/*
* Single-precision vector atan2f(x) function.
*
* Copyright (c) 2021-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.h"
#include "poly_sve_f32.h"
static const struct data
{
float32_t poly[8];
float32_t pi_over_2;
} data = {
/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
[2**-128, 1.0]. */
.poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
-0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f },
.pi_over_2 = 0x1.921fb6p+0f,
};
#define SignMask sv_u32 (0x80000000)
/* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */
static inline svfloat32_t
special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret,
const svbool_t cmp)
{
return sv_call2_f32 (atan2f, y, x, ret, cmp);
}
/* 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)
{
return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
sv_u32 (2 * 0x7f800000lu - 1));
}
/* Fast implementation of SVE atan2f based on atan(x) ~ shift + z + z^3 *
P(z^2) with reduction to [0,1] using z=1/x and shift = pi/2. Maximum
observed error is 2.95 ULP:
_ZGVsMxvv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1
want 0x1.967f00p-1. */
svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, const svbool_t pg)
{
const struct data *data_ptr = ptr_barrier (&data);
svuint32_t ix = svreinterpret_u32 (x);
svuint32_t iy = svreinterpret_u32 (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);
svuint32_t sign_x = svand_x (pg, ix, SignMask);
svuint32_t sign_y = svand_x (pg, iy, SignMask);
svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y);
svfloat32_t ax = svabs_x (pg, x);
svfloat32_t ay = svabs_x (pg, y);
svbool_t pred_xlt0 = svcmplt (pg, x, 0.0);
svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
/* Set up z for call to atan. */
svfloat32_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay);
svfloat32_t d = svsel (pred_aygtax, ay, ax);
svfloat32_t z = svdiv_x (pg, n, d);
/* Work out the correct shift. */
svfloat32_t shift = svsel (pred_xlt0, sv_f32 (-2.0), sv_f32 (0.0));
shift = svsel (pred_aygtax, svadd_x (pg, shift, 1.0), shift);
shift = svmul_x (pg, shift, sv_f32 (data_ptr->pi_over_2));
/* Use split 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 ret = sv_estrin_7_f32_x (pg, z2, z4, z8, data_ptr->poly);
/* ret = shift + z + z^3 * P(z^2). */
svfloat32_t z3 = svmul_x (pg, z2, z);
ret = svmla_x (pg, z, z3, ret);
ret = svadd_m (pg, ret, shift);
/* Account for the sign of x and y. */
ret = svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy));
if (unlikely (svptest_any (pg, cmp_xy)))
return special_case (y, x, ret, cmp_xy);
return ret;
}
/* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */
PL_SIG (SV, F, 2, atan2)
PL_TEST_ULP (SV_NAME_F2 (atan2), 2.45)
PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 0.0, 1.0, 40000)
PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 1.0, 100.0, 40000)
PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 100, inf, 40000)
PL_TEST_INTERVAL (SV_NAME_F2 (atan2), -0, -inf, 40000)
