text: /******************************************************************************
    Copyright (c) 2007-2018, Intel Corp.
    All rights reserved.
  
    Redistribution and use in source and binary forms, with or without 
    modification, are permitted provided that the following conditions are met:
  
      * Redistributions of source code must retain the above copyright notice, 
        this list of conditions and the following disclaimer.
      * Redistributions in binary form must reproduce the above copyright 
        notice, this list of conditions and the following disclaimer in the 
        documentation and/or other materials provided with the distribution.
      * Neither the name of Intel Corporation nor the names of its contributors 
        may be used to endorse or promote products derived from this software 
        without specific prior written permission.
  
    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
    AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
    IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
    ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
    LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
    CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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  ******************************************************************************/
  
  #ifndef _SQRT_MACROS_H_
  #define _SQRT_MACROS_H_
  
  #include "bid_internal.h"
  
  #if DOUBLE_EXTENDED_ON
  
  BID_EXTERN_C BINARY80 SQRT80 (BINARY80);
  
  
  __BID_INLINE__ BID_UINT64
  short_sqrt128 (BID_UINT128 A10) {
    BINARY80 lx, ly, l64;
    int_float f64;
  
    // 2^64
    f64.i = 0x5f800000;
    l64 = (BINARY80) f64.d;
    lx = (BINARY80) A10.w[1] * l64 + (BINARY80) A10.w[0];
    ly = SQRT80 (lx);
    return (BID_UINT64) ly;
  }
  
  
  typedef union BID_ALIGN (16)
       {
         BID_UINT64 w[2];
  	   long double d; 
       } int_dext;
  
  
  __BID_INLINE__ void
  bid_long_sqrt128 (BID_UINT128 * pCS, BID_UINT256 C256) {
    BID_UINT128 CS;
    BID_UINT64 X;
    BID_SINT64 SE;
    BINARY80 l64, lm64, l128, lxL, lx, lS, lSH, lSL, lE, l3, l2,
      l1, l0, lp, lCl;
    int_float f64, fm64;
    int_dext tmp_dext;
  
    // 2^64
    f64.i = 0x5f800000;
    l64 = (BINARY80) f64.d;
  
    l128 = l64 * l64;
    lx = l3 = (BINARY80) C256.w[3] * l64 * l128;
    l2 = (BINARY80) C256.w[2] * l128;
    lx = FENCE (lx + l2);
    l1 = (BINARY80) C256.w[1] * l64;
    lx = FENCE (lx + l1);
    l0 = (BINARY80) C256.w[0];
    lx = FENCE (lx + l0);
    // sqrt(C256)
    lS = SQRT80 (lx);
  
    // get coefficient
    // 2^(-64)
    fm64.i = 0x1f800000;
    lm64 = (BINARY80) fm64.d;
    CS.w[1] = (BID_UINT64) (lS * lm64);
    CS.w[0] = (BID_UINT64) (lS - (BINARY80) CS.w[1] * l64);
  
    //printf("C256=%016I64x %016I64x %016I64x %016I64x, CS=%016I64x %016I64x \n",C256.w[3],C256.w[2],C256.w[1],C256.w[0],CS.w[1],CS.w[0]);
  
    ///////////////////////////////////////
    //  CAUTION!
    //  little endian code only
    //  add solution for big endian
    //////////////////////////////////////
      tmp_dext.d = lS;
  
  #if BID_BIG_ENDIAN
  	tmp_dext.w[0] &= 0xffffffffffff0000ull;
  	tmp_dext.w[1] = 0;
  #else
    //lSH = lS;
    //*((BID_UINT64 *) & lSH) &= 0xffffffff00000000ull;
  	tmp_dext.w[0] &= 0xffffffff00000000ull;
  #endif
  	lSH = tmp_dext.d;
  
    // correction for C256 rounding
    lCl = FENCE (l3 - lx);
    lCl = FENCE (lCl + l2);
    lCl = FENCE (lCl + l1);
    lCl = FENCE (lCl + l0);
  
    lSL = lS - lSH;
  
    //////////////////////////////////////////
    //   Watch for compiler re-ordering
    //
    /////////////////////////////////////////
    // C256-S^2
    lxL = FENCE (lx - lSH * lSH);
    lp = lSH * lSL;
    lp += lp;
    lxL = FENCE (lxL - lp);
    lSL *= lSL;
    lxL = FENCE (lxL - lSL);
    lCl += lxL;
  
