MATHLIB_atanh.cpp

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#define ELEMENT_COUNT(x) c7x::element_count_of<x>::value
 
/******************************************************************************/
/*                                                                            */
/* Includes                                                                   */
/*                                                                            */
/******************************************************************************/
 
#include "MATHLIB_atanh_scalar.h"
#include "MATHLIB_ilut.h"
#include "MATHLIB_lut.h"
#include "MATHLIB_permute.h"
#include "MATHLIB_types.h"
#include "MATHLIB_utility.h"
 
/******************************************************************************/
/*                                                                            */
/* MATHLIB_acosh                                                               */
/*                                                                            */
/******************************************************************************/
 
template <typename T>
static inline MATHLIB_STATUS
MATHLIB_atanh_log(__SE_TEMPLATE_v1 *se0Params, __SA_TEMPLATE_v1 *sa0Params, size_t length, T *pSrc0, T *pDst)
{
   // variables
   MATHLIB_STATUS status       = MATHLIB_SUCCESS; // return function status
   size_t         numBlocks    = 0;               // compute loop's iteration count
   size_t         remNumBlocks = 0;               // when numBlocks is not a multiple of SIMD width
 
   // derive c7x vector type from template typename
   typedef typename c7x::make_full_vector<T>::type vec;
 
   // calculate compute loop's iteration counter
   numBlocks    = length / c7x::element_count_of<vec>::value;
   remNumBlocks = length % c7x::element_count_of<vec>::value;
   if (remNumBlocks) {
      numBlocks++;
   }
 
   //  if (status == MATHLIB_SUCCESS) {
 
   // open SE0, SE1, and SA0 for reading and writing operands
   // MATHLIB_SE0SA0Open(se0Params, sa0Params, pDst);
   MATHLIB_SE0SE1SA0Open(se0Params, sa0Params, pDst, pSrc0);
 
   /**********************************************************************/
   /* Create and assign values for constants employed on pow computation */
   /**********************************************************************/
 
   vec             C1, C2, C3, C4, C5, pol_bound, half;
   c7x::double_vec ln2;
   c7x::uint_vec   zero;
   zero = (c7x::uint_vec) 0;
 
   ln2       = (c7x::double_vec) 0.693147180559945;
   C1        = (vec) -0.2302894f;
   C2        = (vec) 0.1908169f;
   C3        = (vec) -0.2505905f;
   C4        = (vec) 0.3333164f;
   C5        = (vec) -0.5000002f;
   pol_bound = (vec) 0.1f;
   half      = (vec) 0.5f;
 
   // compute loop to perform vector pow
   for (size_t i = 0; i < numBlocks; i++) {
      vec inVec = c7x::strm_eng<0, vec>::get_adv();
 
      /**********************************************************************/
      /* Create variables employed on log computation                       */
      /**********************************************************************/
 
      vec             pol, r1, r2, r3, r4, outVec, inVecOriginal_abs;
      c7x::double_vec inVecVals_odd, inVecVals_even, inVecVals_oddReciprocal, inVecVals_evenReciprocal,
          inVecReciprocalApprox_8_15, inVecReciprocalApprox_0_7, inVecVals_8_15, inVecVals_0_7, rVals_0_7, rVals_8_15,
          TVals_8_15, TVals_0_7, NVals_odd, NVals_even, NVals_0_7, NVals_8_15, pol_0_7, pol_8_15, outVec_8_15,
          outVec_0_7;
      c7x::uint_vec inVecReciprocal_32_63, inVecReciprocalClr_32_63, inVecReciprocalApprox_32_63, indexT,
          upperBitsIndexT, lowerBitsIndexT;
      c7x::int_vec N;
 
      /**********************************************************************/
      /* Calculate Taylor series approximation for log                      */
      /**********************************************************************/
 
      // Split vectors to compute r with double precision
      inVecVals_odd            = __high_float_to_double(inVec);
      inVecVals_even           = __low_float_to_double(inVec);
      inVecVals_oddReciprocal  = __recip(inVecVals_odd);
      inVecVals_evenReciprocal = __recip(inVecVals_even);
 
      // Create floating point reciprocal approximation
      // Upper 32 bits of all inVec reciprocal values
      inVecReciprocal_32_63 = c7x::reinterpret<c7x::uint_vec>(
          __permute_odd_odd_int(MATHLIB_vperm_data_interweave_0_63, c7x::as_uchar_vec(inVecVals_oddReciprocal),
                                c7x::as_uchar_vec(inVecVals_evenReciprocal)));
 
      // Clear bits 0-16 inclusive
      inVecReciprocalClr_32_63 = inVecReciprocal_32_63 & 0xFFFE0000U;
 
