math: Use erff from CORE-MATH

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

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                       85.7363       45.1372       47.35%
x86_64v2                     86.6337       38.5816       55.47%
x86_64v3                     71.3810       34.0843       52.25%
i686                         190.143       97.5014       48.72%
aarch64                      34.9091       14.9320       57.23%
power10                      38.6160        8.5188       77.94%
powerpc                      39.7446       8.45781       78.72%

reciprocal-throughput         master       patched  improvement
x86_64                       35.1739       14.7603       58.04%
x86_64v2                     34.5976       11.2283       67.55%
x86_64v3                     27.3260        9.8550       63.94%
i686                         91.0282       30.8840       66.07%
aarch64                      22.5831        6.9615       69.17%
power10                      18.0386        3.0918       82.86%
powerpc                      20.7277       3.63396       82.47%

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, 247 insertions, 235 deletions

diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
index 4979769b58..fc10f7f80d 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -991,7 +991,6 @@ ldouble: 5
 
 Function: "erf":
 double: 1
-float: 1
 ldouble: 1
 
 Function: "erf_advsimd":
diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps
index a2b5404f9d..bbb3a5c459 100644
--- a/sysdeps/alpha/fpu/libm-test-ulps
+++ b/sysdeps/alpha/fpu/libm-test-ulps
@@ -909,22 +909,18 @@ ldouble: 5
 
 Function: "erf":
 double: 1
-float: 1
 ldouble: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 ldouble: 2
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 ldouble: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 ldouble: 2
 
 Function: "erfc":
diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
index c6f3646797..9e422da289 100644
--- a/sysdeps/arc/fpu/libm-test-ulps
+++ b/sysdeps/arc/fpu/libm-test-ulps
@@ -733,19 +733,15 @@ float: 6
 
 Function: "erf":
 double: 1
-float: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 2
 
 Function: "erf_upward":
 double: 2
-float: 2
 
 Function: "erfc":
 double: 5
diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
index 6319012db5..2c24fdf663 100644
--- a/sysdeps/arc/nofpu/libm-test-ulps
+++ b/sysdeps/arc/nofpu/libm-test-ulps
@@ -177,7 +177,6 @@ float: 2
 
 Function: "erf":
 double: 1
-float: 1
 
 Function: "erfc":
 double: 5
diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
index d9317046a9..153cd1f3d7 100644
--- a/sysdeps/arm/libm-test-ulps
+++ b/sysdeps/arm/libm-test-ulps
@@ -726,19 +726,15 @@ float: 3
 
 Function: "erf":
 double: 1
-float: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 
 Function: "erfc":
 double: 5
diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps
index c3a3db9bcb..d276db245b 100644
--- a/sysdeps/csky/fpu/libm-test-ulps
+++ b/sysdeps/csky/fpu/libm-test-ulps
@@ -719,19 +719,15 @@ float: 3
 
 Function: "erf":
 double: 1
-float: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 
 Function: "erfc":
 double: 5
diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps
index 68a74bf1d0..ea08fd5378 100644
--- a/sysdeps/csky/nofpu/libm-test-ulps
+++ b/sysdeps/csky/nofpu/libm-test-ulps
@@ -717,19 +717,15 @@ float: 3
 
 Function: "erf":
 double: 1
-float: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 
 Function: "erfc":
 double: 5
diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
index a3e66291a0..a16f86ac8b 100644
--- a/sysdeps/hppa/fpu/libm-test-ulps
+++ b/sysdeps/hppa/fpu/libm-test-ulps
@@ -742,20 +742,16 @@ float: 3
 
 Function: "erf":
 double: 1
-float: 1
 ldouble: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 
 Function: "erfc":
 double: 5
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index a77ded2648..041c180f7a 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1078,25 +1078,21 @@ ldouble: 3
 
 Function: "erf":
 double: 1
-float: 1
 float128: 1
 ldouble: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 float128: 2
 ldouble: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 float128: 1
 ldouble: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 float128: 2
 ldouble: 1
 
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
index a9cd01bf03..e3ee0c61f6 100644
--- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
+++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
@@ -1081,25 +1081,21 @@ ldouble: 3
 
