/* * $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 * 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\n" " .even\n" " .globl _MathIeeeDoubTransBase\n" " .globl ___asin\n" "___asin:\n" " movel a6,sp@-\n" " movel "A4(_MathIeeeDoubTransBase)",a6\n" " moveml sp@(8),d0/d1\n" " jsr a6@(-114:W)\n" " movel sp@+,a6\n" " rts\n" ); /****************************************************************************/ #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 */