math: Use erfcf from CORE-MATH

The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance to the generic erfcf.

The code was adapted to glibc style and to use the definition of
math_config.h.

Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (M1,
gcc 13.2.1), and powerpc (POWER10, gcc 13.2.1):

latency                       master       patched  improvement
x86_64                       98.8796       66.2142       33.04%
x86_64v2                     98.9617       67.4221       31.87%
x86_64v3                     87.4161       53.1754       39.17%
aarch64                      33.8336       22.0781       34.75%
power10                      21.1750       13.5864       35.84%
powerpc                      21.4694       13.8149       35.65%

reciprocal-throughput         master       patched  improvement
x86_64                       48.5620       27.6731       43.01%
x86_64v2                     47.9497       28.3804       40.81%
x86_64v3                     42.0255       18.1355       56.85%
aarch64                      24.3938       13.4041       45.05%
power10                      10.4919        6.1881       41.02%
powerpc                       11.763       6.76468       42.49%

Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>

27 files changed, 178 insertions, 249 deletions

diff --git a/SHARED-FILES b/SHARED-FILES
index ccc5179..e6e29bc 100644
--- a/SHARED-FILES
+++ b/SHARED-FILES
@@ -276,3 +276,7 @@ sysdeps/ieee754/flt-32/s_erff.c
   (file src/binary32/erf/erff.c in CORE-MATH)
   - The code was adapted to use glibc code style and internal
     functions to handle errno, overflow, and underflow.
+sysdeps/ieee754/flt-32/s_erfcf.c
+  (file src/binary32/erfc/erfcf.c in CORE-MATH)
+  - The code was adapted to use glibc code style and internal
+    functions to handle errno, overflow, and underflow.
diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps
index bbb3a5c..3678bc3 100644
--- a/sysdeps/alpha/fpu/libm-test-ulps
+++ b/sysdeps/alpha/fpu/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 4
 
 Function: "erfc_downward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
index 9e422da..68d67b6 100644
--- a/sysdeps/arc/fpu/libm-test-ulps
+++ b/sysdeps/arc/fpu/libm-test-ulps
@@ -745,19 +745,15 @@ double: 2
 
 Function: "erfc":
 double: 5
-float: 5
 
 Function: "erfc_downward":
 double: 4
-float: 4
 
 Function: "erfc_towardzero":
 double: 4
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 5
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
index 2c24fdf..dc2499b 100644
--- a/sysdeps/arc/nofpu/libm-test-ulps
+++ b/sysdeps/arc/nofpu/libm-test-ulps
@@ -180,7 +180,6 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
index 153cd1f..000a5af 100644
--- a/sysdeps/arm/libm-test-ulps
+++ b/sysdeps/arm/libm-test-ulps
@@ -738,19 +738,15 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps
index d276db2..ed373cd 100644
--- a/sysdeps/csky/fpu/libm-test-ulps
+++ b/sysdeps/csky/fpu/libm-test-ulps
@@ -731,19 +731,15 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps
index ea08fd5..48a8c73 100644
--- a/sysdeps/csky/nofpu/libm-test-ulps
+++ b/sysdeps/csky/nofpu/libm-test-ulps
@@ -729,19 +729,15 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
index a16f86a..9c298ac 100644
--- a/sysdeps/hppa/fpu/libm-test-ulps
+++ b/sysdeps/hppa/fpu/libm-test-ulps
@@ -755,20 +755,16 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 1
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 041c180..5284078 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1098,25 +1098,21 @@ ldouble: 1
 
 Function: "erfc":
 double: 5
-float: 3
 float128: 4
 ldouble: 5
 
 Function: "erfc_downward":
 double: 5
-float: 6
 float128: 5
 ldouble: 4
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 float128: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 float128: 5
 ldouble: 5
 
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
index e3ee0c6..da00d80 100644
--- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
+++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
@@ -1101,25 +1101,21 @@ ldouble: 1
 
