math: Use atan2pif from CORE-MATH

The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance to the generic atan2pif.

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):

latency                 master        patched   improvement
x86_64                 79.4006        70.8726        10.74%
x86_64v2               77.5136        69.1424        10.80%
x86_64v3               71.8050        68.1637         5.07%
aarch64 (Neoverse)     27.8363        24.7700        11.02%
power8                 39.3893        17.2929        56.10%
power10                19.7200        16.8187        14.71%

reciprocal-throughput   master        patched   improvement
x86_64                 38.3457        30.9471        19.29%
x86_64v2               37.4023        30.3112        18.96%
x86_64v3               33.0713        24.4891        25.95%
aarch64 (Neoverse)     19.3683        15.3259        20.87%
power8                 19.5507        8.27165        57.69%
power10                9.05331        7.63775        15.64%

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

18 files changed, 238 insertions, 59 deletions

diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
index abb0611..be29b37 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -158,22 +158,18 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan_advsimd":
diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
index 35aebba..1383c88 100644
--- a/sysdeps/arc/fpu/libm-test-ulps
+++ b/sysdeps/arc/fpu/libm-test-ulps
@@ -90,19 +90,15 @@ double: 8
 
 Function: "atan2pi":
 double: 1
-float: 1
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 
 Function: "atan_downward":
 double: 1
diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
index 325546e..9028f5c 100644
--- a/sysdeps/arc/nofpu/libm-test-ulps
+++ b/sysdeps/arc/nofpu/libm-test-ulps
@@ -24,7 +24,6 @@ double: 1
 
 Function: "atan2pi":
 double: 1
-float: 1
 
 Function: "atanh":
 double: 2
diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
index 0927fdb..e1c538f 100644
--- a/sysdeps/arm/libm-test-ulps
+++ b/sysdeps/arm/libm-test-ulps
@@ -87,19 +87,15 @@ double: 1
 
 Function: "atan2pi":
 double: 1
-float: 1
 
 Function: "atan2pi_downward":
 double: 1
-float: 3
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 3
 
 Function: "atan_downward":
 double: 1
diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
index 02cc3b5..796da7b 100644
--- a/sysdeps/hppa/fpu/libm-test-ulps
+++ b/sysdeps/hppa/fpu/libm-test-ulps
@@ -87,19 +87,15 @@ double: 1
 
 Function: "atan2pi":
 double: 1
-float: 1
 
 Function: "atan2pi_downward":
 double: 1
-float: 3
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 3
 
 Function: "atan_downward":
 double: 1
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 69d0eb1..4f687c7 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -146,25 +146,21 @@ ldouble: 1
 
 Function: "atan2pi":
 double: 1
-float: 1
 float128: 3
 ldouble: 1
 
 Function: "atan2pi_downward":
 double: 2
-float: 2
 float128: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 float128: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 2
-float: 2
 float128: 2
 ldouble: 2
 
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
index 392d7d2..f24c87b 100644
--- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
+++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
@@ -146,25 +146,21 @@ ldouble: 1
 
 Function: "atan2pi":
 double: 1
-float: 1
 float128: 3
 ldouble: 2
 
 Function: "atan2pi_downward":
 double: 2
-float: 2
 float128: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 float128: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 2
-float: 2
 float128: 2
 ldouble: 2
 
