/*
 * Helper for single-precision routines which calculate exp(x) - 1 and do not
 * need special-case handling
 *
 * Copyright (c) 2022-2023, Arm Limited.
 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
 */

#ifndef PL_MATH_V_EXPM1F_INLINE_H
#define PL_MATH_V_EXPM1F_INLINE_H

#include "v_math.h"
#include "math_config.h"
#include "poly_advsimd_f32.h"

struct v_expm1f_data
{
  float32x4_t poly[5];
  float32x4_t invln2_and_ln2, shift;
  int32x4_t exponent_bias;
};

/* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
   log(2)/2]. Exponent bias is asuint(1.0f).
   invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0.  */
#define V_EXPM1F_DATA                                                         \
  {                                                                           \
    .poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5),     \
	      V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) },                      \
    .shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000),                \
    .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 },   \
  }

static inline float32x4_t
expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
{
  /* Helper routine for calculating exp(x) - 1.
     Copied from v_expm1f_1u6.c, with all special-case handling removed - the
     calling routine should handle special values if required.  */

  /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
  float32x4_t j = vsubq_f32 (
      vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift);
  int32x4_t i = vcvtq_s32_f32 (j);
  float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1);
  f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2);

  /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
     Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses
     Horner.  */
  float32x4_t f2 = vmulq_f32 (f, f);
  float32x4_t f4 = vmulq_f32 (f2, f2);
  float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly);
  p = vfmaq_f32 (f, f2, p);

  /* t = 2^i.  */
  int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
  float32x4_t t = vreinterpretq_f32_s32 (u);
  /* expm1(x) ~= p * t + (t - 1).  */
  return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
}

#endif // PL_MATH_V_EXPM1F_INLINE_H