+2011-06-28 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
+
+ * sysdeps/powerpc/fpu/e_hypot.c: optimizations for POWER5 and POWER6.
+ * sysdeps/powerpc/fpu/e_hypotf.c: likewise.
+
+2011-06-28 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
+
+ * sysdeps/powerpc/fpu/e_rem_pio2f.c: splitting the code on k_rem_pio2f.c
+ * sysdeps/powerpc/fpu/k_rem_pio2f.c: some code from e_rem_pio2f.c.
+
2011-06-15 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
* sysdeps/powerpc/fpu/Makefile: Added new objects.
Boston, MA 02111-1307, USA. */
#include "math.h"
+#include "math_private.h"
static const double two60 = 1.152921504606847e+18;
static const double two500 = 3.2733906078961419e+150;
* is needed.
*/
+#ifdef _ARCH_PWR7
+/* POWER7 isinf and isnan optimization are fast. */
+# define TEST_INF_NAN(x, y) \
+ if (isinf(x) || isinf(y)) \
+ return INFINITY; \
+ if (isnan(x) || isnan(y)) \
+ return NAN;
+# else
+/* For POWER6 and below isinf/isnan triggers LHS and PLT calls are
+ * costly (especially for POWER6). */
+# define GET_TW0_HIGH_WORD(d1,d2,i1,i2) \
+ do { \
+ ieee_double_shape_type gh_u1; \
+ ieee_double_shape_type gh_u2; \
+ gh_u1.value = (d1); \
+ gh_u2.value = (d2); \
+ (i1) = gh_u1.parts.msw; \
+ (i2) = gh_u2.parts.msw; \
+ } while (0)
+
+# define TEST_INF_NAN(x, y) \
+ do { \
+ int32_t hx, hy; \
+ GET_TW0_HIGH_WORD(x, y, hx, hy); \
+ if (hy > hx) { \
+ uint32_t ht = hx; hx = hy; hy = ht; \
+ } \
+ if (hx >= 0x7ff00000) { \
+ if (hx == 0x7ff00000 || hy == 0x7ff00000) \
+ return INFINITY; \
+ return NAN; \
+ } \
+ } while (0)
+
+#endif
+
+
double
__ieee754_hypot (double x, double y)
{
- double j;
+ x = fabs (x);
+ y = fabs (y);
+
+ TEST_INF_NAN (x, y);
- if (isinf(x) || isinf(y))
- {
- return INFINITY;
- }
- if (isnan(x) || isnan(y))
- {
- return NAN;
- }
- x = __builtin_fabs (x);
- y = __builtin_fabs (y);
if (y > x)
{
- j = x;
+ double t = x;
x = y;
- y = j;
+ y = t;
}
if (y == 0.0 || (x / y) > two60)
{
{
x *= twoM600;
y *= twoM600;
- return __builtin_sqrt (x * x + y * y) / twoM600;
+ return sqrt (x * x + y * y) / twoM600;
}
if (y < twoM500)
{
{
x *= two1022;
y *= two1022;
- return __builtin_sqrt (x * x + y * y) / two1022;
+ return sqrt (x * x + y * y) / two1022;
}
else
{
x *= two600;
y *= two600;
- return __builtin_sqrt (x * x + y * y) / two600;
+ return sqrt (x * x + y * y) / two600;
}
}
- return __builtin_sqrt (x * x + y * y);
+ return sqrt (x * x + y * y);
}
Boston, MA 02111-1307, USA. */
#include "math.h"
+#include "math_private.h"
-/* __ieee754_hypotf(x,y)
- *
- * This a FP only version without any FP->INT conversion.
- * It is similar to default C version, making appropriates
- * overflow and underflows checks as well scaling when it
- * is needed.
- */
static const float two30 = 1.0737418e09;
static const float two50 = 1.1259000e15;
static const float twoM60 = 6.7762644e-21;
static const float pdnum = 1.1754939e-38;
+
+/* __ieee754_hypotf(x,y)
+ *
+ * This a FP only version without any FP->INT conversion.
+ * It is similar to default C version, making appropriates
+ * overflow and underflows checks as well scaling when it
+ * is needed.
