path: root/compute/ncnn/src/layer/arm/neon_mathfun.h

/* NEON implementation of sin, cos, exp and log
 *
 *   Inspired by Intel Approximate Math library, and based on the
 *   corresponding algorithms of the cephes math library
 */

/* Copyright (C) 2011  Julien Pommier
 *
 *  This software is provided 'as-is', without any express or implied
 *  warranty.  In no event will the authors be held liable for any damages
 *  arising from the use of this software.
 *
 *  Permission is granted to anyone to use this software for any purpose,
 *  including commercial applications, and to alter it and redistribute it
 *  freely, subject to the following restrictions:
 *
 *  1. The origin of this software must not be misrepresented; you must not
 *     claim that you wrote the original software. If you use this software
 *     in a product, an acknowledgment in the product documentation would be
 *     appreciated but is not required.
 *  2. Altered source versions must be plainly marked as such, and must not be
 *     misrepresented as being the original software.
 *  3. This notice may not be removed or altered from any source distribution.
 *
 *  (this is the zlib license)
 */

#include <arm_neon.h>

#define c_inv_mant_mask ~0x7f800000u
#define c_cephes_SQRTHF 0.707106781186547524
#define c_cephes_log_p0 7.0376836292E-2
#define c_cephes_log_p1 -1.1514610310E-1
#define c_cephes_log_p2 1.1676998740E-1
#define c_cephes_log_p3 -1.2420140846E-1
#define c_cephes_log_p4 +1.4249322787E-1
#define c_cephes_log_p5 -1.6668057665E-1
#define c_cephes_log_p6 +2.0000714765E-1
#define c_cephes_log_p7 -2.4999993993E-1
#define c_cephes_log_p8 +3.3333331174E-1
#define c_cephes_log_q1 -2.12194440e-4
#define c_cephes_log_q2 0.693359375

/* natural logarithm computed for 4 simultaneous float
 *   return NaN for x <= 0
 */
static inline float32x4_t log_ps(float32x4_t x)
{
  float32x4_t one = vdupq_n_f32(1);

  x = vmaxq_f32(x, vdupq_n_f32(0)); /* force flush to zero on denormal values */
  uint32x4_t invalid_mask = vcleq_f32(x, vdupq_n_f32(0));

  int32x4_t ux = vreinterpretq_s32_f32(x);

  int32x4_t emm0 = vshrq_n_s32(ux, 23);

  /* keep only the fractional part */
  ux = vandq_s32(ux, vdupq_n_s32(c_inv_mant_mask));
  ux = vorrq_s32(ux, vreinterpretq_s32_f32(vdupq_n_f32(0.5f)));
  x = vreinterpretq_f32_s32(ux);

  emm0 = vsubq_s32(emm0, vdupq_n_s32(0x7f));
  float32x4_t e = vcvtq_f32_s32(emm0);

  e = vaddq_f32(e, one);

  /* part2:
   *     if( x < SQRTHF ) {
   *       e -= 1;
   *       x = x + x - 1.0;
   *     } else { x = x - 1.0; }
   */
  uint32x4_t mask = vcltq_f32(x, vdupq_n_f32(c_cephes_SQRTHF));
  float32x4_t tmp = vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(x), mask));
  x = vsubq_f32(x, one);
  e = vsubq_f32(e, vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(one), mask)));
  x = vaddq_f32(x, tmp);

  float32x4_t z = vmulq_f32(x, x);

  float32x4_t y = vdupq_n_f32(c_cephes_log_p0);
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p1));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p2));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p3));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p4));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p5));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p6));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p7));
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p8));
  y = vmulq_f32(y, x);

  y = vmulq_f32(y, z);

  tmp = vmulq_f32(e, vdupq_n_f32(c_cephes_log_q1));
  y = vaddq_f32(y, tmp);

  tmp = vmulq_f32(z, vdupq_n_f32(0.5f));
  y = vsubq_f32(y, tmp);

  tmp = vmulq_f32(e, vdupq_n_f32(c_cephes_log_q2));
  x = vaddq_f32(x, y);
  x = vaddq_f32(x, tmp);
  x = vreinterpretq_f32_u32(
      vorrq_u32(vreinterpretq_u32_f32(x), invalid_mask)); // negative arg will be NAN
  return x;
}

