POK
e_rem_pio2.c
1 /*
2  * POK header
3  *
4  * The following file is a part of the POK project. Any modification should
5  * made according to the POK licence. You CANNOT use this file or a part of
6  * this file is this part of a file for your own project
7  *
8  * For more information on the POK licence, please see our LICENCE FILE
9  *
10  * Please follow the coding guidelines described in doc/CODING_GUIDELINES
11  *
12  * Copyright (c) 2007-2009 POK team
13  *
14  * Created by julien on Fri Jan 30 14:41:34 2009
15  */
16 
17 /* @(#)e_rem_pio2.c 5.1 93/09/24 */
18 /*
19  * ====================================================
20  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
21  *
22  * Developed at SunPro, a Sun Microsystems, Inc. business.
23  * Permission to use, copy, modify, and distribute this
24  * software is freely granted, provided that this notice
25  * is preserved.
26  * ====================================================
27  */
28 
29 /* __ieee754_rem_pio2(x,y)
30  *
31  * return the remainder of x rem pi/2 in y[0]+y[1]
32  * use __kernel_rem_pio2()
33  */
34 
35 #ifdef POK_NEEDS_LIBMATH
36 
37 #include <libm.h>
38 #include "math_private.h"
39 
40 /*
41  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
42  */
43 static const int32_t two_over_pi[] = {
44 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
45 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
46 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
47 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
48 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
49 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
50 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
51 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
52 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
53 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
54 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
55 };
56 
57 static const int32_t npio2_hw[] = {
58 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
59 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
60 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
61 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
62 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
63 0x404858EB, 0x404921FB,
64 };
65 
66 /*
67  * invpio2: 53 bits of 2/pi
68  * pio2_1: first 33 bit of pi/2
69  * pio2_1t: pi/2 - pio2_1
70  * pio2_2: second 33 bit of pi/2
71  * pio2_2t: pi/2 - (pio2_1+pio2_2)
72  * pio2_3: third 33 bit of pi/2
73  * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
74  */
75 
76 static const double
77 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
78 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
79 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
80 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
81 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
82 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
83 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
84 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
85 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
86 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
87 
88 int32_t
89 __ieee754_rem_pio2(double x, double *y)
90 {
91  double z,w,t,r,fn;
92  double tx[3];
93  int32_t e0,i,j,nx,n,ix,hx;
94  uint32_t low;
95 
96  z = 0;
97  GET_HIGH_WORD(hx,x); /* high word of x */
98  ix = hx&0x7fffffff;
99  if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
100  {y[0] = x; y[1] = 0; return 0;}
101  if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
102  if(hx>0) {
103  z = x - pio2_1;
104  if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
105  y[0] = z - pio2_1t;
106  y[1] = (z-y[0])-pio2_1t;
107  } else { /* near pi/2, use 33+33+53 bit pi */
108  z -= pio2_2;
109  y[0] = z - pio2_2t;
110  y[1] = (z-y[0])-pio2_2t;
111  }
112  return 1;
113  } else { /* negative x */
114  z = x + pio2_1;
115  if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
116  y[0] = z + pio2_1t;
117  y[1] = (z-y[0])+pio2_1t;
118  } else { /* near pi/2, use 33+33+53 bit pi */
119  z += pio2_2;
120  y[0] = z + pio2_2t;
121  y[1] = (z-y[0])+pio2_2t;
122  }
123  return -1;
124  }
125  }
126  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
127  t = fabs(x);
128  n = (int32_t) (t*invpio2+half);
129  fn = (double)n;
130  r = t-fn*pio2_1;
131  w = fn*pio2_1t; /* 1st round good to 85 bit */
132  if(n<32&&ix!=npio2_hw[n-1]) {
133  y[0] = r-w; /* quick check no cancellation */
134  } else {
135  uint32_t high;
136  j = ix>>20;
137  y[0] = r-w;
138  GET_HIGH_WORD(high,y[0]);
139  i = j-((high>>20)&0x7ff);
140  if(i>16) { /* 2nd iteration needed, good to 118 */
141  t = r;
142  w = fn*pio2_2;
143  r = t-w;
144  w = fn*pio2_2t-((t-r)-w);
145  y[0] = r-w;
146  GET_HIGH_WORD(high,y[0]);
147  i = j-((high>>20)&0x7ff);
148  if(i>49) { /* 3rd iteration need, 151 bits acc */
149  t = r; /* will cover all possible cases */
150  w = fn*pio2_3;
151  r = t-w;
152  w = fn*pio2_3t-((t-r)-w);
153  y[0] = r-w;
154  }
155  }
156  }
157  y[1] = (r-y[0])-w;
158  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
159  else return n;
160  }
161  /*
162  * all other (large) arguments
163  */
164  if(ix>=0x7ff00000) { /* x is inf or NaN */
165  y[0]=y[1]=x-x; return 0;
166  }
167  /* set z = scalbn(|x|,ilogb(x)-23) */
168  GET_LOW_WORD(low,x);
169  SET_LOW_WORD(z,low);
170  e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
171  SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
172  for(i=0;i<2;i++) {
173  tx[i] = (double)((int32_t)(z));
174  z = (z-tx[i])*two24;
175  }
176  tx[2] = z;
177  nx = 3;
178  while(tx[nx-1]==zero) nx--; /* skip zero term */
179  n = __kernel_rem_pio2(tx,y,e0,nx,2,(int*)two_over_pi);
180  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
181  return n;
182 }
183 #endif