AArch64: Implement AdvSIMD and SVE atan2pi/f

Implement double and single precision variants of the C23 routine atan2pi
for both AdvSIMD and SVE.

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

bits/libm-simd-decl-stubs.h

@@ -406,4 +406,15 @@
 #define __DECL_SIMD_atanpif32x
 #define __DECL_SIMD_atanpif64x
 #define __DECL_SIMD_atanpif128x
+
+#define __DECL_SIMD_atan2pi
+#define __DECL_SIMD_atan2pif
+#define __DECL_SIMD_atan2pil
+#define __DECL_SIMD_atan2pif16
+#define __DECL_SIMD_atan2pif32
+#define __DECL_SIMD_atan2pif64
+#define __DECL_SIMD_atan2pif128
+#define __DECL_SIMD_atan2pif32x
+#define __DECL_SIMD_atan2pif64x
+#define __DECL_SIMD_atan2pif128x
 #endif

math/bits/mathcalls.h

@@ -77,6 +77,7 @@ __MATHCALL (atanpi,, (_Mdouble_ __x));
 __MATHCALL_VEC (atanpi,, (_Mdouble_ __x));
 /* Arc tangent of Y/X, divided by pi.  */
 __MATHCALL (atan2pi,, (_Mdouble_ __y, _Mdouble_ __x));
+__MATHCALL_VEC (atan2pi,, (_Mdouble_ __y, _Mdouble_ __x));
 
 /* Cosine of pi * X.  */
 __MATHCALL_VEC (cospi,, (_Mdouble_ __x));

sysdeps/aarch64/fpu/Makefile

@@ -8,6 +8,7 @@ libmvec-supported-funcs = acos \
                           atanh \
                           atanpi \
                           atan2 \
+                          atan2pi \
                           cbrt \
                           cos \
                           cosh \

sysdeps/aarch64/fpu/Versions

@@ -173,5 +173,10 @@ libmvec {
     _ZGVnN4v_atanpif;
     _ZGVsMxv_atanpi;
     _ZGVsMxv_atanpif;
+    _ZGVnN2vv_atan2pi;
+    _ZGVnN2vv_atan2pif;
+    _ZGVnN4vv_atan2pif;
+    _ZGVsMxvv_atan2pi;
+    _ZGVsMxvv_atan2pif;
   }
 }

sysdeps/aarch64/fpu/advsimd_f32_protos.h

@@ -50,3 +50,4 @@ libmvec_hidden_proto (V_NAME_F1(tan));
 libmvec_hidden_proto (V_NAME_F1(tanh));
 libmvec_hidden_proto (V_NAME_F1(tanpi));
 libmvec_hidden_proto (V_NAME_F2(atan2));
+libmvec_hidden_proto (V_NAME_F2(atan2pi));

