+++ /dev/null
-/** @file\r
- Compute the 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_log.c 5.1 93/09/24\r
- NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp\r
-**/\r
-#include <LibConfig.h>\r
-#include <sys/EfiCdefs.h>\r
-\r
-#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */\r
- // potential divide by 0 -- near line 118, (x-x)/zero is on purpose\r
- #pragma warning ( disable : 4723 )\r
-#endif\r
-\r
-/* __ieee754_log(x)\r
- * Return the logrithm of x\r
- *\r
- * Method :\r
- * 1. Argument Reduction: find k and f such that\r
- * x = 2^k * (1+f),\r
- * where sqrt(2)/2 < 1+f < sqrt(2) .\r
- *\r
- * 2. Approximation of log(1+f).\r
- * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)\r
- * = 2s + 2/3 s**3 + 2/5 s**5 + .....,\r
- * = 2s + s*R\r
- * We use a special Reme algorithm on [0,0.1716] to generate\r
- * a polynomial of degree 14 to approximate R The maximum error\r
- * of this polynomial approximation is bounded by 2**-58.45. In\r
- * other words,\r
- * 2 4 6 8 10 12 14\r
- * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s\r
- * (the values of Lg1 to Lg7 are listed in the program)\r
- * and\r
- * | 2 14 | -58.45\r
- * | Lg1*s +...+Lg7*s - R(z) | <= 2\r
- * | |\r
- * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.\r
- * In order to guarantee error in log below 1ulp, we compute log\r
- * by\r
- * log(1+f) = f - s*(f - R) (if f is not too large)\r
- * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)\r
- *\r
- * 3. Finally, log(x) = k*ln2 + log(1+f).\r
- * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))\r
- * Here ln2 is split into two floating point number:\r
- * ln2_hi + ln2_lo,\r
- * where n*ln2_hi is always exact for |n| < 2000.\r
- *\r
- * Special cases:\r
- * log(x) is NaN with signal if x < 0 (including -INF) ;\r
- * log(+INF) is +INF; log(0) is -INF with signal;\r
- * log(NaN) is that NaN with no signal.\r
- *\r
- * Accuracy:\r
- * according to an error analysis, the error is always less than\r
- * 1 ulp (unit in the last place).\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
-ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */\r
-ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */\r
-two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */\r
-Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */\r
-Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */\r
-Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */\r
-Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */\r
-Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */\r
-Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */\r
-Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */\r
-\r
-static const double zero = 0.0;\r
-\r
-double\r
-__ieee754_log(double x)\r
-{\r
- double hfsq,f,s,z,R,w,t1,t2,dk;\r
- int32_t k,hx,i,j;\r
- u_int32_t lx;\r
-\r
- EXTRACT_WORDS(hx,lx,x);\r
-\r
- k=0;\r
- if (hx < 0x00100000) { /* x < 2**-1022 */\r
- if (((hx&0x7fffffff)|lx)==0)\r
- return -two54/zero; /* log(+-0)=-inf */\r
- if (hx<0) {\r
- errno = EDOM;\r
- return (x-x)/zero; /* log(-#) = NaN */\r
- }\r
- k -= 54; x *= two54; /* subnormal number, scale up x */\r
- GET_HIGH_WORD(hx,x);\r
- }\r
- if (hx >= 0x7ff00000) return x+x;\r
- k += (hx>>20)-1023;\r
- hx &= 0x000fffff;\r
- i = (hx+0x95f64)&0x100000;\r
- SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */\r
- k += (i>>20);\r
- f = x-1.0;\r
- if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */\r
- if(f==zero) { if(k==0) return zero; else {dk=(double)k;\r
- return dk*ln2_hi+dk*ln2_lo;}\r
- }\r
- R = f*f*(0.5-0.33333333333333333*f);\r
- if(k==0) return f-R; else {dk=(double)k;\r
- return dk*ln2_hi-((R-dk*ln2_lo)-f);}\r
- }\r
- s = f/(2.0+f);\r
- dk = (double)k;\r
- z = s*s;\r
- i = hx-0x6147a;\r
- w = z*z;\r
- j = 0x6b851-hx;\r
- t1= w*(Lg2+w*(Lg4+w*Lg6));\r
- t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));\r
- i |= j;\r
- R = t2+t1;\r
- if(i>0) {\r
- hfsq=0.5*f*f;\r
- if(k==0) return f-(hfsq-s*(hfsq+R)); else\r
- return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);\r
- } else {\r
- if(k==0) return f-s*(f-R); else\r
- return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);\r
- }\r
-}\r
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