diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/e_powl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/e_powl.c | 441 |
1 files changed, 0 insertions, 441 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_powl.c b/sysdeps/ieee754/ldbl-128ibm/e_powl.c deleted file mode 100644 index feeaa8ce21..0000000000 --- a/sysdeps/ieee754/ldbl-128ibm/e_powl.c +++ /dev/null @@ -1,441 +0,0 @@ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* Expansions and modifications for 128-bit long double are - Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> - and are incorporated herein by permission of the author. The author - reserves the right to distribute this material elsewhere under different - copying permissions. These modifications are distributed here under - the following terms: - - This library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - This 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 - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, write to the Free Software - Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ - -/* __ieee754_powl(x,y) return x**y - * - * n - * Method: Let x = 2 * (1+f) - * 1. Compute and return log2(x) in two pieces: - * log2(x) = w1 + w2, - * where w1 has 113-53 = 60 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision - * arithmetic, where |y'|<=0.5. - * 3. Return x**y = 2**n*exp(y'*log2) - * - * Special cases: - * 1. (anything) ** 0 is 1 - * 2. (anything) ** 1 is itself - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN - * - */ - -#include "math.h" -#include "math_private.h" - -static const long double bp[] = { - 1.0L, - 1.5L, -}; - -/* log_2(1.5) */ -static const long double dp_h[] = { - 0.0, - 5.8496250072115607565592654282227158546448E-1L -}; - -/* Low part of log_2(1.5) */ -static const long double dp_l[] = { - 0.0, - 1.0579781240112554492329533686862998106046E-16L -}; - -static const long double zero = 0.0L, - one = 1.0L, - two = 2.0L, - two113 = 1.0384593717069655257060992658440192E34L, - huge = 1.0e3000L, - tiny = 1.0e-3000L; - -/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2)) - z = (x-1)/(x+1) - 1 <= x <= 1.25 - Peak relative error 2.3e-37 */ -static const long double LN[] = -{ - -3.0779177200290054398792536829702930623200E1L, - 6.5135778082209159921251824580292116201640E1L, - -4.6312921812152436921591152809994014413540E1L, - 1.2510208195629420304615674658258363295208E1L, - -9.9266909031921425609179910128531667336670E-1L -}; -static const long double LD[] = -{ - -5.129862866715009066465422805058933131960E1L, - 1.452015077564081884387441590064272782044E2L, - -1.524043275549860505277434040464085593165E2L, - 7.236063513651544224319663428634139768808E1L, - -1.494198912340228235853027849917095580053E1L - /* 1.0E0 */ -}; - -/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2))) - 0 <= x <= 0.5 - Peak relative error 5.7e-38 */ -static const long double PN[] = -{ - 5.081801691915377692446852383385968225675E8L, - 9.360895299872484512023336636427675327355E6L, - 4.213701282274196030811629773097579432957E4L, - 5.201006511142748908655720086041570288182E1L, - 9.088368420359444263703202925095675982530E-3L, -}; -static const long double PD[] = -{ - 3.049081015149226615468111430031590411682E9L, - 1.069833887183886839966085436512368982758E8L, - 8.259257717868875207333991924545445705394E5L, - 1.872583833284143212651746812884298360922E3L, - /* 1.0E0 */ -}; - -static const long double - /* ln 2 */ - lg2 = 6.9314718055994530941723212145817656807550E-1L, - lg2_h = 6.9314718055994528622676398299518041312695E-1L, - lg2_l = 2.3190468138462996154948554638754786504121E-17L, - ovt = 