* Copyright (c) 1985 Regents of the University of California.
* Use and reproduction of this software are granted in accordance with
* the terms and conditions specified in the Berkeley Software License
* Agreement (in particular, this entails acknowledgement of the programs'
* source, and inclusion of this notice) with the additional understanding
* that all recipients should regard themselves as participants in an
* ongoing research project and hence should feel obligated to report
* their experiences (good or bad) with these elementary function codes,
* using "sendbug 4bsd-bugs@BERKELEY", to the authors.
"@(#)sinh.c 4.3 (Berkeley) 8/21/85; 1.5 (ucb.elefunt) %G%";
* RETURN THE HYPERBOLIC SINE OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
* Required system supported functions :
* Required kernel functions:
* expm1(x) ...return exp(x)-1
* 1. reduce x to non-negative by sinh(-x) = - sinh(x).
* expm1(x) + expm1(x)/(expm1(x)+1)
* 0 <= x <= lnovfl : sinh(x) := --------------------------------
* lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
* lnovfl+ln2 < x < INF : overflow to INF
* sinh(x) is x if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite argument.
* sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
* a test run with 1,024,000 random arguments on a VAX, the maximum
* observed error was 1.93 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
#if (defined(VAX)||defined(TAHOE))
#define _0x(A,B) 0x/**/A/**/B
#define _0x(A,B) 0x/**/B/**/A
/* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */
/* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */
/* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */
static long mln2hix
[] = { _0x(0f33
,43b0
), _0x(2bdb
,c7e2
)};
static long mln2lox
[] = { _0x(1b60
,a70f
), _0x(582a
,279e
)};
static long lnovflx
[] = { _0x(0f33
,43b0
), _0x(2bda
,c7e2
)};
#define mln2hi (*(double*)mln2hix)
#define mln2lo (*(double*)mln2lox)
#define lnovfl (*(double*)lnovflx)
mln2hi
= 7.0978271289338397310E2
, /*Hex 2^ 10 * 1.62E42FEFA39EF */
mln2lo
= 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */
lnovfl
= 7.0978271289338397310E2
; /*Hex 2^ 9 * 1.62E42FEFA39EF */
#if (defined(VAX)||defined(TAHOE))
static double one
=1.0, half
=1.0/2.0 ;
double expm1(), t
, scalb(), copysign(), sign
;
#if (!defined(VAX)&&!defined(TAHOE))
if(x
!=x
) return(x
); /* x is NaN */
{t
=expm1(x
); return(copysign((t
+t
/(one
+t
))*half
,sign
));}
/* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
to avoid unnecessary overflow */
return(copysign(scalb(one
+expm1((x
-mln2hi
)-mln2lo
),max
),sign
));
else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */