math: Use erfc from CORE-MATH

The current implementation precision shows the following accuracy, on
three ranges ([-DBL_MAX,5], [-5,5], [5,DBL_MAX]) with 10e9 uniform
randomly generated numbers for each range (first column is the
accuracy in ULP, with '0' being correctly rounded, second is the
number of samples with the corresponding precision):

* Range [-DBL_MAX, -5]
 * FE_TONEAREST
     0:      10000000000 100.00%
 * FE_UPWARD
     0:      10000000000 100.00%
 * FE_DOWNWARD
     0:      10000000000 100.00%
 * FE_TOWARDZERO
     0:      10000000000 100.00%

* Range [-5, 5]
 * FE_TONEAREST
     0:       8069309665  80.69%
     1:       1882910247  18.83%
     2:         47485296   0.47%
     3:           293749   0.00%
     4:             1043   0.00%
 * FE_UPWARD
     0:       5540301026  55.40%
     1:       2026739127  20.27%
     2:       1774882486  17.75%
     3:        567324466   5.67%
     4:         86913847   0.87%
     5:          3820789   0.04%
     6:            18259   0.00%
 * FE_DOWNWARD
     0:       5520969586  55.21%
     1:       2057293099  20.57%
     2:       1778334818  17.78%
     3:        557521494   5.58%
     4:         82473927   0.82%
     5:          3393276   0.03%
     6:            13800   0.00%
 * FE_TOWARDZERO
     0:       6220287175  62.20%
     1:       2323846149  23.24%
     2:       1251999920  12.52%
     3:        190748245   1.91%
     4:         12996232   0.13%
     5:           122279   0.00%

* Range [5, DBL_MAX]
 * FE_TONEAREST
     0:      10000000000 100.00%
 * FE_UPWARD
     0:      10000000000 100.00%
 * FE_DOWNWARD
     0:      10000000000 100.00%
 * FE_TOWARDZERO
     0:      10000000000 100.00%

The CORE-MATH implementation is correctly rounded for any rounding mode.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).

Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1,
gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1) shows:

reciprocal-throughput        master        patched   improvement
x86_64                      49.0980       267.0660      -443.94%
x86_64v2                    49.3220       257.6310      -422.34%
x86_64v3                    42.9539        84.9571       -97.79%
aarch64                     28.7266        52.9096       -84.18%
power10                     14.1673        25.1273       -77.36%

Latency                      master        patched   improvement
x86_64                      95.6640       269.7060      -181.93%
x86_64v2                    95.8296       260.4860      -171.82%
x86_64v3                    91.1658       112.7150       -23.64%
aarch64                     37.0745        58.6791       -58.27%
power10                     23.3197        31.5737       -35.39%

Checked on x86_64-linux-gnu, aarch64-linux-gnu, and
powerpc64le-linux-gnu.

Reviewed-by: DJ Delorie <dj@redhat.com>

2 files changed, 72 insertions, 0 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 3921666dbd..fcf19cc1e6 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -5729,6 +5729,9 @@ erfc 0x2.56af04p+0
 erfc 0x2.b7f8cb76737d2af98dead7c4c5eep+0
 erfc 0x2.dfb9b4p+0
 erfc 0x1.e33c9ep+0
+
+erfc 0x1.a8f7bfbd15495p+4
+
 # the next value generates larger error bounds on x86_64 (binary64)
 erfc 0x1.3ffcbf39febb4p+0
 
