Fix the inaccuracy of j0f/j1f/y0f/y1f [BZ #14469, #14470, #14471, #14472]

For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.

The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average.  Two different algorithms are used:

* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
  degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)

* for large inputs, an asymptotic formula from [1] is used

[1] Fast and Accurate Bessel Function Computation,
    John Harrison, Proceedings of Arith 19, 2009.

Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).

Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella  <adhemerval.zanella@linaro.org>

1 files changed, 50 insertions, 0 deletions

diff --git a/math/auto-libm-test-out-y0 b/math/auto-libm-test-out-y0
index 8ebb585170..f9742b0f69 100644
--- a/math/auto-libm-test-out-y0
+++ b/math/auto-libm-test-out-y0
@@ -820,6 +820,56 @@ y0 0xd.3432bp-4
 = y0 tonearest ibm128 0xd.3432bp-4 : -0xf.fdd871793bc71f92d6b137b44p-8 : inexact-ok
 = y0 towardzero ibm128 0xd.3432bp-4 : -0xf.fdd871793bc71f92d6b137b44p-8 : inexact-ok
 = y0 upward ibm128 0xd.3432bp-4 : -0xf.fdd871793bc71f92d6b137b44p-8 : inexact-ok
+y0 0x1.33eaacp+5 xfail:binary64 xfail:intel96 xfail-rounding:ibm128-libgcc
+= y0 downward binary32 0x2.67d558p+4 : 0xf.6b0ep-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 tonearest binary32 0x2.67d558p+4 : 0xf.6b0ep-16 : xfail:binary64 xfail:intel96 inexact-ok
+= y0 towardzero binary32 0x2.67d558p+4 : 0xf.6b0ep-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 upward binary32 0x2.67d558p+4 : 0xf.6b0e1p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 downward binary64 0x2.67d558p+4 : 0xf.6b0e005e95ad8p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 tonearest binary64 0x2.67d558p+4 : 0xf.6b0e005e95ad8p-16 : xfail:binary64 xfail:intel96 inexact-ok
+= y0 towardzero binary64 0x2.67d558p+4 : 0xf.6b0e005e95ad8p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 upward binary64 0x2.67d558p+4 : 0xf.6b0e005e95aep-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 downward intel96 0x2.67d558p+4 : 0xf.6b0e005e95ad82ap-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 tonearest intel96 0x2.67d558p+4 : 0xf.6b0e005e95ad82ap-16 : xfail:binary64 xfail:intel96 inexact-ok
+= y0 towardzero intel96 0x2.67d558p+4 : 0xf.6b0e005e95ad82ap-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 upward intel96 0x2.67d558p+4 : 0xf.6b0e005e95ad82bp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 downward m68k96 0x2.67d558p+4 : 0xf.6b0e005e95ad82ap-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 tonearest m68k96 0x2.67d558p+4 : 0xf.6b0e005e95ad82ap-16 : xfail:binary64 xfail:intel96 inexact-ok
+= y0 towardzero m68k96 0x2.67d558p+4 : 0xf.6b0e005e95ad82ap-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 upward m68k96 0x2.67d558p+4 : 0xf.6b0e005e95ad82bp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 downward binary128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b86p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 tonearest binary128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b86p-16 : xfail:binary64 xfail:intel96 inexact-ok
+= y0 towardzero binary128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b86p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 upward binary128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b868p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 downward ibm128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b8p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 tonearest ibm128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b8p-16 : xfail:binary64 xfail:intel96 inexact-ok
+= y0 towardzero ibm128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6b8p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y0 upward ibm128 0x2.67d558p+4 : 0xf.6b0e005e95ad82a5093316a6bcp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+y0 0x1.a681cep-1 xfail-rounding:ibm128-libgcc
+= y0 downward binary32 0xd.340e7p-4 : -0xf.ffff8p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 tonearest binary32 0xd.340e7p-4 : -0xf.ffff8p-8 : inexact-ok
+= y0 towardzero binary32 0xd.340e7p-4 : -0xf.ffff7p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 upward binary32 0xd.340e7p-4 : -0xf.ffff7p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 downward binary64 0xd.340e7p-4 : -0xf.ffff7f7e5aba8p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 tonearest binary64 0xd.340e7p-4 : -0xf.ffff7f7e5aba8p-8 : inexact-ok
+= y0 towardzero binary64 0xd.340e7p-4 : -0xf.ffff7f7e5abap-8 : xfail:ibm128-libgcc inexact-ok
+= y0 upward binary64 0xd.340e7p-4 : -0xf.ffff7f7e5abap-8 : xfail:ibm128-libgcc inexact-ok
+= y0 downward intel96 0xd.340e7p-4 : -0xf.ffff7f7e5aba736p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 tonearest intel96 0xd.340e7p-4 : -0xf.ffff7f7e5aba736p-8 : inexact-ok
+= y0 towardzero intel96 0xd.340e7p-4 : -0xf.ffff7f7e5aba735p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 upward intel96 0xd.340e7p-4 : -0xf.ffff7f7e5aba735p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 downward m68k96 0xd.340e7p-4 : -0xf.ffff7f7e5aba736p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 tonearest m68k96 0xd.340e7p-4 : -0xf.ffff7f7e5aba736p-8 : inexact-ok
+= y0 towardzero m68k96 0xd.340e7p-4 : -0xf.ffff7f7e5aba735p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 upward m68k96 0xd.340e7p-4 : -0xf.ffff7f7e5aba735p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 downward binary128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25de8p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 tonearest binary128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25dep-8 : inexact-ok
+= y0 towardzero binary128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25dep-8 : xfail:ibm128-libgcc inexact-ok
+= y0 upward binary128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25dep-8 : xfail:ibm128-libgcc inexact-ok
+= y0 downward ibm128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b26p-8 : xfail:ibm128-libgcc inexact-ok
+= y0 tonearest ibm128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25cp-8 : inexact-ok
+= y0 towardzero ibm128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25cp-8 : xfail:ibm128-libgcc inexact-ok
+= y0 upward ibm128 0xd.340e7p-4 : -0xf.ffff7f7e5aba735ccb0b13b25cp-8 : xfail:ibm128-libgcc inexact-ok
 y0 min
 = y0 downward binary32 0x4p-128 : -0x3.7ac89cp+4 : inexact-ok
 = y0 tonearest binary32 0x4p-128 : -0x3.7ac89cp+4 : inexact-ok