SDL  2.0
k_rem_pio2.c File Reference
#include "math_libm.h"
#include "math_private.h"
#include "SDL_assert.h"
+ Include dependency graph for k_rem_pio2.c:

Go to the source code of this file.

Functions

 libm_hidden_proto (scalbn)
 
int attribute_hidden __kernel_rem_pio2 (x, y, int e0, int nx, int prec, ipio2)
 

Variables

static double PIo2 []
 
static double zero = 0.0
 
static double one = 1.0
 
static double two24 = 1.67772160000000000000e+07
 
static double twon24 = 5.96046447753906250000e-08
 

Function Documentation

int attribute_hidden __kernel_rem_pio2 ( x  ,
y  ,
int  e0,
int  nx,
int  prec,
ipio2   
)

Definition at line 176 of file k_rem_pio2.c.

References floor, i, j, one, scalbn, SDL_arraysize, SDL_assert, two24, twon24, and zero.

Referenced by __ieee754_rem_pio2().

181 {
182  int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih;
183  double z, fw, f[20], fq[20], q[20];
184 
185  /* initialize jk */
186  SDL_assert((prec >= 0) && (prec < SDL_arraysize(init_jk)));
187  jk = init_jk[prec];
188  SDL_assert((jk >= 2) && (jk <= 6));
189  jp = jk;
190 
191  /* determine jx,jv,q0, note that 3>q0 */
192  SDL_assert(nx > 0);
193  jx = nx - 1;
194  jv = (e0 - 3) / 24;
195  if (jv < 0)
196  jv = 0;
197  q0 = e0 - 24 * (jv + 1);
198 
199  /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
200  j = jv - jx;
201  m = jx + jk;
202  for (i = 0; i <= m; i++, j++)
203  f[i] = (j < 0) ? zero : (double) ipio2[j];
204 
205  /* compute q[0],q[1],...q[jk] */
206  for (i = 0; i <= jk; i++) {
207  for (j = 0, fw = 0.0; j <= jx; j++)
208  fw += x[j] * f[jx + i - j];
209  q[i] = fw;
210  }
211 
212  jz = jk;
213  recompute:
214  /* distill q[] into iq[] reversingly */
215  for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) {
216  fw = (double) ((int32_t) (twon24 * z));
217  iq[i] = (int32_t) (z - two24 * fw);
218  z = q[j - 1] + fw;
219  }
220 
221  /* compute n */
222  z = scalbn(z, q0); /* actual value of z */
223  z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */
224  n = (int32_t) z;
225  z -= (double) n;
226  ih = 0;
227  if (q0 > 0) { /* need iq[jz-1] to determine n */
228  i = (iq[jz - 1] >> (24 - q0));
229  n += i;
230  iq[jz - 1] -= i << (24 - q0);
231  ih = iq[jz - 1] >> (23 - q0);
232  } else if (q0 == 0)
233  ih = iq[jz - 1] >> 23;
234  else if (z >= 0.5)
235  ih = 2;
236 
237  if (ih > 0) { /* q > 0.5 */
238  n += 1;
239  carry = 0;
240  for (i = 0; i < jz; i++) { /* compute 1-q */
241  j = iq[i];
242  if (carry == 0) {
243  if (j != 0) {
244  carry = 1;
245  iq[i] = 0x1000000 - j;
246  }
247  } else
248  iq[i] = 0xffffff - j;
249  }
250  if (q0 > 0) { /* rare case: chance is 1 in 12 */
251  switch (q0) {
252  case 1:
253  iq[jz - 1] &= 0x7fffff;
254  break;
255  case 2:
256  iq[jz - 1] &= 0x3fffff;
257  break;
258  }
259  }
260  if (ih == 2) {
261  z = one - z;
262  if (carry != 0)
263  z -= scalbn(one, q0);
264  }
265  }
266 
267  /* check if recomputation is needed */
268  if (z == zero) {
269  j = 0;
270  for (i = jz - 1; i >= jk; i--)
271  j |= iq[i];
272  if (j == 0) { /* need recomputation */
273  for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
274 
275  for (i = jz + 1; i <= jz + k; i++) { /* add q[jz+1] to q[jz+k] */
276  f[jx + i] = (double) ipio2[jv + i];
277  for (j = 0, fw = 0.0; j <= jx; j++)
278  fw += x[j] * f[jx + i - j];
279  q[i] = fw;
280  }
281  jz += k;
282  goto recompute;
283  }
284  }
285 
286  /* chop off zero terms */
287  if (z == 0.0) {
288  jz -= 1;
289  q0 -= 24;
290  while (iq[jz] == 0) {
291  jz--;
292  q0 -= 24;
293  }
294  } else { /* break z into 24-bit if necessary */
295  z = scalbn(z, -q0);
296  if (z >= two24) {
297  fw = (double) ((int32_t) (twon24 * z));
298  iq[jz] = (int32_t) (z - two24 * fw);
299  jz += 1;
300  q0 += 24;
301  iq[jz] = (int32_t) fw;
302  } else
303  iq[jz] = (int32_t) z;
304  }
305 
306  /* convert integer "bit" chunk to floating-point value */
307  fw = scalbn(one, q0);
308  for (i = jz; i >= 0; i--) {
309  q[i] = fw * (double) iq[i];
310  fw *= twon24;
311  }
312 
313  /* compute PIo2[0,...,jp]*q[jz,...,0] */
314  for (i = jz; i >= 0; i--) {
315  for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
316  fw += PIo2[k] * q[i + k];
317  fq[jz - i] = fw;
318  }
319 
320  /* compress fq[] into y[] */
321  switch (prec) {
322  case 0:
323  fw = 0.0;
324  for (i = jz; i >= 0; i--)
325  fw += fq[i];
326  y[0] = (ih == 0) ? fw : -fw;
327  break;
328  case 1:
329  case 2:
330  fw = 0.0;
331  for (i = jz; i >= 0; i--)
332  fw += fq[i];
333  y[0] = (ih == 0) ? fw : -fw;
334  fw = fq[0] - fw;
335  for (i = 1; i <= jz; i++)
336  fw += fq[i];
337  y[1] = (ih == 0) ? fw : -fw;
338  break;
339  case 3: /* painful */
340  for (i = jz; i > 0; i--) {
341  fw = fq[i - 1] + fq[i];
342  fq[i] += fq[i - 1] - fw;
343  fq[i - 1] = fw;
344  }
345  for (i = jz; i > 1; i--) {
346  fw = fq[i - 1] + fq[i];
347  fq[i] += fq[i - 1] - fw;
348  fq[i - 1] = fw;
349  }
350  for (fw = 0.0, i = jz; i >= 2; i--)
351  fw += fq[i];
352  if (ih == 0) {
353  y[0] = fq[0];
354  y[1] = fq[1];
355  y[2] = fw;
356  } else {
357  y[0] = -fq[0];
358  y[1] = -fq[1];
359  y[2] = -fw;
360  }
361  }
362  return n & 7;
363 }
static double PIo2[]
Definition: k_rem_pio2.c:150
GLdouble n
signed int int32_t
GLdouble GLdouble GLdouble GLdouble q
Definition: SDL_opengl.h:2080
const GLfloat * m
GLfloat f
static double one
Definition: k_rem_pio2.c:167
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
#define scalbn
Definition: math_private.h:40
static double two24
Definition: k_rem_pio2.c:167
GLbyte nx
static double twon24
Definition: k_rem_pio2.c:168
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:42
#define SDL_assert(condition)
Definition: SDL_assert.h:167
static double zero
Definition: k_rem_pio2.c:167
GLdouble GLdouble z
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
#define SDL_arraysize(array)
Definition: SDL_stdinc.h:93
#define floor
Definition: math_private.h:37
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:42
libm_hidden_proto ( scalbn  )

Definition at line 139 of file k_rem_pio2.c.

References PIo2.

142  { 2, 3, 4, 6 }; /* initial value for jk */
143 #else
144  static int init_jk[] = { 2, 3, 4, 6 };

Variable Documentation

double one = 1.0
static

Definition at line 167 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().

double PIo2[]
static
Initial value:
= {
1.57079625129699707031e+00,
7.54978941586159635335e-08,
5.39030252995776476554e-15,
3.28200341580791294123e-22,
1.27065575308067607349e-29,
1.22933308981111328932e-36,
2.73370053816464559624e-44,
2.16741683877804819444e-51,
}

Definition at line 150 of file k_rem_pio2.c.

Referenced by libm_hidden_proto().

double two24 = 1.67772160000000000000e+07
static

Definition at line 167 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().

double twon24 = 5.96046447753906250000e-08
static

Definition at line 168 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().

double zero = 0.0
static

Definition at line 167 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().