      // Concatenate cleared bit reciprocal with zero bits
      inVecReciprocalApprox_8_15 = c7x::reinterpret<c7x::double_vec>(__permute_high_high(
          MATHLIB_vperm_data_interweave_0_63, c7x::as_uchar_vec(inVecReciprocalClr_32_63), c7x::as_uchar_vec(zero)));
      inVecReciprocalApprox_0_7  = c7x::reinterpret<c7x::double_vec>(__permute_low_low(
           MATHLIB_vperm_data_interweave_0_63, c7x::as_uchar_vec(inVecReciprocalClr_32_63), c7x::as_uchar_vec(zero)));
 
      // Split inVec into two vectors with double precision
      inVecVals_0_7  = c7x::reinterpret<c7x::double_vec>(__permute_low_low(
           MATHLIB_vperm_data_dp_interweave_0_63, c7x::as_uchar_vec(inVecVals_odd), c7x::as_uchar_vec(inVecVals_even)));
      inVecVals_8_15 = c7x::reinterpret<c7x::double_vec>(__permute_high_high(
          MATHLIB_vperm_data_dp_interweave_0_63, c7x::as_uchar_vec(inVecVals_odd), c7x::as_uchar_vec(inVecVals_even)));
 
      // Calculate r in double precision
      rVals_0_7  = (inVecReciprocalApprox_0_7 * inVecVals_0_7) - 1.0;
      rVals_8_15 = (inVecReciprocalApprox_8_15 * inVecVals_8_15) - 1.0;
 
      // Convert r to float, compute r to the power of 2, 3, 4
      r1 = c7x::reinterpret<vec>(__permute_even_even_int(MATHLIB_vperm_data_0_63,
                                                         c7x::as_uchar_vec(__double_to_float(rVals_8_15)),
                                                         c7x::as_uchar_vec(__double_to_float(rVals_0_7))));
      r2 = r1 * r1;
      r3 = r1 * r2;
      r4 = r2 * r2;
 
      // Compute Taylor series polynomial
      pol = (C5 * r2) + ((C4 * r3) + ((((C2 * r1) + C3) + (C1 * r2)) * r4));
 
      /**********************************************************************/
      /* Calculate N                                                        */
      /**********************************************************************/
 
      // Upper 32 bits of all inVec reciprocal approximation values
      inVecReciprocalApprox_32_63 = c7x::reinterpret<c7x::uint_vec>(
          __permute_odd_odd_int(MATHLIB_vperm_data_0_63, c7x::as_uchar_vec(inVecReciprocalApprox_8_15),
                                c7x::as_uchar_vec(inVecReciprocalApprox_0_7)));
 
      N = c7x::convert<c7x::int_vec>(((inVecReciprocalApprox_32_63 << 1) >> 21) - 1023);
 
      // Covert N to double precision for later calculation with LUT values
      NVals_odd  = __high_int_to_double(N);
      NVals_even = __low_int_to_double(N);
      NVals_0_7  = c7x::reinterpret<c7x::double_vec>(__permute_low_low(
           MATHLIB_vperm_data_dp_interweave_0_63, c7x::as_uchar_vec(NVals_odd), c7x::as_uchar_vec(NVals_even)));
      NVals_8_15 = c7x::reinterpret<c7x::double_vec>(__permute_high_high(
          MATHLIB_vperm_data_dp_interweave_0_63, c7x::as_uchar_vec(NVals_odd), c7x::as_uchar_vec(NVals_even)));
 
      /**********************************************************************/
      /* Determine LUT values                                               */
      /**********************************************************************/
 
      // Calculate LUT index
      indexT = (((inVecReciprocalApprox_32_63 << 12) >> 29) + MATHLIB_LOGTABLE_OFFSET);
 
      // Read from LUT and reconstruct double values split into two vectors
      upperBitsIndexT = MATHLIB_LUTReadUpperBits(indexT);
      lowerBitsIndexT = MATHLIB_LUTReadLowerBits(indexT);
 
      TVals_8_15 = c7x::reinterpret<c7x::double_vec>(__permute_high_high(
          MATHLIB_vperm_data_interweave_0_63, c7x::as_uchar_vec(upperBitsIndexT), c7x::as_uchar_vec(lowerBitsIndexT)));
      TVals_0_7  = c7x::reinterpret<c7x::double_vec>(__permute_low_low(
           MATHLIB_vperm_data_interweave_0_63, c7x::as_uchar_vec(upperBitsIndexT), c7x::as_uchar_vec(lowerBitsIndexT)));
 
      // Calculate an adjusted T
      TVals_8_15 = TVals_8_15 - (ln2 * NVals_8_15);
      TVals_0_7  = TVals_0_7 - (ln2 * NVals_0_7);
 
      /**********************************************************************/
      /* Calculate output with adjusted LUT and Taylor series values        */
      /**********************************************************************/
 
