[PATCH 10/15] math: Use atan2pif from CORE-MATH

DJ Delorie dj@redhat.com
Sat Feb 8 04:20:27 GMT 2025


LGTM but one question:

> +	return 0.0f * sgnf[uy >> 31];

Is this reliable under gcc's optimizer?  I've seen copysign() used for
this purpose elsewhere...

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

Adhemerval Zanella <adhemerval.zanella@linaro.org> writes:
> diff --git a/SHARED-FILES b/SHARED-FILES
> index e700f4b155..b403a2a6f0 100644
> --- a/SHARED-FILES
> +++ b/SHARED-FILES
> @@ -342,3 +342,7 @@ sysdeps/ieee754/flt-32/s_asinpif.c:
>    (src/binary32/asinpi/asinpif.c in CORE-MATH)
>    - the code was adapted to use glibc code style and internal
>      functions to handle errno, overflow, and underflow.
> +sysdeps/ieee754/flt-32/s_atan2pif.c:
> +  (src/binary32/atan2pi/atan2pif.c in CORE-MATH)
> +  - the code was adapted to use glibc code style and internal
> +    functions to handle errno, overflow, and underflow.

Ok.

> diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
> diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
> diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
> diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
> diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
> diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
> diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps

Ok.

> diff --git a/sysdeps/ieee754/flt-32/s_atan2pif.c b/sysdeps/ieee754/flt-32/s_atan2pif.c
> +/* 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"

Ok.

> +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;
> +}

Ok.

> +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;
> +}

Ok.

> +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);

Ok.

> +  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];
> +    }

Ok.

> +  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];
> +    }

Ok.

> +  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];
> +    }

Ok.

> +  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];

Ok.

> +  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;
> +	    }

Ok.

> +	  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;
> +	    }
> +	}
> +    }

Ok.

> +  float rf = r;
> +  if (__glibc_unlikely (rf == 0.0f && y != 0.0f))
> +    __set_errno (ERANGE);
> +  return rf;
> +}
> +libm_alias_float (__atan2pi, atan2pi)

Ok.

> diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
> diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
> diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps
> diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps
> diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
> diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
> diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
> diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
> diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
> diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps

Ok.



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