sysdeps/aarch64/fpu/atan2pi_advsimd.c

@@ -0,0 +1,175 @@
+/* Double-Precision vector (Advanced SIMD) inverse tan2pi 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
+{
+  float64_t c2, c4, c6, c8, c10, c12, c14, c16, c18, c20;
+  float64x2_t c0;
+  uint64x2_t zeroinfnan;
+  float64x2_t c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
+} data = {
+  /* Coefficients of polynomial P such that atan(x)~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,
+  .zeroinfnan = V2 (2 * 0x7ff0000000000000ul - 1),
+};
+
+#define SignMask v_u64 (0x8000000000000000)
+#define OneOverPi v_f64 (0x1.45f306dc9c883p-2)
+
+/* Special cases i.e. 0, infinity, NaN (fall back to scalar calls).  */
+static float64x2_t VPCS_ATTR NOINLINE
+special_case (float64x2_t y, float64x2_t x, float64x2_t ret,
+	      uint64x2_t sign_xy, uint64x2_t cmp)
+{
+  /* Account for the sign of x and y.  */
+  ret = vreinterpretq_f64_u64 (
+      veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy));
+
+  /* Since we have no scalar fallback for atan2pi,
+     we can instead make a call to atan2f and divide by pi.  */
+  ret = v_call2_f64 (atan2, y, x, ret, cmp);
+
+  /* Only divide the special cases by pi, and leave the rest unchanged.  */
+  return vbslq_f64 (cmp, vmulq_f64 (ret, OneOverPi), ret);
+}
+
+/* Returns 1 if input is the bit representation of 0, infinity or nan.  */
+static inline uint64x2_t
+zeroinfnan (uint64x2_t i, const struct data *d)
+{
+  /* (2 * i - 1) >= (2 * asuint64 (INFINITY) - 1).  */
+  return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)), d->zeroinfnan);
+}
+
+/* Fast implementation of vector atan2pi.
+   Maximum observed error is 3.04 ulps:
+   _ZGVnN2vv_atan2pi (0x1.1e0733532ce28p+5, 0x1.2d803379cca1fp+5)
+   got 0x1.eed60c1e89317p-3 want 0x1.eed60c1e89314p-3.  */
+float64x2_t VPCS_ATTR V_NAME_D2 (atan2pi) (float64x2_t y, float64x2_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  uint64x2_t ix = vreinterpretq_u64_f64 (x);
+  uint64x2_t iy = vreinterpretq_u64_f64 (y);
+
+  uint64x2_t special_cases
+      = vorrq_u64 (zeroinfnan (ix, d), zeroinfnan (iy, d));
+
+  uint64x2_t sign_x = vandq_u64 (ix, SignMask);
+  uint64x2_t sign_y = vandq_u64 (iy, SignMask);
+  uint64x2_t sign_xy = veorq_u64 (sign_x, sign_y);
+
+  float64x2_t ax = vabsq_f64 (x);
+  float64x2_t ay = vabsq_f64 (y);
+
+  uint64x2_t pred_xlt0 = vcltzq_f64 (x);
+  uint64x2_t pred_aygtax = vcgtq_f64 (ay, ax);
+
+  /* Set up z for evaluation of atanpi.  */
+  float64x2_t num = vbslq_f64 (pred_aygtax, vnegq_f64 (ax), ay);
+  float64x2_t den = vbslq_f64 (pred_aygtax, ay, ax);
+  float64x2_t z = vdivq_f64 (num, den);
+
+  /* Work out the correct shift for atan2pi:
+     -1.0 when x < 0  and ax < ay
+     -0.5 when x < 0  and ax > ay
+      0   when x >= 0 and ax < ay
+      0.5 when x >= 0 and ax > ay.  */
+  float64x2_t shift = vreinterpretq_f64_u64 (
+      vandq_u64 (pred_xlt0, vreinterpretq_u64_f64 (v_f64 (-1.0))));
+  float64x2_t shift2 = vreinterpretq_f64_u64 (
+      vandq_u64 (pred_aygtax, vreinterpretq_u64_f64 (v_f64 (0.5))));
+  shift = vaddq_f64 (shift, shift2);
+
+  /* Calculate the polynomial approximation.  */
+  float64x2_t z2 = vmulq_f64 (z, z);
+  float64x2_t z3 = vmulq_f64 (z2, 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 poly = vfmaq_f64 (p18, z16, p920);
+
+  /* y = shift + z * P(z^2).  */
+  float64x2_t ret = vfmaq_f64 (shift, z, d->c0);
+  ret = vfmaq_f64 (ret, z3, poly);
+
+  if (__glibc_unlikely (v_any_u64 (special_cases)))
+    return special_case (y, x, ret, sign_xy, special_cases);
+
+  /* Account for the sign of x and y.  */
+  return vreinterpretq_f64_u64 (
+      veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy));
+}