diff --git a/sysdeps/ieee754/flt-32/s_atan2pif.c b/sysdeps/ieee754/flt-32/s_atan2pif.c
new file mode 100644
index 0000000..8c9cbc13
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/s_atan2pif.c
@@ -0,0 +1,238 @@
+/* Correctly-rounded half revolution arctangent function of two binary32 values.
+
+Copyright (c) 2022-2025 Alexei Sibidanov.
+
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/atan2pi/atan2pif.c, revision dbebee1).
+
+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 <math.h>
+#include <stdint.h>
+#include <errno.h>
+#include <libm-alias-float.h>
+#include "math_config.h"
+
+static inline double
+muldd (double xh, double xl, double ch, double cl, double *l)
+{
+  double ahlh = ch * xl;
+  double alhh = cl * xh;
+  double ahhh = ch * xh;
+  double ahhl = fma (ch, xh, -ahhh);
+  ahhl += alhh + ahlh;
+  ch = ahhh + ahhl;
+  *l = (ahhh - ch) + ahhl;
+  return ch;
+}
+
+static double
+polydd (double xh, double xl, int n, const double c[][2], double *l)
+{
+  int i = n - 1;
+  double ch = c[i][0], cl = c[i][1];
+  while (--i >= 0)
+    {
+      ch = muldd (xh, xl, ch, cl, &cl);
+      double th = ch + c[i][0], tl = (c[i][0] - th) + ch;
+      ch = th;
+      cl += tl + c[i][1];
+    }
+  *l = cl;
+  return ch;
+}
+
+float
+__atan2pif (float y, float x)
+{
+  static const double cn[] =
+    {
+      0x1.45f306dc9c883p-2, 0x1.988d83a142adap-1, 0x1.747bebf492057p-1,
+      0x1.2cc5645094ff3p-2, 0x1.a0521c711ab66p-5, 0x1.881b8058b9a0dp-9,
+      0x1.b16ff514a0afp-16
+    };
+  static const double cd[] =
+    {
+      0x1p+0,               0x1.6b8b143a3f6dap+1, 0x1.8421201d18ed5p+1,
+      0x1.8221d086914ebp+0, 0x1.670657e3a07bap-2, 0x1.0f4951fd1e72dp-5,
+      0x1.b3874b8798286p-11
+    };
+  static const double m[] = { 0, 1 };
+  static const double off[]
+      = { 0.0f, 0.5f, 1.0f, 0.5f, -0.0f, -0.5f, -1.0f, -0.5f };
+  static const float sgnf[] = { 1, -1 };
+  static const double sgn[] = { 1, -1 };
+  uint32_t ux = asuint (x);
+  uint32_t uy = asuint (y);
+  uint32_t ax = ux & (~0u >> 1);
+  uint32_t ay = uy & (~0u >> 1);
+  if (__glibc_unlikely (ay >= (0xff << 23) || ax >= (0xff << 23)))
+    {
+      if (ay > (0xff << 23))
+	return x + y; /* nan */
+      if (ax > (0xff << 23))
+	return x + y; /* nan */
+      uint32_t yinf = ay == (0xff << 23);
+      uint32_t xinf = ax == (0xff << 23);
+      if (yinf & xinf)
+	{
+	  if (ux >> 31)
+	    return 0.75f * sgnf[uy >> 31];
+	  else
+	    return 0.25f * sgnf[uy >> 31];
+	}
+      if (xinf)
+	{
+	  if (ux >> 31)
+	    return sgnf[uy >> 31];
+	  else
+	    return 0.0f * sgnf[uy >> 31];
+	}
+      if (yinf)
+	return 0.5f * sgnf[uy >> 31];
+    }
+  if (__glibc_unlikely (ay == 0))
+    {
+      if (__glibc_unlikely (!(ay | ax)))
+	{
+	  uint32_t i = (uy >> 31) * 4 + (ux >> 31) * 2;
+	  return off[i];
+	}
+      if (!(ux >> 31))
+	return 0.0f * sgnf[uy >> 31];
+    }
+  if (__glibc_unlikely (ax == ay))
+    {
+      static const float s[] = { 0.25, 0.75, -0.25, -0.75 };
+      uint32_t i = (uy >> 31) * 2 + (ux >> 31);
+      return s[i];
+    }
+  uint32_t gt = ay > ax, i = (uy >> 31) * 4 + (ux >> 31) * 2 + gt;
+
+  double zx = x, zy = y;
+  double z = (m[gt] * zx + m[1 - gt] * zy) / (m[gt] * zy + m[1 - gt] * zx);
+  double r = cn[0], z2 = z*z;
+  z *= sgn[gt];
+  /* avoid spurious underflow in the polynomial evaluation excluding extremely
+     small arguments */
+  if (__glibc_likely (z2 > 0x1p-54))
+    {
+      double z4 = z2*z2, z8 = z4*z4;
+      double cn0 =     r + z2*cn[1];
+      double cn2 = cn[2] + z2*cn[3];
+      double cn4 = cn[4] + z2*cn[5];
+      double cn6 = cn[6];
+      cn0 += z4*cn2;
+      cn4 += z4*cn6;
+      cn0 += z8*cn4;
+      double cd0 = cd[0] + z2*cd[1];
+      double cd2 = cd[2] + z2*cd[3];
+      double cd4 = cd[4] + z2*cd[5];
+      double cd6 = cd[6];
+      cd0 += z4*cd2;
+      cd4 += z4*cd6;
