projects / unix-history / blame
| Commit | Line | Data |
|---|---|---|
| 3de6acd5 ZAL |
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[] = "@(#)acosh.c 1.1 (ELEFUNT) %G%"; | |
| 16 | #endif not lint | |
| 17 | ||
| 18 | /* ACOSH(X) | |
| 19 | * RETURN THE INVERSE HYPERBOLIC COSINE OF X | |
| 20 | * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) | |
| 21 | * CODED IN C BY K.C. NG, 2/16/85; | |
| 22 | * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85. | |
| 23 | * | |
| 24 | * Required system supported functions : | |
| 25 | * sqrt(x) | |
| 26 | * | |
| 27 | * Required kernel function: | |
| 28 | * log1p(x) ...return log(1+x) | |
| 29 | * | |
| 30 | * Method : | |
| 31 | * Based on | |
| 32 | * acosh(x) = log [ x + sqrt(x*x-1) ] | |
| 33 | * we have | |
| 34 | * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else | |
| 35 | * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . | |
| 36 | * These formulae avoid the over/underflow complication. | |
| 37 | * | |
| 38 | * Special cases: | |
| 39 | * acosh(x) is NaN with signal if x<1. | |
| 40 | * acosh(NaN) is NaN without signal. | |
| 41 | * | |
| 42 | * Accuracy: | |
| 43 | * acosh(x) returns the exact inverse hyperbolic cosine of x nearly | |
| 44 | * rounded. In a test run with 512,000 random arguments on a VAX, the | |
| 45 | * maximum observed error was 3.30 ulps (units of the last place) at | |
| 46 | * x=1.0070493753568216 . | |
| 47 | * | |
| 48 | * Constants: | |
| 49 | * The hexadecimal values are the intended ones for the following constants. | |
| 50 | * The decimal values may be used, provided that the compiler will convert | |
| 51 | * from decimal to binary accurately enough to produce the hexadecimal values | |
| 52 | * shown. | |
| 53 | */ | |
| 54 | ||
| 55 | #ifdef VAX /* VAX D format */ | |
| 56 | /* static double */ | |
| 57 | /* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ | |
| 58 | /* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */ | |
| 59 | static long ln2hix[] = { 0x72174031, 0x0000f7d0}; | |
| 60 | static long ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1}; | |
| 61 | #define ln2hi (*(double*)ln2hix) | |
| 62 | #define ln2lo (*(double*)ln2lox) | |
| 63 | #else /* IEEE double */ | |
| 64 | static double | |
| 65 | ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ | |
| 66 | ln2lo = 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */ | |
| 67 | #endif | |
| 68 | ||
| 69 | double acosh(x) | |
| 70 | double x; | |
| 71 | { | |
| 72 | double log1p(),sqrt(),t,big=1.E20; /* big+1==big */ | |
| 73 | ||
| 74 | #ifndef VAX | |
| 75 | if(x!=x) return(x); /* x is NaN */ | |
| 76 | #endif | |
| 77 | ||
| 78 | /* return log1p(x) + log(2) if x is large */ | |
| 79 | if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} | |
| 80 | ||
| 81 | t=sqrt(x-1.0); | |
| 82 | return(log1p(t*(t+sqrt(x+1.0)))); | |
| 83 | } |