Searched hist:151969 (Results 1 - 4 of 4) sorted by relevance
| /freebsd-11.0-release/lib/msun/src/ | ||
| H A D | k_tan.c | diff 151969 Wed Nov 02 14:01:45 MST 2005 bde Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x) so that it can be faster for tiny x and avoided for reduced x. This improves things a little differently than for cosine and sine. We still need to reclassify x in the "kernel" functions, but we get an extra optimization for tiny x, and an overall optimization since tiny reduced x rarely happens. We also get optimizations for space and style. A large block of poorly duplicated code to fix a special case is no longer needed. This supersedes the fixes in k_sin.c revs 1.9 and 1.11 and k_sinf.c 1.8 and 1.10. Fixed wrong constant for the cutoff for "tiny" in tanf(). It was 2**-28, but should be almost the same as the cutoff in sinf() (2**-12). The incorrect cutoff protected us from the bugs fixed in k_sinf.c 1.8 and 1.10, except 4 cases of reduced args passed the cutoff and needed special handling in theory although not in practice. Now we essentially use a cutoff of 0 for the case of reduced args, so we now have 0 special args instead of 4. This change makes no difference to the results for sinf() (since it only changes the algorithm for the 4 special args and the results for those happen not to change), but it changes lots of results for sin(). Exhaustive testing is impossible for sin(), but exhaustive testing for sinf() (relative to a version with the old algorithm and a fixed cutoff) shows that the changes in the error are either reductions or from 0.5-epsilon ulps to 0.5+epsilon ulps. The new method just uses some extra terms in approximations so it tends to give more accurate results, and there are apparently no problems from having extra accuracy. On amd64 with -O1, on all float args the error range in ulps is reduced from (0.500, 0.665] to [0.335, 0.500) in 24168 cases and increased from 0.500-epsilon to 0.500+epsilon in 24 cases. Non- exhaustive testing by ucbtest shows no differences. |
| H A D | s_tan.c | diff 151969 Wed Nov 02 14:01:45 MST 2005 bde Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x) so that it can be faster for tiny x and avoided for reduced x. This improves things a little differently than for cosine and sine. We still need to reclassify x in the "kernel" functions, but we get an extra optimization for tiny x, and an overall optimization since tiny reduced x rarely happens. We also get optimizations for space and style. A large block of poorly duplicated code to fix a special case is no longer needed. This supersedes the fixes in k_sin.c revs 1.9 and 1.11 and k_sinf.c 1.8 and 1.10. Fixed wrong constant for the cutoff for "tiny" in tanf(). It was 2**-28, but should be almost the same as the cutoff in sinf() (2**-12). The incorrect cutoff protected us from the bugs fixed in k_sinf.c 1.8 and 1.10, except 4 cases of reduced args passed the cutoff and needed special handling in theory although not in practice. Now we essentially use a cutoff of 0 for the case of reduced args, so we now have 0 special args instead of 4. This change makes no difference to the results for sinf() (since it only changes the algorithm for the 4 special args and the results for those happen not to change), but it changes lots of results for sin(). Exhaustive testing is impossible for sin(), but exhaustive testing for sinf() (relative to a version with the old algorithm and a fixed cutoff) shows that the changes in the error are either reductions or from 0.5-epsilon ulps to 0.5+epsilon ulps. The new method just uses some extra terms in approximations so it tends to give more accurate results, and there are apparently no problems from having extra accuracy. On amd64 with -O1, on all float args the error range in ulps is reduced from (0.500, 0.665] to [0.335, 0.500) in 24168 cases and increased from 0.500-epsilon to 0.500+epsilon in 24 cases. Non- exhaustive testing by ucbtest shows no differences. |
| H A D | s_tanf.c | diff 151969 Wed Nov 02 14:01:45 MST 2005 bde Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x) so that it can be faster for tiny x and avoided for reduced x. This improves things a little differently than for cosine and sine. We still need to reclassify x in the "kernel" functions, but we get an extra optimization for tiny x, and an overall optimization since tiny reduced x rarely happens. We also get optimizations for space and style. A large block of poorly duplicated code to fix a special case is no longer needed. This supersedes the fixes in k_sin.c revs 1.9 and 1.11 and k_sinf.c 1.8 and 1.10. Fixed wrong constant for the cutoff for "tiny" in tanf(). It was 2**-28, but should be almost the same as the cutoff in sinf() (2**-12). The incorrect cutoff protected us from the bugs fixed in k_sinf.c 1.8 and 1.10, except 4 cases of reduced args passed the cutoff and needed special handling in theory although not in practice. Now we essentially use a cutoff of 0 for the case of reduced args, so we now have 0 special args instead of 4. This change makes no difference to the results for sinf() (since it only changes the algorithm for the 4 special args and the results for those happen not to change), but it changes lots of results for sin(). Exhaustive testing is impossible for sin(), but exhaustive testing for sinf() (relative to a version with the old algorithm and a fixed cutoff) shows that the changes in the error are either reductions or from 0.5-epsilon ulps to 0.5+epsilon ulps. The new method just uses some extra terms in approximations so it tends to give more accurate results, and there are apparently no problems from having extra accuracy. On amd64 with -O1, on all float args the error range in ulps is reduced from (0.500, 0.665] to [0.335, 0.500) in 24168 cases and increased from 0.500-epsilon to 0.500+epsilon in 24 cases. Non- exhaustive testing by ucbtest shows no differences. |
| H A D | k_tanf.c | diff 151969 Wed Nov 02 14:01:45 MST 2005 bde Moved the optimization for tiny x from __kernel_tan[f](x) to tan[f](x) so that it can be faster for tiny x and avoided for reduced x. This improves things a little differently than for cosine and sine. We still need to reclassify x in the "kernel" functions, but we get an extra optimization for tiny x, and an overall optimization since tiny reduced x rarely happens. We also get optimizations for space and style. A large block of poorly duplicated code to fix a special case is no longer needed. This supersedes the fixes in k_sin.c revs 1.9 and 1.11 and k_sinf.c 1.8 and 1.10. Fixed wrong constant for the cutoff for "tiny" in tanf(). It was 2**-28, but should be almost the same as the cutoff in sinf() (2**-12). The incorrect cutoff protected us from the bugs fixed in k_sinf.c 1.8 and 1.10, except 4 cases of reduced args passed the cutoff and needed special handling in theory although not in practice. Now we essentially use a cutoff of 0 for the case of reduced args, so we now have 0 special args instead of 4. This change makes no difference to the results for sinf() (since it only changes the algorithm for the 4 special args and the results for those happen not to change), but it changes lots of results for sin(). Exhaustive testing is impossible for sin(), but exhaustive testing for sinf() (relative to a version with the old algorithm and a fixed cutoff) shows that the changes in the error are either reductions or from 0.5-epsilon ulps to 0.5+epsilon ulps. The new method just uses some extra terms in approximations so it tends to give more accurate results, and there are apparently no problems from having extra accuracy. On amd64 with -O1, on all float args the error range in ulps is reduced from (0.500, 0.665] to [0.335, 0.500) in 24168 cases and increased from 0.500-epsilon to 0.500+epsilon in 24 cases. Non- exhaustive testing by ucbtest shows no differences. |
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