AArch64: Implement AdvSIMD and SVE atanpi/f

Implement double and single precision variants of the C23 routine atanpi
for both AdvSIMD and SVE.

Reviewed-by: Wilco Dijkstra  <Wilco.Dijkstra@arm.com>

bits/libm-simd-decl-stubs.h

@@ -395,4 +395,15 @@
 #define __DECL_SIMD_asinpif32x
 #define __DECL_SIMD_asinpif64x
 #define __DECL_SIMD_asinpif128x
+
+#define __DECL_SIMD_atanpi
+#define __DECL_SIMD_atanpif
+#define __DECL_SIMD_atanpil
+#define __DECL_SIMD_atanpif16
+#define __DECL_SIMD_atanpif32
+#define __DECL_SIMD_atanpif64
+#define __DECL_SIMD_atanpif128
+#define __DECL_SIMD_atanpif32x
+#define __DECL_SIMD_atanpif64x
+#define __DECL_SIMD_atanpif128x
 #endif

math/bits/mathcalls.h

@@ -74,6 +74,7 @@ __MATHCALL (asinpi,, (_Mdouble_ __x));
 __MATHCALL_VEC (asinpi,, (_Mdouble_ __x));
 /* Arc tangent of X, divided by pi.  */
 __MATHCALL (atanpi,, (_Mdouble_ __x));
+__MATHCALL_VEC (atanpi,, (_Mdouble_ __x));
 /* Arc tangent of Y/X, divided by pi.  */
 __MATHCALL (atan2pi,, (_Mdouble_ __y, _Mdouble_ __x));
 

sysdeps/aarch64/fpu/Makefile

@@ -6,6 +6,7 @@ libmvec-supported-funcs = acos \
                           asinpi \
                           atan \
                           atanh \
+                          atanpi \
                           atan2 \
                           cbrt \
                           cos \

sysdeps/aarch64/fpu/Versions

@@ -168,5 +168,10 @@ libmvec {
     _ZGVnN4v_asinpif;
     _ZGVsMxv_asinpi;
     _ZGVsMxv_asinpif;
+    _ZGVnN2v_atanpi;
+    _ZGVnN2v_atanpif;
+    _ZGVnN4v_atanpif;
+    _ZGVsMxv_atanpi;
+    _ZGVsMxv_atanpif;
   }
 }

sysdeps/aarch64/fpu/advsimd_f32_protos.h

@@ -25,6 +25,7 @@ libmvec_hidden_proto (V_NAME_F1(asinh));
 libmvec_hidden_proto (V_NAME_F1(asinpi));
 libmvec_hidden_proto (V_NAME_F1(atan));
 libmvec_hidden_proto (V_NAME_F1(atanh));
+libmvec_hidden_proto (V_NAME_F1(atanpi));
 libmvec_hidden_proto (V_NAME_F1(cbrt));
 libmvec_hidden_proto (V_NAME_F1(cos));
 libmvec_hidden_proto (V_NAME_F1(cosh));

