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c-kzg-4844
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Handle many missing (step 3)

This commit is contained in:
Ben Edgington 2021-03-03 17:43:31 +00:00
parent 8fbea3b3ef
commit f09d1a70b2
3 changed files with 113 additions and 114 deletions
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132
src/zero_poly.c
View File

@ -31,8 +31,8 @@
* Uses straightforward multiplication to calculate the product of `(x - r^i)` where `r` is a root of unity and the `i`s
* are the indices at which it must evaluate to zero. This results in a polynomial of degree @p len_indices.
*
* @param[out] dst The resulting leaf, length @p len_dst
* @param[in] len_dst Length of the output leaf, @p dst
* @param[out] dst The resulting polynomial, length @p len_dst
* @param[in] len_dst Length of the output polynomial, @p dst
* @param[in] indices Array of missing indices of length @p len_indices
* @param[in] len_indices Length of the missing indices array, @p indices
* @param[in] stride Stride length through the powers of the root of unity
@ -42,8 +42,8 @@
*
* @todo rework to pass polynomials in and out
*/
C_KZG_RET do_zero_poly_mul_leaf(fr_t *dst, uint64_t len_dst, const uint64_t *indices, uint64_t len_indices,
uint64_t stride, const FFTSettings *fs) {
C_KZG_RET do_zero_poly_mul_partial(fr_t *dst, uint64_t len_dst, const uint64_t *indices, uint64_t len_indices,
uint64_t stride, const FFTSettings *fs) {
CHECK(len_dst >= len_indices + 1);
@ -80,12 +80,12 @@ C_KZG_RET do_zero_poly_mul_leaf(fr_t *dst, uint64_t len_dst, const uint64_t *ind
* @retval C_CZK_OK All is well
* @retval C_CZK_BADARGS Invalid parameters were supplied
*/
C_KZG_RET pad_p(fr_t *out, uint64_t out_len, const fr_t *p, uint64_t p_len) {
CHECK(out_len >= p_len);
for (uint64_t i = 0; i < p_len; i++) {
out[i] = p[i];
C_KZG_RET pad_p(fr_t *out, uint64_t out_len, const poly *p) {
CHECK(out_len >= p->length);
for (uint64_t i = 0; i < p->length; i++) {
out[i] = p->coeffs[i];
}
for (uint64_t i = p_len; i < out_len; i++) {
for (uint64_t i = p->length; i < out_len; i++) {
out[i] = fr_zero;
}
return C_KZG_OK;
@ -109,15 +109,15 @@ C_KZG_RET pad_p(fr_t *out, uint64_t out_len, const fr_t *p, uint64_t p_len) {
* @retval C_CZK_BADARGS Invalid parameters were supplied
* @retval C_CZK_ERROR An internal error occurred
*/
C_KZG_RET reduce_leaves(poly *out, uint64_t len_out, fr_t *scratch, uint64_t len_scratch, const poly *leaves,
uint64_t leaf_count, const FFTSettings *fs) {
C_KZG_RET reduce_partials(poly *out, uint64_t len_out, fr_t *scratch, uint64_t len_scratch, const poly *partials,
uint64_t partial_count, const FFTSettings *fs) {
CHECK(is_power_of_two(len_out));
CHECK(len_scratch >= 3 * len_out);
CHECK(leaf_count > 0);
CHECK(partial_count > 0);
// The degree of the output polynomial is the sum of the degrees of the input polynomials.
uint64_t out_degree = 0;
for (int i = 0; i < leaf_count; i++) {
out_degree += leaves[i].length - 1;
for (int i = 0; i < partial_count; i++) {
out_degree += partials[i].length - 1;
}
CHECK(out_degree + 1 <= len_out);
@ -126,12 +126,12 @@ C_KZG_RET reduce_leaves(poly *out, uint64_t len_out, fr_t *scratch, uint64_t len
fr_t *mul_eval_ps = scratch + len_out;
fr_t *p_eval = scratch + 2 * len_out;
// Do the last leaf first: it may be shorter than the others and the padding can remain in place for the rest.
TRY(pad_p(p_padded, len_out, leaves[leaf_count - 1].coeffs, leaves[leaf_count - 1].length));
// Do the last partial first: it may be shorter than the others and the padding can remain in place for the rest.
