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, 75 insertions, 0 deletions

diff --git a/math/auto-libm-test-out-y1 b/math/auto-libm-test-out-y1
index af68e6c05a..ab920d1542 100644
--- a/math/auto-libm-test-out-y1
+++ b/math/auto-libm-test-out-y1
@@ -795,6 +795,81 @@ y1 0x1p-10000
 = y1 tonearest binary128 0x1p-10000 : -0xa.2f9836e4e441529fc2757d1f535p+9996 : inexact-ok
 = y1 towardzero binary128 0x1p-10000 : -0xa.2f9836e4e441529fc2757d1f5348p+9996 : inexact-ok
 = y1 upward binary128 0x1p-10000 : -0xa.2f9836e4e441529fc2757d1f5348p+9996 : inexact-ok
+y1 0x1.065194p+7 xfail-rounding:binary64 xfail-rounding:intel96 xfail-rounding:ibm128-libgcc
+= y1 downward binary32 0x8.328cap+4 : -0x3.2fe874p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 tonearest binary32 0x8.328cap+4 : -0x3.2fe87p-16 : inexact-ok
+= y1 towardzero binary32 0x8.328cap+4 : -0x3.2fe87p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 upward binary32 0x8.328cap+4 : -0x3.2fe87p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 downward binary64 0x8.328cap+4 : -0x3.2fe87001a1df4p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 tonearest binary64 0x8.328cap+4 : -0x3.2fe87001a1df4p-16 : inexact-ok
+= y1 towardzero binary64 0x8.328cap+4 : -0x3.2fe87001a1df2p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 upward binary64 0x8.328cap+4 : -0x3.2fe87001a1df2p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 downward intel96 0x8.328cap+4 : -0x3.2fe87001a1df3754p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 tonearest intel96 0x8.328cap+4 : -0x3.2fe87001a1df375p-16 : inexact-ok
+= y1 towardzero intel96 0x8.328cap+4 : -0x3.2fe87001a1df375p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 upward intel96 0x8.328cap+4 : -0x3.2fe87001a1df375p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 downward m68k96 0x8.328cap+4 : -0x3.2fe87001a1df3754p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 tonearest m68k96 0x8.328cap+4 : -0x3.2fe87001a1df375p-16 : inexact-ok
+= y1 towardzero m68k96 0x8.328cap+4 : -0x3.2fe87001a1df375p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 upward m68k96 0x8.328cap+4 : -0x3.2fe87001a1df375p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 downward binary128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aecb2p-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 tonearest binary128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aecb2p-16 : inexact-ok
+= y1 towardzero binary128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aecbp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 upward binary128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aecbp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 downward ibm128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aedp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 tonearest ibm128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aedp-16 : inexact-ok
+= y1 towardzero ibm128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aecp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+= y1 upward ibm128 0x8.328cap+4 : -0x3.2fe87001a1df375068d0356aecp-16 : xfail:binary64 xfail:intel96 xfail:ibm128-libgcc inexact-ok
+y1 0x1.c1badep+0 xfail-rounding:ibm128-libgcc
+= y1 downward binary32 0x1.c1badep+0 : -0x3.ff6378p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 tonearest binary32 0x1.c1badep+0 : -0x3.ff6374p-4 : inexact-ok
+= y1 towardzero binary32 0x1.c1badep+0 : -0x3.ff6374p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 upward binary32 0x1.c1badep+0 : -0x3.ff6374p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 downward binary64 0x1.c1badep+0 : -0x3.ff6375c9f4404p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 tonearest binary64 0x1.c1badep+0 : -0x3.ff6375c9f4402p-4 : inexact-ok
+= y1 towardzero binary64 0x1.c1badep+0 : -0x3.ff6375c9f4402p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 upward binary64 0x1.c1badep+0 : -0x3.ff6375c9f4402p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 downward intel96 0x1.c1badep+0 : -0x3.ff6375c9f440230cp-4 : xfail:ibm128-libgcc inexact-ok
