diff options
Diffstat (limited to 'sysdeps/powerpc/fpu/e_rem_pio2f.c')
| -rw-r--r-- | sysdeps/powerpc/fpu/e_rem_pio2f.c | 248 |
1 files changed, 245 insertions, 3 deletions
diff --git a/sysdeps/powerpc/fpu/e_rem_pio2f.c b/sysdeps/powerpc/fpu/e_rem_pio2f.c index 9325eeb27d..5b6e7b60ef 100644 --- a/sysdeps/powerpc/fpu/e_rem_pio2f.c +++ b/sysdeps/powerpc/fpu/e_rem_pio2f.c @@ -19,18 +19,71 @@ Boston, MA 02111-1307, USA. */ #include <math.h> +#include <stdint.h> -#include "math_private.h" #include "s_float_bitwise.h" -/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */ -int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx); +static int32_t __fp_kernel_rem_pio2f (float *, float *, float, int32_t); /* __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, @@ -42,9 +95,24 @@ static const float npio2_hw[] = { 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; @@ -187,3 +255,177 @@ __ieee754_rem_pio2f (float x, float *y) } 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; +} |