TRY(pad_p(p_padded, len_out, &partials[partial_count - 1]));
TRY(fft_fr(mul_eval_ps, p_padded, false, len_out, fs));
for (uint64_t i = 0; i < leaf_count - 1; i++) {
TRY(pad_p(p_padded, leaves[i].length, leaves[i].coeffs, leaves[i].length));
for (uint64_t i = 0; i < partial_count - 1; i++) {
TRY(pad_p(p_padded, partials[i].length, &partials[i]));
TRY(fft_fr(p_eval, p_padded, false, len_out, fs));
for (uint64_t j = 0; j < len_out; j++) {
fr_mul(&mul_eval_ps[j], &mul_eval_ps[j], &p_eval[j]);
@ -149,7 +149,7 @@ C_KZG_RET reduce_leaves(poly *out, uint64_t len_out, fr_t *scratch, uint64_t len
* indices.
*
* This is done by simply multiplying together `(x - r^i)` for all the `i` that are missing indices, using a combination
* of direct multiplication (#do_zero_poly_mul_leaf) and multiplication via convolution (#reduce_leaves).
* of direct multiplication (#do_zero_poly_mul_partial) and multiplication via convolution (#reduce_partials).
*
* Also calculates the FFT (the "evaluation polynomial").
*
@ -172,7 +172,7 @@ C_KZG_RET reduce_leaves(poly *out, uint64_t len_out, fr_t *scratch, uint64_t len
* @retval C_CZK_ERROR An internal error occurred
* @retval C_CZK_MALLOC Memory allocation failed
*
* @todo What is the performance impact of tuning `per_leaf_poly` and `reduction factor`?
* @todo What is the performance impact of tuning `degree_of_partial` and `reduction factor`?
*/
C_KZG_RET zero_polynomial_via_multiplication(fr_t *zero_eval, fr_t *zero_poly, uint64_t *zero_poly_len, uint64_t length,
const uint64_t *missing_indices, uint64_t len_missing,
@ -189,83 +189,81 @@ C_KZG_RET zero_polynomial_via_multiplication(fr_t *zero_eval, fr_t *zero_poly, u
CHECK(length <= fs->max_width);
CHECK(is_power_of_two(length));
uint64_t per_leaf_poly = 64; // Tunable parameter. Must be a power of two.
uint64_t per_leaf = per_leaf_poly - 1;
uint64_t degree_of_partial = 64; // Tunable parameter. Must be a power of two.
uint64_t missing_per_partial = degree_of_partial - 1;
uint64_t domain_stride = fs->max_width / length;
uint64_t leaf_count = (len_missing + per_leaf - 1) / per_leaf;
uint64_t n = next_power_of_two(leaf_count * per_leaf_poly);
uint64_t partial_count = (len_missing + missing_per_partial - 1) / missing_per_partial;
uint64_t n = next_power_of_two(partial_count * degree_of_partial);
if (n > length) n = length;
if (len_missing <= per_leaf) {
TRY(do_zero_poly_mul_leaf(zero_poly, length, missing_indices, len_missing, domain_stride, fs));
if (len_missing <= missing_per_partial) {
TRY(do_zero_poly_mul_partial(zero_poly, length, missing_indices, len_missing, domain_stride, fs));
TRY(fft_fr(zero_eval, zero_poly, false, length, fs));
*zero_poly_len = len_missing + 1;
} else {
// Work space for building and reducing the leaves
// Work space for building and reducing the partials
fr_t *work;
TRY(new_fr_array(&work, next_power_of_two(leaf_count * per_leaf_poly)));
TRY(new_fr_array(&work, next_power_of_two(partial_count * degree_of_partial)));
// Build the leaves.
// Build the partials.
// Just allocate pointers here since we're re-using `work` for the leaf processing
// Combining leaves can be done mostly in-place, using a scratchpad.
poly *leaves;
TRY(new_poly_array(&leaves, leaf_count));
// Just allocate pointers here since we're re-using `work` for the partial processing
// Combining partials can be done mostly in-place, using a scratchpad.
