diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/e_powf.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_powf.c | 171 |
1 files changed, 70 insertions, 101 deletions
diff --git a/sysdeps/ieee754/flt-32/e_powf.c b/sysdeps/ieee754/flt-32/e_powf.c index 13b49de..3f06020 100644 --- a/sysdeps/ieee754/flt-32/e_powf.c +++ b/sysdeps/ieee754/flt-32/e_powf.c @@ -1,6 +1,22 @@ /* e_powf.c -- float version of e_pow.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ +/* Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C 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. + + 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 + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ /* * ==================================================== @@ -20,8 +36,6 @@ static const float huge = 1.0e+30, tiny = 1.0e-30; static const float bp[] = {1.0, 1.5,}, -dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ -dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ zero = 0.0, one = 1.0, two = 2.0, @@ -38,28 +52,24 @@ P2 = -2.7777778450e-03, /* 0xbb360b61 */ P3 = 6.6137559770e-05, /* 0x388ab355 */ P4 = -1.6533901999e-06, /* 0xb5ddea0e */ P5 = 4.1381369442e-08, /* 0x3331bb4c */ -lg2 = 6.9314718246e-01, /* 0x3f317218 */ -lg2_h = 6.93145752e-01, /* 0x3f317200 */ -lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ -ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ -cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ -cp_h = 0xf.64p-4, /* cp high 12 bits. */ -cp_l = -0x7.b11e3p-16, /* 2/(3ln2) - cp_h. */ -ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ -ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ -ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ +ovt = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */ + +static const double + dp[] = { 0.0, 0x1.2b803473f7ad1p-1, }, /* log2(1.5) */ + lg2 = M_LN2, + cp = 2.0/3.0/M_LN2, + invln2 = 1.0/M_LN2; float __ieee754_powf(float x, float y) { - float z,ax,z_h,z_l,p_h,p_l; - float y1,t1,t2,r,s,t,u,v,w; + float z, ax, s; + double d1, d2; int32_t i,j,k,yisint,n; - int32_t hx,hy,ix,iy,is; + int32_t hx,hy,ix,iy; - GET_FLOAT_WORD(hx,x); GET_FLOAT_WORD(hy,y); - ix = hx&0x7fffffff; iy = hy&0x7fffffff; + iy = hy&0x7fffffff; /* y==zero: x**0 = 1 */ if(iy==0 && !issignaling (x)) return one; @@ -68,26 +78,14 @@ __ieee754_powf(float x, float y) if(x == 1.0 && !issignaling (y)) return one; if(x == -1.0 && isinf(y)) return one; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + /* +-NaN return x+y */ if(__builtin_expect(ix > 0x7f800000 || iy > 0x7f800000, 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(iy>=0x4b800000) yisint = 2; /* even integer y */ - else if(iy>=0x3f800000) { - k = (iy>>23)-0x7f; /* exponent */ - j = iy>>(23-k); - if((j<<(23-k))==iy) yisint = 2-(j&1); - } - } - /* special value of y */ if (__builtin_expect(iy==0x7f800000, 0)) { /* y is +-inf */ if (ix==0x3f800000) @@ -106,6 +104,21 @@ __ieee754_powf(float x, float y) return __ieee754_sqrtf(x); } + /* 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(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + ax = fabsf(x); /* special value of x */ if(__builtin_expect(ix==0x7f800000||ix==0||ix==0x3f800000, 0)){ @@ -131,16 +144,10 @@ __ieee754_powf(float x, float y) if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; /* now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ - t = ax-1; /* t has 20 trailing zeros */ - w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); - u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ - v = t*ivln2_l-w*ivln2; - t1 = u+v; - GET_FLOAT_WORD(is,t1); - SET_FLOAT_WORD(t1,is&0xfffff000); - t2 = v-(t1-u); + d2 = ax-1; /* d2 has 20 trailing zeros. */ + d2 = d2 * invln2 - + (d2 * d2) * (0.5 - d2 * (0.333333333333 - d2 * 0.25)) * invln2; } else { - float s2,s_h,s_l,t_h,t_l; /* Avoid internal underflow for tiny y. The exact value of y does not matter if |y| <= 2**-32. */ if (iy < 0x2f800000) @@ -158,69 +165,37 @@ __ieee754_powf(float x, float y) else {k=0;n+=1;ix -= 0x00800000;} SET_FLOAT_WORD(ax,ix); - /* 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; - GET_FLOAT_WORD(is,s_h); - SET_FLOAT_WORD(s_h,is&0xfffff000); - /* t_h=ax+bp[k] High */ - SET_FLOAT_WORD (t_h, - ((((ix>>1)|0x20000000)+0x00400000+(k<<21)) - & 0xfffff000)); - 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; - r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); - r += s_l*(s_h+s); - s2 = s_h*s_h; - t_h = (float)3.0+s2+r; - GET_FLOAT_WORD(is,t_h); - SET_FLOAT_WORD(t_h,is&0xfffff000); - t_l = r-((t_h-(float)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; - GET_FLOAT_WORD(is,p_h); - SET_FLOAT_WORD(p_h,is&0xfffff000); - 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 = (float)n; - t1 = (((z_h+z_l)+dp_h[k])+t); - GET_FLOAT_WORD(is,t1); - SET_FLOAT_WORD(t1,is&0xfffff000); - t2 = z_l-(((t1-t)-dp_h[k])-z_h); + /* compute d1 = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + d1 = (ax-(double)bp[k])/(ax+(double)bp[k]); + /* compute d2 = log(ax) */ + d2 = d1 * d1; + d2 = 3.0 + d2 + d2*d2*(L1+d2*(L2+d2*(L3+d2*(L4+d2*(L5+d2*L6))))); + /* 2/(3log2)*(d2+...) */ + d2 = d1*d2*cp; + /* log2(ax) = (d2+..)*2/(3*log2) */ + d2 = d2+dp[k]+(double)n; } s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ 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) */ - GET_FLOAT_WORD(is,y); - SET_FLOAT_WORD(y1,is&0xfffff000); - p_l = (y-y1)*t1+y*t2; - p_h = y1*t1; - z = p_l+p_h; + /* compute y * d2 */ + d1 = y * d2; + z = d1; GET_FLOAT_WORD(j,z); if (__builtin_expect(j>0x43000000, 0)) /* if z > 128 */ return s*huge*huge; /* overflow */ else if (__builtin_expect(j==0x43000000, 0)) { /* if z == 128 */ - if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + if(ovt>(z-d1)) return s*huge*huge; /* overflow */ } else if (__builtin_expect((j&0x7fffffff)>0x43160000, 0))/* z <= -150 */ return s*tiny*tiny; /* underflow */ else if (__builtin_expect((u_int32_t) j==0xc3160000, 0)){/* z == -150*/ - if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + if(0.0<=(z-d1)) return s*tiny*tiny; /* underflow */ } /* - * compute 2**(p_h+p_l) + * compute 2**d1 */ i = j&0x7fffffff; k = (i>>23)-0x7f; @@ -228,22 +203,16 @@ __ieee754_powf(float x, float y) if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ n = j+(0x00800000>>(k+1)); k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ - SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + SET_FLOAT_WORD(z,n&~(0x007fffff>>k)); n = ((n&0x007fffff)|0x00800000)>>(23-k); if(j<0) n = -n; - p_h -= t; + d1 -= z; } - t = p_l+p_h; - GET_FLOAT_WORD(is,t); - SET_FLOAT_WORD(t,is&0xfffff000); - u = t*lg2_h; - v = (p_l-(t-p_h))*lg2+t*lg2_l; - z = u+v; - w = v-(z-u); - t = z*z; - t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); - r = (z*t1)/(t1-two)-(w+z*w); - z = one-(r-z); + d1 = d1 * lg2; + d2 = d1*d1; + d2 = d1 - d2*(P1+d2*(P2+d2*(P3+d2*(P4+d2*P5)))); + d2 = (d1*d2)/(d2-two); + z = one - (d2-d1); GET_FLOAT_WORD(j,z); j += (n<<23); if((j>>23)<=0) /* subnormal output */ |