library/math_asin.c
/*
* $Id: math_asin.c,v 1.7 2006-01-08 12:04:23 obarthel Exp $
*
* :ts=4
*
* Portable ISO 'C' (1994) runtime library for the Amiga computer
* Copyright (c) 2002-2015 by Olaf Barthel <obarthel (at) gmx.net>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* - Neither the name of Olaf Barthel nor the names of contributors
* may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
*/
#ifndef _MATH_HEADERS_H
#include "math_headers.h"
#endif /* _MATH_HEADERS_H */
/****************************************************************************/
#if defined(FLOATING_POINT_SUPPORT)
/****************************************************************************/
#if defined(IEEE_FLOATING_POINT_SUPPORT)
/****************************************************************************/
#if defined(__GNUC__)
/****************************************************************************/
#if defined(SMALL_DATA)
#define A4(x) "a4@(" #x ":W)"
#elif defined(SMALL_DATA32)
#define A4(x) "a4@(" #x ":L)"
#else
#define A4(x) #x
#endif /* SMALL_DATA */
/****************************************************************************/
double __asin(double x);
/****************************************************************************/
asm("
.text
.even
.globl _MathIeeeDoubTransBase
.globl ___asin
___asin:
movel a6,sp@-
movel "A4(_MathIeeeDoubTransBase)",a6
moveml sp@(8),d0/d1
jsr a6@(-114:W)
movel sp@+,a6
rts
");
/****************************************************************************/
#else
/****************************************************************************/
INLINE STATIC const double
__asin(double x)
{
double result;
result = IEEEDPAsin(x);
return(result);
}
/****************************************************************************/
#endif /* __GNUC__ */
/****************************************************************************/
#endif /* IEEE_FLOATING_POINT_SUPPORT */
/****************************************************************************/
#if defined(M68881_FLOATING_POINT_SUPPORT)
INLINE STATIC const double
__asin(double x)
{
double result;
__asm ("fasin%.x %1,%0"
: "=f" (result)
: "f" (x));
return(result);
}
#endif /* M68881_FLOATING_POINT_SUPPORT */
/****************************************************************************/
#if defined(PPC_FLOATING_POINT_SUPPORT)
static const double
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
huge = 1.000e+300,
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
INLINE STATIC double
__asin(double x)
{
double t,w,p,q,c,r,s;
int hx,ix;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>= 0x3ff00000) /* |x|>= 1 */
{
unsigned int lx;
GET_LOW_WORD(lx,x);
if(((ix-0x3ff00000)|lx)==0) /* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
}
else if (ix<0x3fe00000) /* |x|<0.5 */
{
if(ix<0x3e400000) /* if |x| < 2**-27 */
{
if(huge+x>one)
return x; /* return x with inexact if x!=0*/
}
else
{
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
}
/* 1> |x|>= 0.5 */
w = one-fabs(x);
t = w*0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = sqrt(t);
if(ix>=0x3FEF3333) /* if |x| > 0.975 */
{
w = p/q;
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
}
else
{
w = s;
SET_LOW_WORD(w,0);
c = (t-w*w)/(s+w);
r = p/q;
p = 2.0*s*r-(pio2_lo-2.0*c);
q = pio4_hi-2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0)
return t;
else
return -t;
}
#endif /* PPC_FLOATING_POINT_SUPPORT */
/****************************************************************************/
double
asin(double x)
{
double result;
if(-1.0 <= x && x <= 1.0)
{
result = __asin(x);
}
else
{
result = 0;
__set_errno(EDOM);
}
return(result);
}
/****************************************************************************/
#endif /* FLOATING_POINT_SUPPORT */