/* * Copyright (c) 2002 Apple Computer, Inc. All rights reserved. * * @APPLE_LICENSE_HEADER_START@ * * Copyright (c) 1999-2003 Apple Computer, Inc. All Rights Reserved. * * This file contains Original Code and/or Modifications of Original Code * as defined in and that are subject to the Apple Public Source License * Version 2.0 (the 'License'). You may not use this file except in * compliance with the License. Please obtain a copy of the License at * http://www.opensource.apple.com/apsl/ and read it before using this * file. * * The Original Code and all software distributed under the License are * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. * Please see the License for the specific language governing rights and * limitations under the License. * * @APPLE_LICENSE_HEADER_END@ */ /******************************************************************************* * * * File atan2.c, * * Function atan2(y/x), * * Implementation of arc tangent of ( y / x ) for the PowerPC. * * * * Copyright c 1991-2001 Apple Computer, Inc. All rights reserved. * * * * Written by Ali Sazegari, started on November 1991, * * Modified and ported by Robert A. Murley (ram) for Mac OS X. * * * * A MathLib v4 file. * * * * December 03 1992: first rs6000 port. * * January 05 1993: added the environmental controls. * * July 07 1993: fixed the argument of __fpclassifyd. * * July 11 1993: changed feholdexcept to _feprocentry to set rounding * * to zero. removed the constant nan, fixed all edge * * cases to reflect the fpce-nceg requirements. * * September19 1994: changed all the environemntal enquiries to __setflm. * * October 06 1994: initialized CurrentEnvironment to correct an invalid * * flag problem. * * July 23 2001: replaced __setflm with fegetenvd/fesetenvd; * * replaced DblInHex typedef with hexdouble. * * September 07 2001: added #ifdef __ppc__. * * September 09 2001: added more comments. * * September 10 2001: added macros to detect PowerPC and correct compiler. * * September 18 2001: added <CoreServices/CoreServices.h> to get to <fp.h> * * and <fenv.h>. * * September 25 2001: removed fenv_access pragma. * * October 05 2001: added const double pi. * * October 08 2001: removed <CoreServices/CoreServices.h>. * * changed compiler errors to warnings. * * November 06 2001: commented out warning about Intel architectures. * * * * W A R N I N G: * * These routines require a 64-bit double precision IEEE-754 model. * * They are written for PowerPC only and are expecting the compiler * * to generate the correct sequence of multiply-add fused instructions. * * * * These routines are not intended for 32-bit Intel architectures. * * * * A version of gcc higher than 932 is required. * * * * GCC compiler options: * * optimization level 3 (-O3) * * -fschedule-insns -finline-functions -funroll-all-loops * * * *******************************************************************************/ #ifdef __APPLE_CC__ #if __APPLE_CC__ > 930 #include "math.h" #include "fenv_private.h" #include "fp_private.h" static const double pi = 3.141592653589793116e+00; /******************************************************************************* * Functions needed for the computation. * *******************************************************************************/ /* the following fp.h functions are used: */ /* atan, __fpclassifyd, copysign and __signbitd. */ /******************************************************************************* * This function is odd. The positive interval is computed and for * * negative values, the sign is reflected in the computation. * *******************************************************************************/ double atan2 ( double y, double x ) { register double result; hexdouble