#define c_exp_hi 88.3762626647949f
#define c_exp_lo -88.3762626647949f

#define c_cephes_LOG2EF 1.44269504088896341
#define c_cephes_exp_C1 0.693359375
#define c_cephes_exp_C2 -2.12194440e-4

#define c_cephes_exp_p0 1.9875691500E-4
#define c_cephes_exp_p1 1.3981999507E-3
#define c_cephes_exp_p2 8.3334519073E-3
#define c_cephes_exp_p3 4.1665795894E-2
#define c_cephes_exp_p4 1.6666665459E-1
#define c_cephes_exp_p5 5.0000001201E-1

/* exp() computed for 4 float at once */
static inline float32x4_t exp_ps(float32x4_t x)
{
  float32x4_t tmp, fx;

  float32x4_t one = vdupq_n_f32(1);
  x = vminq_f32(x, vdupq_n_f32(c_exp_hi));
  x = vmaxq_f32(x, vdupq_n_f32(c_exp_lo));

  /* express exp(x) as exp(g + n*log(2)) */
  fx = vmlaq_f32(vdupq_n_f32(0.5f), x, vdupq_n_f32(c_cephes_LOG2EF));

  /* perform a floorf */
  tmp = vcvtq_f32_s32(vcvtq_s32_f32(fx));

  /* if greater, substract 1 */
  uint32x4_t mask = vcgtq_f32(tmp, fx);
  mask = vandq_u32(mask, vreinterpretq_u32_f32(one));

  fx = vsubq_f32(tmp, vreinterpretq_f32_u32(mask));

  tmp = vmulq_f32(fx, vdupq_n_f32(c_cephes_exp_C1));
  float32x4_t z = vmulq_f32(fx, vdupq_n_f32(c_cephes_exp_C2));
  x = vsubq_f32(x, tmp);
  x = vsubq_f32(x, z);

  static const float cephes_exp_p[6] = {c_cephes_exp_p0, c_cephes_exp_p1, c_cephes_exp_p2,
                                        c_cephes_exp_p3, c_cephes_exp_p4, c_cephes_exp_p5};
  float32x4_t y = vld1q_dup_f32(cephes_exp_p + 0);
  float32x4_t c1 = vld1q_dup_f32(cephes_exp_p + 1);
  float32x4_t c2 = vld1q_dup_f32(cephes_exp_p + 2);
  float32x4_t c3 = vld1q_dup_f32(cephes_exp_p + 3);
  float32x4_t c4 = vld1q_dup_f32(cephes_exp_p + 4);
  float32x4_t c5 = vld1q_dup_f32(cephes_exp_p + 5);

  y = vmulq_f32(y, x);
  z = vmulq_f32(x, x);

  y = vaddq_f32(y, c1);
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, c2);
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, c3);
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, c4);
  y = vmulq_f32(y, x);
  y = vaddq_f32(y, c5);

  y = vmulq_f32(y, z);
  y = vaddq_f32(y, x);
  y = vaddq_f32(y, one);

  /* build 2^n */
  int32x4_t mm;
  mm = vcvtq_s32_f32(fx);
  mm = vaddq_s32(mm, vdupq_n_s32(0x7f));
  mm = vshlq_n_s32(mm, 23);
  float32x4_t pow2n = vreinterpretq_f32_s32(mm);

  y = vmulq_f32(y, pow2n);
  return y;
}

#define c_minus_cephes_DP1 -0.78515625
#define c_minus_cephes_DP2 -2.4187564849853515625e-4
#define c_minus_cephes_DP3 -3.77489497744594108e-8
#define c_sincof_p0 -1.9515295891E-4
#define c_sincof_p1 8.3321608736E-3
#define c_sincof_p2 -1.6666654611E-1
#define c_coscof_p0 2.443315711809948E-005
#define c_coscof_p1 -1.388731625493765E-003
#define c_coscof_p2 4.166664568298827E-002
#define c_cephes_FOPI 1.27323954473516 // 4 / M_PI

/* evaluation of 4 sines & cosines at once.
 *
 *   The code is the exact rewriting of the cephes sinf function.
 *   Precision is excellent as long as x < 8192 (I did not bother to
 *   take into account the special handling they have for greater values
 *   -- it does not return garbage for arguments over 8192, though, but
 *   the extra precision is missing).
 *
 *   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
 *   surprising but correct result.
 *
 *   Note also that when you compute sin(x), cos(x) is available at
 *   almost no extra price so both sin_ps and cos_ps make use of
 *   sincos_ps..
 */
static inline void sincos_ps(float32x4_t x, float32x4_t *ysin, float32x4_t *ycos)
{
  // any x
  float32x4_t xmm1, xmm2, xmm3, y;

  uint32x4_t emm2;

  uint32x4_t sign_mask_sin, sign_mask_cos;
  sign_mask_sin = vcltq_f32(x, vdupq_n_f32(0));
  x = vabsq_f32(x);