poly *partials;
TRY(new_poly_array(&partials, partial_count));
uint64_t offset = 0, out_offset = 0, max = len_missing;
for (int i = 0; i < leaf_count; i++) {
uint64_t end = offset + per_leaf;
for (int i = 0; i < partial_count; i++) {
uint64_t end = offset + missing_per_partial;
if (end > max) end = max;
leaves[i].coeffs = &work[out_offset];
leaves[i].length = per_leaf_poly;
TRY(do_zero_poly_mul_leaf(leaves[i].coeffs, per_leaf_poly, &missing_indices[offset], end - offset,
domain_stride, fs));
offset += per_leaf;
out_offset += per_leaf_poly;
partials[i].coeffs = &work[out_offset];
partials[i].length = degree_of_partial;
TRY(do_zero_poly_mul_partial(partials[i].coeffs, degree_of_partial, &missing_indices[offset], end - offset,
domain_stride, fs));
offset += missing_per_partial;
out_offset += degree_of_partial;
}
// Adjust the length of the last leaf
// leaf_lengths[leaf_count - 1] = 1 + len_missing % per_leaf;
leaves[leaf_count - 1].length = 1 + len_missing - (leaf_count - 1) * per_leaf;
// Adjust the length of the last partial
partials[partial_count - 1].length = 1 + len_missing - (partial_count - 1) * missing_per_partial;
// Now reduce all the leaves to a single poly
// Reduce all the partials to a single poly
int reduction_factor = 4; // must be a power of 2 (TODO why?)
int reduction_factor = 4; // must be a power of 2 (for sake of the FFTs in reduce partials)
fr_t *scratch;
TRY(new_fr_array(&scratch, n * 3));
while (leaf_count > 1) {
uint64_t reduced_count = (leaf_count + reduction_factor - 1) / reduction_factor;
uint64_t leaf_size = next_power_of_two(leaves[0].length);
while (partial_count > 1) {
uint64_t reduced_count = (partial_count + reduction_factor - 1) / reduction_factor;
uint64_t partial_size = next_power_of_two(partials[0].length);
for (uint64_t i = 0; i < reduced_count; i++) {
uint64_t start = i * reduction_factor;
uint64_t end = start + reduction_factor;
// E.g. if we *started* with 2 leaves, we won't have more than that since it is already a power
// of 2. If we had 3, it would have been rounded up anyway. So just pick the end
uint64_t out_end = end * leaf_size;
uint64_t out_end = end * partial_size;
if (out_end > n) out_end = n;
fr_t *reduced = work + start * leaf_size;
uint64_t reduced_len = out_end - start * leaf_size;
fr_t *reduced = work + start * partial_size;
uint64_t reduced_len = out_end - start * partial_size;
if (reduced_len > length) reduced_len = length;
if (end > leaf_count) end = leaf_count;
uint64_t leaves_slice_len = end - start;
if (leaves_slice_len > 1) {
leaves[i].coeffs = reduced;
TRY(reduce_leaves(&leaves[i], reduced_len, scratch, n * 3, &leaves[start], leaves_slice_len, fs));
if (end > partial_count) end = partial_count;
uint64_t partials_slice = end - start;
partials[i].coeffs = reduced;
if (partials_slice > 1) {
TRY(reduce_partials(&partials[i], reduced_len, scratch, n * 3, &partials[start], partials_slice,
fs));
} else {
leaves[i].coeffs = reduced;
leaves[i].length = leaves[start].length;
partials[i].length = partials[start].length;
}
}
leaf_count = reduced_count;
partial_count = reduced_count;
}
*zero_poly_len = leaves[0].length;
for (uint64_t i = 0; i < length; i++) {
zero_poly[i] = i < *zero_poly_len ? leaves[0].coeffs[i] : fr_zero;
}
// Process final output
TRY(pad_p(zero_poly, length, &partials[0]));
TRY(fft_fr(zero_eval, zero_poly, false, length, fs));
*zero_poly_len = partials[0].length;
free(work);
free(leaves);
free(partials);
free(scratch);
}

10
src/zero_poly.h
View File

@ -17,17 +17,17 @@
/**
* @file zero_poly.h
*
* Methods for constructing zero polynomials and reconstructing polynomials from partial evaluations on a subgroup
* Methods for constructing polynomials that evaluate to zero for given lists of powers of roots of unity.
