1<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> 2<html> 3<head> 4 <title>GMP Itemized Development Tasks</title> 5 <link rel="shortcut icon" href="favicon.ico"> 6 <link rel="stylesheet" href="gmp.css"> 7 <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> 8</head> 9 10<center> 11 <h1> 12 GMP Itemized Development Tasks 13 </h1> 14</center> 15 16<font size=-1> 17<pre> 18Copyright 2000-2004, 2006, 2008, 2009 Free Software Foundation, Inc. 19 20This file is part of the GNU MP Library. 21 22The GNU MP Library is free software; you can redistribute it and/or modify 23it under the terms of either: 24 25 * the GNU Lesser General Public License as published by the Free 26 Software Foundation; either version 3 of the License, or (at your 27 option) any later version. 28 29or 30 31 * the GNU General Public License as published by the Free Software 32 Foundation; either version 2 of the License, or (at your option) any 33 later version. 34 35or both in parallel, as here. 36 37The GNU MP Library is distributed in the hope that it will be useful, but 38WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 39or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 40for more details. 41 42You should have received copies of the GNU General Public License and the 43GNU Lesser General Public License along with the GNU MP Library. If not, 44see https://www.gnu.org/licenses/. 45</pre> 46</font> 47 48<hr> 49<!-- NB. timestamp updated automatically by emacs --> 50 This file current as of 29 Jan 2014. An up-to-date version is available at 51 <a href="https://gmplib.org/tasks.html">https://gmplib.org/tasks.html</a>. 52 Please send comments about this page to gmp-devel<font>@</font>gmplib.org. 53 54<p> These are itemized GMP development tasks. Not all the tasks 55 listed here are suitable for volunteers, but many of them are. 56 Please see the <a href="projects.html">projects file</a> for more 57 sizeable projects. 58 59<p> CAUTION: This file needs updating. Many of the tasks here have 60either already been taken care of, or have become irrelevant. 61 62<h4>Correctness and Completeness</h4> 63<ul> 64<li> <code>_LONG_LONG_LIMB</code> in gmp.h is not namespace clean. Reported 65 by Patrick Pelissier. 66 <br> 67 We sort of mentioned <code>_LONG_LONG_LIMB</code> in past releases, so 68 need to be careful about changing it. It used to be a define 69 applications had to set for long long limb systems, but that in 70 particular is no longer relevant now that it's established automatically. 71<li> The various reuse.c tests need to force reallocation by calling 72 <code>_mpz_realloc</code> with a small (1 limb) size. 73<li> One reuse case is missing from mpX/tests/reuse.c: 74 <code>mpz_XXX(a,a,a)</code>. 75<li> Make the string reading functions allow the `0x' prefix when the base is 76 explicitly 16. They currently only allow that prefix when the base is 77 unspecified (zero). 78<li> <code>mpf_eq</code> is not always correct, when one operand is 79 1000000000... and the other operand is 0111111111..., i.e., extremely 80 close. There is a special case in <code>mpf_sub</code> for this 81 situation; put similar code in <code>mpf_eq</code>. [In progress.] 82<li> <code>mpf_eq</code> doesn't implement what gmp.texi specifies. It should 83 not use just whole limbs, but partial limbs. [In progress.] 84<li> <code>mpf_set_str</code> doesn't validate it's exponent, for instance 85 garbage 123.456eX789X is accepted (and an exponent 0 used), and overflow 86 of a <code>long</code> is not detected. 87<li> <code>mpf_add</code> doesn't check for a carry from truncated portions of 88 the inputs, and in that respect doesn't implement the "infinite precision 89 followed by truncate" specified in the manual. 90<li> Windows DLLs: tests/mpz/reuse.c and tests/mpf/reuse.c initialize global 91 variables with pointers to <code>mpz_add</code> etc, which doesn't work 92 when those routines are coming from a DLL (because they're effectively 93 function pointer global variables themselves). Need to rearrange perhaps 94 to a set of calls to a test function rather than iterating over an array. 95<li> <code>mpz_pow_ui</code>: Detect when the result would be more memory than 96 a <code>size_t</code> can represent and raise some suitable exception, 97 probably an alloc call asking for <code>SIZE_T_MAX</code>, and if that 98 somehow succeeds then an <code>abort</code>. Various size overflows of 99 this kind are not handled gracefully, probably resulting in segvs. 100 <br> 101 In <code>mpz_n_pow_ui</code>, detect when the count of low zero bits 102 exceeds an <code>unsigned long</code>. There's a (small) chance of this 103 happening but still having enough memory to represent the value. 104 Reported by Winfried Dreckmann in for instance <code>mpz_ui_pow_ui (x, 105 4UL, 1431655766UL)</code>. 106<li> <code>mpf</code>: Detect exponent overflow and raise some exception. 107 It'd be nice to allow the full <code>mp_exp_t</code> range since that's 108 how it's been in the past, but maybe dropping one bit would make it 109 easier to test if e1+e2 goes out of bounds. 110</ul> 111 112 113 114<h4>Machine Independent Optimization</h4> 115<ul> 116<li> <code>mpf_cmp</code>: For better cache locality, don't test for low zero 117 limbs until the high limbs fail to give an ordering. Reduce code size by 118 turning the three <code>mpn_cmp</code>'s into a single loop stopping when 119 the end of one operand is reached (and then looking for a non-zero in the 120 rest of the other). 121<li> <code>mpf_mul_2exp</code>, <code>mpf_div_2exp</code>: The use of 122 <code>mpn_lshift</code> for any size<=prec means repeated 123 <code>mul_2exp</code> and <code>div_2exp</code> calls accumulate low zero 124 limbs until size==prec+1 is reached. Those zeros will slow down 125 subsequent operations, especially if the value is otherwise only small. 126 If low bits of the low limb are zero, use <code>mpn_rshift</code> so as 127 to not increase the size. 128<li> <code>mpn_dc_sqrtrem</code>, <code>mpn_sqrtrem2</code>: Don't use 129 <code>mpn_add_1</code> and <code>mpn_sub_1</code> for 1 limb operations, 130 instead <code>ADDC_LIMB</code> and <code>SUBC_LIMB</code>. 131<li> <code>mpn_sqrtrem2</code>: Use plain variables for <code>sp[0]</code> and 132 <code>rp[0]</code> calculations, so the compiler needn't worry about 133 aliasing between <code>sp</code> and <code>rp</code>. 