OpenCores
URL https://opencores.org/ocsvn/openrisc_me/openrisc_me/trunk

Subversion Repositories openrisc_me

[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libm/] [machine/] [spu/] [headers/] [acosd2.h] - Blame information for rev 207

Details | Compare with Previous | View Log

Line No. Rev Author Line
1 207 jeremybenn
/* --------------------------------------------------------------  */
2
/* (C)Copyright 2006,2008,                                         */
3
/* International Business Machines Corporation                     */
4
/* All Rights Reserved.                                            */
5
/*                                                                 */
6
/* Redistribution and use in source and binary forms, with or      */
7
/* without modification, are permitted provided that the           */
8
/* following conditions are met:                                   */
9
/*                                                                 */
10
/* - Redistributions of source code must retain the above copyright*/
11
/*   notice, this list of conditions and the following disclaimer. */
12
/*                                                                 */
13
/* - Redistributions in binary form must reproduce the above       */
14
/*   copyright notice, this list of conditions and the following   */
15
/*   disclaimer in the documentation and/or other materials        */
16
/*   provided with the distribution.                               */
17
/*                                                                 */
18
/* - Neither the name of IBM Corporation nor the names of its      */
19
/*   contributors may be used to endorse or promote products       */
20
/*   derived from this software without specific prior written     */
21
/*   permission.                                                   */
22
/*                                                                 */
23
/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND          */
24
/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,     */
25
/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF        */
26
/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE        */
27
/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR            */
28
/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,    */
29
/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT    */
30
/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;    */
31
/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)        */
32
/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN       */
33
/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR    */
34
/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,  */
35
/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              */
36
/* --------------------------------------------------------------  */
37
/* PROLOG END TAG zYx                                              */
38
#ifdef __SPU__
39
 
40
#ifndef _ACOSD2_H_
41
#define _ACOSD2_H_      1
42
 
43
#include "simdmath.h"
44
#include <spu_intrinsics.h>
45
#include "sqrtd2.h"
46
#include "divd2.h"
47
 
48
/*
49
 * FUNCTION
50
 *      vector double _acosd2(vector double x)
51
 *
52
 * DESCRIPTION
53
 *      Compute the arc cosine of the vector of double precision elements
54
 *      specified by x, returning the resulting angles in radians. The input
55
 *      elements are to be in the closed interval [-1, 1]. Values outside
56
 *      this range result in a invalid operation execption being latched in
57
 *      the FPSCR register and a NAN is returned.
58
 *
59
 *      The basic algorithm computes the arc cosine using PI/2 - asind2(x).
60
 *      However, as |x| approaches 1, there is a cancellation error in
61
 *      subtracting asind2(x) from PI/2, so we simplify the evaluation
62
 *      instead of layering acosd2 on top of asind2.
63
 *
64
 *      This yields the basic algorithm of:
65
 *
66
 *         absx = (x < 0.0) ? -x : x;
67
 *
68
 *         if (absx > 0.5) {
69
 *           if (x < 0) {
70
 *             addend = SM_PI;
71
 *             multiplier = -2.0;
72
 *           } else {
73
 *             addend = 0.0;
74
 *             multiplier = 2.0;
75
 *           }
76
 *
77
 *           x = sqrt(-0.5 * absx + 0.5);
78
 *         } else {
79
 *           addend = SM_PI_2;
80
 *           multiplier = -1.0;
81
 *         }
82
 *
83
 *          x2 = x * x;
84
 *          x3 = x2 * x;
85
 *
86
 *          p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0;
87
 *
88
 *          q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;;
89
 *
90
 *          pq = p / q;
91
 *
92
 *          result = (x3*pq + x)*multiplier - addend;
93
 *
94
 *      Where P5-P0 and Q5-Q0 are the polynomial coeficients. See asind2
95
 *      for additional details.
96
 */
97
static __inline vector double _acosd2(vector double x)
98
{
99
  vec_uint4   x_gt_half, x_eq_half;
100
  vec_double2 x_neg;                    // input x is negative
101
  vec_double2 x_abs;                    // absolute value of x
102
  vec_double2 x_trans;                  // transformed x when |x| > 0.5
103
  vec_double2 x2, x3;                   // x squared and x cubed, respectively.
104
  vec_double2 result;
105
  vec_double2 multiplier, addend;
106
  vec_double2 p, q, pq;
107
  vec_double2 half = spu_splats(0.5);
108
  vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL);
109
  vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11});
110
 
111
  // Compute the absolute value of x
112
  x_abs = spu_andc(x, sign);
113
 
114
  // Perform transformation for the case where |x| > 0.5. We rely on
115
  // sqrtd2 producing a NAN is |x| > 1.0.
116
  x_trans = _sqrtd2(spu_nmsub(x_abs, half, half));
117
 
118
  // Determine the correct addend and multiplier.
119
  x_neg = (vec_double2)spu_rlmaska((vec_int4)spu_shuffle(x, x, splat_hi), -31);
120
 
121
  x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half);
122
  x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half);
123
  x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4)));
124
  x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi);
125
 
126
  addend = spu_sel(spu_splats(SM_PI_2), spu_and(spu_splats(SM_PI), x_neg), (vec_ullong2)x_gt_half);
127
 
128
  multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half);
129
 
130
  // Select whether to use the x or the transformed x for the polygon evaluation.
131
  // if |x| > 0.5 use x_trans
132
  // else         use x
133
 
134
  x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half);
135
 
136
  // Compute the polynomials.
137
 
138
  x2 = spu_mul(x, x);
139
  x3 = spu_mul(x2, x);
140
 
141
  p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661));
142
  p = spu_madd(p, x2, spu_splats(5.444622390564711410273));
143
  p = spu_madd(p, x2, spu_splats(-16.26247967210700244449));
144
  p = spu_madd(p, x2, spu_splats(19.56261983317594739197));
145
  p = spu_madd(p, x2, spu_splats(-8.198089802484824371615));
146
 
147
  q = spu_add(x2, spu_splats(-14.74091372988853791896));
148
  q = spu_madd(q, x2, spu_splats(70.49610280856842141659));
149
  q = spu_madd(q, x2, spu_splats(-147.1791292232726029859));
150
  q = spu_madd(q, x2, spu_splats(139.5105614657485689735));
151
  q = spu_madd(q, x2, spu_splats(-49.18853881490881290097));
152
 
153
  // Compute the rational solution p/q and final multiplication and addend 
154
  // correction.
155
  pq = _divd2(p, q);
156
 
157
  result = spu_madd(spu_madd(x3, pq, x), multiplier, addend);
158
 
159
  return (result);
160
}
161
 
162
#endif /* _ACOSD2_H_ */
163
#endif /* __SPU__ */
164
 

powered by: WebSVN 2.1.0

© copyright 1999-2024 OpenCores.org, equivalent to Oliscience, all rights reserved. OpenCores®, registered trademark.