sysdeps/aarch64/fpu/atan2pi_sve.c

@@ -0,0 +1,159 @@
+/* Double-Precision vector (SVE) inverse tan2pi 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 "math_config.h"
+#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;
+} 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 = 0.5,
+};
+
+#define OneOverPi sv_f64 (0x1.45f306dc9c883p-2)
+
+/* Special cases i.e. 0, infinity, nan (fall back to scalar calls).  */
+static svfloat64_t NOINLINE
+special_case (svfloat64_t y, svfloat64_t x, svfloat64_t ret,
+	      const svbool_t cmp)
+{
+  ret = sv_call2_f64 (atan2, y, x, ret, cmp);
+  return svmul_f64_m (cmp, ret, OneOverPi);
+}
+
+/* Returns a predicate indicating true if the input is the bit representation
+   of 0, infinity or nan.  */
+static inline svbool_t
+zeroinfnan (svuint64_t i, const svbool_t pg)
+{
+  return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
+		  sv_u64 (2 * asuint64 (INFINITY) - 1));
+}
+
+/* Fast implementation of SVE atan2pi.
+   Maximum observed error is 3.11 ulps:
+   _ZGVsMxvv_atan2pi (0x1.ef284a877f6b5p+6, 0x1.03fdde8242b17p+7)
+   got 0x1.f00f800163079p-3 want 0x1.f00f800163076p-3.  */
+svfloat64_t SV_NAME_D2 (atan2pi) (svfloat64_t y, 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 iy = svreinterpret_u64 (y);
+
+  svbool_t cmp_x = zeroinfnan (ix, pg);
+  svbool_t cmp_y = zeroinfnan (iy, pg);
+  svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y);
+
+  svfloat64_t ax = svabs_x (pg, x);
+  svfloat64_t ay = svabs_x (pg, y);
+  svuint64_t iax = svreinterpret_u64 (ax);
+  svuint64_t iay = svreinterpret_u64 (ay);
+
+  svuint64_t sign_x = sveor_x (pg, ix, iax);
+  svuint64_t sign_y = sveor_x (pg, iy, iay);
+  svuint64_t sign_xy = sveor_x (pg, sign_x, sign_y);
+
+  svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
+
+  /* Set up z for evaluation of atanpi.  */
+  svfloat64_t num = svsel (pred_aygtax, svneg_x (pg, ax), ay);
+  svfloat64_t den = svsel (pred_aygtax, ay, ax);
+  svfloat64_t z = svdiv_x (pg, num, den);
+
+  /* Work out the correct shift for atan2pi:
+     -1.0 when x < 0  and ax < ay
+     -0.5 when x < 0  and ax > ay
+      0   when x >= 0 and ax < ay
+      0.5 when x >= 0 and ax > ay.  */
+  svfloat64_t shift = svreinterpret_f64 (svlsr_x (pg, sign_x, 1));
+  shift = svmul_x (ptrue, shift, sv_f64 (d->shift_val));
+  shift = svsel (pred_aygtax, sv_f64 (d->shift_val), shift);
+  shift = svreinterpret_f64 (svorr_x (pg, sign_x, svreinterpret_u64 (shift)));
+
+  /* Use split Estrin scheme for P(z^2) with deg(P)=19.  */
+  svfloat64_t z2 = svmul_x (pg, z, z);
+  svfloat64_t z3 = svmul_x (pg, z2, z);
+  svfloat64_t z4 = svmul_x (pg, z2, z2);
+  svfloat64_t z8 = svmul_x (pg, z4, z4);
+  svfloat64_t z16 = svmul_x (pg, 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 poly = svmla_x (pg, p18, z16, p920);
+
+  svfloat64_t ret = svmla_x (pg, shift, z, sv_f64 (d->c0));
+  ret = svmla_x (pg, ret, z3, poly);
+
+  /* Account for the sign of x and y.  */
+  if (__glibc_unlikely (svptest_any (pg, cmp_xy)))
+    return special_case (
+	y, x,
+	svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy)),
+	cmp_xy);
+  return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy));
+}