  /* scale by 4/Pi */
  y = vmulq_f32(x, vdupq_n_f32(c_cephes_FOPI));

  /* store the integer part of y in mm0 */
  emm2 = vcvtq_u32_f32(y);
  /* j=(j+1) & (~1) (see the cephes sources) */
  emm2 = vaddq_u32(emm2, vdupq_n_u32(1));
  emm2 = vandq_u32(emm2, vdupq_n_u32(~1));
  y = vcvtq_f32_u32(emm2);

  /* get the polynom selection mask
   *     there is one polynom for 0 <= x <= Pi/4
   *     and another one for Pi/4<x<=Pi/2
   *
   *     Both branches will be computed.
   */
  uint32x4_t poly_mask = vtstq_u32(emm2, vdupq_n_u32(2));

  /* The magic pass: "Extended precision modular arithmetic"
   *     x = ((x - y * DP1) - y * DP2) - y * DP3; */
  xmm1 = vmulq_n_f32(y, c_minus_cephes_DP1);
  xmm2 = vmulq_n_f32(y, c_minus_cephes_DP2);
  xmm3 = vmulq_n_f32(y, c_minus_cephes_DP3);
  x = vaddq_f32(x, xmm1);
  x = vaddq_f32(x, xmm2);
  x = vaddq_f32(x, xmm3);

  sign_mask_sin = veorq_u32(sign_mask_sin, vtstq_u32(emm2, vdupq_n_u32(4)));
  sign_mask_cos = vtstq_u32(vsubq_u32(emm2, vdupq_n_u32(2)), vdupq_n_u32(4));

  /* Evaluate the first polynom  (0 <= x <= Pi/4) in y1,
   *     and the second polynom      (Pi/4 <= x <= 0) in y2 */
  float32x4_t z = vmulq_f32(x, x);
  float32x4_t y1, y2;

  y1 = vmulq_n_f32(z, c_coscof_p0);
  y2 = vmulq_n_f32(z, c_sincof_p0);
  y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p1));
  y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p1));
  y1 = vmulq_f32(y1, z);
  y2 = vmulq_f32(y2, z);
  y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p2));
  y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p2));
  y1 = vmulq_f32(y1, z);
  y2 = vmulq_f32(y2, z);
  y1 = vmulq_f32(y1, z);
  y2 = vmulq_f32(y2, x);
  y1 = vsubq_f32(y1, vmulq_f32(z, vdupq_n_f32(0.5f)));
  y2 = vaddq_f32(y2, x);
  y1 = vaddq_f32(y1, vdupq_n_f32(1));

  /* select the correct result from the two polynoms */
  float32x4_t ys = vbslq_f32(poly_mask, y1, y2);
  float32x4_t yc = vbslq_f32(poly_mask, y2, y1);
  *ysin = vbslq_f32(sign_mask_sin, vnegq_f32(ys), ys);
  *ycos = vbslq_f32(sign_mask_cos, yc, vnegq_f32(yc));
}

static inline float32x4_t sin_ps(float32x4_t x)
{
  float32x4_t ysin, ycos;
  sincos_ps(x, &ysin, &ycos);
  return ysin;
}

static inline float32x4_t cos_ps(float32x4_t x)
{
  float32x4_t ysin, ycos;
  sincos_ps(x, &ysin, &ycos);
  return ycos;
}

static inline float32x4_t div_ps(float32x4_t a, float32x4_t b)
{
  float32x4_t reciprocal = vrecpeq_f32(b);
  reciprocal = vmulq_f32(vrecpsq_f32(b, reciprocal), reciprocal);
  //     reciprocal = vmulq_f32(vrecpsq_f32(b, reciprocal), reciprocal);
  return vmulq_f32(a, reciprocal);
}

static inline float32x4_t pow_ps(float32x4_t a, float32x4_t b)
{
  // pow(x, m) = exp(m * log(x))
  return exp_ps(vmulq_f32(b, log_ps(a)));
}