/* * Copyright (c) 2002 Apple Computer, Inc. All rights reserved. * * @APPLE_LICENSE_HEADER_START@ * * The contents of this file constitute Original Code as defined in and * are subject to the Apple Public Source License Version 1.1 (the * "License"). You may not use this file except in compliance with the * License. Please obtain a copy of the License at * http://www.apple.com/publicsource and read it before using this file. * * This 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 OR NON-INFRINGEMENT. Please see the * License for the specific language governing rights and limitations * under the License. * * @APPLE_LICENSE_HEADER_END@ */ /******************************************************************************* * * * File logb.c, * * Functions logb. * * Implementation of IEEE-754 logb for the PowerPC platforms. * * * * Copyright © 1991-2001 Apple Computer, Inc. All rights reserved. * * * * Written by A. Sazegari, started on June 1991. * * Modified and ported by Robert A. Murley (ram) for Mac OS X. * * * * A MathLib v4 file. * * * * Change History (most recent last): * * * * August 26 1991: removed CFront Version 1.1d17 warnings. * * August 27 1991: no errors reported by the test suite. * * November 11 1991: changed CLASSEXTENDED to the macro CLASSIFY and * * + or - infinity to constants. * * November 18 1991: changed the macro CLASSIFY to CLASSEXTENDEDint to * * improve performance. * * February 07 1992: changed bit operations to macros ( object size is * * unchanged ). * * September 24 1992: took the "#include support.h" out. * * December 03 1992: first rs/6000 port. * * August 30 1992: set the divide by zero for the zero argument case. * * October 05 1993: corrected the environment. * * October 17 1994: replaced all environmental functions with __setflm. * * May 28 1997: made speed improvements. * * April 30 2001: first mac os x port using gcc. * * July 16 2001: replaced __setflm with FEGETENVD/FESETENVD. * * August 28 2001: added description of logb function. * * September 06 2001: added #if __ppc__. * * September 09 2001: added more comments. * * September 10 2001: added macros to detect PowerPC and correct compiler. * * 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 * * * ******************************************************************************** * The C math library offers a similar function called "frexp". It is * * different in details from logb, but similar in spirit. This current * * implementation of logb follows the recommendation in IEEE Standard 854 * * which is different in its handling of denormalized numbers from the IEEE * * Standard 754. * *******************************************************************************/ #include "math.h" #include "fenv.h" #include "fp_private.h" #include "fenv_private.h" static const double twoTo52 = 0x1.0p+52; // 4.50359962737049600e15; static const double klTod = 4503601774854144.0; // 0x1.000008p52 static const hexdouble minusInf = HEXDOUBLE(0xfff00000, 0x00000000); static const float twoTo23 = 0x1.0p+23; // 8388608.0e0; static const hexsingle minusInff = { 0xff800000 }; /******************************************************************************* * L O G B * ******************************************************************************** * * * logb extracts the exponent of its argument, as a signed integral * * value. A subnormal argument is treated as though it were first * * normalized. Thus * * 1 <= x * 2^( - Logb ( x ) ) < 2 * *******************************************************************************/ double logb ( double x ) { hexdouble xInHex; int32_t shiftedExp; xInHex.d = x; __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; if (unlikely( shiftedExp == 2047 )) { // NaN or INF if ( ( ( xInHex.i.hi & 0x80000000 ) == 0 ) || ( x != x ) ) return x; // NaN or +INF return x else return -x; // -INF returns +INF } if (likely( shiftedExp != 0 )) // normal number shiftedExp -= 1023; // unbias exponent else if ( x == 0.0 ) { // zero hexdouble OldEnvironment; FEGETENVD_GRP( OldEnvironment.d ); // raise zero divide for DOMAIN error OldEnvironment.i.lo |= FE_DIVBYZERO; FESETENVD_GRP( OldEnvironment.d ); return ( minusInf.d ); // return -infinity } else { // subnormal number xInHex.d *= twoTo52; // scale up __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; shiftedExp -= 1075; // unbias exponent } if (unlikely( shiftedExp == 0 )) // zero result return ( 0.0 ); else { // nonzero result xInHex.d = klTod; __NOOP; __NOOP; __NOOP; xInHex.i.lo += shiftedExp; return ( xInHex.d - klTod ); } } int ilogb ( double x ) { hexdouble xInHex; int32_t shiftedExp; xInHex.d = x; __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; if (unlikely( shiftedExp == 2047 )) { // NaN or INF if (x != x) return FP_ILOGBNAN; else { feraiseexcept( FE_INVALID ); // raise invalid for DOMAIN error return INT32_MAX; } } if (likely( shiftedExp != 0 )) // normal number shiftedExp -= 1023; // unbias exponent else if ( x == 0.0 ) { // zero feraiseexcept( FE_INVALID ); // raise invalid for DOMAIN error return FP_ILOGB0; // return -infinity } else { // subnormal number xInHex.d *= twoTo52; // scale up __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.i.hi & 0x7ff00000 ) >> 20; shiftedExp -= 1075; // unbias exponent } return shiftedExp; } float logbf ( float x ) { hexsingle xInHex; int32_t shiftedExp; xInHex.fval = x; __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.lval & 0x7f800000 ) >> 23; if (unlikely( shiftedExp == 255 )) { // NaN or INF if ( ( ( xInHex.lval & 0x80000000 ) == 0 ) || ( x != x ) ) return x; // NaN or +INF return x else return -x; // -INF returns +INF } if (likely( shiftedExp != 0 )) // normal number shiftedExp -= 127; // unbias exponent else if ( x == 0.0 ) { // zero hexdouble OldEnvironment; FEGETENVD_GRP( OldEnvironment.d ); // raise zero divide for DOMAIN error OldEnvironment.i.lo |= FE_DIVBYZERO; FESETENVD_GRP( OldEnvironment.d ); return ( minusInff.fval ); // return -infinity } else { // subnormal number xInHex.fval *= twoTo23; // scale up __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.lval & 0x7f800000 ) >> 23; shiftedExp -= 150; // unbias exponent } return (float)shiftedExp; } int ilogbf ( float x ) { hexsingle xInHex; int32_t shiftedExp; xInHex.fval = x; __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.lval & 0x7f800000 ) >> 23; if (unlikely( shiftedExp == 255 )) { // NaN or INF if (x != x) return FP_ILOGBNAN; else { feraiseexcept( FE_INVALID ); // raise invalid for DOMAIN error return INT32_MAX; } } if (likely( shiftedExp != 0 )) // normal number shiftedExp -= 127; // unbias exponent else if ( x == 0.0 ) { // zero feraiseexcept( FE_INVALID ); // raise invalid for DOMAIN error return FP_ILOGB0; // return -infinity } else { // subnormal number xInHex.fval *= twoTo23; // scale up __NOOP; __NOOP; __NOOP; shiftedExp = ( xInHex.lval & 0x7f800000 ) >> 23; shiftedExp -= 150; // unbias exponent } return shiftedExp; }