 Function: "erfc":
 double: 5
-float: 3
 float128: 4
 ldouble: 5
 
 Function: "erfc_downward":
 double: 5
-float: 6
 float128: 5
 ldouble: 4
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 float128: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 float128: 5
 ldouble: 5
 
diff --git a/sysdeps/ieee754/flt-32/s_erfcf.c b/sysdeps/ieee754/flt-32/s_erfcf.c
index fdba278..3dae2a0 100644
--- a/sysdeps/ieee754/flt-32/s_erfcf.c
+++ b/sysdeps/ieee754/flt-32/s_erfcf.c
@@ -1,173 +1,187 @@
-/* s_erfcf.c -- float version of s_erfc.c.
- */
+/* Correctly-rounded complementary error function for the binary32 format
 
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
+Copyright (c) 2023, 2024 Alexei Sibidanov.
 
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
-#endif
+This file is part of the CORE-MATH project
+project (file src/binary32/erfc/erfcf.c revision bc385c2).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
 
 #include <errno.h>
-#include <fix-int-fp-convert-zero.h>
-#include <libm-alias-float.h>
-#include <math-narrow-eval.h>
 #include <math.h>
-#include <math_private.h>
-
+#include <stdint.h>
+#include <libm-alias-float.h>
+#include "math_config.h"
 
