gcc/gmp/doc/tasks.html - Issue 3050029: [gcc] GCC 4.5.0=>4.5.1

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Issue 3050029: [gcc] GCC 4.5.0=>4.5.1 (Closed) Base URL: ssh://git@gitrw.chromium.org:9222/nacl-toolchain.git

Patch Set: Created 10 years, 5 months ago

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-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

-<html>

-<head>

- <title>GMP Itemized Development Tasks</title>

- <link rel="shortcut icon" href="favicon.ico">

- <link rel="stylesheet" href="gmp.css">

- <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">

-</head>

-<center>

- <h1>

- GMP Itemized Development Tasks

- </h1>

-</center>

-<font size=-1>

-<pre>

-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>

-

- 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> &lt= 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 &gt&gt 32) == 0) { x &lt&lt= 32; cnt += 32; }

- if ((x &gt&gt 48) == 0) { x &lt&lt= 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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