+ */
+
+#ifdef _ARCH_PWR7
+/* POWER7 isinf and isnan optimizations are fast. */
+# define TEST_INF_NAN(x, y) \
+ if (isinff(x) || isinff(y)) \
+ return INFINITY; \
+ if (isnanf(x) || isnanf(y)) \
+ return NAN;
+# else
+/* For POWER6 and below isinf/isnan triggers LHS and PLT calls are
+ * costly (especially for POWER6). */
+# define GET_TWO_FLOAT_WORD(f1,f2,i1,i2) \
+ do { \
+ ieee_float_shape_type gf_u1; \
+ ieee_float_shape_type gf_u2; \
+ gf_u1.value = (f1); \
+ gf_u2.value = (f2); \
+ (i1) = gf_u1.word; \
+ (i2) = gf_u2.word; \
+ } while (0)
+
+# define TEST_INF_NAN(x, y) \
+ do { \
+ int32_t hx, hy; \
+ GET_TWO_FLOAT_WORD(x, y, hx, hy); \
+ if (hy > hx) { \
+ uint32_t ht = hx; hx = hy; hy = ht; \
+ } \
+ if (hx >= 0x7f800000) { \
+ if (hx == 0x7f800000 || hy == 0x7f800000) \
+ return INFINITY; \
+ return NAN; \
+ } \
+ } while (0)
+#endif
+
+
float
__ieee754_hypotf (float x, float y)
{
- float j;
+ x = fabsf (x);
+ y = fabsf (y);
+
+ TEST_INF_NAN (x, y);
- if (isinff(x) || isinff(y))
- {
- return INFINITY;
- }
- if (isnanf(x) || isnanf(y))
- {
- return NAN;
- }
- x = __builtin_fabsf (x);
- y = __builtin_fabsf (y);
if (y > x)
{
- j = x;
- x = y;
- y = j;
+ float t = y;
+ y = x;
+ x = t;
}
if (y == 0.0 || (x / y) > two30)
{
{
x *= twoM60;
y *= twoM60;
- return __builtin_sqrtf (x * x + y * y) / twoM60;
+ return sqrtf (x * x + y * y) / twoM60;
}
if (y < twoM50)
{
{
x *= two126;
y *= two126;
- return __builtin_sqrtf (x * x + y * y) / two126;
+ return sqrtf (x * x + y * y) / two126;
}
else
{
x *= two60;
y *= two60;
- return __builtin_sqrtf (x * x + y * y) / two60;
+ return sqrtf (x * x + y * y) / two60;
}
}
- return __builtin_sqrtf (x * x + y * y);
+ return sqrtf (x * x + y * y);
}
Boston, MA 02111-1307, USA. */
#include <math.h>
-#include <stdint.h>
+#include "math_private.h"
#include "s_float_bitwise.h"
-static int32_t __fp_kernel_rem_pio2f (float *, float *, float, int32_t);
+/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */
+int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx);
/* __ieee754_rem_pio2f(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
*/
-static const float two_over_pi[] = {
- 1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
- 7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
- 2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
- 2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
- 2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
- 6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
- 2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
- 2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
- 1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
- 6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
- 6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
- 9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
- 2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
- 1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
- 2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
- 4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
- 2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
- 1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
- 5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
- 1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
- 1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
- 1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
- 3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
- 2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
- 2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
- 9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
- 1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
- 3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
- 7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
- 1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
- 1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
- 2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
- 6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