-static const float
-tiny	    = 1e-30,
-half=  5.0000000000e-01, /* 0x3F000000 */
-one =  1.0000000000e+00, /* 0x3F800000 */
-two =  2.0000000000e+00, /* 0x40000000 */
-	/* c = (subfloat)0.84506291151 */
-erx =  8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to  erf on [0,0.84375]
- */
-pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
-pp1  = -3.2504209876e-01, /* 0xbea66beb */
-pp2  = -2.8481749818e-02, /* 0xbce9528f */
-pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
-pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
-qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
-qq2  =  6.5022252500e-02, /* 0x3d852a63 */
-qq3  =  5.0813062117e-03, /* 0x3ba68116 */
-qq4  =  1.3249473704e-04, /* 0x390aee49 */
-qq5  = -3.9602282413e-06, /* 0xb684e21a */
-/*
- * Coefficients for approximation to  erf  in [0.84375,1.25]
- */
-pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
-pa1  =  4.1485610604e-01, /* 0x3ed46805 */
-pa2  = -3.7220788002e-01, /* 0xbebe9208 */
-pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
-pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
-pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
-pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
-qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
-qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
-qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
-qa4  =  1.2617121637e-01, /* 0x3e013307 */
-qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
-qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
-/*
- * Coefficients for approximation to  erfc in [1.25,1/0.35]
- */
-ra0  = -9.8649440333e-03, /* 0xbc21a093 */
-ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
-ra2  = -1.0558626175e+01, /* 0xc128f022 */
-ra3  = -6.2375331879e+01, /* 0xc2798057 */
-ra4  = -1.6239666748e+02, /* 0xc322658c */
-ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
-ra6  = -8.1287437439e+01, /* 0xc2a2932b */
-ra7  = -9.8143291473e+00, /* 0xc11d077e */
-sa1  =  1.9651271820e+01, /* 0x419d35ce */
-sa2  =  1.3765776062e+02, /* 0x4309a863 */
-sa3  =  4.3456588745e+02, /* 0x43d9486f */
-sa4  =  6.4538726807e+02, /* 0x442158c9 */
-sa5  =  4.2900814819e+02, /* 0x43d6810b */
-sa6  =  1.0863500214e+02, /* 0x42d9451f */
-sa7  =  6.5702495575e+00, /* 0x40d23f7c */
-sa8  = -6.0424413532e-02, /* 0xbd777f97 */
-/*
- * Coefficients for approximation to  erfc in [1/.35,28]
- */
-rb0  = -9.8649431020e-03, /* 0xbc21a092 */
-rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
-rb2  = -1.7757955551e+01, /* 0xc18e104b */
-rb3  = -1.6063638306e+02, /* 0xc320a2ea */
-rb4  = -6.3756646729e+02, /* 0xc41f6441 */
-rb5  = -1.0250950928e+03, /* 0xc480230b */
-rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
-sb1  =  3.0338060379e+01, /* 0x41f2b459 */
-sb2  =  3.2579251099e+02, /* 0x43a2e571 */
-sb3  =  1.5367296143e+03, /* 0x44c01759 */
-sb4  =  3.1998581543e+03, /* 0x4547fdbb */
-sb5  =  2.5530502930e+03, /* 0x451f90ce */
-sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
-sb7  = -2.2440952301e+01; /* 0xc1b38712 */