134<li> <code>mpn_sqrtrem</code>: Some work can be saved in the last step when 135 the remainder is not required, as noted in Paul's paper. 136<li> <code>mpq_add</code>, <code>mpq_sub</code>: The gcd fits a single limb 137 with high probability and in this case <code>binvert_limb</code> could 138 be used to calculate the inverse just once for the two exact divisions 139 "op1.den / gcd" and "op2.den / gcd", rather than letting 140 <code>mpn_bdiv_q_1</code> do it each time. This would require calling 141 <code>mpn_pi1_bdiv_q_1</code>. 142<li> <code>mpn_gcdext</code>: Don't test <code>count_leading_zeros</code> for 143 zero, instead check the high bit of the operand and avoid invoking 144 <code>count_leading_zeros</code>. This is an optimization on all 145 machines, and significant on machines with slow 146 <code>count_leading_zeros</code>, though it's possible an already 147 normalized operand might not be encountered very often. 148<li> Rewrite <code>umul_ppmm</code> to use floating-point for generating the 149 most significant limb (if <code>GMP_LIMB_BITS</code> <= 52 bits). 150 (Peter Montgomery has some ideas on this subject.) 151<li> Improve the default <code>umul_ppmm</code> code in longlong.h: Add partial 152 products with fewer operations. 153<li> Consider inlining <code>mpz_set_ui</code>. This would be both small and 154 fast, especially for compile-time constants, but would make application 155 binaries depend on having 1 limb allocated to an <code>mpz_t</code>, 156 preventing the "lazy" allocation scheme below. 157<li> Consider inlining <code>mpz_[cft]div_ui</code> and maybe 158 <code>mpz_[cft]div_r_ui</code>. A <code>__gmp_divide_by_zero</code> 159 would be needed for the divide by zero test, unless that could be left to 160 <code>mpn_mod_1</code> (not sure currently whether all the risc chips 161 provoke the right exception there if using mul-by-inverse). 162<li> Consider inlining: <code>mpz_fits_s*_p</code>. The setups for 163 <code>LONG_MAX</code> etc would need to go into gmp.h, and on Cray it 164 might, unfortunately, be necessary to forcibly include <limits.h> 165 since there's no apparent way to get <code>SHRT_MAX</code> with an 166 expression (since <code>short</code> and <code>unsigned short</code> can 167 be different sizes). 168<li> <code>mpz_powm</code> and <code>mpz_powm_ui</code> aren't very fast on one 169 or two limb moduli, due to a lot of function call overheads. These could 170 perhaps be handled as special cases. 171<li> Make sure <code>mpz_powm_ui</code> is never slower than the corresponding 172 computation using <code>mpz_powm</code>. 173<li> <code>mpz_powm</code> REDC should do multiplications by <code>g[]</code> 174 using the division method when they're small, since the REDC form of a 175 small multiplier is normally a full size product. Probably would need a 176 new tuned parameter to say what size multiplier is "small", as a function 177 of the size of the modulus. 178<li> <code>mpn_gcd</code> might be able to be sped up on small to moderate 179 sizes by improving <code>find_a</code>, possibly just by providing an 180 alternate implementation for CPUs with slowish 181 <code>count_leading_zeros</code>. 182<li> <code>mpf_set_str</code> produces low zero limbs when a string has a 183 fraction but is exactly representable, eg. 0.5 in decimal. These could be 184 stripped to save work in later operations. 185<li> <code>mpz_and</code>, <code>mpz_ior</code> and <code>mpz_xor</code> should 186 use <code>mpn_and_n</code> etc for the benefit of the small number of 187 targets with native versions of those routines. Need to be careful not to 188 pass size==0. Is some code sharing possible between the <code>mpz</code> 189 routines? 190<li> <code>mpf_add</code>: Don't do a copy to avoid overlapping operands 191 unless it's really necessary (currently only sizes are tested, not 192 whether r really is u or v). 193<li> <code>mpf_add</code>: Under the check for v having no effect on the 194 result, perhaps test for r==u and do nothing in that case, rather than 195 currently it looks like an <code>MPN_COPY_INCR</code> will be done to 196 reduce prec+1 limbs to prec. 197<li> <code>mpf_div_ui</code>: Instead of padding with low zeros, call 198 <code>mpn_divrem_1</code> asking for fractional quotient limbs. 199<li> <code>mpf_div_ui</code>: Eliminate <code>TMP_ALLOC</code>. When r!=u 200 there's no overlap and the division can be called on those operands. 201 When r==u and is prec+1 limbs, then it's an in-place division. If r==u 202 and not prec+1 limbs, then move the available limbs up to prec+1 and do 203 an in-place there. 204<li> <code>mpf_div_ui</code>: Whether the high quotient limb is zero can be 205 determined by testing the dividend for high<divisor. When non-zero, the 206 division can be done on prec dividend limbs instead of prec+1. The result 207 size is also known before the division, so that can be a tail call (once 208 the <code>TMP_ALLOC</code> is eliminated). 209<li> <code>mpn_divrem_2</code> could usefully accept unnormalized divisors and 210 shift the dividend on-the-fly, since this should cost nothing on 211 superscalar processors and avoid the need for temporary copying in 212 <code>mpn_tdiv_qr</code>. 213<li> <code>mpf_sqrt</code>: If r!=u, and if u doesn't need to be padded with 214 zeros, then there's no need for the tp temporary. 215<li> <code>mpq_cmp_ui</code> could form the <code>num1*den2</code> and 216 <code>num2*den1</code> products limb-by-limb from high to low and look at 217 each step for values differing by more than the possible carry bit from 218 the uncalculated portion. 219<li> <code>mpq_cmp</code> could do the same high-to-low progressive multiply 220 and compare. The benefits of karatsuba and higher multiplication 221 algorithms are lost, but if it's assumed only a few high limbs will be 222 needed to determine an order then that's fine. 223<li> <code>mpn_add_1</code>, <code>mpn_sub_1</code>, <code>mpn_add</code>, 224 <code>mpn_sub</code>: Internally use <code>__GMPN_ADD_1</code> etc 225 instead of the functions, so they get inlined on all compilers, not just 226 gcc and others with <code>inline</code> recognised in gmp.h. 227 <code>__GMPN_ADD_1</code> etc are meant mostly to support application 228 inline <code>mpn_add_1</code> etc and if they don't come out good for 229 internal uses then special forms can be introduced, for instance many 230 internal uses are in-place. Sometimes a block of code is executed based 231 on the carry-out, rather than using it arithmetically, and those places 232 might want to do their own loops entirely. 