sysdeps/aarch64/fpu/atanpi_advsimd.c

@@ -0,0 +1,117 @@
+/* Double-Precision vector (Advanced SIMD) inverse tanpi function
+
+   Copyright (C) 2025 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "v_math.h"
+
+static const struct data
+{
+  double c2, c4, c6, c8, c10, c12, c14, c16, c18, c20;
+  float64x2_t c0, c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
+} data = {
+  /* Coefficients of polynomial P such that atanpi(x)~x*P(x^2) on
+	      [2^-1022, 1.0].  */
+  .c0 = V2 (0x1.45f306dc9c883p-2), .c1 = V2 (-0x1.b2995e7b7ba4ap-4),
+  .c2 = 0x1.04c26be3d2c1p-4,	   .c3 = V2 (-0x1.7483759c17ea1p-5),
+  .c4 = 0x1.21bb95c315d57p-5,	   .c5 = V2 (-0x1.da1bdc3d453f3p-6),
+  .c6 = 0x1.912d20459b4bfp-6,	   .c7 = V2 (-0x1.5bbd4545cad1fp-6),
+  .c8 = 0x1.331b83bec30a1p-6,	   .c9 = V2 (-0x1.13d6457f44de3p-6),
+  .c10 = 0x1.f8e802974db94p-7,	   .c11 = V2 (-0x1.d7e173ab04a1ap-7),
+  .c12 = 0x1.bdfa47d6a4f28p-7,	   .c13 = V2 (-0x1.9ba78f3232ceep-7),
+  .c14 = 0x1.5e6044590ab4fp-7,	   .c15 = V2 (-0x1.01ccfdeb9f77fp-7),
+  .c16 = 0x1.345cf0d4eb1c1p-8,	   .c17 = V2 (-0x1.19e5f00f67e3ap-9),
+  .c18 = 0x1.6d3035ac7625bp-11,	   .c19 = V2 (-0x1.286bb9ae4ed79p-13),
+  .c20 = 0x1.c37ec36da0e1ap-17,
+};
+
+#define SignMask v_u64 (0x8000000000000000)
+
+/* Fast implementation of vector atanpi.
+   atanpi(x) ~ shift + z * P(z^2) with reduction to [0,1] using
+   z=1/x and shift = +-1/2. Maximum observed error is 2.76 ulps:
+   _ZGVnN2v_atanpi(0x1.fa2d6912cd64fp-1) got 0x1.fc45a51bd497fp-3
+					want 0x1.fc45a51bd497cp-3.  */
+float64x2_t VPCS_ATTR V_NAME_D1 (atanpi) (float64x2_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  uint64x2_t ix = vreinterpretq_u64_f64 (x);
+  uint64x2_t sign = vandq_u64 (ix, SignMask);
+
+  /* Argument Reduction:
+     y := arctanpi(x) for |x| < 1
+     y := arctanpi(-1/x) + 1/2 for x > 1
+     y := arctanpi(-1/x) - 1/2 for x < -1
+     Hence, use z=-1/a if |x|>=|-1|, otherwise z=a.  */
+  uint64x2_t red = vcagtq_f64 (x, v_f64 (-1.0));
+  float64x2_t z = vbslq_f64 (red, vdivq_f64 (v_f64 (-1.0), x), x);