*/
#include "c_kzg.h"
#include "fft_common.h"
#include "poly.h"
C_KZG_RET do_zero_poly_mul_leaf(fr_t *dst, uint64_t len_dst, const uint64_t *indices, uint64_t len_indices,
uint64_t stride, const FFTSettings *fs);
C_KZG_RET reduce_leaves(poly *dst, uint64_t len_dst, fr_t *scratch, uint64_t len_scratch, const poly *leaves,
uint64_t leaf_count, const FFTSettings *fs);
C_KZG_RET do_zero_poly_mul_partial(fr_t *dst, uint64_t len_dst, const uint64_t *indices, uint64_t len_indices,
uint64_t stride, const FFTSettings *fs);
C_KZG_RET reduce_partials(poly *dst, uint64_t len_dst, fr_t *scratch, uint64_t len_scratch, const poly *partials,
uint64_t partial_count, const FFTSettings *fs);
C_KZG_RET zero_polynomial_via_multiplication(fr_t *zero_eval, fr_t *zero_poly, uint64_t *zero_poly_len, uint64_t length,
const uint64_t *missing_indices, uint64_t len_missing,
const FFTSettings *fs);

85
src/zero_poly_test.c
View File

@ -60,30 +60,30 @@ uint64_t expected_poly_u64[16][4] = {
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}};
void test_reduce_leaves(void) {
void test_reduce_partials(void) {
FFTSettings fs;
TEST_CHECK(C_KZG_OK == new_fft_settings(&fs, 4));
fr_t from_tree_reduction_coeffs[16], from_direct[9], scratch[48];
poly from_tree_reduction;
from_tree_reduction.coeffs = from_tree_reduction_coeffs;
// Via reduce_leaves
// Via reduce_partials
poly leaves[4];
fr_t leaf0[3], leaf1[3], leaf2[3], leaf3[3];
leaves[0].coeffs = leaf0, leaves[0].length = 3;
leaves[1].coeffs = leaf1, leaves[1].length = 3;
leaves[2].coeffs = leaf2, leaves[2].length = 3;
leaves[3].coeffs = leaf3, leaves[3].length = 3;
const uint64_t leaf_indices[4][2] = {{1, 3}, {7, 8}, {9, 10}, {12, 13}};
poly partials[4];
fr_t partial0[3], partial1[3], partial2[3], partial3[3];
partials[0].coeffs = partial0, partials[0].length = 3;
partials[1].coeffs = partial1, partials[1].length = 3;
partials[2].coeffs = partial2, partials[2].length = 3;
partials[3].coeffs = partial3, partials[3].length = 3;
const uint64_t partial_indices[4][2] = {{1, 3}, {7, 8}, {9, 10}, {12, 13}};
for (int i = 0; i < 4; i++) {
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_leaf(leaves[i].coeffs, 3, leaf_indices[i], 2, 1, &fs));
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_partial(partials[i].coeffs, 3, partial_indices[i], 2, 1, &fs));
}
TEST_CHECK(C_KZG_OK == reduce_leaves(&from_tree_reduction, 16, scratch, 48, leaves, 4, &fs));
TEST_CHECK(C_KZG_OK == reduce_partials(&from_tree_reduction, 16, scratch, 48, partials, 4, &fs));
// Direct
uint64_t indices[] = {1, 3, 7, 8, 9, 10, 12, 13};
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_leaf(from_direct, 9, indices, 8, 1, &fs));
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_partial(from_direct, 9, indices, 8, 1, &fs));
// Compare
for (int i = 0; i < 9; i++) {
@ -93,7 +93,7 @@ void test_reduce_leaves(void) {
free_fft_settings(&fs);
}
void reduce_leaves_random(void) {
void reduce_partials_random(void) {
for (int scale = 5; scale < 13; scale++) {
for (int ii = 1; ii <= 7; ii++) {
float missing_ratio = 0.1 * ii;
@ -110,24 +110,24 @@ void reduce_leaves_random(void) {
}
shuffle(missing, point_count);
// Build the leaves
poly *leaves;
const int points_per_leaf = 63;
uint64_t indices[points_per_leaf];
uint64_t leaf_count = (missing_count + points_per_leaf - 1) / points_per_leaf;
TEST_CHECK(C_KZG_OK == new_poly_array(&leaves, leaf_count));
for (uint64_t i = 0; i < leaf_count; i++) {
uint64_t start = i * points_per_leaf;
uint64_t end = start + points_per_leaf;
// Build the partials
poly *partials;
const int missing_per_partial = 63;
uint64_t indices[missing_per_partial];
uint64_t partial_count = (missing_count + missing_per_partial - 1) / missing_per_partial;
TEST_CHECK(C_KZG_OK == new_poly_array(&partials, partial_count));
for (uint64_t i = 0; i < partial_count; i++) {
uint64_t start = i * missing_per_partial;