233<li> <code>__gmp_extract_double</code> on 64-bit systems could use just one 234 bitfield for the mantissa extraction, not two, when endianness permits. 235 Might depend on the compiler allowing <code>long long</code> bit fields 236 when that's the only actual 64-bit type. 237<li> tal-notreent.c could keep a block of memory permanently allocated. 238 Currently the last nested <code>TMP_FREE</code> releases all memory, so 239 there's an allocate and free every time a top-level function using 240 <code>TMP</code> is called. Would need 241 <code>mp_set_memory_functions</code> to tell tal-notreent.c to release 242 any cached memory when changing allocation functions though. 243<li> <code>__gmp_tmp_alloc</code> from tal-notreent.c could be partially 244 inlined. If the current chunk has enough room then a couple of pointers 245 can be updated. Only if more space is required then a call to some sort 246 of <code>__gmp_tmp_increase</code> would be needed. The requirement that 247 <code>TMP_ALLOC</code> is an expression might make the implementation a 248 bit ugly and/or a bit sub-optimal. 249<pre> 250#define TMP_ALLOC(n) 251 ((ROUND_UP(n) > current->end - current->point ? 252 __gmp_tmp_increase (ROUND_UP (n)) : 0), 253 current->point += ROUND_UP (n), 254 current->point - ROUND_UP (n)) 255</pre> 256<li> <code>__mp_bases</code> has a lot of data for bases which are pretty much 257 never used. Perhaps the table should just go up to base 16, and have 258 code to generate data above that, if and when required. Naturally this 259 assumes the code would be smaller than the data saved. 260<li> <code>__mp_bases</code> field <code>big_base_inverted</code> is only used 261 if <code>USE_PREINV_DIVREM_1</code> is true, and could be omitted 262 otherwise, to save space. 263<li> <code>mpz_get_str</code>, <code>mtox</code>: For power-of-2 bases, which 264 are of course fast, it seems a little silly to make a second pass over 265 the <code>mpn_get_str</code> output to convert to ASCII. Perhaps combine 266 that with the bit extractions. 267<li> <code>mpz_gcdext</code>: If the caller requests only the S cofactor (of 268 A), and A<B, then the code ends up generating the cofactor T (of B) and 269 deriving S from that. Perhaps it'd be possible to arrange to get S in 270 the first place by calling <code>mpn_gcdext</code> with A+B,B. This 271 might only be an advantage if A and B are about the same size. 272<li> <code>mpz_n_pow_ui</code> does a good job with small bases and stripping 273 powers of 2, but it's perhaps a bit too complicated for what it gains. 274 The simpler <code>mpn_pow_1</code> is a little faster on small exponents. 275 (Note some of the ugliness in <code>mpz_n_pow_ui</code> is due to 276 supporting <code>mpn_mul_2</code>.) 277 <br> 278 Perhaps the stripping of 2s in <code>mpz_n_pow_ui</code> should be 279 confined to single limb operands for simplicity and since that's where 280 the greatest gain would be. 281 <br> 282 Ideally <code>mpn_pow_1</code> and <code>mpz_n_pow_ui</code> would be 283 merged. The reason <code>mpz_n_pow_ui</code> writes to an 284 <code>mpz_t</code> is that its callers leave it to make a good estimate 285 of the result size. Callers of <code>mpn_pow_1</code> already know the 286 size by separate means (<code>mp_bases</code>). 287<li> <code>mpz_invert</code> should call <code>mpn_gcdext</code> directly. 288</ul> 289 290 291<h4>Machine Dependent Optimization</h4> 292<ul> 293<li> <code>invert_limb</code> on various processors might benefit from the 294 little Newton iteration done for alpha and ia64. 295<li> Alpha 21264: <code>mpn_addlsh1_n</code> could be implemented with 296 <code>mpn_addmul_1</code>, since that code at 3.5 is a touch faster than 297 a separate <code>lshift</code> and <code>add_n</code> at 298 1.75+2.125=3.875. Or very likely some specific <code>addlsh1_n</code> 299 code could beat both. 300<li> Alpha 21264: Improve feed-in code for <code>mpn_mul_1</code>, 301 <code>mpn_addmul_1</code>, and <code>mpn_submul_1</code>. 302<li> Alpha 21164: Rewrite <code>mpn_mul_1</code>, <code>mpn_addmul_1</code>, 303 and <code>mpn_submul_1</code> for the 21164. This should use both integer 304 multiplies and floating-point multiplies. For the floating-point 305 operations, the single-limb multiplier should be split into three 21-bit 306 chunks, or perhaps even better in four 16-bit chunks. Probably possible 307 to reach 9 cycles/limb. 308<li> Alpha: GCC 3.4 will introduce <code>__builtin_ctzl</code>, 309 <code>__builtin_clzl</code> and <code>__builtin_popcountl</code> using 310 the corresponding CIX <code>ct</code> instructions, and 311 <code>__builtin_alpha_cmpbge</code>. These should give GCC more 312 information about scheduling etc than the <code>asm</code> blocks 313 currently used in longlong.h and gmp-impl.h. 314<li> Alpha Unicos: Apparently there's no <code>alloca</code> on this system, 315 making <code>configure</code> choose the slower 316 <code>malloc-reentrant</code> allocation method. Is there a better way? 317 Maybe variable-length arrays per notes below. 318<li> Alpha Unicos 21164, 21264: <code>.align</code> is not used since it pads 319 with garbage. Does the code get the intended slotting required for the 320 claimed speeds? <code>.align</code> at the start of a function would 321 presumably be safe no matter how it pads. 322<li> ARM V5: <code>count_leading_zeros</code> can use the <code>clz</code> 323 instruction. For GCC 3.4 and up, do this via <code>__builtin_clzl</code> 324 since then gcc knows it's "predicable". 325<li> Itanium: GCC 3.4 introduces <code>__builtin_popcount</code> which can be 326 used instead of an <code>asm</code> block. The builtin should give gcc 327 more opportunities for scheduling, bundling and predication. 328 <code>__builtin_ctz</code> similarly (it just uses popcount as per 329 current longlong.h). 330<li> UltraSPARC/64: Optimize <code>mpn_mul_1</code>, <code>mpn_addmul_1</code>, 331 for s2 < 2^32 (or perhaps for any zero 16-bit s2 chunk). Not sure how 332 much this can improve the speed, though, since the symmetry that we rely 333 on is lost. Perhaps we can just gain cycles when s2 < 2^16, or more 334 accurately, when two 16-bit s2 chunks which are 16 bits apart are zero. 335<li> UltraSPARC/64: Write native <code>mpn_submul_1</code>, analogous to 336 <code>mpn_addmul_1</code>. 