+static const double E[] =
+  {
+    0x1p+0,               0x1.0163da9fb3335p+0, 0x1.02c9a3e778061p+0,
+    0x1.04315e86e7f85p+0, 0x1.059b0d3158574p+0, 0x1.0706b29ddf6dep+0,
+    0x1.0874518759bc8p+0, 0x1.09e3ecac6f383p+0, 0x1.0b5586cf9890fp+0,
+    0x1.0cc922b7247f7p+0, 0x1.0e3ec32d3d1a2p+0, 0x1.0fb66affed31bp+0,
+    0x1.11301d0125b51p+0, 0x1.12abdc06c31ccp+0, 0x1.1429aaea92dep+0,
+    0x1.15a98c8a58e51p+0, 0x1.172b83c7d517bp+0, 0x1.18af9388c8deap+0,
+    0x1.1a35beb6fcb75p+0, 0x1.1bbe084045cd4p+0, 0x1.1d4873168b9aap+0,
+    0x1.1ed5022fcd91dp+0, 0x1.2063b88628cd6p+0, 0x1.21f49917ddc96p+0,
+    0x1.2387a6e756238p+0, 0x1.251ce4fb2a63fp+0, 0x1.26b4565e27cddp+0,
+    0x1.284dfe1f56381p+0, 0x1.29e9df51fdee1p+0, 0x1.2b87fd0dad99p+0,
+    0x1.2d285a6e4030bp+0, 0x1.2ecafa93e2f56p+0, 0x1.306fe0a31b715p+0,
+    0x1.32170fc4cd831p+0, 0x1.33c08b26416ffp+0, 0x1.356c55f929ff1p+0,
+    0x1.371a7373aa9cbp+0, 0x1.38cae6d05d866p+0, 0x1.3a7db34e59ff7p+0,
+    0x1.3c32dc313a8e5p+0, 0x1.3dea64c123422p+0, 0x1.3fa4504ac801cp+0,
+    0x1.4160a21f72e2ap+0, 0x1.431f5d950a897p+0, 0x1.44e086061892dp+0,
+    0x1.46a41ed1d0057p+0, 0x1.486a2b5c13cdp+0,  0x1.4a32af0d7d3dep+0,
+    0x1.4bfdad5362a27p+0, 0x1.4dcb299fddd0dp+0, 0x1.4f9b2769d2ca7p+0,
+    0x1.516daa2cf6642p+0, 0x1.5342b569d4f82p+0, 0x1.551a4ca5d920fp+0,
+    0x1.56f4736b527dap+0, 0x1.58d12d497c7fdp+0, 0x1.5ab07dd485429p+0,
+    0x1.5c9268a5946b7p+0, 0x1.5e76f15ad2148p+0, 0x1.605e1b976dc09p+0,
+    0x1.6247eb03a5585p+0, 0x1.6434634ccc32p+0,  0x1.6623882552225p+0,
+    0x1.68155d44ca973p+0, 0x1.6a09e667f3bcdp+0, 0x1.6c012750bdabfp+0,
+    0x1.6dfb23c651a2fp+0, 0x1.6ff7df9519484p+0, 0x1.71f75e8ec5f74p+0,
+    0x1.73f9a48a58174p+0, 0x1.75feb564267c9p+0, 0x1.780694fde5d3fp+0,
+    0x1.7a11473eb0187p+0, 0x1.7c1ed0130c132p+0, 0x1.7e2f336cf4e62p+0,
+    0x1.80427543e1a12p+0, 0x1.82589994cce13p+0, 0x1.8471a4623c7adp+0,
+    0x1.868d99b4492edp+0, 0x1.88ac7d98a6699p+0, 0x1.8ace5422aa0dbp+0,
+    0x1.8cf3216b5448cp+0, 0x1.8f1ae99157736p+0, 0x1.9145b0b91ffc6p+0,
+    0x1.93737b0cdc5e5p+0, 0x1.95a44cbc8520fp+0, 0x1.97d829fde4e5p+0,
+    0x1.9a0f170ca07bap+0, 0x1.9c49182a3f09p+0,  0x1.9e86319e32323p+0,
+    0x1.a0c667b5de565p+0, 0x1.a309bec4a2d33p+0, 0x1.a5503b23e255dp+0,
+    0x1.a799e1330b358p+0, 0x1.a9e6b5579fdbfp+0, 0x1.ac36bbfd3f37ap+0,
+    0x1.ae89f995ad3adp+0, 0x1.b0e07298db666p+0, 0x1.b33a2b84f15fbp+0,
+    0x1.b59728de5593ap+0, 0x1.b7f76f2fb5e47p+0, 0x1.ba5b030a1064ap+0,
+    0x1.bcc1e904bc1d2p+0, 0x1.bf2c25bd71e09p+0, 0x1.c199bdd85529cp+0,
+    0x1.c40ab5fffd07ap+0, 0x1.c67f12e57d14bp+0, 0x1.c8f6d9406e7b5p+0,
+    0x1.cb720dcef9069p+0, 0x1.cdf0b555dc3fap+0, 0x1.d072d4a07897cp+0,
+    0x1.d2f87080d89f2p+0, 0x1.d5818dcfba487p+0, 0x1.d80e316c98398p+0,
+    0x1.da9e603db3285p+0, 0x1.dd321f301b46p+0,  0x1.dfc97337b9b5fp+0,
+    0x1.e264614f5a129p+0, 0x1.e502ee78b3ff6p+0, 0x1.e7a51fbc74c83p+0,
+    0x1.ea4afa2a490dap+0, 0x1.ecf482d8e67f1p+0, 0x1.efa1bee615a27p+0,
+    0x1.f252b376bba97p+0, 0x1.f50765b6e454p+0,  0x1.f7bfdad9cbe14p+0,
+    0x1.fa7c1819e90d8p+0, 0x1.fd3c22b8f71f1p+0
+  };
 