+= y1 tonearest intel96 0x1.c1badep+0 : -0x3.ff6375c9f440230cp-4 : inexact-ok
+= y1 towardzero intel96 0x1.c1badep+0 : -0x3.ff6375c9f4402308p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 upward intel96 0x1.c1badep+0 : -0x3.ff6375c9f4402308p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 downward m68k96 0x1.c1badep+0 : -0x3.ff6375c9f440230cp-4 : xfail:ibm128-libgcc inexact-ok
+= y1 tonearest m68k96 0x1.c1badep+0 : -0x3.ff6375c9f440230cp-4 : inexact-ok
+= y1 towardzero m68k96 0x1.c1badep+0 : -0x3.ff6375c9f4402308p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 upward m68k96 0x1.c1badep+0 : -0x3.ff6375c9f4402308p-4 : xfail:ibm128-libgcc inexact-ok
+= y1 downward binary128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1ebp-4 : xfail:ibm128-libgcc inexact-ok
+= y1 tonearest binary128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1ebp-4 : inexact-ok
+= y1 towardzero binary128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1eaep-4 : xfail:ibm128-libgcc inexact-ok
+= y1 upward binary128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1eaep-4 : xfail:ibm128-libgcc inexact-ok
+= y1 downward ibm128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1fp-4 : xfail:ibm128-libgcc inexact-ok
+= y1 tonearest ibm128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1fp-4 : inexact-ok
+= y1 towardzero ibm128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1ep-4 : xfail:ibm128-libgcc inexact-ok
+= y1 upward ibm128 0x1.c1badep+0 : -0x3.ff6375c9f440230a8962842c1ep-4 : xfail:ibm128-libgcc inexact-ok
+y1 0x1.c1bc2ep+0
+= y1 downward binary32 0x1.c1bc2ep+0 : -0x3.ff56acp-4 : inexact-ok
+= y1 tonearest binary32 0x1.c1bc2ep+0 : -0x3.ff56a8p-4 : inexact-ok
+= y1 towardzero binary32 0x1.c1bc2ep+0 : -0x3.ff56a8p-4 : inexact-ok
+= y1 upward binary32 0x1.c1bc2ep+0 : -0x3.ff56a8p-4 : inexact-ok
+= y1 downward binary64 0x1.c1bc2ep+0 : -0x3.ff56a991ca78ap-4 : inexact-ok
+= y1 tonearest binary64 0x1.c1bc2ep+0 : -0x3.ff56a991ca788p-4 : inexact-ok
+= y1 towardzero binary64 0x1.c1bc2ep+0 : -0x3.ff56a991ca788p-4 : inexact-ok
+= y1 upward binary64 0x1.c1bc2ep+0 : -0x3.ff56a991ca788p-4 : inexact-ok
+= y1 downward intel96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd8p-4 : inexact-ok
+= y1 tonearest intel96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd4p-4 : inexact-ok
+= y1 towardzero intel96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd4p-4 : inexact-ok
+= y1 upward intel96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd4p-4 : inexact-ok
+= y1 downward m68k96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd8p-4 : inexact-ok
+= y1 tonearest m68k96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd4p-4 : inexact-ok
+= y1 towardzero m68k96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd4p-4 : inexact-ok
+= y1 upward m68k96 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd4p-4 : inexact-ok
+= y1 downward binary128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd5084138201442p-4 : inexact-ok
+= y1 tonearest binary128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd5084138201442p-4 : inexact-ok
+= y1 towardzero binary128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd508413820144p-4 : inexact-ok
+= y1 upward binary128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd508413820144p-4 : inexact-ok
+= y1 downward ibm128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd50841382015p-4 : inexact-ok
+= y1 tonearest ibm128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd50841382014p-4 : inexact-ok
+= y1 towardzero ibm128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd50841382014p-4 : inexact-ok
+= y1 upward ibm128 0x1.c1bc2ep+0 : -0x3.ff56a991ca788cd50841382014p-4 : inexact-ok
 y1 min
 = y1 downward binary32 0x4p-128 : -0x2.8be61p+124 : inexact-ok
 = y1 tonearest binary32 0x4p-128 : -0x2.8be60cp+124 : inexact-ok