Mod poly and mpn_mod random generation by dlesnoff · Pull Request #2448 · flintlib/flint

dlesnoff · 2025-10-29T16:56:45Z

Follow-up of #2430 .
Adds a rand function:

nmod_poly
nmod_poly_mat
mpn_mod
fmpz_mod_poly

It seems that implementations of nmod_mpoly randtest functions generate uniformly random coefficients.
I did not add rand functions for basic types like fmpz_mod nor nmod.
I plan to add a rand function for mpn_mod_poly and mpn_mod_mat.
Please forgive me, I based my branch on my previously non-merged branch and it needs some cleanup.

fredrik-johansson · 2025-10-29T17:09:09Z

Please forgive me, I based my branch on my previously non-merged branch and it needs some cleanup.

I think you need to rebase on main and force-push to get a clean diff.

vneiger · 2025-10-29T21:44:30Z

    }
 }

+void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m) {


The current behaviour does not have uniform distribution (it is more likely to generate 1 than other values). Maybe generate uniformly in [0,m-2] (being careful with m=1 or such corner cases), and then add 1?

Does m stands for uniform? For me, it stands for modulus since the element is upper bounded by a modulus and is not just a random element with a set number of bits. Sorry, I did not meant to make something uniform.
The functions fmpz_mod_poly_randtest used randm. I prefered creating a randm_nonzero function than using randtest_nonzero.

What I meant is that currently, fmpz_randm generates a uniform integer in [0, m) (all values have equal probability), as can be seen from the code. The fact that the distribution is uniform is not explicitly indicated in the documentation, but that's ok, it is the "canonical distribution" for a finite set.

So if a fmpz_randm_nonzero function is added, it seems to me that it should also have uniform distribution (choosing uniformly in [1, m)), unless this is tricky to make. In this case it is not tricky: apply fmpz_randm with m-1 to get a uniform choice in [0, m-1), and then add 1, this gives you a uniform choice in [1, m).

vneiger · 2025-10-29T21:47:44Z

    fmpz_mod_poly_fit_length(poly, len, ctx);
    _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));


Why this change, or why using nonzero almost everywhere?

To have at least a randfull-like functionality. See my comments above.

As suggested in other functions, I think that in these randtest functions we may as well rely on the existing fmpz_randtest_mod.

vneiger · 2025-10-29T21:59:00Z

I cancelled the CI workflow because they were still in testing after almost 4 hours. Please review the code carefully to see what changes to existing functions could have led to this, thanks! (I pointed at some modifications in my comments, but there may be others)

dlesnoff · 2025-10-30T10:05:15Z

fmpz_randtest does not generate a coefficient with increased sparsity (here, 0 with increased probability) but generates a coefficient using a number of bits. For mod functions, it requires to be reduced after being generated.
fmpz_randm generates directly a coefficient in the range [0, m) where m is a bound, but I am unsure if this function has some pseudo-uniformity guarantee (the algorithm is unspecified).
So randtest has a slight different meaning for fmpz than for structures in mod n source files.

There is probably an infinite loop, I'll do a manual bisect.

The randtest functions are using `randm` which generates positive coefficients in [0, m) range with m the modulus given by the context. The documentation told that the coefficients are randomly signed, so I fixed that. I introduced a `randm_nonzero` function in fmpz to ensure that coefficients are nonzero and replaced all occurences of `randm` in `fmpz_mod_poly_randtest` functions by this new function. Apart from the `rand` function, this introduces a `rand_monic` and a `rand_irreducible` function.

I added _fmpz_mod_vec_rand with the intent to use it in _mpn_mod_vec_rand but did not use it in the end. This reverts commit f98e52c.

dlesnoff · 2025-10-30T11:34:05Z

The tests halt indefinitely after gr_special_fac. ~~I am unsure if it's related to my PR.~~
This commit is the culprit: Add fmpz_mod_poly_rand, rand_monic, irred funcs

dlesnoff · 2025-10-30T14:26:28Z

Ok, I guess that if a polynomial has nonzero coefficients, it is irreducible with much less probability. This could slow down the tests. I should indeed give up on a "randfull-like" functionality for fmpz_mod_poly_randtest functions but then what would be the point of making another rand function?

vneiger · 2025-10-30T16:48:03Z

 .. function:: void nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len)

-    Generates a random polynomial with length up to ``len``.
+    Generates a random and sparse with increased probability polynomial with length up to ``len``.