uint64_t end = start + missing_per_partial;
if (end > missing_count) end = missing_count;
uint64_t leaf_size = end - start;
TEST_CHECK(C_KZG_OK == new_fr_array(&leaves[i].coeffs, leaf_size + 1));
for (int j = 0; j < leaf_size; j++) {
indices[j] = missing[i * points_per_leaf + j];
uint64_t partial_size = end - start;
TEST_CHECK(C_KZG_OK == new_fr_array(&partials[i].coeffs, partial_size + 1));
for (int j = 0; j < partial_size; j++) {
indices[j] = missing[i * missing_per_partial + j];
}
leaves[i].length = leaf_size + 1;
TEST_CHECK(C_KZG_OK ==
do_zero_poly_mul_leaf(leaves[i].coeffs, leaves[i].length, indices, leaf_size, 1, &fs));
partials[i].length = partial_size + 1;
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_partial(partials[i].coeffs, partials[i].length, indices,
partial_size, 1, &fs));
}
// From tree reduction
@ -135,14 +135,14 @@ void reduce_leaves_random(void) {
TEST_CHECK(C_KZG_OK == new_poly(&from_tree_reduction, point_count));
fr_t *scratch;
TEST_CHECK(C_KZG_OK == new_fr_array(&scratch, point_count * 3));
TEST_CHECK(C_KZG_OK == reduce_leaves(&from_tree_reduction, point_count, scratch, point_count * 3, leaves,
leaf_count, &fs));
TEST_CHECK(C_KZG_OK == reduce_partials(&from_tree_reduction, point_count, scratch, point_count * 3,
partials, partial_count, &fs));
// From direct
fr_t *from_direct;
TEST_CHECK(C_KZG_OK == new_fr_array(&from_direct, missing_count + 1));
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_leaf(from_direct, missing_count + 1, missing, missing_count,
fs.max_width / point_count, &fs));
TEST_CHECK(C_KZG_OK == do_zero_poly_mul_partial(from_direct, missing_count + 1, missing, missing_count,
fs.max_width / point_count, &fs));
for (uint64_t i = 0; i < missing_count + 1; i++) {
TEST_CHECK(fr_equal(&from_tree_reduction.coeffs[i], &from_direct[i]));
@ -151,10 +151,10 @@ void reduce_leaves_random(void) {
free_poly(&from_tree_reduction);
free(from_direct);
free(scratch);
for (uint64_t i = 0; i < leaf_count; i++) {
free_poly(&leaves[i]);
for (uint64_t i = 0; i < partial_count; i++) {
free_poly(&partials[i]);
}
free(leaves);
free(partials);
free(missing);
free_fft_settings(&fs);
}
@ -260,7 +260,7 @@ void zero_poly_random(void) {
}
}
// TODO: fix up the edge cases - zero_poly... fails for very large numbers of missing indices
// We know it doesn't work when all indices are missing
if (len_missing == fs.max_width) {
free_fft_settings(&fs);
continue;
@ -284,8 +284,6 @@ void zero_poly_random(void) {
fr_t out;
eval_poly(&out, &p, &fs.expanded_roots_of_unity[missing[i]]);
ret = TEST_CHECK(fr_is_zero(&out));
TEST_MSG("Failed for scale = %d, len_missing = %d, zero_poly_len = %lu", scale, len_missing,
zero_poly_len);
TEST_MSG("Failed for missing[%d] = %lu", i, missing[i]);
}
@ -328,6 +326,9 @@ void zero_poly_all_but_one(void) {
TEST_CHECK(C_KZG_OK == zero_polynomial_via_multiplication(zero_eval, zero_poly, &zero_poly_len, fs.max_width,
missing, len_missing, &fs));
TEST_CHECK(len_missing + 1 == zero_poly_len);
TEST_MSG("ZeroPolyLen: expected %d, got %lu", len_missing + 1, zero_poly_len);
poly p;
p.length = zero_poly_len;
p.coeffs = zero_poly;
@ -376,7 +377,7 @@ void zero_poly_252(void) {
TEST_CHECK(C_KZG_OK == zero_polynomial_via_multiplication(zero_eval, zero_poly, &zero_poly_len, fs.max_width,
missing, len_missing, &fs));
TEST_CHECK(253 == zero_poly_len);
TEST_CHECK(len_missing + 1 == zero_poly_len);
TEST_MSG("ZeroPolyLen: expected %d, got %lu", len_missing + 1, zero_poly_len);
poly p;
@ -409,9 +410,9 @@ void zero_poly_252(void) {
TEST_LIST = {
{"ZERO_POLY_TEST", title},
{"test_reduce_leaves", test_reduce_leaves},
{"test_reduce_partials", test_reduce_partials},
{"check_test_data", check_test_data},
{"reduce_leaves_random", reduce_leaves_random},
{"reduce_partials_random", reduce_partials_random},
{"zero_poly_known", zero_poly_known},
{"zero_poly_random", zero_poly_random},
{"zero_poly_all_but_one", zero_poly_all_but_one},