glibc/sysdeps/ieee754/flt-32/s_sincosf.h

/* Used by sinf, cosf and sincosf functions.
   Copyright (C) 2018-2019 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
   <http://www.gnu.org/licenses/>.  */

#include <stdint.h>
#include <math.h>
#include "math_config.h"
#include <sincosf_poly.h>

/* 2PI * 2^-64.  */
static const double pi63 = 0x1.921FB54442D18p-62;
/* PI / 4.  */
static const double pio4 = 0x1.921FB54442D18p-1;

/* Polynomial data (the cosine polynomial is negated in the 2nd entry).  */
extern const sincos_t __sincosf_table[2] attribute_hidden;

/* Table with 4/PI to 192 bit precision.  */
extern const uint32_t __inv_pio4[] attribute_hidden;

/* Top 12 bits of the float representation with the sign bit cleared.  */
static inline uint32_t
abstop12 (float x)
{
  return (asuint (x) >> 20) & 0x7ff;
}

/* Fast range reduction using single multiply-subtract.  Return the modulo of
   X as a value between -PI/4 and PI/4 and store the quadrant in NP.
   The values for PI/2 and 2/PI are accessed via P.  Since PI/2 as a double
   is accurate to 55 bits and the worst-case cancellation happens at 6 * PI/4,
   the result is accurate for |X| <= 120.0.  */
static inline double
reduce_fast (double x, const sincos_t *p, int *np)
{
  double r;
#if TOINT_INTRINSICS
  /* Use fast round and lround instructions when available.  */
  r = x * p->hpi_inv;
  *np = converttoint (r);
  return x - roundtoint (r) * p->hpi;
#else
  /* Use scaled float to int conversion with explicit rounding.
     hpi_inv is prescaled by 2^24 so the quadrant ends up in bits 24..31.
     This avoids inaccuracies introduced by truncating negative values.  */
  r = x * p->hpi_inv;
  int n = ((int32_t)r + 0x800000) >> 24;
  *np = n;
  return x - n * p->hpi;
#endif
}

/* Reduce the range of XI to a multiple of PI/2 using fast integer arithmetic.
   XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored).
   Return the modulo between -PI/4 and PI/4 and store the quadrant in NP.
   Reduction uses a table of 4/PI with 192 bits of precision.  A 32x96->128 bit
   multiply computes the exact 2.62-bit fixed-point modulo.  Since the result
   can have at most 29 leading zeros after the binary point, the double
   precision result is accurate to 33 bits.  */
static inline double
reduce_large (uint32_t xi, int *np)
{
  const uint32_t *arr = &__inv_pio4[(xi >> 26) & 15];
  int shift = (xi >> 23) & 7;
  uint64_t n, res0, res1, res2;

  xi = (xi & 0xffffff) | 0x800000;
  xi <<= shift;

  res0 = xi * arr[0];
  res1 = (uint64_t)xi * arr[4];
  res2 = (uint64_t)xi * arr[8];
  res0 = (res2 >> 32) | (res0 << 32);
  res0 += res1;

  n = (res0 + (1ULL << 61)) >> 62;
  res0 -= n << 62;
  double x = (int64_t)res0;
  *np = n;
  return x * pi63;
}