sysdeps/aarch64/fpu/atan2pif_advsimd.c

@@ -0,0 +1,138 @@
+/* Single-Precision vector (Advanced SIMD) inverse tan2pi 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
+{
+  float32x4_t c1, c3, c5, c7;
+  float c2, c4, c6, c8;
+  float32x4_t c0;
+  uint32x4_t comp_const;
+} data = {
+  /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+     [2^-128, 1.0].
+     Generated using fpminimax between FLT_MIN and 1.  */
+  .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,	    .comp_const = V4 (2 * 0x7f800000lu - 1),
+};
+
+#define SignMask v_u32 (0x80000000)
+#define OneOverPi v_f32 (0x1.45f307p-2)
+
+/* Special cases i.e. 0, infinity and nan (fall back to scalar calls).  */
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t y, float32x4_t x, float32x4_t ret,
+	      uint32x4_t sign_xy, uint32x4_t cmp)
+{
+  /* Account for the sign of y.  */
+  ret = vreinterpretq_f32_u32 (
+      veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy));
+
+  /* Since we have no scalar fallback for atan2pif,
+     we can instead make a call to atan2f and divide by pi.  */
+  ret = v_call2_f32 (atan2f, y, x, ret, cmp);
+
+  /* Only divide the special cases by pi, and leave the rest unchanged.  */
+  return vbslq_f32 (cmp, vmulq_f32 (ret, OneOverPi), ret);
+}
+
+/* Returns 1 if input is the bit representation of 0, infinity or nan.  */
+static inline uint32x4_t
+zeroinfnan (uint32x4_t i, const struct data *d)
+{
+  /* 2 * i - 1 >= 2 * 0x7f800000lu - 1.  */
+  return vcgeq_u32 (vsubq_u32 (vshlq_n_u32 (i, 1), v_u32 (1)), d->comp_const);
+}
+
+/* Fast implementation of vector atan2f. Maximum observed error is 2.89 ULP:
+   _ZGVnN4vv_atan2pif (0x1.bd397p+54, 0x1.e79a4ap+54) got 0x1.e2678ep-3
+						     want 0x1.e26794p-3.  */
+float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2pi) (float32x4_t y,
+						    float32x4_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  uint32x4_t ix = vreinterpretq_u32_f32 (x);
+  uint32x4_t iy = vreinterpretq_u32_f32 (y);
+
+  uint32x4_t special_cases
+      = vorrq_u32 (zeroinfnan (ix, d), zeroinfnan (iy, d));
+
+  uint32x4_t sign_x = vandq_u32 (ix, SignMask);
+  uint32x4_t sign_y = vandq_u32 (iy, SignMask);
+  uint32x4_t sign_xy = veorq_u32 (sign_x, sign_y);
+
+  float32x4_t ax = vabsq_f32 (x);
+  float32x4_t ay = vabsq_f32 (y);
+
+  uint32x4_t pred_xlt0 = vcltzq_f32 (x);
+  uint32x4_t pred_aygtax = vcgtq_f32 (ay, ax);
+
+  /* Set up z for evaluation of atanpif.  */
+  float32x4_t num = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay);
+  float32x4_t den = vbslq_f32 (pred_aygtax, ay, ax);
+  float32x4_t z = vdivq_f32 (num, den);
+
+  /* Work out the correct shift for atan2pi:
+     -1.0 when x < 0  and ax < ay
+     -0.5 when x < 0  and ax > ay
+      0   when x >= 0 and ax < ay
+      0.5 when x >= 0 and ax > ay.  */
+  float32x4_t shift = vreinterpretq_f32_u32 (
+      vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-1.0f))));
+  float32x4_t shift2 = vreinterpretq_f32_u32 (
+      vandq_u32 (pred_aygtax, vreinterpretq_u32_f32 (v_f32 (0.5f))));
+  shift = vaddq_f32 (shift, shift2);
+
+  /* Calculate the polynomial approximation.  */
+  float32x4_t z2 = vmulq_f32 (z, z);
+  float32x4_t z3 = vmulq_f32 (z2, z);
+  float32x4_t z4 = vmulq_f32 (z2, z2);
+  float32x4_t z8 = vmulq_f32 (z4, z4);
+
+  float32x4_t c2468 = vld1q_f32 (&d->c2);
+
+  float32x4_t p12 = vfmaq_laneq_f32 (d->c1, z2, c2468, 0);
+  float32x4_t p34 = vfmaq_laneq_f32 (d->c3, z2, c2468, 1);
+  float32x4_t p56 = vfmaq_laneq_f32 (d->c5, z2, c2468, 2);
+  float32x4_t p78 = vfmaq_laneq_f32 (d->c7, z2, c2468, 3);
+  float32x4_t p14 = vfmaq_f32 (p12, z4, p34);
+  float32x4_t p58 = vfmaq_f32 (p56, z4, p78);
+
+  float32x4_t poly = vfmaq_f32 (p14, z8, p58);
+
+  /* y = shift + z * P(z^2).  */
+  float32x4_t ret = vfmaq_f32 (shift, z, d->c0);
+  ret = vfmaq_f32 (ret, z3, poly);
+
+  if (__glibc_unlikely (v_any_u32 (special_cases)))
+    {
+      return special_case (y, x, ret, sign_xy, special_cases);
+    }
+
+  /* Account for the sign of y.  */
+  return vreinterpretq_f32_u32 (
+      veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy));
+}
+libmvec_hidden_def (V_NAME_F2 (atan2pi))
+HALF_WIDTH_ALIAS_F2 (atan2pi)

