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remp2.c File Reference
#include "prim.h"
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Functions

int32_t rempio2 (double x, double *y)
 

Variables

static const int two_over_pi []
 
static const int npio2_hw []
 
static const double zero = 0.00000000000000000000e+00
 
static const double half = 5.00000000000000000000e-01
 
static const double two24 = 1.67772160000000000000e+07
 
static const double invpio2 = 6.36619772367581382433e-01
 
static const double pio2_1 = 1.57079632673412561417e+00
 
static const double pio2_1t = 6.07710050650619224932e-11
 
static const double pio2_2 = 6.07710050630396597660e-11
 
static const double pio2_2t = 2.02226624879595063154e-21
 
static const double pio2_3 = 2.02226624871116645580e-21
 
static const double pio2_3t = 8.47842766036889956997e-32
 

Function Documentation

◆ rempio2()

int32_t rempio2 ( double  x,
double *  y 
)

Definition at line 104 of file remp2.c.

References __kernel_rem_pio2(), fabs(), half, invpio2, npio2_hw, pio2_1, pio2_1t, pio2_2, pio2_2t, pio2_3, pio2_3t, two24, two_over_pi, and zero.

Referenced by cos(), sin(), and tan().

105 {
106  double z = 0.,w,t,r,fn;
107  double tx[3];
108  int32_t i,j,n,ix,hx;
109  int e0,nx;
110  uint32_t low;
111 
112  GET_HIGH_WORD(hx,x); /* high word of x */
113  ix = hx&0x7fffffff;
114  if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
115  {
116  y[0] = x;
117  y[1] = 0;
118  return 0;
119  }
120  if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
121  if(hx>0) {
122  z = x - pio2_1;
123  if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
124  y[0] = z - pio2_1t;
125  y[1] = (z-y[0])-pio2_1t;
126  } else { /* near pi/2, use 33+33+53 bit pi */
127  z -= pio2_2;
128  y[0] = z - pio2_2t;
129  y[1] = (z-y[0])-pio2_2t;
130  }
131  return 1;
132  } else { /* negative x */
133  z = x + pio2_1;
134  if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
135  y[0] = z + pio2_1t;
136  y[1] = (z-y[0])+pio2_1t;
137  } else { /* near pi/2, use 33+33+53 bit pi */
138  z += pio2_2;
139  y[0] = z + pio2_2t;
140  y[1] = (z-y[0])+pio2_2t;
141  }
142  return -1;
143  }
144  }
145  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
146  t = fabs(x);
147  n = (int32_t) (t*invpio2+half);
148  fn = (double)n;
149  r = t-fn*pio2_1;
150  w = fn*pio2_1t; /* 1st round good to 85 bit */
151  if(n<32&&ix!=npio2_hw[n-1]) {
152  y[0] = r-w; /* quick check no cancellation */
153  } else {
154  uint32_t high;
155 
156  j = ix>>20;
157  y[0] = r-w;
158  GET_HIGH_WORD(high, y[0]);
159  i = j-((high>>20)&0x7ff);
160  if(i>16) { /* 2nd iteration needed, good to 118 */
161  t = r;
162  w = fn*pio2_2;
163  r = t-w;
164  w = fn*pio2_2t-((t-r)-w);
165  y[0] = r-w;
166  GET_HIGH_WORD(high,y[0]);
167  i = j-((high>>20)&0x7ff);
168  if(i>49) { /* 3rd iteration need, 151 bits acc */
169  t = r; /* will cover all possible cases */
170  w = fn*pio2_3;
171  r = t-w;
172  w = fn*pio2_3t-((t-r)-w);
173  y[0] = r-w;
174  }
175  }
176  }
177  y[1] = (r-y[0])-w;
178  if(hx<0) {
179  y[0] = -y[0];
180  y[1] = -y[1];
181  return -n;
182  }
183  else return n;
184  }
185  /*
186  * all other (large) arguments
187  */
188  if(ix>=0x7ff00000) { /* x is inf or NaN */
189  y[0]=y[1]=x-x;
190  return 0;
191  }
192  /* set z = scalbn(|x|,ilogb(x)-23) */
193  GET_LOW_WORD(low,x);
194  SET_LOW_WORD(z,low);
195  e0 = (int32_t)(ix>>20)-1046; /* e0 = ilogb(z)-23; */
196  SET_HIGH_WORD(z,ix - (e0<<20));
197  for(i=0; i<2; i++) {
198  tx[i] = (double)((int32_t)(z));
199  z = (z-tx[i])*two24;
200  }
201  tx[2] = z;
202  nx = 3;
203  while(tx[nx-1]==zero) nx--; /* skip zero term */
204  n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
205  if(hx<0) {
206  y[0] = -y[0];
207  y[1] = -y[1];
208  return -n;
209  }
210  return n;
211 }
pio2_3
static const double pio2_3
Definition: remp2.c:101
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Get the more significant 32 bit int from a double.
Definition: prim.h:167
zero
static const double zero
Definition: remp2.c:93
half
static const double half
Definition: remp2.c:94
pio2_2t
static const double pio2_2t
Definition: remp2.c:100
GET_LOW_WORD
#define GET_LOW_WORD(i, d)
Get the less significant 32 bit int from a double.
Definition: prim.h:177
pio2_1t
static const double pio2_1t
Definition: remp2.c:98
pio2_1
static const double pio2_1
Definition: remp2.c:97
__kernel_rem_pio2
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
Kernel reduction function.
Definition: kremp2.c:184
invpio2
static const double invpio2
Definition: remp2.c:96
two_over_pi
static const int two_over_pi[]
Definition: remp2.c:59
two24
static const double two24
Definition: remp2.c:95
pio2_2
static const double pio2_2
Definition: remp2.c:99
npio2_hw
static const int npio2_hw[]
Definition: remp2.c:73
SET_LOW_WORD
#define SET_LOW_WORD(d, v)
Set the less significant 32 bits of a double from an int.
Definition: prim.h:209
SET_HIGH_WORD
#define SET_HIGH_WORD(d, v)
Set the more significant 32 bits of a double from an int.
Definition: prim.h:198
fabs
double fabs(double x)
Returns the absolute value of x.
Definition: fabs.c:51
pio2_3t
static const double pio2_3t
Definition: remp2.c:102
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Variable Documentation

◆ half

const double half = 5.00000000000000000000e-01
static

Definition at line 94 of file remp2.c.

Referenced by rempio2().

◆ invpio2

const double invpio2 = 6.36619772367581382433e-01
static

Definition at line 96 of file remp2.c.

Referenced by rempio2().

◆ npio2_hw

const int npio2_hw[]
static
Initial value:
= {
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
}

Definition at line 73 of file remp2.c.

Referenced by rempio2().

◆ pio2_1

const double pio2_1 = 1.57079632673412561417e+00
static

Definition at line 97 of file remp2.c.

Referenced by rempio2().

◆ pio2_1t

const double pio2_1t = 6.07710050650619224932e-11
static

Definition at line 98 of file remp2.c.

Referenced by rempio2().

◆ pio2_2

const double pio2_2 = 6.07710050630396597660e-11
static

Definition at line 99 of file remp2.c.

Referenced by rempio2().

◆ pio2_2t

const double pio2_2t = 2.02226624879595063154e-21
static

Definition at line 100 of file remp2.c.

Referenced by rempio2().

◆ pio2_3

const double pio2_3 = 2.02226624871116645580e-21
static

Definition at line 101 of file remp2.c.

Referenced by rempio2().

◆ pio2_3t

const double pio2_3t = 8.47842766036889956997e-32
static

Definition at line 102 of file remp2.c.

Referenced by rempio2().

◆ two24

const double two24 = 1.67772160000000000000e+07
static

Definition at line 95 of file remp2.c.

Referenced by rempio2().

◆ two_over_pi

const int two_over_pi[]
static
Initial value:
= {
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
}

Definition at line 59 of file remp2.c.

Referenced by rempio2().

◆ zero

const double zero = 0.00000000000000000000e+00
static

Definition at line 93 of file remp2.c.

Referenced by rempio2().