      // Split polynomial result into two vectors with double precision
      pol_0_7  = c7x::reinterpret<c7x::double_vec>(__permute_low_low(MATHLIB_vperm_data_dp_interweave_0_63,
                                                                     c7x::as_uchar_vec(__high_float_to_double(pol)),
                                                                     c7x::as_uchar_vec(__low_float_to_double(pol))));
      pol_8_15 = c7x::reinterpret<c7x::double_vec>(__permute_high_high(MATHLIB_vperm_data_dp_interweave_0_63,
                                                                       c7x::as_uchar_vec(__high_float_to_double(pol)),
                                                                       c7x::as_uchar_vec(__low_float_to_double(pol))));
 
      // Add LUT values and Taylor series values
      outVec_0_7  = rVals_0_7 + TVals_0_7 + pol_0_7;
      outVec_8_15 = rVals_8_15 + TVals_8_15 + pol_8_15;
 
      // Combine output vector into one floating point result
      outVec = c7x::reinterpret<vec>(__permute_even_even_int(MATHLIB_vperm_data_0_63,
                                                             c7x::as_uchar_vec(__double_to_float(outVec_8_15)),
                                                             c7x::as_uchar_vec(__double_to_float(outVec_0_7))));
 
      outVec = outVec * half;
 
      /**********************************************************************/
      /* Determine algorithm for specific input         */
      /**********************************************************************/
 
      // #if !defined(MATHLIB_FAST)
      vec inVecOriginal  = c7x::strm_eng<1, vec>::get_adv();
      inVecOriginal_abs  = __abs(inVecOriginal);
      __vpred cmp_le_pol = __cmp_le_pred(inVecOriginal_abs, pol_bound);
      outVec             = __select(cmp_le_pol, inVec, outVec);
      // #endif
 
      // Store atanh computation result in
      __vpred tmp  = c7x::strm_agen<0, vec>::get_vpred();
      vec    *addr = c7x::strm_agen<0, vec>::get_adv(pDst);
      __vstore_pred(tmp, addr, outVec);
   }
   MATHLIB_SE0SE1SA0Close();
   //  }
   return status;
}
 
template <typename T>
static inline MATHLIB_STATUS
MATHLIB_atanh_cond(__SE_TEMPLATE_v1 *se0Params, __SA_TEMPLATE_v1 *sa0Params, size_t length, T *pSrc0, T *pDst)
{
   // variables
   MATHLIB_STATUS status       = MATHLIB_SUCCESS; // return function status
   size_t         numBlocks    = 0;               // compute loop's iteration count
   size_t         remNumBlocks = 0;               // when numBlocks is not a multiple of SIMD width
 
   // derive c7x vector type from template typename
   typedef typename c7x::make_full_vector<T>::type vec;
 
   // calculate compute loop's iteration counter
   numBlocks    = length / c7x::element_count_of<vec>::value;
   remNumBlocks = length % c7x::element_count_of<vec>::value;
   if (remNumBlocks) {
      numBlocks++;
   }
 
   //  if (status == MATHLIB_SUCCESS) {
 
   // open SE0, SE1, and SA0 for reading and writing operands
   // MATHLIB_SE0SA0Open(se0Params, sa0Params, pDst);
   MATHLIB_SE0SE1SA0Open(se0Params, sa0Params, pDst, pSrc0);
 
   /**********************************************************************/
   /* Create and assign values for constants employed on pow computation */
   /**********************************************************************/
 
   vec limit, zeroF, inf;
 
   limit = (vec) 1.0f;
   zeroF = (vec) 0.0f;
   inf   = (vec) 0x7F800000u;
 
   // compute loop to perform vector pow
   for (size_t i = 0; i < numBlocks; i++) {
      vec inVec         = c7x::strm_eng<0, vec>::get_adv();
      vec inVecOriginal = c7x::strm_eng<1, vec>::get_adv();
 
      vec outVec, sign;
 
      vec inVecOriginal_abs = __abs(inVecOriginal);
 
      __vpred cmp_limit = __cmp_eq_pred(inVecOriginal_abs, limit);
      outVec            = __select(cmp_limit, inf, inVec);
 
      sign                = (vec) 1.0;
      __vpred cmp_lt_zero = __cmp_lt_pred(inVecOriginal, zeroF);
      sign                = __select(cmp_lt_zero, -sign, sign);
 
      outVec = outVec * sign;
 
      // Store exp computation result in
      __vpred tmp  = c7x::strm_agen<0, vec>::get_vpred();
      vec    *addr = c7x::strm_agen<0, vec>::get_adv(pDst);
      __vstore_pred(tmp, addr, outVec);
   }
   MATHLIB_SE0SE1SA0Close();
   //  }
   return status;
}
 
template <typename vecType> static inline vecType divspMod_atanh(vecType a, vecType b)
{
   vecType res, r0, d0, d1, p0, p1, Two;
 
