memory on AIX and Darwin. In SVR4
+ they're returned in registers, except that draft SVR4 had said memory, so
+ it'd be prudent to check which is done. We can jam the compiler into the
+ right mode if we know how, since all this is purely internal to libgmp.
+ (gcc has an option, though of course gcc doesn't matter since we use
+ inline asm there.)
+</ul>
+
+<h4>New Functionality</h4>
+<ul>
+<li> Maybe add <code>mpz_crr</code> (Chinese Remainder Reconstruction).
+<li> Let `0b' and `0B' mean binary input everywhere.
+<li> <code>mpz_init</code> and <code>mpq_init</code> could do lazy allocation.
+ Set <code>ALLOC(var)</code> to 0 to indicate nothing allocated, and let
+ <code>_mpz_realloc</code> do the initial alloc. Set
+ <code>z->_mp_d</code> to a dummy that <code>mpz_get_ui</code> and
+ similar can unconditionally fetch from. Niels Möller has had a go at
+ this.
+ <br>
+ The advantages of the lazy scheme would be:
+ <ul>
+ <li> Initial allocate would be the size required for the first value
+ stored, rather than getting 1 limb in <code>mpz_init</code> and then
+ more or less immediately reallocating.
+ <li> <code>mpz_init</code> would only store magic values in the
+ <code>mpz_t</code> fields, and could be inlined.
+ <li> A fixed initializer could even be used by applications, like
+ <code>mpz_t z = MPZ_INITIALIZER;</code>, which might be convenient
+ for globals.
+ </ul>
+ The advantages of the current scheme are:
+ <ul>
+ <li> <code>mpz_set_ui</code> and other similar routines needn't check the
+ size allocated and can just store unconditionally.
+ <li> <code>mpz_set_ui</code> and perhaps others like
+ <code>mpz_tdiv_r_ui</code> and a prospective
+ <code>mpz_set_ull</code> could be inlined.
+ </ul>
+<li> Add <code>mpf_out_raw</code> and <code>mpf_inp_raw</code>. Make sure
+ format is portable between 32-bit and 64-bit machines, and between
+ little-endian and big-endian machines. A format which MPFR can use too
+ would be good.
+<li> <code>mpn_and_n</code> ... <code>mpn_copyd</code>: Perhaps make the mpn
+ logops and copys available in gmp.h, either as library functions or
+ inlines, with the availability of library functions instantiated in the
+ generated gmp.h at build time.
+<li> <code>mpz_set_str</code> etc variants taking string lengths rather than
+ null-terminators.
+<li> <code>mpz_andn</code>, <code>mpz_iorn</code>, <code>mpz_nand</code>,
+ <code>mpz_nior</code>, <code>mpz_xnor</code> might be useful additions,
+ if they could share code with the current such functions (which should be
+ possible).
+<li> <code>mpz_and_ui</code> etc might be of use sometimes. Suggested by
+ Niels Möller.
+<li> <code>mpf_set_str</code> and <code>mpf_inp_str</code> could usefully
+ accept 0x, 0b etc when base==0. Perhaps the exponent could default to
+ decimal in this case, with a further 0x, 0b etc allowed there.
+ Eg. 0xFFAA@0x5A. A leading "0" for octal would match the integers, but
+ probably something like "0.123" ought not mean octal.
+<li> <code>GMP_LONG_LONG_LIMB</code> or some such could become a documented
+ feature of gmp.h, so applications could know whether to
+ <code>printf</code> a limb using <code>%lu</code> or <code>%Lu</code>.
+<li> <code>GMP_PRIdMP_LIMB</code> and similar defines following C99
+ <inttypes.h> might be of use to applications printing limbs. But
+ if <code>GMP_LONG_LONG_LIMB</code> or whatever is added then perhaps this
+ can easily enough be left to applications.
+<li> <code>gmp_printf</code> could accept <code>%b</code> for binary output.
+ It'd be nice if it worked for plain <code>int</code> etc too, not just
+ <code>mpz_t</code> etc.
+<li> <code>gmp_printf</code> in fact could usefully accept an arbitrary base,
+ for both integer and float conversions. A base either in the format
+ string or as a parameter with <code>*</code> should be allowed. Maybe
+ <code>&13b</code> (b for base) or something like that.
+<li> <code>gmp_printf</code> could perhaps accept <code>mpq_t</code> for float
+ conversions, eg. <code>"%.4Qf"</code>. This would be merely for
+ convenience, but still might be useful. Rounding would be the same as
+ for an <code>mpf_t</code> (ie. currently round-to-nearest, but not
+ actually documented). Alternately, perhaps a separate
+ <code>mpq_get_str_point</code> or some such might be more use. Suggested
+ by Pedro Gimeno.
