diff options
Diffstat (limited to 'sysdeps/powerpc')
| -rw-r--r-- | sysdeps/powerpc/fpu/e_hypot.c | 65 | ||||
| -rw-r--r-- | sysdeps/powerpc/fpu/e_hypotf.c | 82 | ||||
| -rw-r--r-- | sysdeps/powerpc/fpu/e_rem_pio2f.c | 248 | ||||
| -rw-r--r-- | sysdeps/powerpc/fpu/k_rem_pio2f.c | 274 |
4 files changed, 287 insertions, 382 deletions
diff --git a/sysdeps/powerpc/fpu/e_hypot.c b/sysdeps/powerpc/fpu/e_hypot.c index 22bd56371e..c09c0c8b46 100644 --- a/sysdeps/powerpc/fpu/e_hypot.c +++ b/sysdeps/powerpc/fpu/e_hypot.c @@ -19,7 +19,6 @@ 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; @@ -37,56 +36,26 @@ static const double pdnum = 2.225073858507201e-308; * 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) { - x = fabs (x); - y = fabs (y); - - TEST_INF_NAN (x, y); + double j; + 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) { - double t = x; + j = x; x = y; - y = t; + y = j; } if (y == 0.0 || (x / y) > two60) { @@ -96,7 +65,7 @@ __ieee754_hypot (double x, double y) { x *= twoM600; y *= twoM600; - return sqrt (x * x + y * y) / twoM600; + return __builtin_sqrt (x * x + y * y) / twoM600; } if (y < twoM500) { @@ -104,14 +73,14 @@ __ieee754_hypot (double x, double y) { x *= two1022; y *= two1022; - return sqrt (x * x + y * y) / two1022; + return __builtin_sqrt (x * x + y * y) / two1022; } else { x *= two600; y *= two600; - return sqrt (x * x + y * y) / two600; + return __builtin_sqrt (x * x + y * y) / two600; } } - return sqrt (x * x + y * y); + return __builtin_sqrt (x * x + y * y); } diff --git a/sysdeps/powerpc/fpu/e_hypotf.c b/sysdeps/powerpc/fpu/e_hypotf.c index 3e6c597cc9..55eb2cb0c8 100644 --- a/sysdeps/powerpc/fpu/e_hypotf.c +++ b/sysdeps/powerpc/fpu/e_hypotf.c @@ -19,17 +19,6 @@ Boston, MA 02111-1307, USA. */ #include "math.h" -#include "math_private.h" - - -static const float two30 = 1.0737418e09; -static const float two50 = 1.1259000e15; -static const float two60 = 1.1529221e18; -static const float two126 = 8.5070592e+37; -static const float twoM50 = 8.8817842e-16; -static const float twoM60 = 6.7762644e-21; -static const float pdnum = 1.1754939e-38; - /* __ieee754_hypotf(x,y) * @@ -39,55 +28,34 @@ static const float pdnum = 1.1754939e-38; * 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 - +static const float two30 = 1.0737418e09; +static const float two50 = 1.1259000e15; +static const float two60 = 1.1529221e18; +static const float two126 = 8.5070592e+37; +static const float twoM50 = 8.8817842e-16; +static const float twoM60 = 6.7762644e-21; +static const float pdnum = 1.1754939e-38; float __ieee754_hypotf (float x, float y) { - x = fabsf (x); - y = fabsf (y); - - TEST_INF_NAN (x, y); + float j; + 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) { - float t = y; - y = x; - x = t; + j = x; + x = y; + y = j; } if (y == 0.0 || (x / y) > two30) { @@ -97,7 +65,7 @@ __ieee754_hypotf (float x, float y) { x *= twoM60; y *= twoM60; - return sqrtf (x * x + y * y) / twoM60; + return __builtin_sqrtf (x * x + y * y) / twoM60; } if (y < twoM50) { @@ -105,14 +73,14 @@ __ieee754_hypotf (float x, float y) { x *= two126; y *= two126; - return sqrtf (x * x + y * y) / two126; + return __builtin_sqrtf (x * x + y * y) / two126; } else { x *= two60; y *= two60; - return sqrtf (x * x + y * y) / two60; + return __builtin_sqrtf (x * x + y * y) / two60; } } - return sqrtf (x * x + y * y); + return __builtin_sqrtf (x * x + y * y); } 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; +} diff --git a/sysdeps/powerpc/fpu/k_rem_pio2f.c b/sysdeps/powerpc/fpu/k_rem_pio2f.c deleted file mode 100644 index 9635340219..0000000000 --- a/sysdeps/powerpc/fpu/k_rem_pio2f.c +++ /dev/null @@ -1,274 +0,0 @@ -/* 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; -} |