diff options
Diffstat (limited to 'usr/src/lib/libm/common/C/acos.c')
| -rw-r--r-- | usr/src/lib/libm/common/C/acos.c | 154 |
1 files changed, 154 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/C/acos.c b/usr/src/lib/libm/common/C/acos.c new file mode 100644 index 0000000000..523217a470 --- /dev/null +++ b/usr/src/lib/libm/common/C/acos.c @@ -0,0 +1,154 @@ +/* + * CDDL HEADER START + * + * The contents of this file are subject to the terms of the + * Common Development and Distribution License (the "License"). + * You may not use this file except in compliance with the License. + * + * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE + * or http://www.opensolaris.org/os/licensing. + * See the License for the specific language governing permissions + * and limitations under the License. + * + * When distributing Covered Code, include this CDDL HEADER in each + * file and include the License file at usr/src/OPENSOLARIS.LICENSE. + * If applicable, add the following below this CDDL HEADER, with the + * fields enclosed by brackets "[]" replaced with your own identifying + * information: Portions Copyright [yyyy] [name of copyright owner] + * + * CDDL HEADER END + */ + +/* + * Copyright 2011 Nexenta Systems, Inc. All rights reserved. + */ +/* + * Copyright 2006 Sun Microsystems, Inc. All rights reserved. + * Use is subject to license terms. + */ + +#pragma weak acos = __acos + +/* INDENT OFF */ +/* + * acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ +/* INDENT ON */ + +#include "libm_synonyms.h" /* __acos, __sqrt, __isnan */ +#include "libm_protos.h" /* _SVID_libm_error */ +#include "libm_macros.h" +#include <math.h> + +/* INDENT OFF */ +static const double xxx[] = { +/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ +/* pi */ 3.14159265358979311600e+00, /* 400921FB, 54442D18 */ +/* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */ +/* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */ +/* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */ +/* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */ +/* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */ +/* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */ +/* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */ +/* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */ +/* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */ +/* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */ +/* qS3 */ -6.88283971605453293030e-01, /* BFE6066C, 1B8D0159 */ +/* qS4 */ 7.70381505559019352791e-02 /* 3FB3B8C5, B12E9282 */ +}; +#define one xxx[0] +#define pi xxx[1] +#define pio2_hi xxx[2] +#define pio2_lo xxx[3] +#define pS0 xxx[4] +#define pS1 xxx[5] +#define pS2 xxx[6] +#define pS3 xxx[7] +#define pS4 xxx[8] +#define pS5 xxx[9] +#define qS1 xxx[10] +#define qS2 xxx[11] +#define qS3 xxx[12] +#define qS4 xxx[13] +/* INDENT ON */ + +double +acos(double x) { + double z, p, q, r, w, s, c, df; + int hx, ix; + + hx = ((int *) &x)[HIWORD]; + ix = hx & 0x7fffffff; + if (ix >= 0x3ff00000) { /* |x| >= 1 */ + if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) { + /* |x| == 1 */ + if (hx > 0) /* acos(1) = 0 */ + return (0.0); + else /* acos(-1) = pi */ + return (pi + 2.0 * pio2_lo); + } else if (isnan(x)) +#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) + return (ix >= 0x7ff80000 ? x : (x - x) / (x - x)); + /* assumes sparc-like QNaN */ +#else + return (x - x) / (x - x); /* acos(|x|>1) is NaN */ +#endif + else + return (_SVID_libm_err(x, x, 1)); + } + if (ix < 0x3fe00000) { /* |x| < 0.5 */ + if (ix <= 0x3c600000) + return (pio2_hi + pio2_lo); /* if |x| < 2**-57 */ + z = x * x; + p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + + z * (pS4 + z * pS5))))); + q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); + r = p / q; + return (pio2_hi - (x - (pio2_lo - x * r))); + } else if (hx < 0) { + /* x < -0.5 */ + z = (one + x) * 0.5; + p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + + z * (pS4 + z * pS5))))); + q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); + s = sqrt(z); + r = p / q; + w = r * s - pio2_lo; + return (pi - 2.0 * (s + w)); + } else { + /* x > 0.5 */ + z = (one - x) * 0.5; + s = sqrt(z); + df = s; + ((int *) &df)[LOWORD] = 0; + c = (z - df * df) / (s + df); + p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + + z * (pS4 + z * pS5))))); + q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); + r = p / q; + w = r * s + c; + return (2.0 * (df + w)); + } +} |