SDL  2.0
e_rem_pio2.c
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1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /* __ieee754_rem_pio2(x,y)
13  *
14  * return the remainder of x rem pi/2 in y[0]+y[1]
15  * use __kernel_rem_pio2()
16  */
17 
18 #include "math_libm.h"
19 #include "math_private.h"
20 
21 /*
22  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
23  */
24 static const int32_t two_over_pi[] = {
25 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
26 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
27 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
28 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
29 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
30 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
31 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
32 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
33 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
34 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
35 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
36 };
37 
38 static const int32_t npio2_hw[] = {
39 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
40 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
41 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
42 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
43 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
44 0x404858EB, 0x404921FB,
45 };
46 
47 /*
48  * invpio2: 53 bits of 2/pi
49  * pio2_1: first 33 bit of pi/2
50  * pio2_1t: pi/2 - pio2_1
51  * pio2_2: second 33 bit of pi/2
52  * pio2_2t: pi/2 - (pio2_1+pio2_2)
53  * pio2_3: third 33 bit of pi/2
54  * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
55  */
56 
57 static const double
58 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
59 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
60 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
61 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
62 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
63 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
64 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
65 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
66 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
67 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
68 
70 {
71  double z=0.0,w,t,r,fn;
72  double tx[3];
73  int32_t e0,i,j,nx,n,ix,hx;
74  u_int32_t low;
75 
76  GET_HIGH_WORD(hx,x); /* high word of x */
77  ix = hx&0x7fffffff;
78  if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
79  {y[0] = x; y[1] = 0; return 0;}
80  if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
81  if(hx>0) {
82  z = x - pio2_1;
83  if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
84  y[0] = z - pio2_1t;
85  y[1] = (z-y[0])-pio2_1t;
86  } else { /* near pi/2, use 33+33+53 bit pi */
87  z -= pio2_2;
88  y[0] = z - pio2_2t;
89  y[1] = (z-y[0])-pio2_2t;
90  }
91  return 1;
92  } else { /* negative x */
93  z = x + pio2_1;
94  if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
95  y[0] = z + pio2_1t;
96  y[1] = (z-y[0])+pio2_1t;
97  } else { /* near pi/2, use 33+33+53 bit pi */
98  z += pio2_2;
99  y[0] = z + pio2_2t;
100  y[1] = (z-y[0])+pio2_2t;
101  }
102  return -1;
103  }
104  }
105  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
106  t = fabs(x);
107  n = (int32_t) (t*invpio2+half);
108  fn = (double)n;
109  r = t-fn*pio2_1;
110  w = fn*pio2_1t; /* 1st round good to 85 bit */
111  if(n<32&&ix!=npio2_hw[n-1]) {
112  y[0] = r-w; /* quick check no cancellation */
113  } else {
114  u_int32_t high;
115  j = ix>>20;
116  y[0] = r-w;
117  GET_HIGH_WORD(high,y[0]);
118  i = j-((high>>20)&0x7ff);
119  if(i>16) { /* 2nd iteration needed, good to 118 */
120  t = r;
121  w = fn*pio2_2;
122  r = t-w;
123  w = fn*pio2_2t-((t-r)-w);
124  y[0] = r-w;
125  GET_HIGH_WORD(high,y[0]);
126  i = j-((high>>20)&0x7ff);
127  if(i>49) { /* 3rd iteration need, 151 bits acc */
128  t = r; /* will cover all possible cases */
129  w = fn*pio2_3;
130  r = t-w;
131  w = fn*pio2_3t-((t-r)-w);
132  y[0] = r-w;
133  }
134  }
135  }
136  y[1] = (r-y[0])-w;
137  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
138  else return n;
139  }
140  /*
141  * all other (large) arguments
142  */
143  if(ix>=0x7ff00000) { /* x is inf or NaN */
144  y[0]=y[1]=x-x; return 0;
145  }
146  /* set z = scalbn(|x|,ilogb(x)-23) */
147  GET_LOW_WORD(low,x);
148  SET_LOW_WORD(z,low);
149  e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
150  SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
151  for(i=0;i<2;i++) {
152  tx[i] = (double)((int32_t)(z));
153  z = (z-tx[i])*two24;
154  }
155  tx[2] = z;
156  nx = 3;
157  while(tx[nx-1]==zero) nx--; /* skip zero term */
158  n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
159  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
160  return n;
161 }
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:108
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2079
GLdouble GLdouble z
static const double invpio2
Definition: e_rem_pio2.c:61
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1574
signed int int32_t
int32_t attribute_hidden __ieee754_rem_pio2(double x, double *y)
Definition: e_rem_pio2.c:69
static const double pio2_1t
Definition: e_rem_pio2.c:63
static const double pio2_3t
Definition: e_rem_pio2.c:67
#define attribute_hidden
Definition: math_private.h:25
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:136
static const double zero
Definition: e_rem_pio2.c:58
unsigned int u_int32_t
Definition: math_private.h:31
#define SET_LOW_WORD(d, v)
Definition: math_private.h:146
int attribute_hidden __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
Definition: k_rem_pio2.c:150
static const double half
Definition: e_rem_pio2.c:59
static const double two24
Definition: e_rem_pio2.c:60
return Display return Display Bool Bool int int int return Display XEvent Bool(*) XPointer return Display return Display Drawable _Xconst char unsigned int unsigned int return Display Pixmap Pixmap XColor XColor unsigned int unsigned int return Display _Xconst char char int char return Display Visual unsigned int int int char unsigned int unsigned int int in j)
Definition: SDL_x11sym.h:50
GLbyte nx
GLubyte GLubyte GLubyte GLubyte w
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1574
return Display return Display Bool Bool int int int return Display XEvent Bool(*) XPointer return Display return Display Drawable _Xconst char unsigned int unsigned int return Display Pixmap Pixmap XColor XColor unsigned int unsigned int return Display _Xconst char char int char return Display Visual unsigned int int int char unsigned int unsigned int in i)
Definition: SDL_x11sym.h:50
static const int32_t npio2_hw[]
Definition: e_rem_pio2.c:38
#define GET_LOW_WORD(i, d)
Definition: math_private.h:117
GLdouble n
static const double pio2_2
Definition: e_rem_pio2.c:64
static const double pio2_1
Definition: e_rem_pio2.c:62
static const double pio2_3
Definition: e_rem_pio2.c:66
static const int32_t two_over_pi[]
Definition: e_rem_pio2.c:24
double fabs(double x)
Definition: s_fabs.c:22
GLdouble GLdouble t
Definition: SDL_opengl.h:2071
static const double pio2_2t
Definition: e_rem_pio2.c:65