+++ /dev/null
-THINGS TO WORK ON
-
-Note that many of these things mentioned here are already fixed in GMP 2.0.
-
-* Improve speed for non-gcc compilers by defining umul_ppmm, udiv_qrnnd,
- etc, to call __umul_ppmm, __udiv_qrnnd. A typical definition for
- umul_ppmm would be
- #define umul_ppmm(ph,pl,m0,m1) \
- {unsigned long __ph; (pl) = __umul_ppmm (&__ph, (m0), (m1)); (ph) = __ph;}
- In order to maintain just one version of longlong.h (gmp and gcc), this
- has to be done outside of longlong.h.
-
-* Change mpn-routines to not deal with normalisation?
- mpn_add: Unchanged.
- mpn_sub: Remove normalization loop. Does it assume normalised input?
- mpn_mul: Make it return most sign limb, to simplify normalisation.
- Karatsubas algorith will be greatly simplified if mpn_add and
- mpn_sub doesn't normalise their results.
- mpn_div: Still requires strict normalisation.
- Beware of problems with mpn_cmp (and similar), a larger size does not
- ensure that an operand is larger, since it may be "less normalised".
- Normalization has to be moved into mpz-functions.
-
-Bennet Yee at CMU proposes:
-* mpz_{put,get}_raw for memory oriented I/O like other *_raw functions.
-* A function mpfatal that is called for exceptions. The user may override
- the default definition.
-
-* mout should group in 10-digit groups.
-* ASCII dependence?
-* Error reporting from I/O functions (linkoping)?
-
-* Make all computation mpz_* functions return a signed int indicating if
- the result was zero, positive, or negative?
-
-* Implement mpz_cmpabs, mpz_xor, mpz_to_double, mpz_to_si, mpz_lcm,
- mpz_dpb, mpz_ldb, various bit string operations like mpz_cntbits. Also
- mpz_@_si for most @??
-
-Brian Beuning proposes:
- 1. An array of small primes
- 3. A function to factor an MINT
- 4. A routine to look for "small" divisors of an MINT
- 5. A 'multiply mod n' routine based on Montgomery's algorithm.
-
-Doug Lea proposes:
- 1. A way to find out if an integer fits into a signed int, and if so, a
- way to convert it out.
- 2. Similarly for double precision float conversion.
- 3. A function to convert the ratio of two integers to a double. This
- can be useful for mixed mode operations with integers, rationals, and
- doubles.
- 5. Bit-setting, clearing, and testing operations, as in
- mpz_setbit(MP_INT* dest, MP_INT* src, unsigned long bit_number),
- and used, for example in
- mpz_setbit(x, x, 123)
- to directly set the 123rd bit of x.
- If these are supported, you don't first have to set up
- an otherwise unnecessary mpz holding a shifted value, then
- do an "or" operation.
-
-Elliptic curve method descrition in the Chapter `Algorithms in Number
-Theory' in the Handbook of Theoretical Computer Science, Elsevier,
-Amsterdam, 1990. Also in Carl Pomerance's lecture notes on Cryptology and
-Computational Number Theory, 1990.
-
-* New function: mpq_get_ifstr (int_str, frac_str, base,
- precision_in_som_way, rational_number). Convert RATIONAL_NUMBER to a
- string in BASE and put the integer part in INT_STR and the fraction part
- in FRAC_STR. (This function would do a division of the numerator and the
- denominator.)
-
-* Should mpz_powm* handle negative exponents?
-
-* udiv_qrnnd: If the denominator is normalized, the n0 argument has very
- little effect on the quotient. Maybe we can assume it is 0, and
- compensate at a later stage?
-
-* Better sqrt: First calculate the reciprocal square root, then multiply by
- the operand to get the square root. The reciprocal square root can be
- obtained through Newton-Raphson without division. The iteration is x :=
- x*(3-a*x^2)/2, where a is the operand.
-
-* Newton-Raphson using multiplication: We get twice as many correct digits
- in each iteration. So if we square x(k) as part of the iteration, the
- result will have the leading digits in common with the entire result from
- iteration k-1. A _mpn_mul_lowpart could implement this.