337<li> UltraSPARC/64: Write <code>umul_ppmm</code>. Using four 338 "<code>mulx</code>"s either with an asm block or via the generic C code is 339 about 90 cycles. Try using fp operations, and also try using karatsuba 340 for just three "<code>mulx</code>"s. 341<li> UltraSPARC/32: Rewrite <code>mpn_lshift</code>, <code>mpn_rshift</code>. 342 Will give 2 cycles/limb. Trivial modifications of mpn/sparc64 should do. 343<li> UltraSPARC/32: Write special mpn_Xmul_1 loops for s2 < 2^16. 344<li> UltraSPARC/32: Use <code>mulx</code> for <code>umul_ppmm</code> if 345 possible (see commented out code in longlong.h). This is unlikely to 346 save more than a couple of cycles, so perhaps isn't worth bothering with. 347<li> UltraSPARC/32: On Solaris gcc doesn't give us <code>__sparc_v9__</code> 348 or anything to indicate V9 support when -mcpu=v9 is selected. See 349 gcc/config/sol2-sld-64.h. Will need to pass something through from 350 ./configure to select the right code in longlong.h. (Currently nothing 351 is lost because <code>mulx</code> for multiplying is commented out.) 352<li> UltraSPARC/32: <code>mpn_divexact_1</code> and 353 <code>mpn_modexact_1c_odd</code> can use a 64-bit inverse and take 354 64-bits at a time from the dividend, as per the 32-bit divisor case in 355 mpn/sparc64/mode1o.c. This must be done in assembler, since the full 356 64-bit registers (<code>%gN</code>) are not available from C. 357<li> UltraSPARC/32: <code>mpn_divexact_by3c</code> can work 64-bits at a time 358 using <code>mulx</code>, in assembler. This would be the same as for 359 sparc64. 360<li> UltraSPARC: <code>binvert_limb</code> might save a few cycles from 361 masking down to just the useful bits at each point in the calculation, 362 since <code>mulx</code> speed depends on the highest bit set. Either 363 explicit masks or small types like <code>short</code> and 364 <code>int</code> ought to work. 365<li> Sparc64 HAL R1 <code>popc</code>: This chip reputedly implements 366 <code>popc</code> properly (see gcc sparc.md). Would need to recognise 367 it as <code>sparchalr1</code> or something in configure / config.sub / 368 config.guess. <code>popc_limb</code> in gmp-impl.h could use this (per 369 commented out code). <code>count_trailing_zeros</code> could use it too. 370<li> PA64: Improve <code>mpn_addmul_1</code>, <code>mpn_submul_1</code>, and 371 <code>mpn_mul_1</code>. The current code runs at 11 cycles/limb. It 372 should be possible to saturate the cache, which will happen at 8 373 cycles/limb (7.5 for mpn_mul_1). Write special loops for s2 < 2^32; 374 it should be possible to make them run at about 5 cycles/limb. 375<li> PPC601: See which of the power or powerpc32 code runs better. Currently 376 the powerpc32 is used, but only because it's the default for 377 <code>powerpc*</code>. 378<li> PPC630: Rewrite <code>mpn_addmul_1</code>, <code>mpn_submul_1</code>, and 379 <code>mpn_mul_1</code>. Use both integer and floating-point operations, 380 possibly two floating-point and one integer limb per loop. Split operands 381 into four 16-bit chunks for fast fp operations. Should easily reach 9 382 cycles/limb (using one int + one fp), but perhaps even 7 cycles/limb 383 (using one int + two fp). 384<li> PPC630: <code>mpn_rshift</code> could do the same sort of unrolled loop 385 as <code>mpn_lshift</code>. Some judicious use of m4 might let the two 386 share source code, or with a register to control the loop direction 387 perhaps even share object code. 388<li> Implement <code>mpn_mul_basecase</code> and <code>mpn_sqr_basecase</code> 389 for important machines. Helping the generic sqr_basecase.c with an 390 <code>mpn_sqr_diagonal</code> might be enough for some of the RISCs. 391<li> POWER2/POWER2SC: Schedule <code>mpn_lshift</code>/<code>mpn_rshift</code>. 392 Will bring time from 1.75 to 1.25 cycles/limb. 393<li> X86: Optimize non-MMX <code>mpn_lshift</code> for shifts by 1. (See 394 Pentium code.) 395<li> X86: Good authority has it that in the past an inline <code>rep 396 movs</code> would upset GCC register allocation for the whole function. 397 Is this still true in GCC 3? It uses <code>rep movs</code> itself for 398 <code>__builtin_memcpy</code>. Examine the code for some simple and 399 complex functions to find out. Inlining <code>rep movs</code> would be 400 desirable, it'd be both smaller and faster. 401<li> Pentium P54: <code>mpn_lshift</code> and <code>mpn_rshift</code> can come 402 down from 6.0 c/l to 5.5 or 5.375 by paying attention to pairing after 403 <code>shrdl</code> and <code>shldl</code>, see mpn/x86/pentium/README. 404<li> Pentium P55 MMX: <code>mpn_lshift</code> and <code>mpn_rshift</code> 405 might benefit from some destination prefetching. 406<li> PentiumPro: <code>mpn_divrem_1</code> might be able to use a 407 mul-by-inverse, hoping for maybe 30 c/l. 408<li> K7: <code>mpn_lshift</code> and <code>mpn_rshift</code> might be able to 409 do something branch-free for unaligned startups, and shaving one insn 410 from the loop with alternative indexing might save a cycle. 411<li> PPC32: Try using fewer registers in the current <code>mpn_lshift</code>. 412 The pipeline is now extremely deep, perhaps unnecessarily deep. 413<li> Fujitsu VPP: Vectorize main functions, perhaps in assembly language. 414<li> Fujitsu VPP: Write <code>mpn_mul_basecase</code> and 415 <code>mpn_sqr_basecase</code>. This should use a "vertical multiplication 416 method", to avoid carry propagation. splitting one of the operands in 417 11-bit chunks. 418<li> Pentium: <code>mpn_lshift</code> by 31 should use the special rshift 419 by 1 code, and vice versa <code>mpn_rshift</code> by 31 should use the 420 special lshift by 1. This would be best as a jump across to the other 421 routine, could let both live in lshift.asm and omit rshift.asm on finding 422 <code>mpn_rshift</code> already provided. 423<li> Cray T3E: Experiment with optimization options. In particular, 424 -hpipeline3 seems promising. We should at least up -O to -O2 or -O3. 425<li> Cray: <code>mpn_com</code> and <code>mpn_and_n</code> etc very probably 426 wants a pragma like <code>MPN_COPY_INCR</code>. 427<li> Cray vector systems: <code>mpn_lshift</code>, <code>mpn_rshift</code>, 428 <code>mpn_popcount</code> and <code>mpn_hamdist</code> are nice and small 429 and could be inlined to avoid function calls. 