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) 08/21/85"; 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 } 103