Open Access
Table B.1
Precomputed parameters for Taylor-based scaling and squaring algorithm for u=2−53. In each row from left to right we have respectively the number of matrix product in the scaling phase k, the Taylor series polynomial order mk, the Horner-Paterson-Stockmeyer parameters qk and rk, and the number of matrix product Πmk.
| k | mk | qk | rk | θmk |  |
Πm |
|---|---|---|---|---|---|---|
| 1 | 2 | 1 | 2 | 2.5810 × 10−8 | 8.7334 × 10−6 | 1 |
| 2 | 4 | 2 | 2 | 3.3972 × 10−4 | 1.6778 × 10−3 | 2 |
| 3 | 6 | 2 | 3 | 9.0657 × 10−3 | 1.7720 × 10−2 | 3 |
| 4 | 9 | 3 | 3 | 8.9578 × 10−2 | 1.1354 × 10−1 | 4 |
| 5 | 12 | 3 | 4 | 2/9962 × 10−1 | 3.2690 × 10−1 | 5 |
| 6 | 16 | 4 | 4 | 7.80 × 10−1 | 7.8738 × 10−1 | 6 |
| 7 | 20 | 4 | 5 | 1.4383 | 1.4383 | 7 |
| 8 | 25 | 5 | 5 | 2.4286 | 2.4286 | 8 |
| 9 | 30 | 5 | 6 | 3.5397 | 3.5397 | 9 |
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