+
+  /* Shift is calculated as +1/2 or 0, depending on the argument case.  */
+  float64x2_t shift = vreinterpretq_f64_u64 (
+      vandq_u64 (red, vreinterpretq_u64_f64 (v_f64 (0.5))));
+
+  /* Reinsert sign bit from argument into the shift value.  */
+  shift = vreinterpretq_f64_u64 (
+      veorq_u64 (vreinterpretq_u64_f64 (shift), sign));
+
+  /* Calculate polynomial approximation P(z^2) with deg(P)=19.  */
+  float64x2_t z2 = vmulq_f64 (z, z);
+  float64x2_t z4 = vmulq_f64 (z2, z2);
+  float64x2_t z8 = vmulq_f64 (z4, z4);
+  float64x2_t z16 = vmulq_f64 (z8, z8);
+
+  float64x2_t c24 = vld1q_f64 (&d->c2);
+  float64x2_t c68 = vld1q_f64 (&d->c6);
+
+  /* Order-7 Estrin.  */
+  float64x2_t p12 = vfmaq_laneq_f64 (d->c1, z2, c24, 0);
+  float64x2_t p34 = vfmaq_laneq_f64 (d->c3, z2, c24, 1);
+  float64x2_t p56 = vfmaq_laneq_f64 (d->c5, z2, c68, 0);
+  float64x2_t p78 = vfmaq_laneq_f64 (d->c7, z2, c68, 1);
+
+  float64x2_t p14 = vfmaq_f64 (p12, z4, p34);
+  float64x2_t p58 = vfmaq_f64 (p56, z4, p78);
+  float64x2_t p18 = vfmaq_f64 (p14, z8, p58);
+
+  /* Order-11 Estrin.  */
+  float64x2_t c1012 = vld1q_f64 (&d->c10);
+  float64x2_t c1416 = vld1q_f64 (&d->c14);
+  float64x2_t c1820 = vld1q_f64 (&d->c18);
+
+  float64x2_t p910 = vfmaq_laneq_f64 (d->c9, z2, c1012, 0);
+  float64x2_t p1112 = vfmaq_laneq_f64 (d->c11, z2, c1012, 1);
+  float64x2_t p912 = vfmaq_f64 (p910, z4, p1112);
+
+  float64x2_t p1314 = vfmaq_laneq_f64 (d->c13, z2, c1416, 0);
+  float64x2_t p1516 = vfmaq_laneq_f64 (d->c15, z2, c1416, 1);
+  float64x2_t p1316 = vfmaq_f64 (p1314, z4, p1516);
+
+  float64x2_t p1718 = vfmaq_laneq_f64 (d->c17, z2, c1820, 0);
+  float64x2_t p1920 = vfmaq_laneq_f64 (d->c19, z2, c1820, 1);
+  float64x2_t p1720 = vfmaq_f64 (p1718, z4, p1920);
+
+  float64x2_t p916 = vfmaq_f64 (p912, z8, p1316);
+  float64x2_t p920 = vfmaq_f64 (p916, z16, p1720);
+
+  float64x2_t y = vfmaq_f64 (p18, p920, z16);
+
+  y = vfmaq_f64 (d->c0, z2, y);
+
+  /* y = shift + z * p(z^2).  */
+  return vfmaq_f64 (shift, z, y);
+}