 Function: "erf":
 double: 1
-float: 1
 float128: 1
 ldouble: 1
 
 Function: "erf_downward":
 double: 1
-float: 1
 float128: 2
 ldouble: 1
 
 Function: "erf_towardzero":
 double: 1
-float: 1
 float128: 1
 ldouble: 1
 
 Function: "erf_upward":
 double: 1
-float: 1
 float128: 2
 ldouble: 1
 
diff --git a/sysdeps/ieee754/flt-32/s_erff.c b/sysdeps/ieee754/flt-32/s_erff.c
index 61e2555267..025c207962 100644
--- a/sysdeps/ieee754/flt-32/s_erff.c
+++ b/sysdeps/ieee754/flt-32/s_erff.c
@@ -1,154 +1,256 @@
-/* s_erff.c -- float version of s_erf.c.
- */
+/* Correctly-rounded error function for binary32 value.
 
-/*
- * ====================================================
- * 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) 2022-2024 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/erf/erff.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 <float.h>
 #include <math.h>
-#include <math-narrow-eval.h>
-#include <math_private.h>
-#include <math-underflow.h>
+#include <stdint.h>
 #include <libm-alias-float.h>
-#include <fix-int-fp-convert-zero.h>
+#include "math_config.h"
 
-static const float
-tiny	    = 1e-30,
-one =  1.0000000000e+00, /* 0x3F800000 */
-erx =  8.4506291151e-01, /* 0x3f58560b */
-/*
- * Coefficients for approximation to  erf on [0,0.84375]
- */
-efx =  1.2837916613e-01, /* 0x3e0375d4 */
-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 */
-
-float __erff(float x)
+float
+__erff (float x)
 {
-	int32_t hx,ix,i;
-	float R,S,P,Q,s,y,z,r;
-	GET_FLOAT_WORD(hx,x);
-	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) {		/* erf(nan)=nan */
-	    i = ((uint32_t)hx>>31)<<1;
-	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
-	}
-
-	if(ix < 0x3f580000) {		/* |x|<0.84375 */
-	    if(ix < 0x31800000) { 	/* |x|<2**-28 */
-	        if (ix < 0x04000000)
-		  {
-		    /* Avoid spurious underflow.  */
-		    float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
-		    math_check_force_underflow (ret);
-		    return ret;
-		  }
-		return x + efx*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;
-	    return x + x*y;
-	}
-	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) return erx + P/Q; else return -erx - P/Q;
-	}
-	if (ix >= 0x40c00000) {		/* inf>|x|>=6 */
-	    if(hx>=0) return one-tiny; else return tiny-one;
-	}
-	x = fabsf(x);
- 	s = one/(x*x);
-	if(ix< 0x4036DB6E) {	/* |x| < 1/0.35 */
-	    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| >= 1/0.35 */
-	    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&0xfffff000);
-	r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
-	if(hx>=0) return one-r/x; else return  r/x-one;
+  /* for 7 <= i < 63, C[i-7] is a degree-7 polynomial approximation of
+     erf(i/16+1/32+x) for -1/32 <= x <= 1/32 */
+  static const double C[56][8] = {
+    {  0x1.f86faa9428f9cp-2,   0x1.cfc41e36c7dfap-1,  -0x1.b2c7dc53508b9p-2,
+      -0x1.5a9de93fa556ep-3,   0x1.731793dbb01b5p-3,   0x1.133e06426cf18p-6,