OldEnvironment, CurrentEnvironment; CurrentEnvironment.i.lo = 0; /******************************************************************************* * If argument is SNaN then a QNaN has to be returned and the invalid * * flag signaled. * *******************************************************************************/ if ( ( x != x ) || ( y != y ) ) return x + y; fegetenvd( OldEnvironment.d ); fesetenvd( 0.0 ); /******************************************************************************* * The next switch will decipher what sort of argument we have: * * * * atan2 ( ±0, x ) = ±0, if x > 0, * * atan2 ( ±0, +0) = ±0, * * atan2 ( ±0, x ) = ±¹, if x < 0, * * atan2 ( ±0, -0) = ±¹, * * atan2 ( y, ±0 ) = ¹/2, if y > 0, * * atan2 ( y, ±0 ) = -¹/2, if y < 0, * * atan2 ( ±y, ° ) = ±0, for finite y > 0, * * atan2 ( ±°, x ) = ±¹/2, for finite x, * * atan2 ( ±y, -°) = ±¹, for finite y > 0, * * atan2 ( ±°, ° ) = ±¹/4, * * atan2 ( ±°, -°) = ±3¹/4. * * * * note that the non obvious cases are y and x both infinite or both zero. * * for more information, see ÒBranch Cuts for Complex Elementary Functions, * * or much Much Ado About NothingÕs Sign bitÓ, by W. Kahan, Proceedings of * * the joint IMA/SIAM conference on The state of the Art in Numerical * * Analysis, 14-18 April 1986, Clarendon Press (1987). * * * * atan2(y,0) does not raise the divide-by-zero exception, nor does * * atan2(0,0) raise the invalid exception. * *******************************************************************************/ switch ( __fpclassifyd ( x ) ) { case FP_ZERO: CurrentEnvironment.i.lo |= FE_INEXACT; if ( y > 0.0 ) x = + 0.5 * pi; else if ( y < 0.0 ) x = - 0.5 * pi; else { if ( __signbitd ( x ) ) x = copysign ( pi, y ); else { CurrentEnvironment.i.lo &= ~FE_INEXACT; x = y; } } OldEnvironment.i.lo |= CurrentEnvironment.i.lo; fesetenvd( OldEnvironment.d ); return x; case FP_INFINITE: if ( x > 0.0 ) { if ( __isfinited ( y ) ) x = copysign ( 0.0, y ); else { CurrentEnvironment.i.lo |= FE_INEXACT; x = copysign ( 0.25 * pi, y ); } } else { CurrentEnvironment.i.lo |= FE_INEXACT; if ( __isfinited ( y ) ) x = copysign ( pi, y ); else x = copysign ( 0.75 * pi, y ); } OldEnvironment.i.lo |= CurrentEnvironment.i.lo; fesetenvd( OldEnvironment.d ); return x; default: break; } switch ( __fpclassifyd ( y ) ) { case FP_ZERO: if ( x > 0.0 ) x = y; else { CurrentEnvironment.i.lo |= FE_INEXACT; x = copysign ( pi, y ); } OldEnvironment.i.lo |= CurrentEnvironment.i.lo; fesetenvd( OldEnvironment.d ); return x; case FP_INFINITE: CurrentEnvironment.i.lo |= FE_INEXACT; x = copysign ( 0.5 * pi, y ); OldEnvironment.i.lo |= CurrentEnvironment.i.lo; fesetenvd( OldEnvironment.d ); return x; default: break; } /******************************************************************************* * End of the special case section. atan2 is mostly a collection of special * * case functions. Next we will carry out the main computation which at * * this point will only receive normal or denormal numbers. * *******************************************************************************/ result = atan ( __fabs ( y / x ) ); fegetenvd( CurrentEnvironment.d ); CurrentEnvironment.i.lo &= ~( FE_UNDERFLOW | FE_OVERFLOW ); if ( __signbitd ( x ) ) result = pi - result; switch ( __fpclassifyd ( result ) ) { case FP_SUBNORMAL: CurrentEnvironment.i.lo |= FE_UNDERFLOW; /* FALL THROUGH */ case FP_NORMAL: CurrentEnvironment.i.lo |= FE_INEXACT; /* FALL THROUGH */ default: break; } OldEnvironment.i.lo |= CurrentEnvironment.i.lo; fesetenvd( OldEnvironment.d ); return ( copysign ( result, y ) ); } #ifdef notdef float atan2f( float y, float x) { return (float)atan2( y, x ); } #endif #else /* __APPLE_CC__ version */ #warning A higher version than gcc-932 is required. #endif /* __APPLE_CC__ version */ #endif /* __APPLE_CC__ */