- 1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
- 1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
- 3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
- 8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
- 2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
- 2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
- 1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
- 1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
- 9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
- 1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
- 2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
- 1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
- 7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
- 6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
- 2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
- 9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
- 1.40000000e+02, 1.07000000e+02
-};
-
-
static const float npio2_hw[] = {
1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00,
7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01,
4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01
};
-static const float PIo2[] = {
- 1.5703125000e+00, /* 0x3fc90000 */
- 4.5776367188e-04, /* 0x39f00000 */
- 2.5987625122e-05, /* 0x37da0000 */
- 7.5437128544e-08, /* 0x33a20000 */
- 6.0026650317e-11, /* 0x2e840000 */
- 7.3896444519e-13, /* 0x2b500000 */
- 5.3845816694e-15, /* 0x27c20000 */
- 5.6378512969e-18, /* 0x22d00000 */
- 8.3009228831e-20, /* 0x1fc40000 */
- 3.2756352257e-22, /* 0x1bc60000 */
- 6.3331015649e-25, /* 0x17440000 */
-};
static const float zero = 0.0000000000e+00;
-static const float one = 1.0000000000;
static const float two8 = 2.5600000000e+02;
-static const float twon8 = 3.9062500000e-03;
static const float half = 5.0000000000e-01;
static const float invpio2 = 6.3661980629e-01;
}
return i;
}
-
-static int32_t
-__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
-{
- int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
- float z, fw, f[20], fq[20], q[20];
-
- /* initialize jk */
- jp = jk = 9;
-
- /* determine jx,jv,q0, note that 3>q0 */
- jx = nx - 1;
- exp = __float_get_exp (e0) - 127;
- jv = (exp - 3) / 8;
- if (jv < 0)
- jv = 0;
- q0 = exp - 8 * (jv + 1);
-
- /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
- j = jv - jx;
- m = jx + jk;
- for (i = 0; i <= m; i++, j++)
- f[i] = (j < 0) ? zero : two_over_pi[j];
-
- /* compute q[0],q[1],...q[jk] */
- for (i = 0; i <= jk; i++)
- {
- for (j = 0, fw = 0.0; j <= jx; j++)
- fw += x[j] * f[jx + i - j];
- q[i] = fw;
- }
-
- jz = jk;
-recompute:
- /* distill q[] into iq[] reversingly */
- for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
- {
- fw = truncf (twon8 * z);
- iq[i] = (int32_t) (z - two8 * fw);
- z = q[j - 1] + fw;
- }
-
- /* compute n */
- z = __scalbnf (z, q0); /* actual value of z */
- z -= 8.0 * floorf (z * 0.125); /* trim off integer >= 8 */
- n = (int32_t) z;
- z -= truncf (z);
- ih = 0;
- if (q0 > 0)
- { /* need iq[jz-1] to determine n */
- i = (iq[jz - 1] >> (8 - q0));
- n += i;
- iq[jz - 1] -= i << (8 - q0);
- ih = iq[jz - 1] >> (7 - q0);
- }
- else if (q0 == 0)
- ih = iq[jz - 1] >> 8;
- else if (z >= 0.5)
- ih = 2;
-
- if (ih > 0)
- { /* q > 0.5 */
- n += 1;
- carry = 0;
- for (i = 0; i < jz; i++)
- { /* compute 1-q */
- j = iq[i];
- if (carry == 0)
- {
- if (j != 0)
- {
- carry = 1;
- iq[i] = 0x100 - j;
- }
- }
- else
- iq[i] = 0xff - j;
- }
- if (q0 > 0)
- { /* rare case: chance is 1 in 12 */
- switch (q0)
- {
- case 1:
- iq[jz - 1] &= 0x7f;
- break;
- case 2:
- iq[jz - 1] &= 0x3f;
- break;
- }
- }
- if (ih == 2)
- {
- z = one - z;
- if (carry != 0)
- z -= __scalbnf (one, q0);
- }
- }
-
- /* check if recomputation is needed */
- if (z == zero)
- {
- j = 0;
- for (i = jz - 1; i >= jk; i--)
- j |= iq[i];
- if (j == 0)
- { /* need recomputation */
- for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
-
- for (i = jz + 1; i <= jz + k; i++)
- { /* add q[jz+1] to q[jz+k] */
- f[jx + i] = two_over_pi[jv + i];
- for (j = 0, fw = 0.0; j <= jx; j++)