430<li> Cray: Variable length arrays seem to be faster than the tal-notreent.c 431 scheme. Not sure why, maybe they merely give the compiler more 432 information about aliasing (or the lack thereof). Would like to modify 433 <code>TMP_ALLOC</code> to use them, or introduce a new scheme. Memory 434 blocks wanted unconditionally are easy enough, those wanted only 435 sometimes are a problem. Perhaps a special size calculation to ask for a 436 dummy length 1 when unwanted, or perhaps an inlined subroutine 437 duplicating code under each conditional. Don't really want to turn 438 everything into a dog's dinner just because Cray don't offer an 439 <code>alloca</code>. 440<li> Cray: <code>mpn_get_str</code> on power-of-2 bases ought to vectorize. 441 Does it? <code>bits_per_digit</code> and the inner loop over bits in a 442 limb might prevent it. Perhaps special cases for binary, octal and hex 443 would be worthwhile (very possibly for all processors too). 444<li> S390: <code>BSWAP_LIMB_FETCH</code> looks like it could be done with 445 <code>lrvg</code>, as per glibc sysdeps/s390/s390-64/bits/byteswap.h. 446 This is only for 64-bit mode or something is it, since 32-bit mode has 447 other code? Also, is it worth using for <code>BSWAP_LIMB</code> too, or 448 would that mean a store and re-fetch? Presumably that's what comes out 449 in glibc. 450<li> Improve <code>count_leading_zeros</code> for 64-bit machines: 451 <pre> 452 if ((x >> 32) == 0) { x <<= 32; cnt += 32; } 453 if ((x >> 48) == 0) { x <<= 16; cnt += 16; } 454 ... </pre> 455<li> IRIX 6 MIPSpro compiler has an <code>__inline</code> which could perhaps 456 be used in <code>__GMP_EXTERN_INLINE</code>. What would be the right way 457 to identify suitable versions of that compiler? 458<li> IRIX <code>cc</code> is rumoured to have an <code>_int_mult_upper</code> 459 (in <code><intrinsics.h></code> like Cray), but it didn't seem to 460 exist on some IRIX 6.5 systems tried. If it does actually exist 461 somewhere it would very likely be an improvement over a function call to 462 umul.asm. 463<li> <code>mpn_get_str</code> final divisions by the base with 464 <code>udiv_qrnd_unnorm</code> could use some sort of multiply-by-inverse 465 on suitable machines. This ends up happening for decimal by presenting 466 the compiler with a run-time constant, but the same for other bases would 467 be good. Perhaps use could be made of the fact base<256. 468<li> <code>mpn_umul_ppmm</code>, <code>mpn_udiv_qrnnd</code>: Return a 469 structure like <code>div_t</code> to avoid going through memory, in 470 particular helping RISCs that don't do store-to-load forwarding. Clearly 471 this is only possible if the ABI returns a structure of two 472 <code>mp_limb_t</code>s in registers. 473 <br> 474 On PowerPC, structures are returned in memory on AIX and Darwin. In SVR4 475 they're returned in registers, except that draft SVR4 had said memory, so 476 it'd be prudent to check which is done. We can jam the compiler into the 477 right mode if we know how, since all this is purely internal to libgmp. 478 (gcc has an option, though of course gcc doesn't matter since we use 479 inline asm there.) 480</ul> 481 482<h4>New Functionality</h4> 483<ul> 484<li> Maybe add <code>mpz_crr</code> (Chinese Remainder Reconstruction). 485<li> Let `0b' and `0B' mean binary input everywhere. 486<li> <code>mpz_init</code> and <code>mpq_init</code> could do lazy allocation. 487 Set <code>ALLOC(var)</code> to 0 to indicate nothing allocated, and let 488 <code>_mpz_realloc</code> do the initial alloc. Set 489 <code>z->_mp_d</code> to a dummy that <code>mpz_get_ui</code> and 490 similar can unconditionally fetch from. Niels Möller has had a go at 491 this. 492 <br> 493 The advantages of the lazy scheme would be: 494 <ul> 495 <li> Initial allocate would be the size required for the first value 496 stored, rather than getting 1 limb in <code>mpz_init</code> and then 497 more or less immediately reallocating. 498 <li> <code>mpz_init</code> would only store magic values in the 499 <code>mpz_t</code> fields, and could be inlined. 500 <li> A fixed initializer could even be used by applications, like 501 <code>mpz_t z = MPZ_INITIALIZER;</code>, which might be convenient 502 for globals. 503 </ul> 504 The advantages of the current scheme are: 505 <ul> 506 <li> <code>mpz_set_ui</code> and other similar routines needn't check the 507 size allocated and can just store unconditionally. 508 <li> <code>mpz_set_ui</code> and perhaps others like 509 <code>mpz_tdiv_r_ui</code> and a prospective 510 <code>mpz_set_ull</code> could be inlined. 511 </ul> 512<li> Add <code>mpf_out_raw</code> and <code>mpf_inp_raw</code>. Make sure 513 format is portable between 32-bit and 64-bit machines, and between 514 little-endian and big-endian machines. A format which MPFR can use too 515 would be good. 516<li> <code>mpn_and_n</code> ... <code>mpn_copyd</code>: Perhaps make the mpn 517 logops and copys available in gmp.h, either as library functions or 518 inlines, with the availability of library functions instantiated in the 519 generated gmp.h at build time. 520<li> <code>mpz_set_str</code> etc variants taking string lengths rather than 521 null-terminators. 522<li> <code>mpz_andn</code>, <code>mpz_iorn</code>, <code>mpz_nand</code>, 523 <code>mpz_nior</code>, <code>mpz_xnor</code> might be useful additions, 524 if they could share code with the current such functions (which should be 525 possible). 526<li> <code>mpz_and_ui</code> etc might be of use sometimes. Suggested by 527 Niels Möller. 528<li> <code>mpf_set_str</code> and <code>mpf_inp_str</code> could usefully 529 accept 0x, 0b etc when base==0. Perhaps the exponent could default to 530 decimal in this case, with a further 0x, 0b etc allowed there. 531 Eg. 0xFFAA@0x5A. A leading "0" for octal would match the integers, but 532 probably something like "0.123" ought not mean octal. 533<li> <code>GMP_LONG_LONG_LIMB</code> or some such could become a documented 534 feature of gmp.h, so applications could know whether to 535 <code>printf</code> a limb using <code>%lu</code> or <code>%Lu</code>. 536<li> <code>GMP_PRIdMP_LIMB</code> and similar defines following C99 537 <inttypes.h> might be of use to applications printing limbs. But 538 if <code>GMP_LONG_LONG_LIMB</code> or whatever is added then perhaps this 539 can easily enough be left to applications. 540<li> <code>gmp_printf</code> could accept <code>%b</code> for binary output. 