+      -0x1.a12a6289cafd8p-5,   0x1.717d6f1d6f557p-9 },
+    {  0x1.1855a5fd3dd50p-1,   0x1.b3aafcc27502fp-1,  -0x1.cee5ac8e92bb2p-2,
+      -0x1.fa02983ca2d79p-4,   0x1.77cd746cb1922p-3,  -0x1.fa6f277886487p-10,
+      -0x1.8de75458db416p-5,   0x1.00899c98551c9p-7 },
+    {  0x1.32a54cb8db67ap-1,   0x1.96164fafd8de5p-1,  -0x1.e23a7ea0c9ad3p-2,
+      -0x1.3f5ee15671cf4p-4,   0x1.70e468a3d72d9p-3,  -0x1.3da68037cfc99p-6,
+      -0x1.69ed9ba1f9839p-5,   0x1.8cab9244a4ff4p-7 },
+    {  0x1.4b13713ad3513p-1,   0x1.7791b886e7405p-1,  -0x1.ecef423109bf5p-2,
+      -0x1.15c3c5cec6847p-5,   0x1.5f688fc931ba6p-3,  -0x1.1da63ed190037p-5,
+      -0x1.38427ca63cca4p-5,   0x1.fa00e52525e17p-7 },
+    {  0x1.61955607dd15dp-1,   0x1.58a445da7c74ep-1,  -0x1.ef6c246a0f66cp-2,
+       0x1.e83e0d9d61330p-8,   0x1.44cc65535bc9fp-3,  -0x1.87d3c4860435dp-5,
+      -0x1.f90b10501169bp-6,   0x1.22295856d427ap-6 },
+    {  0x1.762870f720c6fp-1,   0x1.39ccc1b136d5cp-1,  -0x1.ea4feea4e4744p-2,
+       0x1.715e5952ebfbap-5,   0x1.22cdbd83c75c4p-3,  -0x1.da50aa1d925b6p-5,
+      -0x1.754dc0a29b4ddp-6,   0x1.350b6bef9392cp-6 },
+    {  0x1.88d1cd474a2e0p-1,   0x1.1b7e98fe26219p-1,  -0x1.de65a22ce1419p-2,
+       0x1.40686a3f16400p-4,   0x1.f6b0cbb216b2bp-4,  -0x1.09c7c903edd57p-4,
+      -0x1.da7529fde641p-7,    0x1.362a7a0588eabp-6 },
+    {  0x1.999d4192a5717p-1,   0x1.fc3ee5d1524b3p-2,  -0x1.cc990045b55c8p-2,
+       0x1.b37338e68b37dp-4,   0x1.a0d120c872ea7p-4,  -0x1.19bb2b07ecff6p-4,
+      -0x1.a110f5f593aafp-8,   0x1.272c15a57720ep-6 },
+    {  0x1.a89c850b7d54dp-1,   0x1.c40b0729ed54ap-2,  -0x1.b5eaaef0a2346p-2,
+       0x1.0847c7dacbae1p-3,   0x1.47de0ba6d18fbp-4,  -0x1.1d9de77a4b648p-4,
+       0x1.30ffbe56f0726p-10,  0x1.0a9cb99feea01p-6 },
+    {  0x1.b5e62fce16096p-1,   0x1.8eed36b886d95p-2,  -0x1.9b64a06e50705p-2,
+       0x1.2bb6e2c744df5p-3,   0x1.dee3261ca61bcp-5,  -0x1.16996004f7da5p-4,
+       0x1.fdff37bae983ep-8,   0x1.c750083e65f9ap-7 },
+    {  0x1.c194b1d49a184p-1,   0x1.5d4fd33729015p-2,  -0x1.7e0f4f045addbp-2,
+       0x1.444bc66c31a1bp-3,   0x1.356dbf16ec8f1p-5,  -0x1.0643de0906cd8p-4,
+       0x1.b281af7bd3a2cp-7,   0x1.6b97eaa2c6abdp-7 },
+    {  0x1.cbc54b476248ep-1,   0x1.2f7cc3fe6f423p-2,  -0x1.5ee8429e36de8p-2,
+       0x1.52a8395f96177p-3,   0x1.313761ba257dcp-6,  -0x1.dcf844d5fed8fp-5,
+       0x1.1e1420f475fa9p-6,   0x1.091c7dc1e18b2p-7 },
+    {  0x1.d4970f9ce00d9p-1,   0x1.059f59af7a905p-2,  -0x1.3eda354de36c3p-2,
+       0x1.57b85ad439779p-3,   0x1.8e913b9778136p-10, -0x1.a2893bd3435f4p-5,
+       0x1.4d3a90e37164ap-6,   0x1.4ce7f6e19a902p-8 },
+    {  0x1.dc29fb60715b0p-1,   0x1.bf8e1b1ca2277p-3,  -0x1.1eb7095e5d6d2p-2,
+       0x1.549ea6f7a64f4p-3,  -0x1.b10f12f3877a3p-7,  -0x1.61420c8f7156ap-5,
+       0x1.674f1f92a8812p-6,   0x1.25543ffd74d52p-9 },
+    {  0x1.e29e22a89d767p-1,   0x1.7bd5c7df3fe99p-3,  -0x1.fe674494077bfp-3,<