newlib-cygwin/newlib/libm/machine/spu/headers/sqrtd2.h

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/* 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__ */