- fw += x[j] * f[jx + i - j];
- q[i] = fw;
- }
- jz += k;
- goto recompute;
- }
- }
-
- /* chop off zero terms */
- if (z == 0.0)
- {
- jz -= 1;
- q0 -= 8;
- while (iq[jz] == 0)
- {
- jz--;
- q0 -= 8;
- }
- }
- else
- { /* break z into 8-bit if necessary */
- z = __scalbnf (z, -q0);
- if (z >= two8)
- {
- fw = truncf (twon8 * z);
- iq[jz] = (int32_t) (z - two8 * fw);
- jz += 1;
- q0 += 8;
- iq[jz] = (int32_t) fw;
- }
- else
- iq[jz] = (int32_t) z;
- }
-
- /* convert integer "bit" chunk to floating-point value */
- fw = __scalbnf (one, q0);
- for (i = jz; i >= 0; i--)
- {
- q[i] = fw * (float) iq[i];
- fw *= twon8;
- }
-
- /* compute PIo2[0,...,jp]*q[jz,...,0] */
- for (i = jz; i >= 0; i--)
- {
- for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
- fw += PIo2[k] * q[i + k];
- fq[jz - i] = fw;
- }
-
- /* compress fq[] into y[] */
- fw = 0.0;
- for (i = jz; i >= 0; i--)
- fw += fq[i];
- y[0] = (ih == 0) ? fw : -fw;
- fw = fq[0] - fw;
- for (i = 1; i <= jz; i++)
- fw += fq[i];
- y[1] = (ih == 0) ? fw : -fw;
-
- return n & 7;
-}
--- /dev/null
+/* k_rem_pio2f.c -- float version of e_rem_pio2.c
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 of the
+ License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <math.h>
+
+#include "math_private.h"
+#include "s_float_bitwise.h"
+
+
+static const float two_over_pi[] = {
+ 1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
+ 7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
+ 2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
+ 2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
+ 2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
+ 6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
+ 2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
+ 2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
+ 1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
+ 6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
+ 6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
+ 9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
+ 2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
+ 1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
+ 2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
+ 4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
+ 2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
+ 1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
+ 5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
+ 1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
+ 1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
+ 1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
+ 3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
+ 2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
+ 2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
+ 9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
+ 1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
+ 3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
+ 7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
+ 1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
+ 1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
+ 2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
+ 6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
+ 1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
+ 1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
+ 3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
+ 8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
+ 2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
+ 2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
+ 1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
+ 1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
+ 9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
+ 1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
+ 2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
+ 1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
+ 7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
+ 6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
