+++ /dev/null
-/** @file\r
- Compute the base 10 logrithm of x.\r
-\r
- Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>\r
- This program and the accompanying materials are licensed and made available under\r
- the terms and conditions of the BSD License that accompanies this distribution.\r
- The full text of the license may be found at\r
- http://opensource.org/licenses/bsd-license.\r
-\r
- THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,\r
- WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.\r
-\r
- * ====================================================\r
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r
- *\r
- * Developed at SunPro, a Sun Microsystems, Inc. business.\r
- * Permission to use, copy, modify, and distribute this\r
- * software is freely granted, provided that this notice\r
- * is preserved.\r
- * ====================================================\r
-\r
- e_pow.c 5.1 93/09/24\r
- NetBSD: e_pow.c,v 1.13 2004/06/30 18:43:15 drochner Exp\r
-**/\r
-#include <LibConfig.h>\r
-#include <sys/EfiCdefs.h>\r
-\r
-#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */\r
- // C4723: potential divide by zero.\r
- #pragma warning ( disable : 4723 )\r
- // C4756: overflow in constant arithmetic\r
- #pragma warning ( disable : 4756 )\r
-#endif\r
-\r
-/* __ieee754_pow(x,y) return x**y\r
- *\r
- * n\r
- * Method: Let x = 2 * (1+f)\r
- * 1. Compute and return log2(x) in two pieces:\r
- * log2(x) = w1 + w2,\r
- * where w1 has 53-24 = 29 bit trailing zeros.\r
- * 2. Perform y*log2(x) = n+y' by simulating multi-precision\r
- * arithmetic, where |y'|<=0.5.\r
- * 3. Return x**y = 2**n*exp(y'*log2)\r
- *\r
- * Special cases:\r
- * 1. (anything) ** 0 is 1\r
- * 2. (anything) ** 1 is itself\r
- * 3. (anything) ** NAN is NAN\r
- * 4. NAN ** (anything except 0) is NAN\r
- * 5. +-(|x| > 1) ** +INF is +INF\r
- * 6. +-(|x| > 1) ** -INF is +0\r
- * 7. +-(|x| < 1) ** +INF is +0\r
- * 8. +-(|x| < 1) ** -INF is +INF\r
- * 9. +-1 ** +-INF is NAN\r
- * 10. +0 ** (+anything except 0, NAN) is +0\r
- * 11. -0 ** (+anything except 0, NAN, odd integer) is +0\r
- * 12. +0 ** (-anything except 0, NAN) is +INF\r
- * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF\r
- * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )\r
- * 15. +INF ** (+anything except 0,NAN) is +INF\r
- * 16. +INF ** (-anything except 0,NAN) is +0\r
- * 17. -INF ** (anything) = -0 ** (-anything)\r
- * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)\r
- * 19. (-anything except 0 and inf) ** (non-integer) is NAN\r
- *\r
- * Accuracy:\r
- * pow(x,y) returns x**y nearly rounded. In particular\r
- * pow(integer,integer)\r
- * always returns the correct integer provided it is\r
- * representable.\r
- *\r
- * Constants :\r
- * The hexadecimal values are the intended ones for the following\r
- * constants. The decimal values may be used, provided that the\r
- * compiler will convert from decimal to binary accurately enough\r
- * to produce the hexadecimal values shown.\r
- */\r
-\r
-#include "math.h"\r
-#include "math_private.h"\r
-#include <errno.h>\r
-\r
-static const double\r
-bp[] = {1.0, 1.5,},\r
-dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */\r
-dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */\r
-zero = 0.0,\r
-one = 1.0,\r
-two = 2.0,\r
-two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */\r
-huge = 1.0e300,\r
-tiny = 1.0e-300,\r
- /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */\r
-L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */\r
-L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */\r