541 It'd be nice if it worked for plain <code>int</code> etc too, not just 542 <code>mpz_t</code> etc. 543<li> <code>gmp_printf</code> in fact could usefully accept an arbitrary base, 544 for both integer and float conversions. A base either in the format 545 string or as a parameter with <code>*</code> should be allowed. Maybe 546 <code>&13b</code> (b for base) or something like that. 547<li> <code>gmp_printf</code> could perhaps accept <code>mpq_t</code> for float 548 conversions, eg. <code>"%.4Qf"</code>. This would be merely for 549 convenience, but still might be useful. Rounding would be the same as 550 for an <code>mpf_t</code> (ie. currently round-to-nearest, but not 551 actually documented). Alternately, perhaps a separate 552 <code>mpq_get_str_point</code> or some such might be more use. Suggested 553 by Pedro Gimeno. 554<li> <code>mpz_rscan0</code> or <code>mpz_revscan0</code> or some such 555 searching towards the low end of an integer might match 556 <code>mpz_scan0</code> nicely. Likewise for <code>scan1</code>. 557 Suggested by Roberto Bagnara. 558<li> <code>mpz_bit_subset</code> or some such to test whether one integer is a 559 bitwise subset of another might be of use. Some sort of return value 560 indicating whether it's a proper or non-proper subset would be good and 561 wouldn't cost anything in the implementation. Suggested by Roberto 562 Bagnara. 563<li> <code>mpf_get_ld</code>, <code>mpf_set_ld</code>: Conversions between 564 <code>mpf_t</code> and <code>long double</code>, suggested by Dan 565 Christensen. Other <code>long double</code> routines might be desirable 566 too, but <code>mpf</code> would be a start. 567 <br> 568 <code>long double</code> is an ANSI-ism, so everything involving it would 569 need to be suppressed on a K&R compiler. 570 <br> 571 There'd be some work to be done by <code>configure</code> to recognise 572 the format in use, MPFR has a start on this. Often <code>long 573 double</code> is the same as <code>double</code>, which is easy but 574 pretty pointless. A single float format detector macro could look at 575 <code>double</code> then <code>long double</code> 576 <br> 577 Sometimes there's a compiler option for the size of a <code>long 578 double</code>, eg. xlc on AIX can use either 64-bit or 128-bit. It's 579 probably simplest to regard this as a compiler compatibility issue, and 580 leave it to users or sysadmins to ensure application and library code is 581 built the same. 582<li> <code>mpz_sqrt_if_perfect_square</code>: When 583 <code>mpz_perfect_square_p</code> does its tests it calculates a square 584 root and then discards it. For some applications it might be useful to 585 return that root. Suggested by Jason Moxham. 586<li> <code>mpz_get_ull</code>, <code>mpz_set_ull</code>, 587 <code>mpz_get_sll</code>, <code>mpz_get_sll</code>: Conversions for 588 <code>long long</code>. These would aid interoperability, though a 589 mixture of GMP and <code>long long</code> would probably not be too 590 common. Since <code>long long</code> is not always available (it's in 591 C99 and GCC though), disadvantages of using <code>long long</code> in 592 libgmp.a would be 593 <ul> 594 <li> Library contents vary according to the build compiler. 595 <li> gmp.h would need an ugly <code>#ifdef</code> block to decide if the 596 application compiler could take the <code>long long</code> 597 prototypes. 598 <li> Some sort of <code>LIBGMP_HAS_LONGLONG</code> might be wanted to 599 indicate whether the functions are available. (Applications using 600 autoconf could probe the library too.) 601 </ul> 602 It'd be possible to defer the need for <code>long long</code> to 603 application compile time, by having something like 604 <code>mpz_set_2ui</code> called with two halves of a <code>long 605 long</code>. Disadvantages of this would be, 606 <ul> 607 <li> Bigger code in the application, though perhaps not if a <code>long 608 long</code> is normally passed as two halves anyway. 609 <li> <code>mpz_get_ull</code> would be a rather big inline, or would have 610 to be two function calls. 611 <li> <code>mpz_get_sll</code> would be a worse inline, and would put the 612 treatment of <code>-0x10..00</code> into applications (see 613 <code>mpz_get_si</code> correctness above). 614 <li> Although having libgmp.a independent of the build compiler is nice, 615 it sort of sacrifices the capabilities of a good compiler to 616 uniformity with inferior ones. 617 </ul> 618 Plain use of <code>long long</code> is probably the lesser evil, if only 619 because it makes best use of gcc. In fact perhaps it would suffice to 620 guarantee <code>long long</code> conversions only when using GCC for both 621 application and library. That would cover free software, and we can 622 worry about selected vendor compilers later. 623 <br> 624 In C++ the situation is probably clearer, we demand fairly recent C++ so 625 <code>long long</code> should be available always. We'd probably prefer 626 to have the C and C++ the same in respect of <code>long long</code> 627 support, but it would be possible to have it unconditionally in gmpxx.h, 628 by some means or another. 629<li> <code>mpz_strtoz</code> parsing the same as <code>strtol</code>. 630 Suggested by Alexander Kruppa. 631</ul> 632 633 634<h4>Configuration</h4> 635 636<ul> 637<li> Alpha ev7, ev79: Add code to config.guess to detect these. Believe ev7 638 will be "3-1307" in the current switch, but need to verify that. (On 639 OSF, current configfsf.guess identifies ev7 using psrinfo, we need to do 640 it ourselves for other systems.) 641<li> Alpha OSF: Libtool (version 1.5) doesn't seem to recognise this system is 642 "pic always" and ends up running gcc twice with the same options. This 643 is wasteful, but harmless. Perhaps a newer libtool will be better. 644<li> ARM: <code>umul_ppmm</code> in longlong.h always uses <code>umull</code>, 645 but is that available only for M series chips or some such? Perhaps it 646 should be configured in some way. 647<li> HPPA: config.guess should recognize 7000, 7100, 7200, and 8x00. 648<li> HPPA: gcc 3.2 introduces a <code>-mschedule=7200</code> etc parameter, 649 which could be driven by an exact hppa cpu type. 650<li> Mips: config.guess should say mipsr3000, mipsr4000, mipsr10000, etc. 651 "hinv -c processor" gives lots of information on Irix. Standard 652 config.guess appends "el" to indicate endianness, but 653 <code>AC_C_BIGENDIAN</code> seems the best way to handle that for GMP. 654<li> PowerPC: The function descriptor nonsense for AIX is currently driven by 655 <code>*-*-aix*</code>. It might be more reliable to do some sort of 656 feature test, examining the compiler output perhaps. It might also be 657 nice to merge the aix.m4 files into powerpc-defs.m4. 