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/* 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)
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