-float __erfcf(float x)
+float
+__erfcf (float xf)
 {
-	int32_t hx,ix;
-	float R,S,P,Q,s,y,z,r;
-	GET_FLOAT_WORD(hx,x);
-	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) {			/* erfc(nan)=nan */
-						/* erfc(+-inf)=0,2 */
-	    float ret = (float)(((uint32_t)hx>>31)<<1)+one/x;
-	    if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f)
-	      return 0.0f;
-	    return ret;
-	}
-
-	if(ix < 0x3f580000) {		/* |x|<0.84375 */
-	    if(ix < 0x32800000)  	/* |x|<2**-26 */
-		return one-x;
-	    z = x*x;
-	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
-	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
-	    y = r/s;
-	    if(hx < 0x3e800000) {  	/* x<1/4 */
-		return one-(x+x*y);
-	    } else {
-		r = x*y;
-		r += (x-half);
-	        return half - r ;
-	    }
+  float axf = fabsf (xf);
+  double axd = axf;
+  double  x2 = axd * axd;
+  uint32_t t = asuint (xf);
+  unsigned int at = t & (~0u >> 1);
+  unsigned int sgn = t >> 31;
+  int64_t i = at > 0x40051000;
+  /* for x < -0x1.ea8f94p+1, erfc(x) rounds to 2 (to nearest) */
+  if (__glibc_unlikely (t > 0xc07547ca))
+    { /* xf < -0x1.ea8f94p+1 */
+      if (__glibc_unlikely (t >= 0xff800000))
+	{ /* -Inf or NaN */
+	  if (t == 0xff800000)
+	    return 2.0f;  /* -Inf */
+	  return xf + xf; /* NaN */
 	}
-	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
-	    s = fabsf(x)-one;
-	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
-	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
-	    if(hx>=0) {
-	        z  = one-erx; return z - P/Q;
-	    } else {
-		z = erx+P/Q; return one+z;
-	    }
+      return 2.0f - 0x1p-25f; /* rounds to 2 or nextbelow(2) */
+    }
+  /* at is the absolute value of xf
+     for x >= 0x1.41bbf8p+3, erfc(x) < 2^-150, thus rounds to 0 or to 2^-149
+     depending on the rounding mode */
+  if (__glibc_unlikely (at >= 0x4120ddfc))
+    { /* |xf| >= 0x1.41bbf8p+3 */
+      if (__glibc_unlikely (at >= 0x7f800000))
+	{ /* +Inf or NaN */
+	  if (at == 0x7f800000)
+	    return 0.0f;  /* +Inf */
+	  return xf + xf; /* NaN */
 	}
-	if (ix < 0x41e00000) {		/* |x|<28 */
-	    x = fabsf(x);
-	    s = one/(x*x);
-	    if(ix< 0x4036DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
-	        R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
-				ra5+s*(ra6+s*ra7))))));
-	        S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
-				sa5+s*(sa6+s*(sa7+s*sa8)))))));
-	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
-		if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
-	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
-				rb5+s*rb6)))));
-	        S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
-				sb5+s*(sb6+s*sb7))))));
-	    }
-	    GET_FLOAT_WORD(ix,x);
-	    SET_FLOAT_WORD(z,ix&0xffffe000);
-	    r  =  __ieee754_expf(-z*z-(float)0.5625)*
-			__ieee754_expf((z-x)*(z+x)+R/S);
-	    if(hx>0) {
-		float ret = math_narrow_eval (r/x);
-		if (ret == 0)
-		    __set_errno (ERANGE);
-		return ret;
-	    } else
-		return two-r/x;
-	} else {
-	    if(hx>0) {
-		__set_errno (ERANGE);
-		return tiny*tiny;
-	    } else
-		return two-tiny;
+      __set_errno (ERANGE);
+      /* 0x1p-149f * 0.25f rounds to 0 or 2^-149 depending on rounding */