sysdeps/aarch64/fpu/atan2pif_sve.c

@@ -0,0 +1,137 @@
+/* Single-Precision vector (SVE) inverse tan2pi 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 c0, c1, c3, c5, c7;
+  float32_t c2, c4, c6, c8;
+  float32_t shift_val;
+  uint32_t comp_const;
+} 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 = 0.5f,
+  .comp_const = 2 * 0x7f800000lu - 1,
+};
+
+#define OneOverPi sv_f32 (0x1.45f307p-2)
+
+/* Special cases i.e. 0, infinity, nan (fall back to scalar calls).  */
+static svfloat32_t NOINLINE
+special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret,
+	      const svbool_t cmp)
+{
+  ret = sv_call2_f32 (atan2f, y, x, ret, cmp);
+  return svmul_f32_x (cmp, ret, OneOverPi);
+}
+
+/* Returns a predicate indicating true if the input is the bit representation
+   of 0, infinity or nan.  */
+static inline svbool_t
+zeroinfnan (svuint32_t i, const svbool_t pg, const struct data *d)
+{
+  return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
+		  sv_u32 (d->comp_const));
+}
+
+/* Fast implementation of SVE atan2pif based on atan(x) ~ shift + z + z^3 *
+   P(z^2) with reduction to [0,1] using z=1/x and shift = 1/2. Maximum
+   observed error is 2.90 ULP:
+   _ZGVsMxvv_atan2pif (0x1.a28542p+5, 0x1.adb7c6p+5) got 0x1.f76524p-3
+						    want 0x1.f7651ep-3.  */
+svfloat32_t SV_NAME_F2 (atan2pi) (svfloat32_t y, svfloat32_t x,
+				  const svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+  svbool_t ptrue = svptrue_b32 ();
+
+  svuint32_t ix = svreinterpret_u32 (x);
+  svuint32_t iy = svreinterpret_u32 (y);
+
+  svbool_t cmp_x = zeroinfnan (ix, pg, d);
+  svbool_t cmp_y = zeroinfnan (iy, pg, d);
+  svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y);
+
+  svfloat32_t ax = svabs_x (pg, x);
+  svfloat32_t ay = svabs_x (pg, y);
+  svuint32_t iax = svreinterpret_u32 (ax);
+  svuint32_t iay = svreinterpret_u32 (ay);
+
+  svuint32_t sign_x = sveor_x (pg, ix, iax);
+  svuint32_t sign_y = sveor_x (pg, iy, iay);
+  svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y);
+
+  svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
+
+  /* Set up z for evaluation of atanpif.  */
+  svfloat32_t num = svsel (pred_aygtax, svneg_x (pg, ax), ay);
+  svfloat32_t den = svsel (pred_aygtax, ay, ax);
+  svfloat32_t z = svdiv_x (ptrue, num, den);
+
+  /* Work out the correct shift for atan2pi:
+     -1.0 when x < 0  and ax < ay
+     -0.5 when x < 0  and ax > ay
+      0   when x >= 0 and ax < ay
+      0.5 when x >= 0 and ax > ay.  */
+  svfloat32_t shift = svreinterpret_f32 (svlsr_x (pg, sign_x, 1));
+  shift = svmul_x (ptrue, shift, sv_f32 (d->shift_val));
+  shift = svsel (pred_aygtax, sv_f32 (d->shift_val), shift);
+  shift = svreinterpret_f32 (svorr_x (pg, sign_x, svreinterpret_u32 (shift)));
+
+  /* Use pure Estrin scheme for P(z^2) with deg(P)=7.  */
+  svfloat32_t z2 = svmul_x (pg, z, z);
+  svfloat32_t z4 = svmul_x (pg, z2, z2);
+  svfloat32_t z8 = svmul_x (pg, 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);
+
+  /* ret = shift + z + z^3 * P(z^2).  */
+  svfloat32_t poly = svmad_x (pg, z2, p18, d->c0);
+  svfloat32_t ret = svmad_x (pg, poly, z, shift);
+
+  if (__glibc_unlikely (svptest_any (pg, cmp_xy)))
+    return special_case (
+	y, x,
+	svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)),
+	cmp_xy);
+
+  /* Account for the sign of x and y.  */
+  return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy));
+}