diff --git a/math/auto-libm-test-out-erfc b/math/auto-libm-test-out-erfc
index 76f922ba03..c9572194fd 100644
--- a/math/auto-libm-test-out-erfc
+++ b/math/auto-libm-test-out-erfc
@@ -4444,6 +4444,75 @@ erfc 0x1.e33c9ep+0
 = erfc tonearest ibm128 0x1.e33c9ep+0 : 0x1.f1cb04b622e6f4d5035449633b8p-8 : inexact-ok
 = erfc towardzero ibm128 0x1.e33c9ep+0 : 0x1.f1cb04b622e6f4d5035449633bp-8 : inexact-ok
 = erfc upward ibm128 0x1.e33c9ep+0 : 0x1.f1cb04b622e6f4d5035449633b8p-8 : inexact-ok
+erfc 0x1.a8f7bfbd15495p+4
+= erfc downward binary32 0x1.a8f7cp+4 : 0x0p+0 : inexact-ok underflow errno-erange
+= erfc tonearest binary32 0x1.a8f7cp+4 : 0x0p+0 : inexact-ok underflow errno-erange
+= erfc towardzero binary32 0x1.a8f7cp+4 : 0x0p+0 : inexact-ok underflow errno-erange
+= erfc upward binary32 0x1.a8f7cp+4 : 0x8p-152 : inexact-ok underflow errno-erange-ok
+= erfc downward binary64 0x1.a8f7cp+4 : 0x1.99edf481adc28p-1024 : inexact-ok underflow errno-erange-ok
+= erfc tonearest binary64 0x1.a8f7cp+4 : 0x1.99edf481adc28p-1024 : inexact-ok underflow errno-erange-ok
+= erfc towardzero binary64 0x1.a8f7cp+4 : 0x1.99edf481adc28p-1024 : inexact-ok underflow errno-erange-ok
+= erfc upward binary64 0x1.a8f7cp+4 : 0x1.99edf481adc2cp-1024 : inexact-ok underflow errno-erange-ok
+= erfc downward intel96 0x1.a8f7cp+4 : 0x1.99edf481adc29f24p-1024 : inexact-ok
+= erfc tonearest intel96 0x1.a8f7cp+4 : 0x1.99edf481adc29f26p-1024 : inexact-ok
+= erfc towardzero intel96 0x1.a8f7cp+4 : 0x1.99edf481adc29f24p-1024 : inexact-ok
+= erfc upward intel96 0x1.a8f7cp+4 : 0x1.99edf481adc29f26p-1024 : inexact-ok
+= erfc downward m68k96 0x1.a8f7cp+4 : 0x1.99edf481adc29f24p-1024 : inexact-ok
+= erfc tonearest m68k96 0x1.a8f7cp+4 : 0x1.99edf481adc29f26p-1024 : inexact-ok
+= erfc towardzero m68k96 0x1.a8f7cp+4 : 0x1.99edf481adc29f24p-1024 : inexact-ok
+= erfc upward m68k96 0x1.a8f7cp+4 : 0x1.99edf481adc29f26p-1024 : inexact-ok
+= erfc downward binary128 0x1.a8f7cp+4 : 0x1.99edf481adc29f25df2cafcf9bbfp-1024 : inexact-ok
+= erfc tonearest binary128 0x1.a8f7cp+4 : 0x1.99edf481adc29f25df2cafcf9bcp-1024 : inexact-ok
+= erfc towardzero binary128 0x1.a8f7cp+4 : 0x1.99edf481adc29f25df2cafcf9bbfp-1024 : inexact-ok
+= erfc upward binary128 0x1.a8f7cp+4 : 0x1.99edf481adc29f25df2cafcf9bcp-1024 : inexact-ok
+= erfc downward ibm128 0x1.a8f7cp+4 : 0x1.99edf481adc28p-1024 : inexact-ok underflow errno-erange-ok
+= erfc tonearest ibm128 0x1.a8f7cp+4 : 0x1.99edf481adc28p-1024 : inexact-ok underflow errno-erange-ok
+= erfc towardzero ibm128 0x1.a8f7cp+4 : 0x1.99edf481adc28p-1024 : inexact-ok underflow errno-erange-ok
+= erfc upward ibm128 0x1.a8f7cp+4 : 0x1.99edf481adc2cp-1024 : inexact-ok underflow errno-erange-ok
+= erfc downward binary32 0x1.a8f7bep+4 : 0x0p+0 : inexact-ok underflow errno-erange
+= erfc tonearest binary32 0x1.a8f7bep+4 : 0x0p+0 : inexact-ok underflow errno-erange
+= erfc towardzero binary32 0x1.a8f7bep+4 : 0x0p+0 : inexact-ok underflow errno-erange
+= erfc upward binary32 0x1.a8f7bep+4 : 0x8p-152 : inexact-ok underflow errno-erange-ok
+= erfc downward binary64 0x1.a8f7bep+4 : 0x1.99f8988d84cbcp-1024 : inexact-ok underflow errno-erange-ok
+= erfc tonearest binary64 0x1.a8f7bep+4 : 0x1.99f8988d84ccp-1024 : inexact-ok underflow errno-erange-ok
+= erfc towardzero binary64 0x1.a8f7bep+4 : 0x1.99f8988d84cbcp-1024 : inexact-ok underflow errno-erange-ok
+= erfc upward binary64 0x1.a8f7bep+4 : 0x1.99f8988d84ccp-1024 : inexact-ok underflow errno-erange-ok
+= erfc downward intel96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06ep-1024 : inexact-ok
+= erfc tonearest intel96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06ep-1024 : inexact-ok
+= erfc towardzero intel96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06ep-1024 : inexact-ok