658<li> config.m4 is generated only by the configure script, it won't be 659 regenerated by config.status. Creating it as an <code>AC_OUTPUT</code> 660 would work, but it might upset "make" to have things like <code>L$</code> 661 get into the Makefiles through <code>AC_SUBST</code>. 662 <code>AC_CONFIG_COMMANDS</code> would be the alternative. With some 663 careful m4 quoting the <code>changequote</code> calls might not be 664 needed, which might free up the order in which things had to be output. 665<li> Automake: Latest automake has a <code>CCAS</code>, <code>CCASFLAGS</code> 666 scheme. Though we probably wouldn't be using its assembler support we 667 could try to use those variables in compatible ways. 668<li> <code>GMP_LDFLAGS</code> could probably be done with plain 669 <code>LDFLAGS</code> already used by automake for all linking. But with 670 a bit of luck the next libtool will pass pretty much all 671 <code>CFLAGS</code> through to the compiler when linking, making 672 <code>GMP_LDFLAGS</code> unnecessary. 673<li> mpn/Makeasm.am uses <code>-c</code> and <code>-o</code> together in the 674 .S and .asm rules, but apparently that isn't completely portable (there's 675 an autoconf <code>AC_PROG_CC_C_O</code> test for it). So far we've not 676 had problems, but perhaps the rules could be rewritten to use "foo.s" as 677 the temporary, or to do a suitable "mv" of the result. The only danger 678 from using foo.s would be if a compile failed and the temporary foo.s 679 then looked like the primary source. Hopefully if the 680 <code>SUFFIXES</code> are ordered to have .S and .asm ahead of .s that 681 wouldn't happen. Might need to check. 682</ul> 683 684 685<h4>Random Numbers</h4> 686<ul> 687<li> <code>_gmp_rand</code> is not particularly fast on the linear 688 congruential algorithm and could stand various improvements. 689 <ul> 690 <li> Make a second seed area within <code>gmp_randstate_t</code> (or 691 <code>_mp_algdata</code> rather) to save some copying. 692 <li> Make a special case for a single limb <code>2exp</code> modulus, to 693 avoid <code>mpn_mul</code> calls. Perhaps the same for two limbs. 694 <li> Inline the <code>lc</code> code, to avoid a function call and 695 <code>TMP_ALLOC</code> for every chunk. 696 <li> Perhaps the <code>2exp</code> and general LC cases should be split, 697 for clarity (if the general case is retained). 698 </ul> 699<li> <code>gmp_randstate_t</code> used for parameters perhaps should become 700 <code>gmp_randstate_ptr</code> the same as other types. 701<li> Some of the empirical randomness tests could be included in a "make 702 check". They ought to work everywhere, for a given seed at least. 703</ul> 704 705 706<h4>C++</h4> 707<ul> 708<li> <code>mpz_class(string)</code>, etc: Use the C++ global locale to 709 identify whitespace. 710 <br> 711 <code>mpf_class(string)</code>: Use the C++ global locale decimal point, 712 rather than the C one. 713 <br> 714 Consider making these variant <code>mpz_set_str</code> etc forms 715 available for <code>mpz_t</code> too, not just <code>mpz_class</code> 716 etc. 717<li> <code>mpq_class operator+=</code>: Don't emit an unnecessary 718 <code>mpq_set(q,q)</code> before <code>mpz_addmul</code> etc. 719<li> Put various bits of gmpxx.h into libgmpxx, to avoid excessive inlining. 720 Candidates for this would be, 721 <ul> 722 <li> <code>mpz_class(const char *)</code>, etc: since they're normally 723 not fast anyway, and we can hide the exception <code>throw</code>. 724 <li> <code>mpz_class(string)</code>, etc: to hide the <code>cstr</code> 725 needed to get to the C conversion function. 726 <li> <code>mpz_class string, char*</code> etc constructors: likewise to 727 hide the throws and conversions. 728 <li> <code>mpz_class::get_str</code>, etc: to hide the <code>char*</code> 729 to <code>string</code> conversion and free. Perhaps 730 <code>mpz_get_str</code> can write directly into a 731 <code>string</code>, to avoid copying. 732 <br> 733 Consider making such <code>string</code> returning variants 734 available for use with plain <code>mpz_t</code> etc too. 735 </ul> 736</ul> 737 738<h4>Miscellaneous</h4> 739<ul> 740<li> <code>mpz_gcdext</code> and <code>mpn_gcdext</code> ought to document 741 what range of values the generated cofactors can take, and preferably 742 ensure the definition uniquely specifies the cofactors for given inputs. 743 A basic extended Euclidean algorithm or multi-step variant leads to 744 |x|<|b| and |y|<|a| or something like that, but there's probably 745 two solutions under just those restrictions. 746<li> demos/factorize.c: use <code>mpz_divisible_ui_p</code> rather than 747 <code>mpz_tdiv_qr_ui</code>. (Of course dividing multiple primes at a 748 time would be better still.) 749<li> The various test programs use quite a bit of the main 750 <code>libgmp</code>. This establishes good cross-checks, but it might be 751 better to use simple reference routines where possible. Where it's not 752 possible some attention could be paid to the order of the tests, so a 753 <code>libgmp</code> routine is only used for tests once it seems to be 754 good. 755<li> <code>MUL_FFT_THRESHOLD</code> etc: the FFT thresholds should allow a 756 return to a previous k at certain sizes. This arises basically due to 757 the step effect caused by size multiples effectively used for each k. 758 Looking at a graph makes it fairly clear. 759<li> <code>__gmp_doprnt_mpf</code> does a rather unattractive round-to-nearest 760 on the string returned by <code>mpf_get_str</code>. Perhaps some variant 761 of <code>mpf_get_str</code> could be made which would better suit. 762</ul> 763 764 765<h4>Aids to Development</h4> 766<ul> 767<li> Add <code>ASSERT</code>s at the start of each user-visible mpz/mpq/mpf 768 function to check the validity of each <code>mp?_t</code> parameter, in 769 particular to check they've been <code>mp?