+      return 0x1p-149f * 0.25f;
+    }
+  if (__glibc_unlikely (at <= 0x3db80000))
+    { /* |x| <= 0x1.7p-4 */
+      if (__glibc_unlikely (t == 0xb76c9f62))
+	return 0x1.00010ap+0f + 0x1p-25f; /* exceptional case */
+      /* for |x| <= 0x1.c5bf88p-26. erfc(x) rounds to 1 (to nearest) */
+      if (__glibc_unlikely (at <= 0x32e2dfc4))
+	{ /* |x| <= 0x1.c5bf88p-26 */
+	  if (__glibc_unlikely (at == 0))
+	    return 1.0f;
+	  static const float d[] = { -0x1p-26, 0x1p-25 };
+	  return 1.0f + d[sgn];
 	}
+      /* around 0, erfc(x) behaves as 1 - (odd polynomial) */
+      static const double c[] =
+	{
+	  0x1.20dd750429b6dp+0, -0x1.812746b03610bp-2, 0x1.ce2f218831d2fp-4,
+	  -0x1.b82c609607dcbp-6, 0x1.553af09b8008ep-8
+	};
+      double f0 = xf
+	    * (c[0] + x2 * (c[1] + x2 * (c[2] + x2 * (c[3] + x2 * (c[4])))));
+      return 1.0 - f0;
+    }
+
+  /* now -0x1.ea8f94p+1 <= x <= 0x1.41bbf8p+3, with |x| > 0x1.7p-4 */
+  const double iln2 = 0x1.71547652b82fep+0;
+  const double ln2h = 0x1.62e42fefap-8;
+  const double ln2l = 0x1.cf79abd6f5dc8p-47;
+  uint64_t jt = asuint64 (fma (x2, iln2, -(1024 + 0x1p-8)));
+  int64_t j = (int64_t) (jt << 12) >> 48;
+  double S = asdouble (((j >> 7) + (0x3ff | sgn << 11)) << 52);
+  static const double ch[] =
+    {
+      -0x1.ffffffffff333p-2, 0x1.5555555556a14p-3, -0x1.55556666659b4p-5,
+      0x1.1111074cc7b22p-7
+    };
+  double d = (x2 + ln2h * j) + ln2l * j;
+  double d2 = d * d;
+  double e0 = E[j & 127];
+  double f = d + d2 * ((ch[0] + d * ch[1]) + d2 * (ch[2] + d * ch[3]));
+  static const double ct[][16] =
+    {
+      {
+	 0x1.c162355429b28p-1,   0x1.d99999999999ap+1,  0x1.da951cece2b85p-2,
+	-0x1.70ef6cff4bcc4p+0,   0x1.3d7f7b3d617dep+1, -0x1.9d0aa47537c51p+1,
+	 0x1.9754ea9a3fcb1p+1,  -0x1.27a5453fcc015p+1,  0x1.1ef2e0531aebap+0,
+	-0x1.eca090f5a1c06p-3,  -0x1.7a3cd173a063cp-4,  0x1.30fa68a68fdddp-4,
+	 0x1.55ad9a326993ap-10, -0x1.07e7b0bb39fbfp-6,  0x1.2328706c0e95p-10,
+	 0x1.d6aa0b7b19cfep-9
+      },
+      {
+	 0x1.137c8983f8516p+2,   0x1.799999999999ap+1,   0x1.05b53aa241333p-3,
+	-0x1.a3f53872bf87p-3,    0x1.de4c30742c9d5p-4,  -0x1.cb24bfa591986p-5,
+	 0x1.666aec059ca5fp-6,  -0x1.a61250eb26b0bp-8,   0x1.2b28b7924b34dp-10,
+	 0x1.41b13a9d45013p-15, -0x1.6dd5e8a273613p-14,  0x1.09ce8ea5e8da5p-16,
+	 0x1.33923b4102981p-18, -0x1.1dfd161e3f984p-19, -0x1.c87618fcae3b3p-23,
+	 0x1.e8a6ffa0ba2c7p-23
+      }
+  };
+  double z = (axd - ct[i][0]) / (axd + ct[i][1]);
+  double z2 = z * z, z4 = z2 * z2;
+  double z8 = z4 * z4;
+  const double *c = ct[i] + 3;
+  double s = (((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]))
+	      + z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])))
+    + z8 * (((c[8] + z * c[9]) + z2 * (c[10] + z * c[11])) + z4 * (c[12]));
+  s = ct[i][2] + z * s;
+  static const double off[] = { 0, 2 };
+  double r = (S * (e0 - f * e0)) * s;
+  double y = off[sgn] + r;
+  return y;
 }
 libm_alias_float (__erfc, erfc)
diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
index b6216828..80112db 100644
--- a/sysdeps/loongarch/lp64/libm-test-ulps
+++ b/sysdeps/loongarch/lp64/libm-test-ulps
@@ -926,22 +926,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 4
 
