Lines Matching +full:- +full:i
19 * y = x - N*pi/2
28 * (2/pi) is represented by an array of 24-bit integers in ipio2[].
32 * pieces of 24-bit integers in double precision format.
33 * x[i] will be the i-th 24 bit of x. The scaled exponent
34 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
38 * e0 = ilogb(z)-23
39 * z = scalbn(z,-e0)
40 * for i = 0,1,2
41 * x[i] = floor(z)
42 * z = (z-x[i])*2**24
47 * 24-bit precision 1
48 * 53-bit precision 2
49 * 64-bit precision 2
50 * 113-bit precision 3
51 * The actual value is the sum of them. Thus for 113-bit
58 * r_tail = w - (r_head - t);
71 * integer array, contains the (24*i)-th to (24*i+23)-th
75 * ipio2[i] * 2^(-24(i+1)).
90 * jx nx - 1
94 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
96 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
97 * Hence jv = max(0,(e0-3)/24).
102 * 24-bits chunk of the product of x and 2/pi.
105 * exponent for q[i] would be q0-24*i.
112 * iq[] integer array by breaking up q[] in 24-bits chunk.
137 _F_64(7.54978941586159635335e-08), /* 0x3E74442D, 0x00000000 */
138 _F_64(5.39030252995776476554e-15), /* 0x3CF84698, 0x80000000 */
139 _F_64(3.28200341580791294123e-22), /* 0x3B78CC51, 0x60000000 */
140 _F_64(1.27065575308067607349e-29), /* 0x39F01B83, 0x80000000 */
141 _F_64(1.22933308981111328932e-36), /* 0x387A2520, 0x40000000 */
142 _F_64(2.73370053816464559624e-44), /* 0x36E38222, 0x80000000 */
143 _F_64(2.16741683877804819444e-51), /* 0x3569F31D, 0x00000000 */
149 twon24 = _F_64(5.96046447753906250000e-08); /* 0x3E700000, 0x00000000 */
152 #pragma GCC diagnostic ignored "-Wpragmas"
153 #pragma GCC diagnostic ignored "-Wunknown-warning-option"
154 #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
156 #pragma GCC diagnostic ignored "-Wanalyzer-use-of-uninitialized-value"
163 __int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; in __kernel_rem_pio2() local
171 jx = nx - 1; in __kernel_rem_pio2()
172 jv = (e0 - 3) / 24; in __kernel_rem_pio2()
175 q0 = e0 - 24 * (jv + 1); in __kernel_rem_pio2()
178 j = jv - jx; in __kernel_rem_pio2()
180 for (i = 0; i <= m; i++, j++) in __kernel_rem_pio2()
181 f[i] = (j < 0) ? zero : (__float64)ipio2[j]; in __kernel_rem_pio2()
184 for (i = 0; i <= jk; i++) { in __kernel_rem_pio2()
186 fw += x[j] * f[jx + i - j]; in __kernel_rem_pio2()
187 q[i] = fw; in __kernel_rem_pio2()
193 for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) { in __kernel_rem_pio2()
195 iq[i] = (__int32_t)(z - two24 * fw); in __kernel_rem_pio2()
196 z = q[j - 1] + fw; in __kernel_rem_pio2()
201 z -= _F_64(8.0) * floor(z * _F_64(0.125)); /* trim off integer >= 8 */ in __kernel_rem_pio2()
203 z -= (__float64)n; in __kernel_rem_pio2()
205 if (q0 > 0) { /* need iq[jz-1] to determine n */ in __kernel_rem_pio2()
206 i = (iq[jz - 1] >> (24 - q0)); in __kernel_rem_pio2()
207 n += i; in __kernel_rem_pio2()