-
-* Peter Montgomery: If 0 <= a, b < p < 2^31 and I want a modular product
- a*b modulo p and the long long type is unavailable, then I can write
-
- typedef signed long slong;
- typedef unsigned long ulong;
- slong a, b, p, quot, rem;
-
- quot = (slong) (0.5 + (double)a * (double)b / (double)p);
- rem = (slong)((ulong)a * (ulong)b - (ulong)p * (ulong)q);
- if (rem < 0} {rem += p; quot--;}
-
-FFT:
-{
- * Multiplication could be done with Montgomery's method combined with
- the "three primes" method described in Lipson. Maybe this would be
- faster than to Nussbaumer's method with 3 (simple) moduli?
-
- * Maybe the modular tricks below are not needed: We are using very
- special numbers, Fermat numbers with a small base and a large exponent,
- and maybe it's possible to just subtract and add?
-
- * Modify Nussbaumer's convolution algorithm, to use 3 words for each
- coefficient, calculating in 3 relatively prime moduli (e.g.
- 0xffffffff, 0x100000000, and 0x7fff on a 32-bit computer). Both all
- operations and CRR would be very fast with such numbers.
-
- * Optimize the Shoenhage-Stassen multiplication algorithm. Take
- advantage of the real valued input to save half of the operations and
- half of the memory. Try recursive variants with large, optimized base
- cases. Use recursive FFT with large base cases, since recursive FFT
- has better memory locality. A normal FFT get 100% cache miss.
-}
-
-* Speed modulo arithmetic, using Montgomery's method or my pre-invertion
- method. In either case, special arithmetic calls would be needed,
- mpz_mmmul, mpz_mmadd, mpz_mmsub, plus some kind of initialization
- functions.
-
-* mpz_powm* should not use division to reduce the result in the loop, but
- instead pre-compute the reciprocal of the MOD argument and do reduced_val
- = val-val*reciprocal(MOD)*MOD, or use Montgomery's method.
-
-* mpz_mod_2expplussi -- to reduce a bignum modulo (2**n)+s
-
-* It would be a quite important feature never to allocate more memory than
- really necessary for a result. Sometimes we can achieve this cheaply, by
- deferring reallocation until the result size is known.
-
-* New macro in longlong.h: shift_rhl that extracts a word by shifting two
- words as a unit. (Supported by i386, i860, HP-PA, RS6000, 29k.) Useful
- for shifting multiple precision numbers.
-
-* The installation procedure should make a test run of multiplication to
- decide the threshold values for algorithm switching between the available
- methods.
-
-* The gcd algorithm could probably be improved with a divide-and-conquer
- (DAC) approach. At least the bulk of the operations should be done with
- single precision.
-
-* Fast output conversion of x to base B:
- 1. Find n, such that (B^n > x).
- 2. Set y to (x*2^m)/(B^n), where m large enough to make 2^n ~~ B^n
- 3. Multiply the low half of y by B^(n/2), and recursively convert the
- result. Truncate the low half of y and convert that recursively.
- Complexity: O(M(n)log(n))+O(D(n))!
-
-* Extensions for floating-point arithmetic.
-
-* Improve special cases for division.
-
- 1. When the divisor is just one word, normalization is not needed for
- most CPUs, and can be done in the division loop for CPUs that need
- normalization.
-
- 2. Even when the result is going to be very small, (i.e. nsize-dsize is
- small) normalization should also be done in the division loop.
-
- To fix this, a new routine mpn_div_unnormalized is needed.
-
-* Never allocate temporary space for a source param that overlaps with a
- destination param needing reallocation. Instead malloc a new block for
- the destination (and free the source before returning to the caller).
-
-* When any of the source operands overlap with the destination, mult (and
- other routines) slow down. This is so because the need of temporary
- allocation (with alloca) and copying. If a new destination were
- malloc'ed instead (and the overlapping source free'd before return) no
- copying would be needed. Is GNU malloc quick enough to make this faster
- even for reasonably small operands?
-\f
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projects / ghc-hetmet.git / blobdiff