   Two = (vecType) 2.0;
 
   p0 = __recip(b);
   d0 = p0 * b;
   r0 = p0;
 
   p1 = Two - d0;
   d1 = r0 * p1;
 
   res = a * d1;
 
   return res;
}
 
// this method performs atanh computation of input vector
template <typename T> static inline void MATHLIB_atanh_vector(size_t length, T *pSrc, T *pDst)
{
   // variables
   size_t numBlocks    = 0; // compute loop's iteration count
   size_t remNumBlocks = 0; // when numBlocks is not a multiple of SIMD width
 
   // derive c7x vector type from template typename
   typedef typename c7x::make_full_vector<float>::type vec;
 
   __SE_TEMPLATE_v1 se0Params = __gen_SE_TEMPLATE_v1();
   __SA_TEMPLATE_v1 sa0Params = __gen_SA_TEMPLATE_v1();
 
   MATHLIB_SE0SA01DSequentialInit(&se0Params, &sa0Params, length, pSrc, pDst);
 
   // calculate compute loop's iteration counter
   numBlocks    = length / c7x::element_count_of<vec>::value;
   remNumBlocks = length % c7x::element_count_of<vec>::value;
   if (remNumBlocks) {
      numBlocks++;
   }
 
   // open SE0, SE1, and SA0 for reading and writing operands
   MATHLIB_SE0SA0Open(&se0Params, &sa0Params, pSrc);
 
   /***********************************************************************/
   /* Create and assign values for constants employed on acosh computation */
   /***********************************************************************/
 
   vec pol_bound, c2, c4;
   pol_bound = (vec) 0.1f;
   c2        = (vec) 0.333327051f;
   c4        = (vec) 0.202017226f;
 
   // compute loop to perform vector acosh
   for (size_t i = 0; i < numBlocks; i++) {
      vec inVec = c7x::strm_eng<0, vec>::get_adv();
 
      /**********************************************************************/
      /* Create variables employed on acosh computation                     */
      /**********************************************************************/
 
      vec x2, x4, pol, outVec, inVec_abs, temp1, temp2;
 
      inVec_abs = __abs(inVec);
 
      // #if !defined(MATHLIB_FAST)
 
      x2 = inVec * inVec;
      x4 = x2 * x2;
 
      // use polynomial estimation for |x| <= 0.1
      //  polynomial to estimate atanh(x) for small inputs
      pol = (c2 * x2) + (c4 * x4);
      pol = (pol * inVec_abs) + inVec_abs;
 
      // #endif
 
      // calculate atanh(x) based on atanh(x) = 0.5*ln((1+ x) / (1- x))
      temp1 = 1.0f + inVec_abs;
      temp2 = 1.0f - inVec_abs;
 
      outVec = divspMod_atanh(temp1, temp2);
 
      // #if !defined(MATHLIB_FAST)
 
      __vpred cmp_le_pol = __cmp_le_pred(inVec_abs, pol_bound);
      outVec             = __select(cmp_le_pol, pol, outVec);
 
      // #endif
 
      __vpred tmp  = c7x::strm_agen<0, vec>::get_vpred();
      vec    *addr = c7x::strm_agen<0, vec>::get_adv(pDst);
      __vstore_pred(tmp, addr, outVec);
   }
 
   MATHLIB_SE0SA0Close();
 
   MATHLIB_atanh_log(&se0Params, &sa0Params, length, pSrc, pDst);
   MATHLIB_atanh_cond(&se0Params, &sa0Params, length, pSrc, pDst);
}
 
// this method performs exponential computation of input vector
template <typename T> MATHLIB_STATUS MATHLIB_atanh(size_t length, T *restrict pSrc, T *restrict pDst)
{
   MATHLIB_STATUS status = MATHLIB_SUCCESS; // return function status
 
   // check for null pointers and non-zero length
   status = MATHLIB_checkParams(length, pSrc, pDst);
 
   if (status == MATHLIB_SUCCESS) {
      MATHLIB_atanh_vector(length, pSrc, pDst);
   }
   return status;
}
 
/******************************************************************************/
/*                                                                            */
/* Explicit templatization for datatypes supported by MATHLIB_acosh            */
/*                                                                            */
/******************************************************************************/
 
// single precision
template MATHLIB_STATUS MATHLIB_atanh<float>(size_t length, float *pSrc, float *pDst);
 
/******************************************************************************/
/*                                                                            */
/* C-interface wrapper functions                                              */
/*                                                                            */
/******************************************************************************/
 
extern "C" {
 
// single-precision wrapper
MATHLIB_STATUS MATHLIB_atanh_sp(size_t length, float *pSrc, float *pDst)
{
   MATHLIB_STATUS status = MATHLIB_atanh(length, pSrc, pDst);
   return status;
}
 
} // extern "C"