8.0085662595372944372e-0017L, - /* 2/(3*log(2)) */ - cp = 9.6179669392597560490661645400126142495110E-1L, - cp_h = 9.6179669392597555432899980587535537779331E-1L, - cp_l = 5.0577616648125906047157785230014751039424E-17L; - -#ifdef __STDC__ -long double -__ieee754_powl (long double x, long double y) -#else -long double -__ieee754_powl (x, y) - long double x, y; -#endif -{ - long double z, ax, z_h, z_l, p_h, p_l; - long double y1, t1, t2, r, s, t, u, v, w; - long double s2, s_h, s_l, t_h, t_l; - int32_t i, j, k, yisint, n; - u_int32_t ix, iy; - int32_t hx, hy; - ieee854_long_double_shape_type o, p, q; - - p.value = x; - hx = p.parts32.w0; - ix = hx & 0x7fffffff; - - q.value = y; - hy = q.parts32.w0; - iy = hy & 0x7fffffff; - - - /* y==zero: x**0 = 1 */ - if ((iy | q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0) - return one; - - /* 1.0**y = 1; -1.0**+-Inf = 1 */ - if (x == one) - return one; - if (x == -1.0L && iy == 0x7ff00000 - && (q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0) - return one; - - /* +-NaN return x+y */ - if ((ix > 0x7ff00000) - || ((ix == 0x7ff00000) - && ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) != 0)) - || (iy > 0x7ff00000) - || ((iy == 0x7ff00000) - && ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) != 0))) - return x + y; - - /* determine if y is an odd int when x < 0 - * yisint = 0 ... y is not an integer - * yisint = 1 ... y is an odd int - * yisint = 2 ... y is an even int - */ - yisint = 0; - if (hx < 0) - { - if ((q.parts32.w2 & 0x7fffffff) >= 0x43400000) /* Low part >= 2^53 */ - yisint = 2; /* even integer y */ - else if (iy >= 0x3ff00000) /* 1.0 */ - { - if (__floorl (y) == y) - { - z = 0.5 * y; - if (__floorl (z) == z) - yisint = 2; - else - yisint = 1; - } - } - } - - /* special value of y */ - if ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0) - { - if (iy == 0x7ff00000 && q.parts32.w1 == 0) /* y is +-inf */ - { - if (((ix - 0x3ff00000) | p.parts32.w1 - | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0) - return y - y; /* inf**+-1 is NaN */ - else if (ix > 0x3ff00000 || fabsl (x) > 1.0L) - /* (|x|>1)**+-inf = inf,0 */ - return (hy >= 0) ? y : zero; - else - /* (|x|<1)**-,+inf = inf,0 */ - return (hy < 0) ? -y : zero; - } - if (iy == 0x3ff00000) - { /* y is +-1 */ - if (hy < 0) - return one / x; - else - return x; - } - if (hy == 0x40000000) - return x * x; /* y is 2 */ - if (hy == 0x3fe00000) - { /* y is 0.5 */ - if (hx >= 0) /* x >= +0 */ - return __ieee754_sqrtl (x); - } - } - - ax = fabsl (x); - /* special value of x */ - if ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0) - { - if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) - { - z = ax; /*x is +-0,+-inf,+-1 */ - if (hy < 0) - z = one / z; /* z = (1/|x|) */ - if (hx < 0) - { - if (((ix - 0x3ff00000) | yisint) == 0) - { - z = (z - z) / (z - z); /* (-1)**non-int is NaN */ - } - else if (yisint == 1) - z = -z; /* (x<0)**odd = -(|x|**odd) */ - } - return z; - } - } - - /* (x<0)**(non-int) is NaN */ - if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) - return (x - x) / (x - x); - - /* |y| is huge. - 2^-16495 = 1/2 of smallest representable value. - If (1 - 1/131072)^y underflows, y > 1.4986e9 */ - if (iy > 0x41d654b0) - { - /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */ - if (iy > 0x47d654b0) - { - if (ix <= 0x3fefffff) - return (hy < 0) ? huge * huge : tiny * tiny; - if (ix >= 0x3ff00000) - return (hy > 0) ? huge * huge : tiny * tiny; - } - /* over/underflow if x is not close to one */ - if (ix < 0x3fefffff) - return (hy < 0) ? huge * huge : tiny * tiny; - if (ix > 0x3ff00000) - return (hy > 0) ? huge * huge : tiny * tiny; - } - - n = 0; - /* take care subnormal number */ - if (ix < 0x00100000) - { - ax *= two113; - n -= 113; - o.value = ax; - ix = o.parts32.w0; - } - n += ((ix) >> 20) - 0x3ff; - j = ix & 0x000fffff; - /* determine interval */ - ix = j | 0x3ff00000; /* normalize ix */ - if (j <= 0x39880) - k = 0; /* |x|<sqrt(3/2) */ - else if (j < 0xbb670) - k = 1; /* |x|<sqrt(3) */ - else - { - k = 0; - n += 1; - ix -= 0x00100000; - } - - o.value = ax; - o.value = __scalbnl (o.value, ((int) ((ix - o.parts32.w0) * 2)) >> 21); - ax = o.value; - - /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ - u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ - v = one / (ax + bp[k]); - s = u * v; - s_h = s; - - o.value = s_h; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - s_h = o.value; - /* t_h=ax+bp[k] High */ - t_h = ax + bp[k]; - o.value = t_h; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - t_h = o.value; - t_l = ax - (t_h - bp[k]); - s_l = v * ((u - s_h * t_h) - s_h * t_l); - /* compute log(ax) */ - s2 = s * s; - u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4]))); - v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2)))); - r = s2 * s2 * u / v; - r += s_l * (s_h + s); - s2 = s_h * s_h; - t_h = 3.0 + s2 + r; - o.value = t_h; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - t_h = o.value; - t_l = r - ((t_h - 3.0) - s2); - /* u+v = s*(1+...) */ - u = s_h * t_h; - v = s_l * t_h + t_l * s; - /* 2/(3log2)*(s+...) */ - p_h = u + v; - o.value = p_h; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - p_h = o.value; - p_l = v - (p_h - u); - z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ - z_l = cp_l * p_h + p_l * cp + dp_l[k]; - /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ - t = (long double) n; - t1 = (((z_h + z_l) + dp_h[k]) + t); - o.value = t1; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - t1 = o.value; - t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); - - /* s (sign of result -ve**odd) = -1 else = 1 */ - s = one; - if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) - s = -one; /* (-ve)**(odd int) */ - - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ - y1 = y; - o.value = y1; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - y1 = o.value; - p_l = (y - y1) * t1 + y * t2; - p_h = y1 * t1; - z = p_l + p_h; - o.value = z; - j = o.parts32.w0; - if (j >= 0x40d00000) /* z >= 16384 */ - { - /* if z > 16384 */ - if (((j - 0x40d00000) | o.parts32.w1 - | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0) - return s * huge * huge; /* overflow */ - else - { - if (p_l + ovt > z - p_h) - return s * huge * huge; /* overflow */ - } - } - else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */ - { - /* z < -16495 */ - if (((j - 0xc0d01bc0) | o.parts32.w1 - | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0) - return s * tiny * tiny; /* underflow */ - else - { - if (p_l <= z - p_h) - return s * tiny * tiny; /* underflow */ - } - } - /* compute 2**(p_h+p_l) */ - i = j & 0x7fffffff; - k = (i >> 20) - 0x3ff; - n = 0; - if (i > 0x3fe00000) - { /* if |z| > 0.5, set n = [z+0.5] */ - n = __floorl (z + 0.5L); - t = n; - p_h -= t; - } - t = p_l + p_h; - o.value = t; - o.parts32.w3 = 0; - o.parts32.w2 &= 0xffff8000; - t = o.value; - u = t * lg2_h; - v = (p_l - (t - p_h)) * lg2 + t * lg2_l; - z = u + v; - w = v - (z - u); - /* exp(z) */ - t = z * z; - u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4]))); - v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t))); - t1 = z - t * u / v; - r = (z * t1) / (t1 - two) - (w + z * w); - z = one - (r - z); - z = __scalbnl (z, n); - return s * z; -} |