sysdeps/aarch64/fpu/atanpi_sve.c

@@ -0,0 +1,127 @@
+/* Double-Precision vector (SVE) inverse tanpi function
+
+   Copyright (C) 2025 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "sv_math.h"
+
+static const struct data
+{
+  float64_t c2, c4, c6, c8, c10, c12, c14, c16, c18, c20;
+  float64_t c0, c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
+  float64_t shift_val, neg_one;
+} data = {
+  /* Coefficients of polnomial P such that atan(x)~x+x*P(x^2) on
+     [2^-1022, 1.0].  */
+  .c0 = 0x1.45f306dc9c883p-2,
+  .c1 = -0x1.b2995e7b7ba4ap-4,
+  .c2 = 0x1.04c26be3d2c1p-4,
+  .c3 = -0x1.7483759c17ea1p-5,
+  .c4 = 0x1.21bb95c315d57p-5,
+  .c5 = -0x1.da1bdc3d453f3p-6,
+  .c6 = 0x1.912d20459b4bfp-6,
+  .c7 = -0x1.5bbd4545cad1fp-6,
+  .c8 = 0x1.331b83bec30a1p-6,
+  .c9 = -0x1.13d6457f44de3p-6,
+  .c10 = 0x1.f8e802974db94p-7,
+  .c11 = -0x1.d7e173ab04a1ap-7,
+  .c12 = 0x1.bdfa47d6a4f28p-7,
+  .c13 = -0x1.9ba78f3232ceep-7,
+  .c14 = 0x1.5e6044590ab4fp-7,
+  .c15 = -0x1.01ccfdeb9f77fp-7,
+  .c16 = 0x1.345cf0d4eb1c1p-8,
+  .c17 = -0x1.19e5f00f67e3ap-9,
+  .c18 = 0x1.6d3035ac7625bp-11,
+  .c19 = -0x1.286bb9ae4ed79p-13,
+  .c20 = 0x1.c37ec36da0e1ap-17,
+  .shift_val = 1.5,
+  .neg_one = -1,
+};
+
+/* Fast implementation of SVE atan.
+   Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to 0,1 using
+   z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
+   error is 2.80 ulps:
+   _ZGVsMxv_atanpi(0x1.f19587d63c76fp-1) got 0x1.f6b1304817d02p-3
+					want 0x1.f6b1304817d05p-3.  */
+svfloat64_t SV_NAME_D1 (atanpi) (svfloat64_t x, const svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  svbool_t ptrue = svptrue_b64 ();
+  svuint64_t ix = svreinterpret_u64 (x);
+  svuint64_t sign = svand_x (pg, ix, 0x8000000000000000);
+
+  /* Argument reduction:
+     y := arctan(x) for x < 1
+     y := pi/2 + arctan(-1/x) for x > 1
+     Hence, use z=-1/a if x>=1, otherwise z=a.  */
+  svbool_t red = svacgt (pg, x, d->neg_one);
+  svfloat64_t z = svsel (red, svdiv_x (pg, sv_f64 (d->neg_one), x), x);
+
+  /* Reuse of -1.0f to reduce constant loads,
+     We need a shift value of 1/2, which is created via -1 + (1 + 1/2).  */
+  svfloat64_t shift
+      = svadd_z (red, sv_f64 (d->neg_one), sv_f64 (d->shift_val));
+
+  /* Reinserts the sign bit of the argument to handle the case of x < -1.  */
+  shift = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (shift), sign));
+
+  /* Use split Estrin scheme for P(z^2) with deg(P)=19.  */
+  svfloat64_t z2 = svmul_x (ptrue, z, z);
+  svfloat64_t z4 = svmul_x (ptrue, z2, z2);
+  svfloat64_t z8 = svmul_x (ptrue, z4, z4);
+  svfloat64_t z16 = svmul_x (ptrue, z8, z8);
+
+  /* Order-7 Estrin.  */
+  svfloat64_t c24 = svld1rq (ptrue, &d->c2);
+  svfloat64_t c68 = svld1rq (ptrue, &d->c6);
+
+  svfloat64_t p12 = svmla_lane (sv_f64 (d->c1), z2, c24, 0);
+  svfloat64_t p34 = svmla_lane (sv_f64 (d->c3), z2, c24, 1);
+  svfloat64_t p56 = svmla_lane (sv_f64 (d->c5), z2, c68, 0);
+  svfloat64_t p78 = svmla_lane (sv_f64 (d->c7), z2, c68, 1);
+
+  svfloat64_t p14 = svmla_x (pg, p12, z4, p34);
+  svfloat64_t p58 = svmla_x (pg, p56, z4, p78);
+  svfloat64_t p18 = svmla_x (pg, p14, z8, p58);
+
+  /* Order-11 Estrin.  */
+  svfloat64_t c1012 = svld1rq (ptrue, &d->c10);
+  svfloat64_t c1416 = svld1rq (ptrue, &d->c14);
+  svfloat64_t c1820 = svld1rq (ptrue, &d->c18);
+
+  svfloat64_t p910 = svmla_lane (sv_f64 (d->c9), z2, c1012, 0);
+  svfloat64_t p1112 = svmla_lane (sv_f64 (d->c11), z2, c1012, 1);
+  svfloat64_t p912 = svmla_x (pg, p910, z4, p1112);
+
+  svfloat64_t p1314 = svmla_lane (sv_f64 (d->c13), z2, c1416, 0);
+  svfloat64_t p1516 = svmla_lane (sv_f64 (d->c15), z2, c1416, 1);
+  svfloat64_t p1316 = svmla_x (pg, p1314, z4, p1516);
+
+  svfloat64_t p1718 = svmla_lane (sv_f64 (d->c17), z2, c1820, 0);
+  svfloat64_t p1920 = svmla_lane (sv_f64 (d->c19), z2, c1820, 1);
+  svfloat64_t p1720 = svmla_x (pg, p1718, z4, p1920);
+
+  svfloat64_t p916 = svmla_x (pg, p912, z8, p1316);
+  svfloat64_t p920 = svmla_x (pg, p916, z16, p1720);
+
+  svfloat64_t y = svmla_x (pg, p18, z16, p920);
+
+  y = svmla_x (pg, sv_f64 (d->c0), z2, y);
+  return svmla_x (pg, shift, z, y);
+}