Suggested change

Generates a random and sparse with increased probability polynomial with length up to ``len``.

Generates a random polynomial with length up to ``len``, with for each coefficient the probability of some special values increased (see :func:`n_randtest`). This function is intended for use in test code.

This is sparse with increased proba, but also special values are more likely than with a uniform distribution. So maybe,

Suggested change

Generates a random and sparse with increased probability polynomial with length up to ``len``.

Generates a random polynomial with length up to ``len``, sparse with increased probability, and with coefficients generated by :func:`n_randtest` .

vneiger · 2025-10-30T17:00:51Z

    }
 }

+void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m) {


What I meant is that currently, fmpz_randm generates a uniform integer in [0, m) (all values have equal probability), as can be seen from the code. The fact that the distribution is uniform is not explicitly indicated in the documentation, but that's ok, it is the "canonical distribution" for a finite set.

So if a fmpz_randm_nonzero function is added, it seems to me that it should also have uniform distribution (choosing uniformly in [1, m)), unless this is tricky to make. In this case it is not tricky: apply fmpz_randm with m-1 to get a uniform choice in [0, m-1), and then add 1, this gives you a uniform choice in [1, m).

vneiger · 2025-10-30T17:02:06Z

+{
+    if (len == 0)
+    {
+        flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_randtest_irreducible). len == 0.\n");


Suggested change

flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_randtest_irreducible). len == 0.\n");

flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_rand_irreducible). len == 0.\n");

There is a mismatch function name / name in exception.

(modified comment after checking the diff more carefully)

vneiger · 2025-10-30T17:05:58Z

    fmpz_mod_poly_fit_length(poly, len, ctx);
    _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));


As suggested in other functions, I think that in these randtest functions we may as well rely on the existing fmpz_randtest_mod.

vneiger · 2025-10-30T17:30:21Z

Ok, I guess that if a polynomial has nonzero coefficients, it is irreducible with much less probability. This could slow down the tests. I should indeed give up on a "randfull-like" functionality for fmpz_mod_poly_randtest functions

This is likely indeed. I haven't looked closely at the test files and the one that is failing, but let's suppose that some test includes working modulo 2, then the new randtest using randm_nonzero will only generate coefficients that are 1 ! I don't think randtest should ban 0.

but then what would be the point of making another rand function?

In my last batch of comments, you can see that I suggest using fmpz_randtest_mod instead of fmpz_randm_nonzero. Then the randtest and rand functions for fmpz_mod_poly would become rather different and I think it would make sense to have both. (However, one question that remains, is whether this change will suffice to solve the "infinite test" issue.)

dlesnoff · 2025-11-03T14:14:05Z

I changed randm_non_zero t to randtest calls. I gave one extra bit for the random generation before taking the modulus. If you think it is not necessary, I will remove it.
~~I have still a few changes to perform.~~

…is it OK?

dlesnoff · 2026-08-06T21:17:47Z

Hello, sorry for not making quickly the last modifications needed to close this PR.

As suggested in other functions, I think that in these randtest functions we may as well rely on the existing fmpz_randtest_mod.

Is this still actual? I can't remember if I did this change. I'll look into it tomorrow.

Pay attention to the previous commit. I remove an invocation to fmpz_bits. It apparently fixes a segfault, but I am not sure why it was invocated in the first place. Could you check out for this during review?

Otherwise, I made two changes:

fix documentation errors
the change so that fmpz_randm_nonzero provides a uniform distribution using the add-one trick suggested by @vneiger

vneiger · 2026-08-07T10:16:50Z

+    Sets `f` to a random polynomial with up to the given length and where
+    each coefficient has up to the given number of bits. The coefficients
+    are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.


