+++ /dev/null
-/* @(#)e_exp.c 5.1 93/09/24 */\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
-#include <LibConfig.h>\r
-#include <sys/EfiCdefs.h>\r
-#if defined(LIBM_SCCS) && !defined(lint)\r
-__RCSID("$NetBSD: e_exp.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");\r
-#endif\r
-\r
-#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */\r
- // C4756: overflow in constant arithmetic\r
- #pragma warning ( disable : 4756 )\r
-#endif\r
-\r
-/* __ieee754_exp(x)\r
- * Returns the exponential of x.\r
- *\r
- * Method\r
- * 1. Argument reduction:\r
- * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.\r
- * Given x, find r and integer k such that\r
- *\r
- * x = k*ln2 + r, |r| <= 0.5*ln2.\r
- *\r
- * Here r will be represented as r = hi-lo for better\r
- * accuracy.\r
- *\r
- * 2. Approximation of exp(r) by a special rational function on\r
- * the interval [0,0.34658]:\r
- * Write\r
- * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...\r
- * We use a special Reme algorithm on [0,0.34658] to generate\r
- * a polynomial of degree 5 to approximate R. The maximum error\r
- * of this polynomial approximation is bounded by 2**-59. In\r
- * other words,\r
- * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5\r
- * (where z=r*r, and the values of P1 to P5 are listed below)\r
- * and\r
- * | 5 | -59\r
- * | 2.0+P1*z+...+P5*z - R(z) | <= 2\r
- * | |\r
- * The computation of exp(r) thus becomes\r
- * 2*r\r
- * exp(r) = 1 + -------\r
- * R - r\r
- * r*R1(r)\r
- * = 1 + r + ----------- (for better accuracy)\r
- * 2 - R1(r)\r
- * where\r
- * 2 4 10\r
- * R1(r) = r - (P1*r + P2*r + ... + P5*r ).\r
- *\r
- * 3. Scale back to obtain exp(x):\r
- * From step 1, we have\r
- * exp(x) = 2^k * exp(r)\r
- *\r
- * Special cases:\r
- * exp(INF) is INF, exp(NaN) is NaN;\r
- * exp(-INF) is 0, and\r
- * for finite argument, only exp(0)=1 is exact.\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
- * Misc. info.\r
- * For IEEE double\r
- * if x > 7.09782712893383973096e+02 then exp(x) overflow\r
- * if x < -7.45133219101941108420e+02 then exp(x) underflow\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
-\r
-static const double\r
-one = 1.0,\r
-halF[2] = {0.5,-0.5,},\r
-huge = 1.0e+300,\r
-twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/\r
-o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */\r
-u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */\r
-ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */\r
- -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */\r
-ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */\r
- -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */\r
-invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */\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
-\r
-\r
-double\r
-__ieee754_exp(double x) /* default IEEE double exp */\r
-{\r
- double y,hi,lo,c,t;\r
- int32_t k,xsb;\r
- u_int32_t hx;\r
-\r
- hi = lo = 0;\r
- k = 0;\r
- GET_HIGH_WORD(hx,x);\r
- xsb = (hx>>31)&1; /* sign bit of x */\r
- hx &= 0x7fffffff; /* high word of |x| */\r
-\r
- /* filter out non-finite argument */\r
- if(hx >= 0x40862E42) { /* if |x|>=709.78... */\r
- if(hx>=0x7ff00000) {\r
- u_int32_t lx;\r
- GET_LOW_WORD(lx,x);\r
- if(((hx&0xfffff)|lx)!=0)\r
- return x+x; /* NaN */\r
- else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */\r
- }\r
- if(x > o_threshold) return huge*huge; /* overflow */\r
- if(x < u_threshold) return twom1000*twom1000; /* underflow */\r
- }\r
-\r
- /* argument reduction */\r
- if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */\r
- if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */\r
- hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;\r
- } else {\r
- k = (int32_t)(invln2*x+halF[xsb]);\r
- t = k;\r
- hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */\r
- lo = t*ln2LO[0];\r
- }\r
- x = hi - lo;\r
- }\r
- else if(hx < 0x3e300000) { /* when |x|<2**-28 */\r
- if(huge+x>one) return one+x;/* trigger inexact */\r
- }\r
- else k = 0;\r
-\r
- /* x is now in primary range */\r
- t = x*x;\r
- c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));\r
- if(k==0) return one-((x*c)/(c-2.0)-x);\r
- else y = one-((lo-(x*c)/(2.0-c))-hi);\r
- if(k >= -1021) {\r
- u_int32_t hy;\r
- GET_HIGH_WORD(hy,y);\r
- SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */\r
- return y;\r
- } else {\r
- u_int32_t hy;\r
- GET_HIGH_WORD(hy,y);\r
- SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */\r
- return y*twom1000;\r
- }\r
-}\r
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