-L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */\r
-L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */\r
-L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */\r
-L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */\r
-P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */\r
-P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */\r
-P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */\r
-P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */\r
-P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */\r
-lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */\r
-lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */\r
-lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */\r
-ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */\r
-cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */\r
-cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */\r
-cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/\r
-ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */\r
-ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/\r
-ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/\r
-\r
-double\r
-__ieee754_pow(double x, double y)\r
-{\r
- double z,ax,z_h,z_l,p_h,p_l;\r
- double y1,t1,t2,r,s,t,u,v,w;\r
- int32_t i,j,k,yisint,n;\r
- int32_t hx,hy,ix,iy;\r
- u_int32_t lx,ly;\r
-\r
- EXTRACT_WORDS(hx,lx,x);\r
- EXTRACT_WORDS(hy,ly,y);\r
- ix = hx&0x7fffffff; iy = hy&0x7fffffff;\r
-\r
- /* y==zero: x**0 = 1 */\r
- if((iy|ly)==0) return one;\r
-\r
- /* +-NaN return x+y */\r
- if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||\r
- iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))\r
- return x+y;\r
-\r
- /* determine if y is an odd int when x < 0\r
- * yisint = 0 ... y is not an integer\r
- * yisint = 1 ... y is an odd int\r
- * yisint = 2 ... y is an even int\r
- */\r
- yisint = 0;\r
- if(hx<0) {\r
- if(iy>=0x43400000) yisint = 2; /* even integer y */\r
- else if(iy>=0x3ff00000) {\r
- k = (iy>>20)-0x3ff; /* exponent */\r
- if(k>20) {\r
- j = ly>>(52-k);\r
- if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1);\r
- } else if(ly==0) {\r
- j = iy>>(20-k);\r
- if((j<<(20-k))==iy) yisint = 2-(j&1);\r
- }\r
- }\r
- }\r
-\r
- /* special value of y */\r
- if(ly==0) {\r
- if (iy==0x7ff00000) { /* y is +-inf */\r
- if(((ix-0x3ff00000)|lx)==0)\r
- return y - y; /* inf**+-1 is NaN */\r
- else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */\r
- return (hy>=0)? y: zero;\r
- else /* (|x|<1)**-,+inf = inf,0 */\r
- return (hy<0)?-y: zero;\r
- }\r
- if(iy==0x3ff00000) { /* y is +-1 */\r
- if(hy<0) return one/x; else return x;\r
- }\r
- if(hy==0x40000000) return x*x; /* y is 2 */\r
- if(hy==0x3fe00000) { /* y is 0.5 */\r
- if(hx>=0) /* x >= +0 */\r
- return __ieee754_sqrt(x);\r
- }\r
- }\r
-\r
- ax = fabs(x);\r
- /* special value of x */\r
- if(lx==0) {\r
- if(ix==0x7ff00000||ix==0||ix==0x3ff00000){\r
- z = ax; /*x is +-0,+-inf,+-1*/\r
- if(hy<0) z = one/z; /* z = (1/|x|) */\r
- if(hx<0) {\r
- if(((ix-0x3ff00000)|yisint)==0) {\r
- z = (z-z)/(z-z); /* (-1)**non-int is NaN */\r
- } else if(yisint==1)\r
- z = -z; /* (x<0)**odd = -(|x|**odd) */\r
- }\r
- return z;\r
- }\r
- }\r
-\r
- n = (hx>>31)+1;\r
-\r
- /* (x<0)**(non-int) is NaN */\r
- if((n|yisint)==0) {\r
- errno = EDOM;\r
- return (x-x)/(x-x);\r
- }\r
-\r
- s = one; /* s (sign of result -ve**odd) = -1 else = 1 */\r
- if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */\r
-\r
- /* |y| is huge */\r
- if(iy>0x41e00000) { /* if |y| > 2**31 */\r
- if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */\r
- if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;\r