+ 2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
+ 9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
+ 1.40000000e+02, 1.07000000e+02
+};
+
+
+static const float PIo2[] = {
+ 1.5703125000e+00, /* 0x3fc90000 */
+ 4.5776367188e-04, /* 0x39f00000 */
+ 2.5987625122e-05, /* 0x37da0000 */
+ 7.5437128544e-08, /* 0x33a20000 */
+ 6.0026650317e-11, /* 0x2e840000 */
+ 7.3896444519e-13, /* 0x2b500000 */
+ 5.3845816694e-15, /* 0x27c20000 */
+ 5.6378512969e-18, /* 0x22d00000 */
+ 8.3009228831e-20, /* 0x1fc40000 */
+ 3.2756352257e-22, /* 0x1bc60000 */
+ 6.3331015649e-25, /* 0x17440000 */
+};
+
+
+static const float zero = 0.0000000000e+00;
+static const float one = 1.0000000000;
+static const float twon8 = 3.9062500000e-03;
+static const float two8 = 2.5600000000e+02;
+
+
+int32_t
+__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
+{
+ int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
+ float z, fw, f[20], fq[20], q[20];
+
+ /* initialize jk */
+ jp = jk = 9;
+
+ /* determine jx,jv,q0, note that 3>q0 */
+ jx = nx - 1;
+ exp = __float_get_exp (e0) - 127;
+ jv = (exp - 3) / 8;
+ if (jv < 0)
+ jv = 0;
+ q0 = exp - 8 * (jv + 1);
+
+ /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
+ j = jv - jx;
+ m = jx + jk;
+ for (i = 0; i <= m; i++, j++)
+ f[i] = (j < 0) ? zero : two_over_pi[j];
+
+ /* compute q[0],q[1],...q[jk] */
+ for (i = 0; i <= jk; i++)
+ {
+ for (j = 0, fw = 0.0; j <= jx; j++)
+ fw += x[j] * f[jx + i - j];
+ q[i] = fw;
+ }
+
+ jz = jk;
+recompute:
+ /* distill q[] into iq[] reversingly */
+ for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
+ {
+ fw = truncf (twon8 * z);
+ iq[i] = (int32_t) (z - two8 * fw);
+ z = q[j - 1] + fw;
+ }
+
+ /* compute n */
+ z = __scalbnf (z, q0); /* actual value of z */
+ z -= 8.0 * floorf (z * 0.125); /* trim off integer >= 8 */
+ n = (int32_t) z;
+ z -= truncf (z);
+ ih = 0;
+ if (q0 > 0)
+ { /* need iq[jz-1] to determine n */
+ i = (iq[jz - 1] >> (8 - q0));
+ n += i;
+ iq[jz - 1] -= i << (8 - q0);
+ ih = iq[jz - 1] >> (7 - q0);
+ }
+ else if (q0 == 0)
+ ih = iq[jz - 1] >> 8;
+ else if (z >= 0.5)
+ ih = 2;
+
+ if (ih > 0)
+ { /* q > 0.5 */
+ n += 1;
+ carry = 0;
+ for (i = 0; i < jz; i++)
+ { /* compute 1-q */
+ j = iq[i];
+ if (carry == 0)
+ {
+ if (j != 0)
+ {
+ carry = 1;
+ iq[i] = 0x100 - j;
+ }
+ }
+ else
+ iq[i] = 0xff - j;
+ }
+ if (q0 > 0)
+ { /* rare case: chance is 1 in 12 */
+ switch (q0)
+ {
+ case 1:
+ iq[jz - 1] &= 0x7f;
+ break;
+ case 2:
+ iq[jz - 1] &= 0x3f;
+ break;
+ }
+ }
+ if (ih == 2)
+ {
+ z = one - z;
+ if (carry != 0)
+ z -= __scalbnf (one, q0);
+ }
+ }
+
+ /* check if recomputation is needed */
+ if (z == zero)
+ {
+ j = 0;
+ for (i = jz - 1; i >= jk; i--)
+ j |= iq[i];
+ if (j == 0)
+ { /* need recomputation */
+ for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
+
+ for (i = jz + 1; i <= jz + k; i++)
+ { /* add q[jz+1] to q[jz+k] */
+ f[jx + i] = two_over_pi[jv + i];
+ for (j = 0, fw = 0.0; j <= jx; j++)
+ fw += x[j] * f[jx + i - j];
+ q[i] = fw;
+ }
+ jz += k;
+ goto recompute;
+ }
+ }
+
+ /* chop off zero terms */
+ if (z == 0.0)
+ {
+ jz -= 1;
+ q0 -= 8;
+ while (iq[jz] == 0)
+ {
+ jz--;
+ q0 -= 8;
+ }
+ }
+ else
+ { /* break z into 8-bit if necessary */
+ z = __scalbnf (z, -q0);
+ if (z >= two8)
+ {
+ fw = truncf (twon8 * z);
+ iq[jz] = (int32_t) (z - two8 * fw);
+ jz += 1;
+ q0 += 8;
+ iq[jz] = (int32_t) fw;
+ }
+ else
+ iq[jz] = (int32_t) z;
+ }
+
+ /* convert integer "bit" chunk to floating-point value */
+ fw = __scalbnf (one, q0);
+ for (i = jz; i >= 0; i--)
+ {
+ q[i] = fw * (float) iq[i];
+ fw *= twon8;
+ }
+
+ /* compute PIo2[0,...,jp]*q[jz,...,0] */
+ for (i = jz; i >= 0; i--)
+ {
+ for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
+ fw += PIo2[k] * q[i + k];
+ fq[jz - i] = fw;
+ }
+
+ /* compress fq[] into y[] */
+ fw = 0.0;
+ for (i = jz; i >= 0; i--)
+ fw += fq[i];
+ y[0] = (ih == 0) ? fw : -fw;
+ fw = fq[0] - fw;
+ for (i = 1; i <= jz; i++)
+ fw += fq[i];
+ y[1] = (ih == 0) ? fw : -fw;
+
+ return n & 7;
+}
projects / thirdparty / glibc.git / commitdiff