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

@@ -69,6 +69,10 @@
 # define __DECL_SIMD_atan2 __DECL_SIMD_aarch64
 # undef __DECL_SIMD_atan2f
 # define __DECL_SIMD_atan2f __DECL_SIMD_aarch64
+# undef __DECL_SIMD_atan2pi
+# define __DECL_SIMD_atan2pi __DECL_SIMD_aarch64
+# undef __DECL_SIMD_atan2pif
+# define __DECL_SIMD_atan2pif __DECL_SIMD_aarch64
 # undef __DECL_SIMD_cbrt
 # define __DECL_SIMD_cbrt __DECL_SIMD_aarch64
 # undef __DECL_SIMD_cbrtf
@@ -188,6 +192,7 @@ typedef __SVBool_t __sv_bool_t;
 #  define __vpcs __attribute__ ((__aarch64_vector_pcs__))
 
 __vpcs __f32x4_t _ZGVnN4vv_atan2f (__f32x4_t, __f32x4_t);
+__vpcs __f32x4_t _ZGVnN4vv_atan2pif (__f32x4_t, __f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_acoshf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_acospif (__f32x4_t);
@@ -222,6 +227,7 @@ __vpcs __f32x4_t _ZGVnN4v_tanhf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_tanpif (__f32x4_t);
 
 __vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t);
+__vpcs __f64x2_t _ZGVnN2vv_atanpi2 (__f64x2_t, __f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_acosh (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_acospi (__f64x2_t);
@@ -261,6 +267,7 @@ __vpcs __f64x2_t _ZGVnN2v_tanpi (__f64x2_t);
 #ifdef __SVE_VEC_MATH_SUPPORTED
 
 __sv_f32_t _ZGVsMxvv_atan2f (__sv_f32_t, __sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxvv_atan2pif (__sv_f32_t, __sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_acoshf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_acospif (__sv_f32_t, __sv_bool_t);
@@ -295,6 +302,7 @@ __sv_f32_t _ZGVsMxv_tanhf (__sv_f32_t, __sv_bool_t);
 __sv_f32_t _ZGVsMxv_tanpif (__sv_f32_t, __sv_bool_t);
 
 __sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxvv_atan2pi (__sv_f64_t, __sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_acosh (__sv_f64_t, __sv_bool_t);
 __sv_f64_t _ZGVsMxv_acospi (__sv_f64_t, __sv_bool_t);

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

@@ -33,6 +33,7 @@ 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_ff (atan2pi_advsimd, _ZGVnN2vv_atan2pi)
 VPCS_VECTOR_WRAPPER (cbrt_advsimd, _ZGVnN2v_cbrt)
 VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)
 VPCS_VECTOR_WRAPPER (cosh_advsimd, _ZGVnN2v_cosh)

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

@@ -52,6 +52,7 @@ 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_ff (atan2pi_sve, _ZGVsMxvv_atan2pi)
 SVE_VECTOR_WRAPPER (cbrt_sve, _ZGVsMxv_cbrt)
 SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)
 SVE_VECTOR_WRAPPER (cosh_sve, _ZGVsMxv_cosh)

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

@@ -33,6 +33,7 @@ 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_ff (atan2pif_advsimd, _ZGVnN4vv_atan2pif)
 VPCS_VECTOR_WRAPPER (cbrtf_advsimd, _ZGVnN4v_cbrtf)
 VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)
 VPCS_VECTOR_WRAPPER (coshf_advsimd, _ZGVnN4v_coshf)

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

@@ -52,6 +52,7 @@ 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_ff (atan2pif_sve, _ZGVsMxvv_atan2pif)
 SVE_VECTOR_WRAPPER (cbrtf_sve, _ZGVsMxv_cbrtf)
 SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)
 SVE_VECTOR_WRAPPER (coshf_sve, _ZGVsMxv_coshf)

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

@@ -154,12 +154,17 @@ 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 _ZGVnN2vv_atan2pi F
+GLIBC_2.42 _ZGVnN2vv_atan2pif F
 GLIBC_2.42 _ZGVnN4v_acospif F
 GLIBC_2.42 _ZGVnN4v_asinpif F
 GLIBC_2.42 _ZGVnN4v_atanpif F
+GLIBC_2.42 _ZGVnN4vv_atan2pif 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
+GLIBC_2.42 _ZGVsMxvv_atan2pi F
+GLIBC_2.42 _ZGVsMxvv_atan2pif F