+<li> <code>mpz_rscan0</code> or <code>mpz_revscan0</code> or some such
+ searching towards the low end of an integer might match
+ <code>mpz_scan0</code> nicely. Likewise for <code>scan1</code>.
+ Suggested by Roberto Bagnara.
+<li> <code>mpz_bit_subset</code> or some such to test whether one integer is a
+ bitwise subset of another might be of use. Some sort of return value
+ indicating whether it's a proper or non-proper subset would be good and
+ wouldn't cost anything in the implementation. Suggested by Roberto
+ Bagnara.
+<li> <code>mpf_get_ld</code>, <code>mpf_set_ld</code>: Conversions between
+ <code>mpf_t</code> and <code>long double</code>, suggested by Dan
+ Christensen. Other <code>long double</code> routines might be desirable
+ too, but <code>mpf</code> would be a start.
+ <br>
+ <code>long double</code> is an ANSI-ism, so everything involving it would
+ need to be suppressed on a K&R compiler.
+ <br>
+ There'd be some work to be done by <code>configure</code> to recognise
+ the format in use, MPFR has a start on this. Often <code>long
+ double</code> is the same as <code>double</code>, which is easy but
+ pretty pointless. A single float format detector macro could look at
+ <code>double</code> then <code>long double</code>
+ <br>
+ Sometimes there's a compiler option for the size of a <code>long
+ double</code>, eg. xlc on AIX can use either 64-bit or 128-bit. It's
+ probably simplest to regard this as a compiler compatibility issue, and
+ leave it to users or sysadmins to ensure application and library code is
+ built the same.
+<li> <code>mpz_sqrt_if_perfect_square</code>: When
+ <code>mpz_perfect_square_p</code> does its tests it calculates a square
+ root and then discards it. For some applications it might be useful to
+ return that root. Suggested by Jason Moxham.
+<li> <code>mpz_get_ull</code>, <code>mpz_set_ull</code>,
+ <code>mpz_get_sll</code>, <code>mpz_get_sll</code>: Conversions for
+ <code>long long</code>. These would aid interoperability, though a
+ mixture of GMP and <code>long long</code> would probably not be too
+ common. Since <code>long long</code> is not always available (it's in
+ C99 and GCC though), disadvantages of using <code>long long</code> in
+ libgmp.a would be
+ <ul>
+ <li> Library contents vary according to the build compiler.
+ <li> gmp.h would need an ugly <code>#ifdef</code> block to decide if the
+ application compiler could take the <code>long long</code>
+ prototypes.
+ <li> Some sort of <code>LIBGMP_HAS_LONGLONG</code> might be wanted to
+ indicate whether the functions are available. (Applications using
+ autoconf could probe the library too.)
+ </ul>
+ It'd be possible to defer the need for <code>long long</code> to
+ application compile time, by having something like
+ <code>mpz_set_2ui</code> called with two halves of a <code>long
+ long</code>. Disadvantages of this would be,
+ <ul>
+ <li> Bigger code in the application, though perhaps not if a <code>long
+ long</code> is normally passed as two halves anyway.
+ <li> <code>mpz_get_ull</code> would be a rather big inline, or would have
+ to be two function calls.
+ <li> <code>mpz_get_sll</code> would be a worse inline, and would put the
+ treatment of <code>-0x10..00</code> into applications (see
+ <code>mpz_get_si</code> correctness above).
+ <li> Although having libgmp.a independent of the build compiler is nice,
+ it sort of sacrifices the capabilities of a good compiler to
+ uniformity with inferior ones.
+ </ul>
+ Plain use of <code>long long</code> is probably the lesser evil, if only
+ because it makes best use of gcc. In fact perhaps it would suffice to
+ guarantee <code>long long</code> conversions only when using GCC for both
+ application and library. That would cover free software, and we can
+ worry about selected vendor compilers later.
+ <br>
+ In C++ the situation is probably clearer, we demand fairly recent C++ so
+ <code>long long</code> should be available always. We'd probably prefer
+ to have the C and C++ the same in respect of <code>long long</code>
+ support, but it would be possible to have it unconditionally in gmpxx.h,
+ by some means or another.
+<li> <code>mpz_strtoz</code> parsing the same as <code>strtol</code>.
+ Suggested by Alexander Kruppa.