+      cd0 += z8*cd4;
+      r = cn0/cd0;
+    }
+  r = z * r + off[i];
+  uint64_t res = asuint64 (r);
+  if (__glibc_unlikely ((res << 1) > 0x6d40000000000000
+			 && ((res + 8) & 0xfffffff) <= 16))
+    {
+      if (ax == ay)
+	{
+	  static const double off2[] = { 0.25, 0.75, -0.25, -0.75 };
+	  r = off2[(uy >> 31) * 2 + (ux >> 31)];
+	}
+      else
+	{
+	  double zh, zl;
+	  if (!gt)
+	    {
+	      zh = zy / zx;
+	      zl = fma (zh, -zx, zy) / zx;
+	    }
+	  else
+	    {
+	      zh = zx / zy;
+	      zl = fma (zh, -zy, zx) / zy;
+	    }
+	  double z2l, z2h = muldd (zh, zl, zh, zl, &z2l);
+	  static const double c[][2] =
+	    {
+	      { 0x1.45f306dc9c883p-2, -0x1.6b01ec5513324p-56 },
+	      { -0x1.b2995e7b7b604p-4, 0x1.e402b0c13eedcp-58 },
+	      { 0x1.04c26be3b06cfp-4, -0x1.571d178a53efp-60 },
+	      { -0x1.7483758e69c03p-5, 0x1.819a6ed7aaf38p-63 },
+	      { 0x1.21bb9452523ffp-5, -0x1.234d866fb9807p-60 },
+	      { -0x1.da1bace3cc54ep-6, -0x1.c84f6ada49294p-64 },
+	      { 0x1.912b1c23345ddp-6, -0x1.534890fbc165p-60 },
+	      { -0x1.5bade52f5f52ap-6, 0x1.f783bafc832f6p-60 },
+	      { 0x1.32c69d084c5cp-6, 0x1.042d155953025p-60 },
+	      { -0x1.127bcfb3e8c7dp-6, -0x1.85aae199a7b6bp-60 },
+	      { 0x1.f0af43b11a731p-7, 0x1.8f0356356663p-61 },
+	      { -0x1.c57e86801029ep-7, 0x1.dcdf3e3b38eb4p-61 },
+	      { 0x1.a136408617ea1p-7, 0x1.a71affb36c6c4p-63 },
+	      { -0x1.824ac7814ba37p-7, 0x1.8928b295c0898p-61 },
+	      { 0x1.6794e32ea5471p-7, 0x1.0b4334fb41e63p-61 },
+	      { -0x1.501d57f643d97p-7, 0x1.516785bf1376ep-61 },
+	      { 0x1.3adf02ff2400ap-7, -0x1.b0e30bb8c8076p-62 },
+	      { -0x1.267702f94faap-7, -0x1.7a4d3a1850cc6p-62 },
+	      { 0x1.10dce97099686p-7, 0x1.fcc208eee2571p-61 },
+	      { -0x1.eee49cdad8002p-8, -0x1.9109b3f1bab82p-64 },
+	      { 0x1.af93bc191a929p-8, 0x1.069fd3b47d7bp-62 },
+	      { -0x1.6240751b54675p-8, -0x1.72dc8cfd03b6fp-62 },
+	      { 0x1.0b61e84080884p-8, 0x1.825824c80941bp-63 },
+	      { -0x1.6a72a8a74e3a5p-9, 0x1.8786a82fd117ep-63 },
+	      { 0x1.aede3217d939dp-10, -0x1.93b626982e1fep-68 },
+	      { -0x1.b66568f09ebeep-11, -0x1.704a39121d0a5p-66 },
+	      { 0x1.73af3977fa973p-12, -0x1.aa050e2244ea3p-68 },
+	      { -0x1.fc69d85ed28c9p-14, 0x1.867f17b764cap-68 },
+	      { 0x1.0c883a9270162p-15, -0x1.6842833896dd9p-70 },
+	      { -0x1.9a0b27b6dfe15p-18, 0x1.427fc2f4e1327p-73 },
+	      { 0x1.91e15e7ab5bdcp-21, -0x1.730dbc6279d0dp-77 },
+	      { -0x1.7b1119c1ff867p-25, 0x1.145f9980759c4p-79 }
+	    };
+	  double pl, ph = polydd (z2h, z2l, 32, c, &pl);
+	  zh *= sgn[gt];
+	  zl *= sgn[gt];
+	  ph = muldd (zh, zl, ph, pl, &pl);
+	  double sh = ph + off[i], sl = ((off[i] - sh) + ph) + pl;
+	  float rf = sh;
+	  double th = rf, dh = sh - th, tm = dh + sl;
+	  r = th + tm;
+	  double d = r - th;
+	  if (!(asuint64 (d) << 12))
+	    {
+	      double ad = fabs (d), am = fabs (tm);
+	      if (ad > am)
+		r -= d * 0x1p-10;
+	      if (ad < am)
+		r += d * 0x1p-10;
+	    }
+	}
+    }
+  float rf = r;
+  if (__glibc_unlikely (rf == 0.0f && y != 0.0f))
+    __set_errno (ERANGE);
+  return rf;
+}
+libm_alias_float (__atan2pi, atan2pi)
diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
index 33dd671..d5adc11 100644
--- a/sysdeps/loongarch/lp64/libm-test-ulps
+++ b/sysdeps/loongarch/lp64/libm-test-ulps
@@ -118,22 +118,18 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan_downward":
diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
index 869ceff..c901b00 100644
--- a/sysdeps/mips/mips64/libm-test-ulps
+++ b/sysdeps/mips/mips64/libm-test-ulps
@@ -118,22 +118,18 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan_downward":
diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps
index 75db236..9934382 100644
--- a/sysdeps/or1k/fpu/libm-test-ulps
+++ b/sysdeps/or1k/fpu/libm-test-ulps
@@ -87,19 +87,15 @@ double: 8
 
