* Copyright (c) 1985 Regents of the University of California.
* %sccs.include.redist.c%
static char sccsid
[] = "@(#)exp.c 5.6 (Berkeley) %G%";
* RETURN THE EXPONENTIAL OF X
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
* CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
* Required system supported functions:
* 1. Argument Reduction: given the input x, find r and integer k such
* x = k*ln2 + r, |r| <= 0.5*ln2 .
* r will be represented as r := z+c for better accuracy.
* exp(r) = 1 + r + r*R1/(2-R1),
* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
* 3. exp(x) = 2^k * exp(r) .
* exp(INF) is INF, exp(NaN) is NaN;
* for finite argument, only exp(0)=1 is exact.
* exp(x) returns the exponential of x nearly rounded. In a test run
* with 1,156,000 random arguments on a VAX, the maximum observed
* error was 0.869 ulps (units in the last place).
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
vc(ln2hi
, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0
, 0, .B17217F7D00000
)
vc(ln2lo
, 1.6465949582897081279E-12 ,bcd5
,2ce7
,d9cc
,e4f1
, -39, .E7BCD5E4F1D9CC
)
vc(lnhuge
, 9.4961163736712506989E1
,ec1d
,43bd
,9010,a73e
, 7, .BDEC1DA73E9010
)
vc(lntiny
,-9.5654310917272452386E1
,4f01
,c3bf
,33af
,d72e
, 7,-.BF4F01D72E33AF
)
vc(invln2
, 1.4426950408889634148E0
,aa3b
,40b8
,17f1
,295c
, 1, .B8AA3B295C17F1
)
vc(p1
, 1.6666666666666602251E-1 ,aaaa
,3f2a
,a9f1
,aaaa
, -2, .AAAAAAAAAAA9F1
)
vc(p2
, -2.7777777777015591216E-3 ,0b60,bc36
,ec94
,b5f5
, -8,-.B60B60B5F5EC94
)
vc(p3
, 6.6137563214379341918E-5 ,b355
,398a
,f15f
,792e
, -13, .8AB355792EF15F
)
vc(p4
, -1.6533902205465250480E-6 ,ea0e
,b6dd
,5f84
,2e93
, -19,-.DDEA0E2E935F84
)
vc(p5
, 4.1381367970572387085E-8 ,bb4b
,3431,2683,95f5
, -24, .B1BB4B95F52683
)
#define ln2hi vccast(ln2hi)
#define ln2lo vccast(ln2lo)
#define lnhuge vccast(lnhuge)
#define lntiny vccast(lntiny)
#define invln2 vccast(invln2)
ic(p1
, 1.6666666666666601904E-1, -3, 1.555555555553E
)
ic(p2
, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93
)
ic(p3
, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C
)
ic(p4
, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1
)
ic(p5
, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0
)
ic(ln2hi
, 6.9314718036912381649E-1, -1, 1.62E42FEE00000
)
ic(ln2lo
, 1.9082149292705877000E-10,-33, 1.A39EF35793C76
)
ic(lnhuge
, 7.1602103751842355450E2
, 9, 1.6602B15B7ECF2
)
ic(lntiny
,-7.5137154372698068983E2
, 9, -1.77AF8EBEAE354
)
ic(invln2
, 1.4426950408889633870E0
, 0, 1.71547652B82FE
)
#if !defined(vax)&&!defined(tahoe)
if(x
!=x
) return(x
); /* x is NaN */
#endif /* !defined(vax)&&!defined(tahoe) */
/* argument reduction : x --> x - k*ln2 */
k
=invln2
*x
+copysign(0.5,x
); /* k=NINT(x/ln2) */
/* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
/* return 2^k*[1+x+x*c/(2+c)] */
c
= x
- z
*(p1
+z
*(p2
+z
*(p3
+z
*(p4
+z
*p5
))));
return scalb(1.0+(hi
-(lo
-(x
*c
)/(2.0-c
))),k
);
/* exp(-big#) underflows to zero */
if(finite(x
)) return(scalb(1.0,-5000));
/* exp(INF) is INF, exp(+big#) overflows to INF */
return( finite(x
) ? scalb(1.0,5000) : x
);