I would suggest to copy-paste the doc of e.g. nmod_poly:

Suggested change

Sets `f` to a random polynomial with up to the given length and where

each coefficient has up to the given number of bits. The coefficients

are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.

Generates a random polynomial with length up to `len`, with uniformly chosen coefficients.

vneiger · 2026-08-07T10:19:13Z

+    Sets `f` to a random monic polynomial with up to the given length and where
+    each coefficient has up to the given number of bits. The coefficients
+    are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.


I would suggest to copy-paste the doc of e.g. nmod_poly:

Suggested change

Sets `f` to a random monic polynomial with up to the given length and where

each coefficient has up to the given number of bits. The coefficients

are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.

Generates a random monic polynomial with length `len`, with uniformly chosen coefficients.

vneiger · 2026-08-07T10:23:29Z

+    Sets `f` to a random irreducible polynomial with up to the given length and where each coefficient has up to the given number of bits. The coefficients
+    are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.


As above, I would suggest something more concise (and there is nothing about number of bits here):

Suggested change

Sets `f` to a random irreducible polynomial with up to the given length and where each coefficient has up to the given number of bits. The coefficients

are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.

Generates a random irreducible polynomial with up to the given length and where the coefficients

are generated uniformly.

vneiger · 2026-08-07T10:28:23Z

    Sets `f` to a random polynomial with up to the given length and where
    each coefficient has up to the given number of bits. The coefficients
-    are signed randomly.
+    are random numbers in `[1, n)`.


Perhaps a small mistake here, I don't think this function has been changed, and the previous doc was correct it seems(?).

vneiger · 2026-08-07T10:29:22Z


+.. function:: void nmod_poly_rand(nmod_poly_t poly, flint_rand_t state, slong len)
+
+    Generates a random polynomial with length up to ``len``.


Suggested change

Generates a random polynomial with length up to ``len``.

Generates a random polynomial with length up to ``len`` and coefficients generated uniformly.

vneiger · 2026-08-07T10:29:45Z

+
+.. function:: void nmod_poly_rand_monic(nmod_poly_t poly, flint_rand_t state, slong len)
+
+    Generates a random monic polynomial with length up to ``len``.


Suggested change

Generates a random monic polynomial with length up to ``len``.

Generates a random monic polynomial of length ``len`` and non-leading coefficients generated uniformly.

vneiger · 2026-08-07T10:30:19Z

+
+.. function:: void nmod_poly_rand_irreducible(nmod_poly_t poly, flint_rand_t state, slong len)
+
+    Generates a random irreducible polynomial with length up to ``len``.


Suggested change

Generates a random irreducible polynomial with length up to ``len``.

Generates a random irreducible polynomial with length up to ``len`` with coefficients generated uniformly.

vneiger · 2026-08-07T10:34:06Z

 .. function:: void nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len)

-    Generates a random polynomial with length up to ``len``.
+    Generates a random and sparse with increased probability polynomial with length up to ``len``.


This is sparse with increased proba, but also special values are more likely than with a uniform distribution. So maybe,

Suggested change

Generates a random and sparse with increased probability polynomial with length up to ``len``.

Generates a random polynomial with length up to ``len``, sparse with increased probability, and with coefficients generated by :func:`n_randtest` .

vneiger · 2026-08-07T10:34:34Z

 .. function:: void nmod_poly_randtest_monic(nmod_poly_t poly, flint_rand_t state, slong len)

-    Generates a random monic polynomial with length ``len``.
+    Generates a random and sparse with increased probability monic polynomial with length ``len``.


See the comment above on a similar function.

vneiger · 2026-08-07T10:36:09Z

Here is a first batch of comments, on the documentation.

vneiger · 2026-08-08T07:44:57Z

+.. function:: void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)
+
+    Generates a random integer in the range `1` to `m - 1` inclusive. Requires
+    `m \geq 2`, otherwise an exception will result.


Suggested change

`m \geq 2`, otherwise an exception will result.

