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/* prime < 260, degrees are decaying but always less than 410. Coefficients can
always be stored in uint8_t. Coefficient sequences are always on the form
[a0, a1, a2, ..., an, 0, 0, ..., 0, 1].
Hence, store prime, degree, number of "non-trivial" coefficients, as well as
the "non-trivial" coefficients. */
/* 260 < prime < 300, degrees = 1, ..., 12. Polynomials are on the form
[b0, 1],
[a0, b1, 1],
[b0, a1, 0, 1],
[a0, b2, a2, 0, 1],
[b0, a3, 0, 0, 0, 1],
[a0, b3, b4, a4, a5, 0, 1],
[b0, a6, 0, 0, 0, 0, 0, 1],
[a0, b6, b7, b8, a7, 0, 0, 0, 1],
[b0, b9, b10, a8, 0, 0, 0, 0, 0, 1],
[a0, b11, b12, b13, b14, b15, 0, 0, 0, 0, 1],
[b0, a9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[a0, a10, b16, a11, b17, a12, a13, a14, 0, 0, 0, 0, 1],
where a0, ..., a14 < 2^8 and b0, ..., b10 < 2^16. Store prime as uint8_t with
offset of 2^8, and store coefficients as 15 uint8_t with 11 uint16_t. */
/* 300 < prime < 1000, degrees = 1, ..., 9.
Polynomials are on the form
[b0, 1],
[a0, b1, 1],
[b0, a1, 0, 1],
[a0, b2, a2, 0, 1],
[b0, a3, 0, 0, 0, 1],
[a0, b3, b4, b5, a4, 0, 1],
[b0, a5, 0, 0, 0, 0, 0, 1],
[a0, b6, b7, b8, a6, 0, 0, 0, 1],
[b0, b9, b10, a7, 0, 0, 0, 0, 0, 1],
where a0, ..., a7 < 2^8 and b0, ..., b10 < 2^16. Store prime as uint16_t, and
store coefficients as 8 uint8_t with 11 uint16_t. */
/* 1000 < prime < 3371, degrees = 1, ..., 7, 9. Some exceptions exists where
degree 7 and 9 does not exist. These are p = 2689, 2797, 2833, 3019, 3163,
3209 and 3331. Polynomials are on the form
[b0, 1],
[a0, b1, 1],
[b0, a1, 0, 1],
[a0, b2, a2, 0, 1],
[b0, a3, 0, 0, 0, 1],
[a0, b3, b4, b5, a4, 0, 1],
[b0, a5, 0, 0, 0, 0, 0, 1],
[b0, b6, b7, a6, 0, 0, 0, 0, 0, 1],
where a0, ..., a6 < 2^8 and b0, ..., b7 < 2^16. Store prime as uint16_t, and
store coefficients as 7 uint8_t with 8 uint16_t. */
/* 3371 <= prime < 11000, degrees = 1, ..., 6.
Polynomials are on the form
[b0, 1],
[a0, b1, 1],
[b0, a1, 0, 1],
[a0, b2, a2, 0, 1],
[b0, a3, 0, 0, 0, 1],
[a0, b3, b4, b5, a4, 0, 1],
where a0, ..., a4 < 2^8 and b0, ..., b5 < 2^16. Store prime as uint16_t, and
store coefficients as 5 uint8_t with 6 uint16_t. */
/* 11000 < prime < 2^16, degrees = 1, ..., 4.
Polynomials are on the form
[b0, 1],
[a0, b1, 1],
[b0, a1, 0, 1],
[a0, b2, a2, 0, 1],
where a0, ..., a2 < 2^8 and b0, ..., b2 < 2^16. Store prime as uint16_t, and
store each prime as 3 uint8_t with 3 uint16_t. */
/* 2^16 < prime, then degrees are all four.
Polynomials are on the form
[a0, b0, a1, 0, 1],
where a0, a1 < 2^8 and b0 < 2^32. Store prime as uint16_t where everything
primes are offset by 2^16, and store coefficients as 2 uint8_t with 1
uint32_t. */
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