sysdeps/aarch64/fpu/atanpif_advsimd.c

@@ -0,0 +1,92 @@
+/* Single-Precision vector (Advanced SIMD) inverse tanpi function
+
+   Copyright (C) 2025 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "v_math.h"
+
+static const struct data
+{
+  uint32x4_t half;
+  float32x4_t neg_one;
+  float32x4_t c0, c1, c3, c5, c7;
+  float c2, c4, c6, c8;
+} data = {
+  /* Polynomial coefficients generated using Remez algorithm,
+     see atanpi.sollya for details.  */
+  .c0 = V4 (0x1.45f306p-2), .c1 = V4 (-0x1.b2975ep-4),
+  .c2 = 0x1.0490e4p-4,	    .c3 = V4 (-0x1.70c272p-5),
+  .c4 = 0x1.0eef52p-5,	    .c5 = V4 (-0x1.6abbbap-6),
+  .c6 = 0x1.78157p-7,	    .c7 = V4 (-0x1.f0b406p-9),
+  .c8 = 0x1.2ae7fep-11,	    .half = V4 (0x3f000000),
+  .neg_one = V4 (-1.0f),
+};
+
+#define SignMask v_u32 (0x80000000)
+
+/* Fast implementation of vector atanpif based on
+   atanpi(x) ~ shift + z * P(z^2) with reduction to [0,1]
+   using z=-1/x and shift = +-1/2.
+   Maximum observed error is 2.59ulps:
+   _ZGVnN4v_atanpif (0x1.f2a89cp-1) got 0x1.f76524p-3
+				   want 0x1.f7651ep-3.  */
+float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (atanpi) (float32x4_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  uint32x4_t ix = vreinterpretq_u32_f32 (x);
+  uint32x4_t sign = vandq_u32 (ix, SignMask);
+
+  /* Argument Reduction:
+     y := arctanpi(x) for |x| < 1
+     y := arctanpi(-1/x) + 1/2 for x > 1
+     y := arctanpi(-1/x) - 1/2 for x < -1
+     Hence, use z=-1/a if |x|>=|-1|, otherwise z=a.  */
+  uint32x4_t red = vcagtq_f32 (x, d->neg_one);
+
+  float32x4_t z = vbslq_f32 (red, vdivq_f32 (d->neg_one, x), x);
+
+  /* Shift is calculated as +1/2 or 0, depending on the argument case.  */
+  float32x4_t shift = vreinterpretq_f32_u32 (vandq_u32 (red, d->half));
+
+  /* Reinsert sign bit from argument into the shift value.  */
+  shift = vreinterpretq_f32_u32 (
+      veorq_u32 (vreinterpretq_u32_f32 (shift), sign));
+
+  /* Uses an Estrin scheme for polynomial approximation.  */
+  float32x4_t z2 = vmulq_f32 (z, z);
+  float32x4_t z4 = vmulq_f32 (z2, z2);
+  float32x4_t z8 = vmulq_f32 (z4, z4);
+
+  float32x4_t even_coeffs = vld1q_f32 (&d->c2);
+
+  float32x4_t p12 = vfmaq_laneq_f32 (d->c1, z2, even_coeffs, 0);
+  float32x4_t p34 = vfmaq_laneq_f32 (d->c3, z2, even_coeffs, 1);
+  float32x4_t p56 = vfmaq_laneq_f32 (d->c5, z2, even_coeffs, 2);
+  float32x4_t p78 = vfmaq_laneq_f32 (d->c7, z2, even_coeffs, 3);
+
+  float32x4_t p14 = vfmaq_f32 (p12, z4, p34);
+  float32x4_t p58 = vfmaq_f32 (p56, z4, p78);
+
+  float32x4_t y = vfmaq_f32 (p14, z8, p58);
+  y = vfmaq_f32 (d->c0, z2, y);
+
+  /* y = shift + z * P(z^2).  */
+  return vfmaq_f32 (shift, z, y);
+}
+libmvec_hidden_def (V_NAME_F1 (atanpi))
+HALF_WIDTH_ALIAS_F1 (atanpi)