 Function: "erfc_downward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
index 3ea3f74..08fbad9 100644
--- a/sysdeps/m68k/m680x0/fpu/libm-test-ulps
+++ b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
@@ -854,22 +854,18 @@ ldouble: 1
 
 Function: "erfc":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "erfc_downward":
 double: 1
-float: 4
 ldouble: 4
 
 Function: "erfc_towardzero":
 double: 1
-float: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 1
-float: 3
 ldouble: 3
 
 Function: "exp10m1":
diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps
index c079a4f..5382a18 100644
--- a/sysdeps/microblaze/libm-test-ulps
+++ b/sysdeps/microblaze/libm-test-ulps
@@ -175,7 +175,6 @@ double: 1
 
 Function: "erfc":
 double: 3
-float: 2
 
 Function: "exp":
 float: 1
diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps
index ebd88e0..0fe27ef 100644
--- a/sysdeps/mips/mips32/libm-test-ulps
+++ b/sysdeps/mips/mips32/libm-test-ulps
@@ -735,19 +735,15 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
index ca658b9..ce7dde2 100644
--- a/sysdeps/mips/mips64/libm-test-ulps
+++ b/sysdeps/mips/mips64/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 4
 
 Function: "erfc_downward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/nios2/libm-test-ulps b/sysdeps/nios2/libm-test-ulps
index 6416c7f..cc63f8f 100644
--- a/sysdeps/nios2/libm-test-ulps
+++ b/sysdeps/nios2/libm-test-ulps
@@ -180,7 +180,6 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps
index fb16068..5677a35 100644
--- a/sysdeps/or1k/fpu/libm-test-ulps
+++ b/sysdeps/or1k/fpu/libm-test-ulps
@@ -735,19 +735,15 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps
index 2742e3b..c7ba12f 100644
--- a/sysdeps/or1k/nofpu/libm-test-ulps
+++ b/sysdeps/or1k/nofpu/libm-test-ulps
@@ -735,19 +735,15 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index b22aaf9..4e448a2 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -1125,25 +1125,21 @@ ldouble: 3
 
 Function: "erfc":
 double: 2
-float: 2
 float128: 4
 ldouble: 3
 
 Function: "erfc_downward":
 double: 4
-float: 4
 float128: 5
 ldouble: 10
 
 Function: "erfc_towardzero":
 double: 3
-float: 3
 float128: 4
 ldouble: 11
 
 Function: "erfc_upward":
 double: 4
-float: 4
 float128: 5
 ldouble: 7
 
diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps
index 98cd67b..d9555e7 100644
--- a/sysdeps/powerpc/nofpu/libm-test-ulps
+++ b/sysdeps/powerpc/nofpu/libm-test-ulps
@@ -935,22 +935,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 3
 
 Function: "erfc_downward":
 double: 5
-float: 6
 ldouble: 10
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 ldouble: 11
 
 Function: "erfc_upward":
 double: 5
-float: 6
 ldouble: 7
 
 Function: "exp":
diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
index 8cfeb7b..23228a8 100644
--- a/sysdeps/riscv/nofpu/libm-test-ulps
+++ b/sysdeps/riscv/nofpu/libm-test-ulps
@@ -922,22 +922,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 4
 
 Function: "erfc_downward":
 double: 3
-float: 4
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 3
 ldouble: 4
 
 Function: "erfc_upward":
 double: 3
-float: 4
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
index f7c6c82..74bde10 100644
--- a/sysdeps/riscv/rvd/libm-test-ulps
+++ b/sysdeps/riscv/rvd/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 2
-float: 2
 ldouble: 4
 
 Function: "erfc_downward":
 double: 4
-float: 4
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 3
 ldouble: 4
 
 Function: "erfc_upward":
 double: 4
-float: 4
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
index 36da5d7..6747fd4 100644
--- a/sysdeps/s390/fpu/libm-test-ulps
+++ b/sysdeps/s390/fpu/libm-test-ulps
@@ -926,22 +926,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 2
-float: 2
 ldouble: 4
 
 Function: "erfc_downward":
 double: 4
-float: 4
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 3
 ldouble: 4
 
 Function: "erfc_upward":
 double: 4
-float: 4
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps
index 6b55797..69fe20b 100644
--- a/sysdeps/sh/libm-test-ulps
+++ b/sysdeps/sh/libm-test-ulps
@@ -361,11 +361,9 @@ double: 1
 
 Function: "erfc":
 double: 5
-float: 2
 
 Function: "erfc_towardzero":
 double: 3
-float: 3
 
 Function: "exp":
 double: 1
diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index 3aed9d4..98f7a07 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -925,22 +925,18 @@ ldouble: 2
 
 Function: "erfc":
 double: 5
-float: 3
 ldouble: 4
 
 Function: "erfc_downward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 ldouble: 5
 
 Function: "exp":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index e00ad56..b7400e9 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1330,25 +1330,21 @@ float: 2
 
 Function: "erfc":
 double: 5
-float: 3
 float128: 4
 ldouble: 5
 
 Function: "erfc_downward":
 double: 5
-float: 6
 float128: 5
 ldouble: 4
 
 Function: "erfc_towardzero":
 double: 3
-float: 4
 float128: 4
 ldouble: 4
 
 Function: "erfc_upward":
 double: 5
-float: 6
 float128: 5
 ldouble: 5