+= erfc upward intel96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe07p-1024 : inexact-ok
+= erfc downward m68k96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06ep-1024 : inexact-ok
+= erfc tonearest m68k96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06ep-1024 : inexact-ok
+= erfc towardzero m68k96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06ep-1024 : inexact-ok
+= erfc upward m68k96 0x1.a8f7bep+4 : 0x1.99f8988d84cbe07p-1024 : inexact-ok
+= erfc downward binary128 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06e999bcdeda04dp-1024 : inexact-ok
+= erfc tonearest binary128 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06e999bcdeda04ep-1024 : inexact-ok
+= erfc towardzero binary128 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06e999bcdeda04dp-1024 : inexact-ok
+= erfc upward binary128 0x1.a8f7bep+4 : 0x1.99f8988d84cbe06e999bcdeda04ep-1024 : inexact-ok
+= erfc downward ibm128 0x1.a8f7bep+4 : 0x1.99f8988d84cbcp-1024 : inexact-ok underflow errno-erange-ok
+= erfc tonearest ibm128 0x1.a8f7bep+4 : 0x1.99f8988d84ccp-1024 : inexact-ok underflow errno-erange-ok
+= erfc towardzero ibm128 0x1.a8f7bep+4 : 0x1.99f8988d84cbcp-1024 : inexact-ok underflow errno-erange-ok
+= erfc upward ibm128 0x1.a8f7bep+4 : 0x1.99f8988d84ccp-1024 : inexact-ok underflow errno-erange-ok
+= erfc downward binary64 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f6568p-1024 : inexact-ok underflow errno-erange-ok
+= erfc tonearest binary64 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656cp-1024 : inexact-ok underflow errno-erange-ok
+= erfc towardzero binary64 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f6568p-1024 : inexact-ok underflow errno-erange-ok
+= erfc upward binary64 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656cp-1024 : inexact-ok underflow errno-erange-ok
+= erfc downward intel96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7fep-1024 : inexact-ok
+= erfc tonearest intel96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a8p-1024 : inexact-ok
+= erfc towardzero intel96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7fep-1024 : inexact-ok
+= erfc upward intel96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a8p-1024 : inexact-ok
+= erfc downward m68k96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7fep-1024 : inexact-ok
+= erfc tonearest m68k96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a8p-1024 : inexact-ok
+= erfc towardzero m68k96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7fep-1024 : inexact-ok
+= erfc upward m68k96 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a8p-1024 : inexact-ok
+= erfc downward binary128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7ffffffffff2272p-1024 : inexact-ok
+= erfc tonearest binary128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7ffffffffff2273p-1024 : inexact-ok
+= erfc towardzero binary128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7ffffffffff2272p-1024 : inexact-ok
+= erfc upward binary128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656a7ffffffffff2273p-1024 : inexact-ok
+= erfc downward ibm128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f6568p-1024 : inexact-ok underflow errno-erange-ok
+= erfc tonearest ibm128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656cp-1024 : inexact-ok underflow errno-erange-ok
+= erfc towardzero ibm128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f6568p-1024 : inexact-ok underflow errno-erange-ok
+= erfc upward ibm128 0x1.a8f7bfbd15495p+4 : 0x1.99ef5883f656cp-1024 : inexact-ok underflow errno-erange-ok
 erfc 0x1.3ffcbf39febb4p+0
 = erfc downward binary32 0x1.3ffccp+0 : 0x1.3bd95ep-4 : inexact-ok
 = erfc tonearest binary32 0x1.3ffccp+0 : 0x1.3bd96p-4 : inexact-ok