cosf.c

/*
 * Single-precision vector cos function.
 *
 * Copyright (c) 2019-2024, Arm Limited.
 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
 */

#include "mathlib.h"
#include "v_math.h"
#include "test_defs.h"
#include "test_sig.h"

static const struct data
{
  float32x4_t poly[4];
  float32x4_t range_val, inv_pi, pi_1, pi_2, pi_3;
} data = {
  /* 1.886 ulp error.  */
  .poly = { V4 (-0x1.555548p-3f), V4 (0x1.110df4p-7f), V4 (-0x1.9f42eap-13f),
	    V4 (0x1.5b2e76p-19f) },

  .pi_1 = V4 (0x1.921fb6p+1f),
  .pi_2 = V4 (-0x1.777a5cp-24f),
  .pi_3 = V4 (-0x1.ee59dap-49f),

  .inv_pi = V4 (0x1.45f306p-2f),
  .range_val = V4 (0x1p20f)
};

#define C(i) d->poly[i]

static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
{
  /* Fall back to scalar code.  */
  y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
  return v_call_f32 (cosf, x, y, cmp);
}

float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (cos) (float32x4_t x)
{
  const struct data *d = ptr_barrier (&data);
  float32x4_t n, r, r2, r3, y;
  uint32x4_t odd, cmp;

#if WANT_SIMD_EXCEPT
  r = vabsq_f32 (x);
  cmp = vcgeq_u32 (vreinterpretq_u32_f32 (r),
		   vreinterpretq_u32_f32 (d->range_val));
  if (unlikely (v_any_u32 (cmp)))
    /* If fenv exceptions are to be triggered correctly, set any special lanes
       to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by
       special-case handler later.  */
    r = vbslq_f32 (cmp, v_f32 (1.0f), r);
#else
  cmp = vcageq_f32 (x, d->range_val);
  r = x;
#endif

  /* n = rint((|x|+pi/2)/pi) - 0.5.  */
  n = vrndaq_f32 (vfmaq_f32 (v_f32 (0.5), r, d->inv_pi));
  odd = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtq_s32_f32 (n)), 31);
  n = vsubq_f32 (n, v_f32 (0.5f));

  /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2).  */
  r = vfmsq_f32 (r, d->pi_1, n);
  r = vfmsq_f32 (r, d->pi_2, n);
  r = vfmsq_f32 (r, d->pi_3, n);

  /* y = sin(r).  */
  r2 = vmulq_f32 (r, r);
  r3 = vmulq_f32 (r2, r);
  y = vfmaq_f32 (C (2), C (3), r2);
  y = vfmaq_f32 (C (1), y, r2);
  y = vfmaq_f32 (C (0), y, r2);
  y = vfmaq_f32 (r, y, r3);

  if (unlikely (v_any_u32 (cmp)))
    return special_case (x, y, odd, cmp);
  return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
}

HALF_WIDTH_ALIAS_F1 (cos)

TEST_SIG (V, F, 1, cos, -3.1, 3.1)
TEST_ULP (V_NAME_F1 (cos), 1.4)
TEST_DISABLE_FENV_IF_NOT (V_NAME_F1 (cos), WANT_SIMD_EXCEPT)
TEST_SYM_INTERVAL (V_NAME_F1 (cos), 0, 0x1p20, 500000)
TEST_SYM_INTERVAL (V_NAME_F1 (cos), 0x1p20, inf, 10000)