_init</code>ed. This might 770 catch elementary mistakes in user programs. Care would need to be taken 771 over <code>MPZ_TMP_INIT</code>ed variables used internally. If nothing 772 else then consistency checks like size<=alloc, ptr not 773 <code>NULL</code> and ptr+size not wrapping around the address space, 774 would be possible. A more sophisticated scheme could track 775 <code>_mp_d</code> pointers and ensure only a valid one is used. Such a 776 scheme probably wouldn't be reentrant, not without some help from the 777 system. 778<li> tune/time.c could try to determine at runtime whether 779 <code>getrusage</code> and <code>gettimeofday</code> are reliable. 780 Currently we pretend in configure that the dodgy m68k netbsd 1.4.1 781 <code>getrusage</code> doesn't exist. If a test might take a long time 782 to run then perhaps cache the result in a file somewhere. 783<li> tune/time.c could choose the default precision based on the 784 <code>speed_unittime</code> determined, independent of the method in use. 785<li> Cray vector systems: CPU frequency could be determined from 786 <code>sysconf(_SC_CLK_TCK)</code>, since it seems to be clock cycle 787 based. Is this true for all Cray systems? Would like some documentation 788 or something to confirm. 789</ul> 790 791 792<h4>Documentation</h4> 793<ul> 794<li> <code>mpz_inp_str</code> (etc) doesn't say when it stops reading digits. 795<li> <code>mpn_get_str</code> isn't terribly clear about how many digits it 796 produces. It'd probably be possible to say at most one leading zero, 797 which is what both it and <code>mpz_get_str</code> currently do. But 798 want to be careful not to bind ourselves to something that might not suit 799 another implementation. 800<li> <code>va_arg</code> doesn't do the right thing with <code>mpz_t</code> 801 etc directly, but instead needs a pointer type like <code>MP_INT*</code>. 802 It'd be good to show how to do this, but we'd either need to document 803 <code>mpz_ptr</code> and friends, or perhaps fallback on something 804 slightly nasty with <code>void*</code>. 805</ul> 806 807 808<h4>Bright Ideas</h4> 809 810<p> The following may or may not be feasible, and aren't likely to get done in the 811near future, but are at least worth thinking about. 812 813<ul> 814<li> Reorganize longlong.h so that we can inline the operations even for the 815 system compiler. When there is no such compiler feature, make calls to 816 stub functions. Write such stub functions for as many machines as 817 possible. 818<li> longlong.h could declare when it's using, or would like to use, 819 <code>mpn_umul_ppmm</code>, and the corresponding umul.asm file could be 820 included in libgmp only in that case, the same as is effectively done for 821 <code>__clz_tab</code>. Likewise udiv.asm and perhaps cntlz.asm. This 822 would only be a very small space saving, so perhaps not worth the 823 complexity. 824<li> longlong.h could be built at configure time by concatenating or 825 #including fragments from each directory in the mpn path. This would 826 select CPU specific macros the same way as CPU specific assembler code. 827 Code used would no longer depend on cpp predefines, and the current 828 nested conditionals could be flattened out. 829<li> <code>mpz_get_si</code> returns 0x80000000 for -0x100000000, whereas it's 830 sort of supposed to return the low 31 (or 63) bits. But this is 831 undocumented, and perhaps not too important. 832<li> <code>mpz_init_set*</code> and <code>mpz_realloc</code> could allocate 833 say an extra 16 limbs over what's needed, so as to reduce the chance of 834 having to do a reallocate if the <code>mpz_t</code> grows a bit more. 835 This could only be an option, since it'd badly bloat memory usage in 836 applications using many small values. 837<li> <code>mpq</code> functions could perhaps check for numerator or 838 denominator equal to 1, on the assumption that integers or 839 denominator-only values might be expected to occur reasonably often. 840<li> <code>count_trailing_zeros</code> is used on more or less uniformly 841 distributed numbers in a couple of places. For some CPUs 842 <code>count_trailing_zeros</code> is slow and it's probably worth handling 843 the frequently occurring 0 to 2 trailing zeros cases specially. 844<li> <code>mpf_t</code> might like to let the exponent be undefined when 845 size==0, instead of requiring it 0 as now. It should be possible to do 846 size==0 tests before paying attention to the exponent. The advantage is 847 not needing to set exp in the various places a zero result can arise, 848 which avoids some tedium but is otherwise perhaps not too important. 849 Currently <code>mpz_set_f</code> and <code>mpf_cmp_ui</code> depend on 850 exp==0, maybe elsewhere too. 851<li> <code>__gmp_allocate_func</code>: Could use GCC <code>__attribute__ 852 ((malloc))</code> on this, though don't know if it'd do much. GCC 3.0 853 allows that attribute on functions, but not function pointers (see info 854 node "Attribute Syntax"), so would need a new autoconf test. This can 855 wait until there's a GCC that supports it. 856<li> <code>mpz_add_ui</code> contains two <code>__GMPN_COPY</code>s, one from 857 <code>mpn_add_1</code> and one from <code>mpn_sub_1</code>. If those two 858 routines were opened up a bit maybe that code could be shared. When a 859 copy needs to be done there's no carry to append for the add, and if the 860 copy is non-empty no high zero for the sub. 861</ul> 862 863 864<h4>Old and Obsolete Stuff</h4> 865 866<p> The following tasks apply to chips or systems that are old and/or obsolete. 867It's unlikely anything will be done about them unless anyone is actively using 868them. 869 870<ul> 871<li> Sparc32: The integer based udiv_nfp.asm used to be selected by 872 <code>configure --nfp</code> but that option is gone now that autoconf is 873 used. The file could go somewhere suitable in the mpn search if any 874 chips might benefit from it, though it's possible we don't currently 875 differentiate enough exact cpu types to do this properly. 876<li> VAX D and G format <code>double</code> floats are straightforward and 877 could perhaps be handled directly in <code>__gmp_extract_double</code> 878 and maybe in <code>mpn_get_d</code>, rather than falling back on the 879 generic code. (Both formats are detected by <code>configure</code>.) 880</ul> 881 882 883<hr> 884 885</body> 886</html> 887 888<!-- 889Local variables: 890eval: (add-hook 'write-file-hooks 'time-stamp) 891time-stamp-start: "This file current as of " 892time-stamp-format: "%:d %3b %:y" 893time-stamp-end: "\\." 894time-stamp-line-limit: 50 895End: 896--> 897