text: // Do not include this header directly.
  // This header defines shared struct spmd_kernel helpers.
  //
  // Copyright 2020-2021 Binomial LLC
  //
  // Licensed under the Apache License, Version 2.0 (the "License");
  // you may not use this file except in compliance with the License.
  // You may obtain a copy of the License at
  //
  //    http://www.apache.org/licenses/LICENSE-2.0
  //
  // Unless required by applicable law or agreed to in writing, software
  // distributed under the License is distributed on an "AS IS" BASIS,
  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  // See the License for the specific language governing permissions and
  // limitations under the License.
  
  // See cppspmd_math.h for detailed error statistics.
  
  CPPSPMD_FORCE_INLINE void reduce_expb(vfloat& arg, vfloat& two_int_a, vint& adjustment);
  CPPSPMD_FORCE_INLINE vfloat tan56(vfloat x);
  CPPSPMD_FORCE_INLINE vfloat tan82(vfloat x);
  
  inline vfloat log2_est(vfloat v);
  
  inline vfloat log_est(vfloat v);
  
  inline vfloat exp2_est(vfloat arg);
  
  inline vfloat exp_est(vfloat arg);
  
  inline vfloat pow_est(vfloat arg1, vfloat arg2);
  
  CPPSPMD_FORCE_INLINE vfloat recip_est1(const vfloat& q);
  CPPSPMD_FORCE_INLINE vfloat recip_est1_pn(const vfloat& q);
  
  inline vfloat mod_angles(vfloat a);
  
  inline vfloat sincos_est_a(vfloat a, bool sin_flag);
  CPPSPMD_FORCE_INLINE vfloat sin_est_a(vfloat a) { return sincos_est_a(a, true); }
  CPPSPMD_FORCE_INLINE vfloat cos_est_a(vfloat a) { return sincos_est_a(a, false); }
  
  inline vfloat sin_est(vfloat a);
  
  inline vfloat cos_est(vfloat a);
  
  // Don't call with values <= 0.
  CPPSPMD_FORCE_INLINE vfloat rsqrt_est1(vfloat x0);
  
  // Don't call with values <= 0.
  CPPSPMD_FORCE_INLINE vfloat rsqrt_est2(vfloat x0);
  
  CPPSPMD_FORCE_INLINE vfloat atan2_est(vfloat y, vfloat x);
  
  CPPSPMD_FORCE_INLINE vfloat atan_est(vfloat x) { return atan2_est(x, vfloat(1.0f)); }
  
  // Don't call this for angles close to 90/270! 
  inline vfloat tan_est(vfloat x);
  
  // https://burtleburtle.net/bob/rand/smallprng.html
  struct rand_context { vint a, b, c, d; };
  
  inline void seed_rand(rand_context& x, vint seed);
  
  // Returns 32-bit unsigned random numbers.
  inline vint get_randu(rand_context& x);
  
  // Returns random numbers between [low, high), or low if low >= high
  inline vint get_randi(rand_context& x, vint low, vint high);
  
  // Returns random numbers between [low, high), or low if low >= high
  inline vfloat get_randf(rand_context& x, vfloat low, vfloat high);
  
  CPPSPMD_FORCE_INLINE void init_reverse_bits(vint& tab1, vint& tab2);
  CPPSPMD_FORCE_INLINE vint reverse_bits(vint k, vint tab1, vint tab2);
  
  CPPSPMD_FORCE_INLINE vint count_leading_zeros(vint x);
  CPPSPMD_FORCE_INLINE vint count_leading_zeros_alt(vint x);
  
  CPPSPMD_FORCE_INLINE vint count_trailing_zeros(vint x);
  
  CPPSPMD_FORCE_INLINE vint count_set_bits(vint x);
  
  void print_vint(vint v);
  void print_vbool(vbool v);
  void print_vint_hex(vint v);
  void print_active_lanes(const char *pPrefix);
  void print_vfloat(vfloat v);
  
  