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Annotation of 43BSD/usr.lib/libm/sinh.c, revision 1.1.1.1

1.1       root        1: /* 
                      2:  * Copyright (c) 1985 Regents of the University of California.
                      3:  * 
                      4:  * Use and reproduction of this software are granted  in  accordance  with
                      5:  * the terms and conditions specified in  the  Berkeley  Software  License
                      6:  * Agreement (in particular, this entails acknowledgement of the programs'
                      7:  * source, and inclusion of this notice) with the additional understanding
                      8:  * that  all  recipients  should regard themselves as participants  in  an
                      9:  * ongoing  research  project and hence should  feel  obligated  to report
                     10:  * their  experiences (good or bad) with these elementary function  codes,
                     11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
                     12:  */
                     13: 
                     14: #ifndef lint
                     15: static char sccsid[] = "@(#)sinh.c     4.3 (Berkeley) 8/21/85";
                     16: #endif not lint
                     17: 
                     18: /* SINH(X)
                     19:  * RETURN THE HYPERBOLIC SINE OF X
                     20:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
                     21:  * CODED IN C BY K.C. NG, 1/8/85; 
                     22:  * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
                     23:  *
                     24:  * Required system supported functions :
                     25:  *     copysign(x,y)
                     26:  *     scalb(x,N)
                     27:  *
                     28:  * Required kernel functions:
                     29:  *     expm1(x)        ...return exp(x)-1
                     30:  *
                     31:  * Method :
                     32:  *     1. reduce x to non-negative by sinh(-x) = - sinh(x).
                     33:  *     2. 
                     34:  *
                     35:  *                                           expm1(x) + expm1(x)/(expm1(x)+1)
                     36:  *         0 <= x <= lnovfl     : sinh(x) := --------------------------------
                     37:  *                                                           2
                     38:  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
                     39:  * lnovfl+ln2 <  x <  INF        :  overflow to INF
                     40:  *     
                     41:  *
                     42:  * Special cases:
                     43:  *     sinh(x) is x if x is +INF, -INF, or NaN.
                     44:  *     only sinh(0)=0 is exact for finite argument.
                     45:  *
                     46:  * Accuracy:
                     47:  *     sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
                     48:  *     a test run with 1,024,000 random arguments on a VAX, the maximum
                     49:  *     observed error was 1.93 ulps (units in the last place).
                     50:  *
                     51:  * Constants:
                     52:  * The hexadecimal values are the intended ones for the following constants.
                     53:  * The decimal values may be used, provided that the compiler will convert
                     54:  * from decimal to binary accurately enough to produce the hexadecimal values
                     55:  * shown.
                     56:  */
                     57: #ifdef VAX
                     58: /* double static */
                     59: /* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
                     60: /* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
                     61: /* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
                     62: static long    mln2hix[] = { 0x0f3343b0, 0x2bdbc7e2};
                     63: static long    mln2lox[] = { 0x1b60a70f, 0x582a279e};
                     64: static long    lnovflx[] = { 0x0f3343b0, 0x2bdac7e2};
                     65: #define   mln2hi    (*(double*)mln2hix)
                     66: #define   mln2lo    (*(double*)mln2lox)
                     67: #define   lnovfl    (*(double*)lnovflx)
                     68: #else  /* IEEE double */
                     69: double static 
                     70: mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
                     71: mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
                     72: lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
                     73: #endif
                     74: 
                     75: #ifdef VAX
                     76: static max = 126                      ;
                     77: #else  /* IEEE double */
                     78: static max = 1023                     ;
                     79: #endif
                     80: 
                     81: 
                     82: double sinh(x)
                     83: double x;
                     84: {
                     85:        static double  one=1.0, half=1.0/2.0 ;
                     86:        double expm1(), t, scalb(), copysign(), sign;
                     87: #ifndef VAX
                     88:        if(x!=x) return(x);     /* x is NaN */
                     89: #endif
                     90:        sign=copysign(one,x);
                     91:        x=copysign(x,one);
                     92:        if(x<lnovfl)
                     93:            {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
                     94: 
                     95:        else if(x <= lnovfl+0.7)
                     96:                /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 
                     97:                        to avoid unnecessary overflow */
                     98:            return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
                     99: 
                    100:        else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
                    101:            return( expm1(x)*sign );
                    102: }

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