208 iq[jz - 1] -= i << (24 - q0); in __kernel_rem_pio2()
209 ih = iq[jz - 1] >> (23 - q0); in __kernel_rem_pio2()
211 ih = iq[jz - 1] >> 23; in __kernel_rem_pio2()
218 for (i = 0; i < jz; i++) { /* compute 1-q */ in __kernel_rem_pio2()
219 j = iq[i]; in __kernel_rem_pio2()
223 iq[i] = 0x1000000 - j; in __kernel_rem_pio2()
226 iq[i] = 0xffffff - j; in __kernel_rem_pio2()
231 iq[jz - 1] &= 0x7fffff; in __kernel_rem_pio2()
234 iq[jz - 1] &= 0x3fffff; in __kernel_rem_pio2()
239 z = one - z; in __kernel_rem_pio2()
241 z -= scalbn(one, (int)q0); in __kernel_rem_pio2()
248 for (i = jz - 1; i >= jk; i--) in __kernel_rem_pio2()
249 j |= iq[i]; in __kernel_rem_pio2()
251 for (k = 1; iq[jk - k] == 0; k++) in __kernel_rem_pio2()
254 for (i = jz + 1; i <= jz + k; i++) { /* add q[jz+1] to q[jz+k] */ in __kernel_rem_pio2()
255 f[jx + i] = (__float64)ipio2[jv + i]; in __kernel_rem_pio2()
257 fw += x[j] * f[jx + i - j]; in __kernel_rem_pio2()
258 q[i] = fw; in __kernel_rem_pio2()
267 jz -= 1; in __kernel_rem_pio2()
268 q0 -= 24; in __kernel_rem_pio2()
270 jz--; in __kernel_rem_pio2()
271 q0 -= 24; in __kernel_rem_pio2()
273 } else { /* break z into 24-bit if necessary */ in __kernel_rem_pio2()
274 z = scalbn(z, -(int)q0); in __kernel_rem_pio2()
277 iq[jz] = (__int32_t)(z - two24 * fw); in __kernel_rem_pio2()
285 /* convert integer "bit" chunk to floating-point value */ in __kernel_rem_pio2()
287 for (i = jz; i >= 0; i--) { in __kernel_rem_pio2()
288 q[i] = fw * (__float64)iq[i]; in __kernel_rem_pio2()
293 for (i = jz; i >= 0; i--) { in __kernel_rem_pio2()
294 for (fw = _F_64(0.0), k = 0; k <= jp && k <= jz - i; k++) in __kernel_rem_pio2()
295 fw += PIo2[k] * q[i + k]; in __kernel_rem_pio2()
296 fq[jz - i] = fw; in __kernel_rem_pio2()
303 for (i = jz; i >= 0; i--) in __kernel_rem_pio2()
304 fw += fq[i]; in __kernel_rem_pio2()
305 y[0] = (ih == 0) ? fw : -fw; in __kernel_rem_pio2()
310 for (i = jz; i >= 0; i--) in __kernel_rem_pio2()
311 fw += fq[i]; in __kernel_rem_pio2()
312 y[0] = (ih == 0) ? fw : -fw; in __kernel_rem_pio2()
313 fw = fq[0] - fw; in __kernel_rem_pio2()
314 for (i = 1; i <= jz; i++) in __kernel_rem_pio2()
315 fw += fq[i]; in __kernel_rem_pio2()
316 y[1] = (ih == 0) ? fw : -fw; in __kernel_rem_pio2()
319 for (i = jz; i > 0; i--) { in __kernel_rem_pio2()
320 fw = fq[i - 1] + fq[i]; in __kernel_rem_pio2()
321 fq[i] += fq[i - 1] - fw; in __kernel_rem_pio2()
322 fq[i - 1] = fw; in __kernel_rem_pio2()
324 for (i = jz; i > 1; i--) { in __kernel_rem_pio2()
325 fw = fq[i - 1] + fq[i]; in __kernel_rem_pio2()
326 fq[i] += fq[i - 1] - fw; in __kernel_rem_pio2()
327 fq[i - 1] = fw; in __kernel_rem_pio2()
329 for (fw = _F_64(0.0), i = jz; i >= 2; i--) in __kernel_rem_pio2()
330 fw += fq[i]; in __kernel_rem_pio2()
336 y[0] = -fq[0]; in __kernel_rem_pio2()
337 y[1] = -fq[1]; in __kernel_rem_pio2()
338 y[2] = -fw; in __kernel_rem_pio2()