Lines Matching +full:25 +full:a
19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
49 * where p(d) = d - 0.5*d*d + ... is a special minimax polynomial of
62 * testing of a float variant of this function showed a maximum final error
63 * of 0.5008 ulps. Non-exhaustive testing of a double variant of this
64 * function showed a maximum final error of 0.5078 ulps (near 1+1.0/256).
67 * degree of p(d)) small by using a large number of intervals. Using
68 * centers of intervals instead of endpoints reduces this maximum by a
69 * factor of 2 for a given number of intervals. p(d) is special only
71 * naturally. The most accurate minimax polynomial of a given degree might
129 * ln2_hi and each F_hi(i) are rounded to a number of bits that
146 * a minimum of 33. We only need about 12 bits in F_hi(i) for
152 * in a float for it automatically satisfies the above constraints.
191 { 0xc68000.0p-24, 0x823f30.0p-25, 0x19bd076f7c434e.0p-79 },
192 { 0xc58000.0p-24, 0x84d52c.0p-25, -0x1a327257af0f46.0p-79 },
193 { 0xc40000.0p-24, 0x88bc74.0p-25, 0x113f23def19c5a.0p-81 },
194 { 0xc30000.0p-24, 0x8b5ae6.0p-25, 0x1759f6e6b37de9.0p-79 },
195 { 0xc20000.0p-24, 0x8dfccb.0p-25, 0x1ad35ca6ed5148.0p-81 },
196 { 0xc10000.0p-24, 0x90a22b.0p-25, 0x1a1d71a87deba4.0p-79 },
197 { 0xbf8000.0p-24, 0x94a0d8.0p-25, -0x139e5210c2b731.0p-80 },
198 { 0xbe8000.0p-24, 0x974f16.0p-25, -0x18f6ebcff3ed73.0p-81 },
199 { 0xbd8000.0p-24, 0x9a00f1.0p-25, -0x1aa268be39aab7.0p-79 },
200 { 0xbc8000.0p-24, 0x9cb672.0p-25, -0x14c8815839c566.0p-79 },
201 { 0xbb0000.0p-24, 0xa0cda1.0p-25, 0x1eaf46390dbb24.0p-81 },
202 { 0xba0000.0p-24, 0xa38c6e.0p-25, 0x138e20d831f698.0p-81 },
203 { 0xb90000.0p-24, 0xa64f05.0p-25, -0x1e8d3c41123616.0p-82 },
204 { 0xb80000.0p-24, 0xa91570.0p-25, 0x1ce28f5f3840b2.0p-80 },
205 { 0xb70000.0p-24, 0xabdfbb.0p-25, -0x186e5c0a424234.0p-79 },
206 { 0xb60000.0p-24, 0xaeadef.0p-25, -0x14d41a0b2a08a4.0p-83 },
207 { 0xb50000.0p-24, 0xb18018.0p-25, 0x16755892770634.0p-79 },
208 { 0xb40000.0p-24, 0xb45642.0p-25, -0x16395ebe59b152.0p-82 },
209 { 0xb30000.0p-24, 0xb73077.0p-25, 0x1abc65c8595f09.0p-80 },
210 { 0xb20000.0p-24, 0xba0ec4.0p-25, -0x1273089d3dad89.0p-79 },
211 { 0xb10000.0p-24, 0xbcf133.0p-25, 0x10f9f67b1f4bbf.0p-79 },
212 { 0xb00000.0p-24, 0xbfd7d2.0p-25, -0x109fab90486409.0p-80 },
213 { 0xaf0000.0p-24, 0xc2c2ac.0p-25, -0x1124680aa43333.0p-79 },
214 { 0xae8000.0p-24, 0xc439b3.0p-25, -0x1f360cc4710fc0.0p-80 },
215 { 0xad8000.0p-24, 0xc72afd.0p-25, -0x132d91f21d89c9.0p-80 },
216 { 0xac8000.0p-24, 0xca20a2.0p-25, -0x16bf9b4d1f8da8.0p-79 },
217 { 0xab8000.0p-24, 0xcd1aae.0p-25, 0x19deb5ce6a6a87.0p-81 },
218 { 0xaa8000.0p-24, 0xd0192f.0p-25, 0x1a29fb48f7d3cb.0p-79 },
219 { 0xaa0000.0p-24, 0xd19a20.0p-25, 0x1127d3c6457f9d.0p-81 },
220 { 0xa90000.0p-24, 0xd49f6a.0p-25, -0x1ba930e486a0ac.0p-81 },
221 { 0xa80000.0p-24, 0xd7a94b.0p-25, -0x1b6e645f31549e.0p-79 },
222 { 0xa70000.0p-24, 0xdab7d0.0p-25, 0x1118a425494b61.0p-80 },
223 { 0xa68000.0p-24, 0xdc40d5.0p-25, 0x1966f24d29d3a3.0p-80 },
224 { 0xa58000.0p-24, 0xdf566d.0p-25, -0x1d8e52eb2248f1.0p-82 },
225 { 0xa48000.0p-24, 0xe270ce.0p-25, -0x1ee370f96e6b68.0p-80 },
226 { 0xa40000.0p-24, 0xe3ffce.0p-25, 0x1d155324911f57.0p-80 },
227 { 0xa30000.0p-24, 0xe72179.0p-25, -0x1fe6e2f2f867d9.0p-80 },
228 { 0xa20000.0p-24, 0xea4812.0p-25, 0x1b7be9add7f4d4.0p-80 },
229 { 0xa18000.0p-24, 0xebdd3d.0p-25, 0x1b3cfb3f7511dd.0p-79 },
230 { 0xa08000.0p-24, 0xef0b5b.0p-25, -0x1220de1f730190.0p-79 },
231 { 0xa00000.0p-24, 0xf0a451.0p-25, -0x176364c9ac81cd.0p-80 },
232 { 0x9f0000.0p-24, 0xf3da16.0p-25, 0x1eed6b9aafac8d.0p-81 },
233 { 0x9e8000.0p-24, 0xf576e9.0p-25, 0x1d593218675af2.0p-79 },
234 { 0x9d8000.0p-24, 0xf8b47c.0p-25, -0x13e8eb7da053e0.0p-84 },
235 { 0x9d0000.0p-24, 0xfa553f.0p-25, 0x1c063259bcade0.0p-79 },
236 { 0x9c0000.0p-24, 0xfd9ac5.0p-25, 0x1ef491085fa3c1.0p-79 },
237 { 0x9b8000.0p-24, 0xff3f8c.0p-25, 0x1d607a7c2b8c53.0p-79 },
506 * lets us avoid using a special method to give the desired
606 * x*G(i)-1 (with a reduced x) can be represented exactly, as
609 * Since x+x_lo is a hi+lo decomposition and subtracting 1
634 * it works in practice. It works even if it gives a wrong
638 * (By exhaustive testing, the worst case is d_hi = 0x1.bp-25.
639 * And if d is only a little tinier than that, we would have