    // correction term
    lE = lCl / (lS + lS);
  
    // get low part of coefficient
    X = CS.w[0];
    if (lCl >= 0) {
      SE = (BID_SINT64) (lE);
      CS.w[0] += SE;
      if (CS.w[0] < X)
        CS.w[1]++;
    } else {
      SE = (BID_SINT64) (-lE);
      CS.w[0] -= SE;
      if (CS.w[0] > X)
        CS.w[1]--;
    }
  
    pCS->w[0] = CS.w[0];
    pCS->w[1] = CS.w[1];
  }
  
  #else
  
  BID_EXTERN_C double sqrt (double);
  
  __BID_INLINE__ BID_UINT64
  short_sqrt128 (BID_UINT128 A10) {
    BID_UINT256 ARS, ARS0, AE0, AE, S;
  
    BID_UINT64 MY, ES, CY;
    double lx, l64;
    int_double f64, ly;
    int ey, k;
  
    // 2^64
    f64.i = 0x43f0000000000000ull;
    l64 = f64.d;
    lx = (double) A10.w[1] * l64 + (double) A10.w[0];
    ly.d = 1.0 / sqrt (lx);
  
    MY = (ly.i & 0x000fffffffffffffull) | 0x0010000000000000ull;
    ey = 0x3ff - (ly.i >> 52);
  
    // A10*RS^2
    __mul_64x128_to_192 (ARS0, MY, A10);
    __mul_64x192_to_256 (ARS, MY, ARS0);
  
    // shr by 2*ey+40, to get a 64-bit value
    k = (ey << 1) + 104 - 64;
    if (k >= 128) {
      if (k > 128)
        ES = (ARS.w[2] >> (k - 128)) | (ARS.w[3] << (192 - k));
      else
        ES = ARS.w[2];
    } else {
      if (k >= 64) {
        ARS.w[0] = ARS.w[1];
        ARS.w[1] = ARS.w[2];
        k -= 64;
      }
      if (k) {
        __shr_128 (ARS, ARS, k);
      }
      ES = ARS.w[0];
    }
  
    ES = ((BID_SINT64) ES) >> 1;
  
    if (((BID_SINT64) ES) < 0) {
      ES = -ES;
  
      // A*RS*eps (scaled by 2^64)
      __mul_64x192_to_256 (AE0, ES, ARS0);
  
      AE.w[0] = AE0.w[1];
      AE.w[1] = AE0.w[2];
      AE.w[2] = AE0.w[3];
  
      __add_carry_out (S.w[0], CY, ARS0.w[0], AE.w[0]);
      __add_carry_in_out (S.w[1], CY, ARS0.w[1], AE.w[1], CY);
      S.w[2] = ARS0.w[2] + AE.w[2] + CY;
    } else {
      // A*RS*eps (scaled by 2^64)
      __mul_64x192_to_256 (AE0, ES, ARS0);
  
      AE.w[0] = AE0.w[1];
      AE.w[1] = AE0.w[2];
      AE.w[2] = AE0.w[3];
  
      __sub_borrow_out (S.w[0], CY, ARS0.w[0], AE.w[0]);
      __sub_borrow_in_out (S.w[1], CY, ARS0.w[1], AE.w[1], CY);
      S.w[2] = ARS0.w[2] - AE.w[2] - CY;
    }
  
    k = ey + 51;
  
    if (k >= 64) {
      if (k >= 128) {
        S.w[0] = S.w[2];
        S.w[1] = 0;
        k -= 128;
      } else {
        S.w[0] = S.w[1];
        S.w[1] = S.w[2];
      }
      k -= 64;
    }
    if (k) {
      __shr_128 (S, S, k);
    }
  
  
    return (BID_UINT64) ((S.w[0] + 1) >> 1);
  
  }
  
  
  
  __BID_INLINE__ void
  bid_long_sqrt128 (BID_UINT128 * pCS, BID_UINT256 C256) {
    BID_UINT512 ARS0, ARS;
    BID_UINT256 ARS00, AE, AE2, S;
    BID_UINT128 ES, ES2, ARS1;
    BID_UINT64 ES32, CY, MY;
    double l64, l128, lx, l2, l1, l0;
    int_double f64, ly;
    int ey, k, k2;
  