sysdeps/aarch64/fpu/atanpif_sve.c

@@ -0,0 +1,89 @@
+/* Single-Precision vector (SVE) inverse tanpi function
+
+   Copyright (C) 2025 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "sv_math.h"
+
+static const struct data
+{
+  float32_t c2, c4, c6, c8;
+  float32_t c0, c1, c3, c5, c7;
+  float32_t shift_val, neg_one;
+} data = {
+  /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+    [2**-128, 1.0].  */
+  .c0 = 0x1.45f306p-2,	.c1 = -0x1.b2975ep-4, .c2 = 0x1.0490e4p-4,
+  .c3 = -0x1.70c272p-5, .c4 = 0x1.0eef52p-5,  .c5 = -0x1.6abbbap-6,
+  .c6 = 0x1.78157p-7,	.c7 = -0x1.f0b406p-9, .c8 = 0x1.2ae7fep-11,
+  .shift_val = 1.5f,	.neg_one = -1.0f,
+};
+
+#define SignMask (0x80000000)
+
+/* Fast implementation of SVE atanpif based on
+   atan(x) ~ shift + z * P(z^2) with reduction to [0,1] using
+   z=-1/x and shift = 1/2.
+   Largest observed error is 2.59 ULP, close to +/-1.0:
+   _ZGVsMxv_atanpif(0x1.f2a89cp-1) got 0x1.f76524p-3
+				  want 0x1.f7651ep-3.  */
+svfloat32_t SV_NAME_F1 (atanpi) (svfloat32_t x, const svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+  svbool_t ptrue = svptrue_b32 ();
+
+  /* No need to trigger special case. Small cases, infs and nans
+     are supported by our approximation technique.  */
+  svuint32_t ix = svreinterpret_u32 (x);
+  svuint32_t sign = svand_x (pg, ix, SignMask);
+
+  /* Argument reduction:
+     y := arctan(x) for x < 1
+     y := arctan(-1/x) + 1/2 for x > +1
+     y := arctan(-1/x) - 1/2 for x < -1
+     Hence, use z=-1/a if |x|>=|-1|, otherwise z=a.  */
+  svbool_t red = svacgt (pg, x, d->neg_one);
+  svfloat32_t z = svsel (red, svdiv_x (ptrue, sv_f32 (d->neg_one), x), x);
+
+  /* Reuse of -1.0f to reduce constant loads,
+     We need a shift value of 1/2, which is created via -1 + (1 + 1/2).  */
+  svfloat32_t shift
+      = svadd_z (red, sv_f32 (d->neg_one), sv_f32 (d->shift_val));
+
+  /* Reinserts the sign bit of the argument to handle the case of x < -1.  */
+  shift = svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (shift), sign));
+
+  svfloat32_t z2 = svmul_x (ptrue, z, z);
+  svfloat32_t z4 = svmul_x (ptrue, z2, z2);
+  svfloat32_t z8 = svmul_x (ptrue, z4, z4);
+
+  svfloat32_t even_coeffs = svld1rq (ptrue, &d->c2);
+
+  svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), z2, even_coeffs, 0);
+  svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), z2, even_coeffs, 1);
+  svfloat32_t p56 = svmla_lane (sv_f32 (d->c5), z2, even_coeffs, 2);
+  svfloat32_t p78 = svmla_lane (sv_f32 (d->c7), z2, even_coeffs, 3);
+
+  svfloat32_t p14 = svmad_x (pg, z4, p34, p12);
+  svfloat32_t p58 = svmad_x (pg, z4, p78, p56);
+
+  svfloat32_t p18 = svmad_x (pg, z8, p58, p14);
+  svfloat32_t y = svmad_x (pg, z2, p18, d->c0);
+
+  /* shift + z * P(z^2).  */
+  return svmad_x (pg, y, z, shift);
+}

sysdeps/aarch64/fpu/bits/math-vector.h

@@ -61,6 +61,10 @@
 # define __DECL_SIMD_atanh __DECL_SIMD_aarch64
 # undef __DECL_SIMD_atanhf
 # define __DECL_SIMD_atanhf __DECL_SIMD_aarch64
+# undef __DECL_SIMD_atanpi
+# define __DECL_SIMD_atanpi __DECL_SIMD_aarch64
+# undef __DECL_SIMD_atanpif
+# define __DECL_SIMD_atanpif __DECL_SIMD_aarch64
 # undef __DECL_SIMD_atan2
 # define __DECL_SIMD_atan2 __DECL_SIMD_aarch64
 # undef __DECL_SIMD_atan2f
@@ -192,6 +196,7 @@ __vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_asinpif (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_atanhf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_atanpif (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_cbrtf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_coshf (__f32x4_t);
@@ -225,6 +230,7 @@ __vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_asinpi (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_atanh (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_atanpi (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_cbrt (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_cosh (__f64x2_t);
@@ -263,6 +269,7 @@ __sv_f32_t _ZGVsMxv_asinhf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_asinpif (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_atanhf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_atanpif (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_cbrtf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_coshf (__sv_f32_t, __sv_bool_t);
@@ -296,6 +303,7 @@ __sv_f64_t _ZGVsMxv_asinh (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_asinpi (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_atanh (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_atanpi (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_cbrt (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_cosh (__sv_f64_t, __sv_bool_t);

sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c

@@ -31,6 +31,7 @@ VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh)
 VPCS_VECTOR_WRAPPER (asinpi_advsimd, _ZGVnN2v_asinpi)
 VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan)
 VPCS_VECTOR_WRAPPER (atanh_advsimd, _ZGVnN2v_atanh)
+VPCS_VECTOR_WRAPPER (atanpi_advsimd, _ZGVnN2v_atanpi)
 VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2)
 VPCS_VECTOR_WRAPPER (cbrt_advsimd, _ZGVnN2v_cbrt)
 VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)

sysdeps/aarch64/fpu/test-double-sve-wrappers.c

@@ -50,6 +50,7 @@ SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh)
 SVE_VECTOR_WRAPPER (asinpi_sve, _ZGVsMxv_asinpi)
 SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan)
 SVE_VECTOR_WRAPPER (atanh_sve, _ZGVsMxv_atanh)
+SVE_VECTOR_WRAPPER (atanpi_sve, _ZGVsMxv_atanpi)
 SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2)
 SVE_VECTOR_WRAPPER (cbrt_sve, _ZGVsMxv_cbrt)
 SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)

sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c

@@ -31,6 +31,7 @@ VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf)
 VPCS_VECTOR_WRAPPER (asinpif_advsimd, _ZGVnN4v_asinpif)
 VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf)
 VPCS_VECTOR_WRAPPER (atanhf_advsimd, _ZGVnN4v_atanhf)
+VPCS_VECTOR_WRAPPER (atanpif_advsimd, _ZGVnN4v_atanpif)
 VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f)
 VPCS_VECTOR_WRAPPER (cbrtf_advsimd, _ZGVnN4v_cbrtf)
 VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)

sysdeps/aarch64/fpu/test-float-sve-wrappers.c

@@ -50,6 +50,7 @@ SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf)
 SVE_VECTOR_WRAPPER (asinpif_sve, _ZGVsMxv_asinpif)
 SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf)
 SVE_VECTOR_WRAPPER (atanhf_sve, _ZGVsMxv_atanhf)
+SVE_VECTOR_WRAPPER (atanpif_sve, _ZGVsMxv_atanpif)
 SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f)
 SVE_VECTOR_WRAPPER (cbrtf_sve, _ZGVsMxv_cbrtf)
 SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)

sysdeps/unix/sysv/linux/aarch64/libmvec.abilist

@@ -152,9 +152,14 @@ GLIBC_2.42 _ZGVnN2v_acospi F
 GLIBC_2.42 _ZGVnN2v_acospif F
 GLIBC_2.42 _ZGVnN2v_asinpi F
 GLIBC_2.42 _ZGVnN2v_asinpif F
+GLIBC_2.42 _ZGVnN2v_atanpi F
+GLIBC_2.42 _ZGVnN2v_atanpif F
 GLIBC_2.42 _ZGVnN4v_acospif F
 GLIBC_2.42 _ZGVnN4v_asinpif F
+GLIBC_2.42 _ZGVnN4v_atanpif F
 GLIBC_2.42 _ZGVsMxv_acospi F
 GLIBC_2.42 _ZGVsMxv_acospif F
 GLIBC_2.42 _ZGVsMxv_asinpi F
 GLIBC_2.42 _ZGVsMxv_asinpif F
+GLIBC_2.42 _ZGVsMxv_atanpi F
+GLIBC_2.42 _ZGVsMxv_atanpif F