+</ul>
+
+
+<h4>Configuration</h4>
+
+<ul>
+<li> Alpha ev7, ev79: Add code to config.guess to detect these. Believe ev7
+ will be "3-1307" in the current switch, but need to verify that. (On
+ OSF, current configfsf.guess identifies ev7 using psrinfo, we need to do
+ it ourselves for other systems.)
+<li> Alpha OSF: Libtool (version 1.5) doesn't seem to recognise this system is
+ "pic always" and ends up running gcc twice with the same options. This
+ is wasteful, but harmless. Perhaps a newer libtool will be better.
+<li> ARM: <code>umul_ppmm</code> in longlong.h always uses <code>umull</code>,
+ but is that available only for M series chips or some such? Perhaps it
+ should be configured in some way.
+<li> HPPA: config.guess should recognize 7000, 7100, 7200, and 8x00.
+<li> HPPA: gcc 3.2 introduces a <code>-mschedule=7200</code> etc parameter,
+ which could be driven by an exact hppa cpu type.
+<li> Mips: config.guess should say mipsr3000, mipsr4000, mipsr10000, etc.
+ "hinv -c processor" gives lots of information on Irix. Standard
+ config.guess appends "el" to indicate endianness, but
+ <code>AC_C_BIGENDIAN</code> seems the best way to handle that for GMP.
+<li> PowerPC: The function descriptor nonsense for AIX is currently driven by
+ <code>*-*-aix*</code>. It might be more reliable to do some sort of
+ feature test, examining the compiler output perhaps. It might also be
+ nice to merge the aix.m4 files into powerpc-defs.m4.
+<li> config.m4 is generated only by the configure script, it won't be
+ regenerated by config.status. Creating it as an <code>AC_OUTPUT</code>
+ would work, but it might upset "make" to have things like <code>L$</code>
+ get into the Makefiles through <code>AC_SUBST</code>.
+ <code>AC_CONFIG_COMMANDS</code> would be the alternative. With some
+ careful m4 quoting the <code>changequote</code> calls might not be
+ needed, which might free up the order in which things had to be output.
+<li> Automake: Latest automake has a <code>CCAS</code>, <code>CCASFLAGS</code>
+ scheme. Though we probably wouldn't be using its assembler support we
+ could try to use those variables in compatible ways.
+<li> <code>GMP_LDFLAGS</code> could probably be done with plain
+ <code>LDFLAGS</code> already used by automake for all linking. But with
+ a bit of luck the next libtool will pass pretty much all
+ <code>CFLAGS</code> through to the compiler when linking, making
+ <code>GMP_LDFLAGS</code> unnecessary.
+<li> mpn/Makeasm.am uses <code>-c</code> and <code>-o</code> together in the
+ .S and .asm rules, but apparently that isn't completely portable (there's
+ an autoconf <code>AC_PROG_CC_C_O</code> test for it). So far we've not
+ had problems, but perhaps the rules could be rewritten to use "foo.s" as
+ the temporary, or to do a suitable "mv" of the result. The only danger
+ from using foo.s would be if a compile failed and the temporary foo.s
+ then looked like the primary source. Hopefully if the
+ <code>SUFFIXES</code> are ordered to have .S and .asm ahead of .s that
+ wouldn't happen. Might need to check.
+</ul>
+
+
+<h4>Random Numbers</h4>
+<ul>
+<li> <code>_gmp_rand</code> is not particularly fast on the linear
+ congruential algorithm and could stand various improvements.
+ <ul>
+ <li> Make a second seed area within <code>gmp_randstate_t</code> (or
+ <code>_mp_algdata</code> rather) to save some copying.
+ <li> Make a special case for a single limb <code>2exp</code> modulus, to
+ avoid <code>mpn_mul</code> calls. Perhaps the same for two limbs.
+ <li> Inline the <code>lc</code> code, to avoid a function call and
+ <code>TMP_ALLOC</code> for every chunk.
+ <li> Perhaps the <code>2exp</code> and general LC cases should be split,
+ for clarity (if the general case is retained).
+ </ul>
+<li> <code>gmp_randstate_t</code> used for parameters perhaps should become
+ <code>gmp_randstate_ptr</code> the same as other types.
+<li> Some of the empirical randomness tests could be included in a "make
+ check". They ought to work everywhere, for a given seed at least.
+</ul>
+
+
+<h4>C++</h4>
+<ul>
+<li> <code>mpz_class(string)</code>, etc: Use the C++ global locale to
+ identify whitespace.
+ <br>
+ <code>mpf_class(string)</code>: Use the C++ global locale decimal point,
+ rather than the C one.
+ <br>
+ Consider making these variant <code>mpz_set_str</code> etc forms
+ available for <code>mpz_t</code> too, not just <code>mpz_class</code>
+ etc.