    // 2^64
    f64.i = 0x43f0000000000000ull;
    l64 = f64.d;
  
    l128 = l64 * l64;
    lx = (double) C256.w[3] * l64 * l128;
    l2 = (double) C256.w[2] * l128;
    lx = FENCE (lx + l2);
    l1 = (double) C256.w[1] * l64;
    lx = FENCE (lx + l1);
    l0 = (double) C256.w[0];
    lx = FENCE (lx + l0);
    // sqrt(C256)
    ly.d = 1.0 / sqrt (lx);
  
    MY = (ly.i & 0x000fffffffffffffull) | 0x0010000000000000ull;
    ey = 0x3ff - (ly.i >> 52);
  
    // A10*RS^2, scaled by 2^(2*ey+104)
    __mul_64x256_to_320 (ARS0, MY, C256);
    __mul_64x320_to_384 (ARS, MY, ARS0);
  
    // shr by k=(2*ey+104)-128
    // expect k is in the range (192, 256) if result in [10^33, 10^34)
    // apply an additional signed shift by 1 at the same time (to get eps=eps0/2)
    k = (ey << 1) + 104 - 128 - 192;
    k2 = 64 - k;
    ES.w[0] = (ARS.w[3] >> (k + 1)) | (ARS.w[4] << (k2 - 1));
    ES.w[1] = (ARS.w[4] >> k) | (ARS.w[5] << k2);
    ES.w[1] = ((BID_SINT64) ES.w[1]) >> 1;
  
    // A*RS >> 192 (for error term computation)
    ARS1.w[0] = ARS0.w[3];
    ARS1.w[1] = ARS0.w[4];
  
    // A*RS>>64
    ARS00.w[0] = ARS0.w[1];
    ARS00.w[1] = ARS0.w[2];
    ARS00.w[2] = ARS0.w[3];
    ARS00.w[3] = ARS0.w[4];
  
    if (((BID_SINT64) ES.w[1]) < 0) {
      ES.w[0] = -ES.w[0];
      ES.w[1] = -ES.w[1];
      if (ES.w[0])
        ES.w[1]--;
  
      // A*RS*eps 
      __mul_128x128_to_256 (AE, ES, ARS1);
  
      __add_carry_out (S.w[0], CY, ARS00.w[0], AE.w[0]);
      __add_carry_in_out (S.w[1], CY, ARS00.w[1], AE.w[1], CY);
      __add_carry_in_out (S.w[2], CY, ARS00.w[2], AE.w[2], CY);
      S.w[3] = ARS00.w[3] + AE.w[3] + CY;
    } else {
      // A*RS*eps 
      __mul_128x128_to_256 (AE, ES, ARS1);
  
      __sub_borrow_out (S.w[0], CY, ARS00.w[0], AE.w[0]);
      __sub_borrow_in_out (S.w[1], CY, ARS00.w[1], AE.w[1], CY);
      __sub_borrow_in_out (S.w[2], CY, ARS00.w[2], AE.w[2], CY);
      S.w[3] = ARS00.w[3] - AE.w[3] - CY;
    }
  
    // 3/2*eps^2, scaled by 2^128
    ES32 = ES.w[1] + (ES.w[1] >> 1);
    __mul_64x64_to_128 (ES2, ES32, ES.w[1]);
    // A*RS*3/2*eps^2
    __mul_128x128_to_256 (AE2, ES2, ARS1);
  
    // result, scaled by 2^(ey+52-64)
    __add_carry_out (S.w[0], CY, S.w[0], AE2.w[0]);
    __add_carry_in_out (S.w[1], CY, S.w[1], AE2.w[1], CY);
    __add_carry_in_out (S.w[2], CY, S.w[2], AE2.w[2], CY);
    S.w[3] = S.w[3] + AE2.w[3] + CY;
  
    // k in (0, 64)
    k = ey + 51 - 128;
    k2 = 64 - k;
    S.w[0] = (S.w[1] >> k) | (S.w[2] << k2);
    S.w[1] = (S.w[2] >> k) | (S.w[3] << k2);
  
    // round to nearest
    S.w[0]++;
    if (!S.w[0])
      S.w[1]++;
  
    pCS->w[0] = (S.w[1] << 63) | (S.w[0] >> 1);
    pCS->w[1] = S.w[1] >> 1;
  
  }
  
  #endif
  #endif
  