- if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;\r
- }\r
- /* over/underflow if x is not close to one */\r
- if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;\r
- if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;\r
- /* now |1-x| is tiny <= 2**-20, suffice to compute\r
- log(x) by x-x^2/2+x^3/3-x^4/4 */\r
- t = ax-one; /* t has 20 trailing zeros */\r
- w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));\r
- u = ivln2_h*t; /* ivln2_h has 21 sig. bits */\r
- v = t*ivln2_l-w*ivln2;\r
- t1 = u+v;\r
- SET_LOW_WORD(t1,0);\r
- t2 = v-(t1-u);\r
- } else {\r
- double ss,s2,s_h,s_l,t_h,t_l;\r
- n = 0;\r
- /* take care subnormal number */\r
- if(ix<0x00100000)\r
- {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }\r
- n += ((ix)>>20)-0x3ff;\r
- j = ix&0x000fffff;\r
- /* determine interval */\r
- ix = j|0x3ff00000; /* normalize ix */\r
- if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */\r
- else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */\r
- else {k=0;n+=1;ix -= 0x00100000;}\r
- SET_HIGH_WORD(ax,ix);\r
-\r
- /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */\r
- u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */\r
- v = one/(ax+bp[k]);\r
- ss = u*v;\r
- s_h = ss;\r
- SET_LOW_WORD(s_h,0);\r
- /* t_h=ax+bp[k] High */\r
- t_h = zero;\r
- SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));\r
- t_l = ax - (t_h-bp[k]);\r
- s_l = v*((u-s_h*t_h)-s_h*t_l);\r
- /* compute log(ax) */\r
- s2 = ss*ss;\r
- r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));\r
- r += s_l*(s_h+ss);\r
- s2 = s_h*s_h;\r
- t_h = 3.0+s2+r;\r
- SET_LOW_WORD(t_h,0);\r
- t_l = r-((t_h-3.0)-s2);\r
- /* u+v = ss*(1+...) */\r
- u = s_h*t_h;\r
- v = s_l*t_h+t_l*ss;\r
- /* 2/(3log2)*(ss+...) */\r
- p_h = u+v;\r
- SET_LOW_WORD(p_h,0);\r
- p_l = v-(p_h-u);\r
- z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */\r
- z_l = cp_l*p_h+p_l*cp+dp_l[k];\r
- /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */\r
- t = (double)n;\r
- t1 = (((z_h+z_l)+dp_h[k])+t);\r
- SET_LOW_WORD(t1,0);\r
- t2 = z_l-(((t1-t)-dp_h[k])-z_h);\r
- }\r
-\r
- /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */\r
- y1 = y;\r
- SET_LOW_WORD(y1,0);\r
- p_l = (y-y1)*t1+y*t2;\r
- p_h = y1*t1;\r
- z = p_l+p_h;\r
- EXTRACT_WORDS(j,i,z);\r
- if (j>=0x40900000) { /* z >= 1024 */\r
- if(((j-0x40900000)|i)!=0) /* if z > 1024 */\r
- return s*huge*huge; /* overflow */\r
- else {\r
- if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */\r
- }\r
- } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */\r
- if(((j-0xc090cc00)|i)!=0) /* z < -1075 */\r
- return s*tiny*tiny; /* underflow */\r
- else {\r
- if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */\r
- }\r
- }\r
- /*\r
- * compute 2**(p_h+p_l)\r
- */\r
- i = j&0x7fffffff;\r
- k = (i>>20)-0x3ff;\r
- n = 0;\r
- if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */\r
- n = j+(0x00100000>>(k+1));\r
- k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */\r
- t = zero;\r
- SET_HIGH_WORD(t,n&~(0x000fffff>>k));\r
- n = ((n&0x000fffff)|0x00100000)>>(20-k);\r
- if(j<0) n = -n;\r
- p_h -= t;\r
- }\r
- t = p_l+p_h;\r
- SET_LOW_WORD(t,0);\r
- u = t*lg2_h;\r
- v = (p_l-(t-p_h))*lg2+t*lg2_l;\r
- z = u+v;\r
- w = v-(z-u);\r
- t = z*z;\r
- t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));\r
- r = (z*t1)/(t1-two)-(w+z*w);\r
- z = one-(r-z);\r
- GET_HIGH_WORD(j,z);\r
- j += (n<<20);\r
- if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */\r
- else SET_HIGH_WORD(z,j);\r
- return s*z;\r
-}\r
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