+<li> <code>mpq_class operator+=</code>: Don't emit an unnecssary
+ <code>mpq_set(q,q)</code> before <code>mpz_addmul</code> etc.
+<li> Put various bits of gmpxx.h into libgmpxx, to avoid excessive inlining.
+ Candidates for this would be,
+ <ul>
+ <li> <code>mpz_class(const char *)</code>, etc: since they're normally
+ not fast anyway, and we can hide the exception <code>throw</code>.
+ <li> <code>mpz_class(string)</code>, etc: to hide the <code>cstr</code>
+ needed to get to the C conversion function.
+ <li> <code>mpz_class string, char*</code> etc constructors: likewise to
+ hide the throws and conversions.
+ <li> <code>mpz_class::get_str</code>, etc: to hide the <code>char*</code>
+ to <code>string</code> conversion and free. Perhaps
+ <code>mpz_get_str</code> can write directly into a
+ <code>string</code>, to avoid copying.
+ <br>
+ Consider making such <code>string</code> returning variants
+ available for use with plain <code>mpz_t</code> etc too.
+ </ul>
+</ul>
+
+<h4>Miscellaneous</h4>
+<ul>
+<li> <code>mpz_gcdext</code> and <code>mpn_gcdext</code> ought to document
+ what range of values the generated cofactors can take, and preferably
+ ensure the definition uniquely specifies the cofactors for given inputs.
+ A basic extended Euclidean algorithm or multi-step variant leads to
+ |x|<|b| and |y|<|a| or something like that, but there's probably
+ two solutions under just those restrictions.
+<li> demos/factorize.c: use <code>mpz_divisible_ui_p</code> rather than
+ <code>mpz_tdiv_qr_ui</code>. (Of course dividing multiple primes at a
+ time would be better still.)
+<li> The various test programs use quite a bit of the main
+ <code>libgmp</code>. This establishes good cross-checks, but it might be
+ better to use simple reference routines where possible. Where it's not
+ possible some attention could be paid to the order of the tests, so a
+ <code>libgmp</code> routine is only used for tests once it seems to be
+ good.
+<li> <code>MUL_FFT_THRESHOLD</code> etc: the FFT thresholds should allow a
+ return to a previous k at certain sizes. This arises basically due to
+ the step effect caused by size multiples effectively used for each k.
+ Looking at a graph makes it fairly clear.
+<li> <code>__gmp_doprnt_mpf</code> does a rather unattractive round-to-nearest
+ on the string returned by <code>mpf_get_str</code>. Perhaps some variant
+ of <code>mpf_get_str</code> could be made which would better suit.
+</ul>
+
+
+<h4>Aids to Development</h4>
+<ul>
+<li> Add <code>ASSERT</code>s at the start of each user-visible mpz/mpq/mpf
+ function to check the validity of each <code>mp?_t</code> parameter, in
+ particular to check they've been <code>mp?_init</code>ed. This might
+ catch elementary mistakes in user programs. Care would need to be taken
+ over <code>MPZ_TMP_INIT</code>ed variables used internally. If nothing
+ else then consistency checks like size<=alloc, ptr not
+ <code>NULL</code> and ptr+size not wrapping around the address space,
+ would be possible. A more sophisticated scheme could track
+ <code>_mp_d</code> pointers and ensure only a valid one is used. Such a
+ scheme probably wouldn't be reentrant, not without some help from the
+ system.
+<li> tune/time.c could try to determine at runtime whether
+ <code>getrusage</code> and <code>gettimeofday</code> are reliable.
+ Currently we pretend in configure that the dodgy m68k netbsd 1.4.1
+ <code>getrusage</code> doesn't exist. If a test might take a long time
+ to run then perhaps cache the result in a file somewhere.
+<li> tune/time.c could choose the default precision based on the
+ <code>speed_unittime</code> determined, independent of the method in use.
+<li> Cray vector systems: CPU frequency could be determined from
+ <code>sysconf(_SC_CLK_TCK)</code>, since it seems to be clock cycle
+ based. Is this true for all Cray systems? Would like some documentation
+ or something to confirm.
+</ul>
+
+
+<h4>Documentation</h4>
+<ul>
+<li> <code>mpz_inp_str</code> (etc) doesn't say when it stops reading digits.
+<li> <code>mpn_get_str</code> isn't terribly clear about how many digits it
+ produces. It'd probably be possible to say at most one leading zero,
+ which is what both it and <code>mpz_get_str</code> currently do. But
+ want to be careful not to bind ourselves to something that might not suit
+ another implementation.