`m \geq 2`, otherwise an exception is thrown.

vneiger · 2026-08-08T07:45:52Z

+{
+    if (fmpz_cmp_ui(m, 2) <= 0)
+    {
+        flint_throw(FLINT_ERROR, "Exception (fmpz_randm_nonzero). m <= 2.\n");


Suggested change

flint_throw(FLINT_ERROR, "Exception (fmpz_randm_nonzero). m <= 2.\n");

flint_throw(FLINT_ERROR, "Exception (fmpz_randm_nonzero). m < 2.\n");

vneiger · 2026-08-08T07:47:02Z

+void
+fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)
+{
+    if (fmpz_cmp_ui(m, 2) <= 0)


Suggested change

if (fmpz_cmp_ui(m, 2) <= 0)

if (fmpz_cmp_ui(m, 2) < 0)

because the issue is when m is strictly less than 2

vneiger · 2026-08-08T07:47:27Z

+    fmpz_randm(f, state, mMinusOne); // 0..m-2
+    fmpz_add_ui(f, f, 1); // 1..m-1


Suggested change

fmpz_randm(f, state, mMinusOne); // 0..m-2

fmpz_add_ui(f, f, 1); // 1..m-1

fmpz_randm(f, state, mMinusOne); /* 0..m-2 */

fmpz_add_ui(f, f, 1); /* 1..m-1 */

vneiger · 2026-08-08T07:53:32Z

 }

+void
+fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)


Suggested change

fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)

fmpz_randm_not_zero(fmpz_t f, flint_rand_t state, const fmpz_t m)

(to follow the naming used elsewhere: fmpq_randtest_not_zero, arf_randtest_not_zero, fq_default_rand_not_zero, etc)

vneiger · 2026-08-08T07:53:45Z


    Generates a random integer in the range `0` to `m - 1` inclusive.

+.. function:: void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)


Suggested change

.. function:: void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)

.. function:: void fmpz_randm_not_zero(fmpz_t f, flint_rand_t state, const fmpz_t m)

vneiger · 2026-08-08T08:10:29Z

+        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
+        fmpz_mod(f->coeffs + i, f->coeffs + i, fmpz_mod_ctx_modulus(ctx));


For these two lines (and all the similar ones below in this file), I would suggest to make use of fmpz_randtest_mod

vneiger · 2026-08-08T08:11:04Z

+{
+    if (len == 0)
+    {
+        flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_randtest_irreducible). len == 0.\n");


There is a mismatch function name / name in exception.

vneiger · 2026-08-08T08:11:38Z

+       fmpz_randtest_unsigned(poly->coeffs + random_idx + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
+       fmpz_mod(poly->coeffs + random_idx + 1, poly->coeffs + random_idx + 1, fmpz_mod_ctx_modulus(ctx));


See above, about using fmpz_randtest_mod

vneiger · 2026-08-08T08:16:28Z

 #include "nmod_poly.h"
 #include "nmod_poly_factor.h"

+// Rand functions -> random dense polynomials with high probability


Suggested change

// Rand functions -> random dense polynomials with high probability

/* rand functions -> coefficients generated uniformly */

vneiger · 2026-08-08T08:21:14Z

Pay attention to the previous commit. I remove an invocation to fmpz_bits. It apparently fixes a segfault, but I am not sure why it was invocated in the first place. Could you check out for this during review?

Yes, your change is fine, and I agree this was an extraneous invocation that was probably added by mistake.

dlesnoff force-pushed the mod_poly-random-generation branch from c1be23c to ba6af38 Compare October 29, 2025 18:07

vneiger reviewed Oct 29, 2025

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Comment thread doc/source/fmpz_poly.rst Outdated

vneiger reviewed Oct 29, 2025

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Comment thread src/fmpz_mod_poly/randtest.c

vneiger reviewed Oct 29, 2025

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fredrik-johansson added new feature workshop 2025v2 labels Oct 30, 2025

dlesnoff added 8 commits October 30, 2025 12:17

Add _nmod_vec_rand

e6f8dcd

Add nmod_poly rand funcs

4ea9a57

Add nmod_poly_mat rand funcs

4f0ef9b

Add fmpz_mod_vec_rand

bb5d986

Add a rand function to mpn_mod

400598a

Add mpn_mod_vec_rand func

9060505

Revert "Add fmpz_mod_vec_rand"

