sqrtd2.h

Newlib 嵌入式 C库 标准实现代码

/* --------------------------------------------------------------  */
/* (C)Copyright 2006,2007,                                         */
/* International Business Machines Corporation,                    */
/* Sony Computer Entertainment, Incorporated,                      */
/* Toshiba Corporation,                                            */
/*                                                                 */
/* 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 IBM Corporation nor the names of its      */
/*   contributors may be used to endorse or promote products       */
/*   derived from this software without specific prior written     */
/*   permission.                                                   */
/* 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 IBM 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 SUBSTITUTE GOODS OR SERVICES;    */
/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)        */
/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN       */
/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR    */
/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,  */
/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              */
/* --------------------------------------------------------------  */
/* PROLOG END TAG zYx                                              */
#ifdef __SPU__
#ifndef _SQRTD2_H_
#define _SQRTD2_H_	1

#include <spu_intrinsics.h>

/*
 * FUNCTION
 *	vector double _sqrtd2(vector double in)
 *
 * DESCRIPTION
 *	The _sqrtd2 function computes the square root of the vector input "in" 
 *	and returns the result. 
 *
 */
static __inline vector double _sqrtd2(vector double in)
{
  vec_int4 bias_exp;
  vec_uint4 exp;
  vec_float4 fx, fg, fy, fd, fe, fy2, fhalf;
  vec_ullong2 nochange, denorm;
  vec_ullong2 mask = spu_splats(0x7FE0000000000000ULL);
  vec_double2 dx, de, dd, dy, dg, dy2, dhalf;
  vec_double2 neg;
  vec_double2 one = spu_splats(1.0);
  vec_double2 two_pow_52 = (vec_double2)spu_splats(0x4330000000000000ULL);

  /* If the input is a denorm, then multiply it by 2^52 so that the input is no
   * longer denormal.
   */
  exp = (vec_uint4)spu_and((vec_ullong2)in, spu_splats(0xFFF0000000000000ULL));
  denorm = (vec_ullong2)spu_cmpeq(exp,0);

  in = spu_mul(in, spu_sel(one, two_pow_52, denorm));

  fhalf = spu_splats(0.5f);
  dhalf = spu_splats(0.5);

  /* Coerce the input, in, into the argument reduced space [0.5, 2.0).
   */
  dx = spu_sel(in, dhalf, mask);

  /* Compute an initial single precision guess for the square root (fg)
   * and half reciprocal (fy2).
   */
  fx = spu_roundtf(dx);

  fy2 = spu_rsqrte(fx);
  fy = spu_mul(fy2, fhalf);
  fg = spu_mul(fy2, fx);	/* 12-bit approximation to sqrt(cx) */
  
  /* Perform one single precision Newton-Raphson iteration to improve 
   * accuracy to about 22 bits.
   */
  fe = spu_nmsub(fy, fg, fhalf);
  fd = spu_nmsub(fg, fg, fx);

  fy = spu_madd(fy2, fe, fy);
  fg = spu_madd(fy, fd, fg);	/* 22-bit approximation */

  dy = spu_extend(fy);
  dg = spu_extend(fg);

  /* Perform two double precision Newton-Raphson iteration to improve 
   * accuracy to about 44 and 88 bits repectively.
   */
  dy2 = spu_add(dy, dy);
  de = spu_nmsub(dy, dg, dhalf);
  dd = spu_nmsub(dg, dg, dx);
  dy = spu_madd(dy2, de, dy);
  dg = spu_madd(dy, dd, dg);	/* 44 bit approximation */

  dd = spu_nmsub(dg, dg, dx);
  dg = spu_madd(dy, dd, dg);	/* full double precision approximation */


  /* Compute the expected exponent assuming that it is not a special value.
   * See special value handling below.
   */
  bias_exp = spu_rlmaska(spu_sub((vec_int4)spu_and((vec_ullong2)in, mask), 
				 (vec_int4)spu_splats(0x3FE0000000000000ULL)),
			 -1);

  /* Adjust the exponent bias if the input was denormalized */
  bias_exp = spu_sub(bias_exp, (vec_int4)spu_and(spu_splats(0x01A0000000000000ULL), denorm));

  dg = (vec_double2)spu_add((vec_int4)dg, bias_exp);

  /* Handle special inputs. These include:
   *
   *   input 		 output
   * =========		=========
   *    -0		  -0
   *     0                 0
   * +infinity 		+infinity
   *    NaN		  NaN
   *    <0		  NaN
   */
  exp = spu_shuffle(exp, exp, ((vec_uchar16) { 0,1,2,3,0,1,2,3, 8,9,10,11,8,9,10,11 }));

  neg = (vec_double2)spu_rlmaska((vec_int4)exp, -31);
  nochange = spu_or((vec_ullong2)spu_cmpeq(exp, 0x7FF00000), 
		    spu_cmpeq(in, spu_splats(0.0)));

  dg = spu_sel(spu_or(dg, neg), in, nochange);

  return (dg);
}
#endif /* _SQRTD2_H_ */
#endif /* __SPU__ */