+<li> <code>va_arg</code> doesn't do the right thing with <code>mpz_t</code>
+ etc directly, but instead needs a pointer type like <code>MP_INT*</code>.
+ It'd be good to show how to do this, but we'd either need to document
+ <code>mpz_ptr</code> and friends, or perhaps fallback on something
+ slightly nasty with <code>void*</code>.
+</ul>
+
+
+<h4>Bright Ideas</h4>
+
+<p> The following may or may not be feasible, and aren't likely to get done in the
+near future, but are at least worth thinking about.
+
+<ul>
+<li> Reorganize longlong.h so that we can inline the operations even for the
+ system compiler. When there is no such compiler feature, make calls to
+ stub functions. Write such stub functions for as many machines as
+ possible.
+<li> longlong.h could declare when it's using, or would like to use,
+ <code>mpn_umul_ppmm</code>, and the corresponding umul.asm file could be
+ included in libgmp only in that case, the same as is effectively done for
+ <code>__clz_tab</code>. Likewise udiv.asm and perhaps cntlz.asm. This
+ would only be a very small space saving, so perhaps not worth the
+ complexity.
+<li> longlong.h could be built at configure time by concatenating or
+ #including fragments from each directory in the mpn path. This would
+ select CPU specific macros the same way as CPU specific assembler code.
+ Code used would no longer depend on cpp predefines, and the current
+ nested conditionals could be flattened out.
+<li> <code>mpz_get_si</code> returns 0x80000000 for -0x100000000, whereas it's
+ sort of supposed to return the low 31 (or 63) bits. But this is
+ undocumented, and perhaps not too important.
+<li> <code>mpz_init_set*</code> and <code>mpz_realloc</code> could allocate
+ say an extra 16 limbs over what's needed, so as to reduce the chance of
+ having to do a reallocate if the <code>mpz_t</code> grows a bit more.
+ This could only be an option, since it'd badly bloat memory usage in
+ applications using many small values.
+<li> <code>mpq</code> functions could perhaps check for numerator or
+ denominator equal to 1, on the assumption that integers or
+ denominator-only values might be expected to occur reasonably often.
+<li> <code>count_trailing_zeros</code> is used on more or less uniformly
+ distributed numbers in a couple of places. For some CPUs
+ <code>count_trailing_zeros</code> is slow and it's probably worth handling
+ the frequently occurring 0 to 2 trailing zeros cases specially.
+<li> <code>mpf_t</code> might like to let the exponent be undefined when
+ size==0, instead of requiring it 0 as now. It should be possible to do
+ size==0 tests before paying attention to the exponent. The advantage is
+ not needing to set exp in the various places a zero result can arise,
+ which avoids some tedium but is otherwise perhaps not too important.
+ Currently <code>mpz_set_f</code> and <code>mpf_cmp_ui</code> depend on
+ exp==0, maybe elsewhere too.
+<li> <code>__gmp_allocate_func</code>: Could use GCC <code>__attribute__
+ ((malloc))</code> on this, though don't know if it'd do much. GCC 3.0
+ allows that attribute on functions, but not function pointers (see info
+ node "Attribute Syntax"), so would need a new autoconf test. This can
+ wait until there's a GCC that supports it.
+<li> <code>mpz_add_ui</code> contains two <code>__GMPN_COPY</code>s, one from
+ <code>mpn_add_1</code> and one from <code>mpn_sub_1</code>. If those two
+ routines were opened up a bit maybe that code could be shared. When a
+ copy needs to be done there's no carry to append for the add, and if the
+ copy is non-empty no high zero for the sub.
+</ul>
+
+
+<h4>Old and Obsolete Stuff</h4>
+
+<p> The following tasks apply to chips or systems that are old and/or obsolete.
+It's unlikely anything will be done about them unless anyone is actively using
+them.
+
+<ul>
+<li> Sparc32: The integer based udiv_nfp.asm used to be selected by
+ <code>configure --nfp</code> but that option is gone now that autoconf is
+ used. The file could go somewhere suitable in the mpn search if any
+ chips might benefit from it, though it's possible we don't currently
+ differentiate enough exact cpu types to do this properly.
+<li> VAX D and G format <code>double</code> floats are straightforward and
+ could perhaps be handled directly in <code>__gmp_extract_double</code>
+ and maybe in <code>mpn_get_d</code>, rather than falling back on the
+ generic code. (Both formats are detected by <code>configure</code>.)
+</ul>
+
+
+<hr>
+
+</body>
+</html>
+
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+time-stamp-line-limit: 50
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