59f5c7d

I added _fmpz_mod_vec_rand with the intent to use it in _mpn_mod_vec_rand but did not use it in the end. This reverts commit f98e52c.

dlesnoff force-pushed the mod_poly-random-generation branch from 21ee353 to 59f5c7d Compare October 30, 2025 11:17

vneiger reviewed Oct 30, 2025

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Replace randm_non_zero by randtest calls

eafe4cf

dlesnoff force-pushed the mod_poly-random-generation branch from f5b0816 to eafe4cf Compare November 3, 2025 13:46

dlesnoff added 3 commits November 3, 2025 16:17

Fix documentation of mpn_mod

4dff27e

Merge branch 'main' into mod_poly-random-generation

692c2b8

Remove +1 to uint pointers

716a13e

albinahlback reviewed Nov 4, 2025

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Comment thread doc/source/fmpz_poly.rst Outdated

dlesnoff added 4 commits August 6, 2026 18:22

Merge branch 'trunk' into mod_poly-random-generation

43cdbc6

Randm is now really uniform

320496a

Remove ctx and move fmpz_mod_poly_rand funcs to correct doc file

606465e

Remove duplicate prototype in nmod_vec.h

440ebee

dlesnoff marked this pull request as draft August 6, 2026 18:51

dlesnoff added 2 commits August 6, 2026 21:27

apply fix fmpz_randm_nonzero

e8ecc0c

Don't get why fmpz_bits was used in this reduction? Fix Segfault but …

2eec4e3

…is it OK?

dlesnoff marked this pull request as ready for review August 6, 2026 21:18

vneiger requested changes Aug 7, 2026

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vneiger reviewed Aug 8, 2026

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	Generates a random and sparse with increased probability polynomial with length up to ``len``.
	Generates a random polynomial with length up to ``len``, with for each coefficient the probability of some special values increased (see :func:`n_randtest`). This function is intended for use in test code.

	flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_randtest_irreducible). len == 0.\n");
	flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_rand_irreducible). len == 0.\n");

		Sets `f` to a random irreducible polynomial with up to the given length and where each coefficient has up to the given number of bits. The coefficients
		are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.


		.. function:: void nmod_poly_rand(nmod_poly_t poly, flint_rand_t state, slong len)

		Generates a random polynomial with length up to ``len``.


		.. function:: void nmod_poly_rand_monic(nmod_poly_t poly, flint_rand_t state, slong len)

		Generates a random monic polynomial with length up to ``len``.

	Generates a random monic polynomial with length up to ``len``.
	Generates a random monic polynomial of length ``len`` and non-leading coefficients generated uniformly.


		.. function:: void nmod_poly_rand_irreducible(nmod_poly_t poly, flint_rand_t state, slong len)

		Generates a random irreducible polynomial with length up to ``len``.

	`m \geq 2`, otherwise an exception will result.
	`m \geq 2`, otherwise an exception is thrown.

		fmpz_randm(f, state, mMinusOne); // 0..m-2
		fmpz_add_ui(f, f, 1); // 1..m-1

	fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)
	fmpz_randm_not_zero(fmpz_t f, flint_rand_t state, const fmpz_t m)


		Generates a random integer in the range `0` to `m - 1` inclusive.

		.. function:: void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)

	.. function:: void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)
	.. function:: void fmpz_randm_not_zero(fmpz_t f, flint_rand_t state, const fmpz_t m)

		fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
		fmpz_mod(f->coeffs + i, f->coeffs + i, fmpz_mod_ctx_modulus(ctx));

		fmpz_randtest_unsigned(poly->coeffs + random_idx + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
		fmpz_mod(poly->coeffs + random_idx + 1, poly->coeffs + random_idx + 1, fmpz_mod_ctx_modulus(ctx));

	// Rand functions -> random dense polynomials with high probability
	/* rand functions -> coefficients generated uniformly */

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