 Function: "atan2pi":
 double: 1
-float: 1
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 
 Function: "atan_downward":
 double: 1
diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps
index a1f7c80..7ff5ee4 100644
--- a/sysdeps/or1k/nofpu/libm-test-ulps
+++ b/sysdeps/or1k/nofpu/libm-test-ulps
@@ -69,7 +69,6 @@ double: 8
 
 Function: "atan2pi":
 double: 1
-float: 1
 
 Function: "atan_downward":
 double: 1
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index fa3cf2e..b1c01b4 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -151,25 +151,21 @@ ldouble: 3
 
 Function: "atan2pi":
 double: 1
-float: 1
 float128: 3
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 float128: 2
 ldouble: 4
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 float128: 2
 ldouble: 5
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 float128: 2
 ldouble: 4
 
diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
index a5184ec..f55df65 100644
--- a/sysdeps/riscv/nofpu/libm-test-ulps
+++ b/sysdeps/riscv/nofpu/libm-test-ulps
@@ -94,7 +94,6 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan_downward":
diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
index 3bfc966..879f5c5 100644
--- a/sysdeps/riscv/rvd/libm-test-ulps
+++ b/sysdeps/riscv/rvd/libm-test-ulps
@@ -118,22 +118,18 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan_downward":
diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
index 7d61bf1..c4a27b9 100644
--- a/sysdeps/s390/fpu/libm-test-ulps
+++ b/sysdeps/s390/fpu/libm-test-ulps
@@ -118,22 +118,18 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan_downward":
diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index 426f458..fbf1507 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -118,22 +118,18 @@ ldouble: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 ldouble: 3
 
 Function: "atan2pi_downward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 2
 ldouble: 2
 
 Function: "atan_downward":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index d4c4bfa..a340df6 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -244,25 +244,21 @@ float: 2
 
 Function: "atan2pi":
 double: 1
-float: 1
 float128: 3
 ldouble: 2
 
 Function: "atan2pi_downward":
 double: 1
-float: 3
 float128: 2
 ldouble: 2
 
 Function: "atan2pi_towardzero":
 double: 1
-float: 2
 float128: 2
 ldouble: 2
 
 Function: "atan2pi_upward":
 double: 1
-float: 3
 float128: 2
 ldouble: 2