/* $XConsortium: ieee.c,v 1.5 94/04/17 20:18:24 rws Exp $ */ /****************************************************************************** NOTICE This software is being provided by AGE Logic, Inc. under the following license. By obtaining, using and/or copying this software, you agree that you have read, understood, and will comply with these terms and conditions: Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose and without fee or royalty and to grant others any or all rights granted herein is hereby granted, provided that you agree to comply with the following copyright notice and statements, including the disclaimer, and that the same appears on all copies and derivative works of the software and documentation you make. "Copyright 1993 by AGE Logic, Inc. THIS SOFTWARE IS PROVIDED "AS IS". AGE LOGIC MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED. By way of example, but not limitation, AGE LOGIC MAKES NO REPRESENTATIONS OR WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OR THAT THE SOFTWARE DOES NOT INFRINGE THIRD-PARTY PROPRIETARY RIGHTS. AGE LOGIC SHALL BEAR NO LIABILITY FOR ANY USE OF THIS SOFTWARE. IN NO EVENT SHALL EITHER PARTY BE LIABLE FOR ANY INDIRECT, INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES, INCLUDING LOSS OF PROFITS, REVENUE, DATA OR USE, INCURRED BY EITHER PARTY OR ANY THIRD PARTY, WHETHER IN AN ACTION IN CONTRACT OR TORT OR BASED ON A WARRANTY, EVEN IF AGE LOGIC OR MIT OR LICENSEES HEREUNDER HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. The name AGE Logic, Inc. may not be used in advertising or publicity pertaining to this software without specific, written prior permission from AGE Logic. Title to this software shall at all times remain with AGE Logic, Inc. ****************************************************************************/ /* Copyright (c) 1993 X Consortium Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE X CONSORTIUM BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Except as contained in this notice, the name of the X Consortium shall not be used in advertising or otherwise to promote the sale, use or other dealings in this Software without prior written authorization from the X Consortium. */ #include "XIElibint.h" #include #define ieeeFloatSignMask 0x80000000 #define ieeeFloatExpMask 0x7F800000 #define ieeeFloatExpShift 23 #define ieeeFloatMantissaMask 0x007FFFFF #define ieeeMantissaSize 23 /* From page 2-8 of spec, IEEE format. This is laid out as: bit 31 = 1 bit for sign (if bit on, negative) bits 23-39 = 8 bit "biased" exponent (see below) bits 0-22 = 23 bit mantissa A "normal" number is formed as (-1)^sign_bit * 2^(exp-127) * (1.0 + .mantissa) That is, the mantissa is interpreted as a fractional binary number between 0 and 2^-1 + 2^-2 + ... + 2^-23. If the exponent is 255, the value is taken as infinity. I stole definition out of TMS Family Code tools, pages 5-22, 5-23 */ /**********************************************************************/ xieTypFloat _XieConvertToIEEE(native) XieFloat native; { #ifndef NATIVE_FP_FORMAT XieFloat really_float = native; /* stupid language */ return *((xieTypFloat *)&really_float); #else xieTypFloat value; int sign; int exponent; int ieee_exp; long ieee_mantissa; double frac_part; if (native == 0.0) return(0); /* frexp() can't handle 0.0 reliably */ /*** frexp() breaks a double into the form "frac_part * 2^exponent" where 1/2 <= |frac_part| < 1. ***/ sign = (native < 0); frac_part = frexp(native,&exponent) * (sign? -1: 1); /*** In IEEE, a normal number is formed as: (-1)^sign_bit * 2^(exp-127) * (1.0 + .mantissa) It is easy for us to figure out the sign bit. To convert to IEEE form, we work with the absolute value of the fractional part, which is between 1/2 and 1. To normalize for IEEE format, the mantissa must be converted to be between 1 and 2 instead of 1/2 and 1. In other words, we re-express frac_part * 2^exponent as 2*frac_part * 2^(exponent-1) Then the IEEE mantissa is 2*frac_part - 1, and the IEEE exponent is given by exponent-1 = exp-127, or exp = 126+exponent. example: The number 0.75 is expressed as f * 2^0, f=0.75. We convert mantissa to 2*0.75 = 1.5 and subtract one to get IEEE mantissa coding of 0.5. The exponent is downgraded to -1 so (1 + 0.5) * 2^-1 is 0.75, which is coded with IEEE bias as -1 = exp-127, yielding exp=126. 0.75 = (1+0.5) * 2^(126-127), and we code 0 for sign bit, 0.5 for mantissa, 126 for the exponent. note: if the exponent becomes larger than 128, then exp+127>255, and we can't code it any more in 8 bits. Therefore if the exponent is >= 128, we set exp=255, which means infinity. ***/ frac_part = 2*frac_part; --exponent; frac_part -= 1; if (exponent >= 128) ieee_exp = 255; else ieee_exp = 127+exponent; /* notice we already decremented exponent by one, above */ /*** Now assemble the number ***/ value = 0; if (sign) value |= ieeeFloatSignMask; value |= (ieee_exp << ieeeFloatExpShift); /*** For the mantissa, we know we have a fractional part between 0 and 1. We want the most significant 23 bits. Just shift 23 places to the left and truncate. ***/ ieee_mantissa = (pow(2.0,23.0) * frac_part); value |= ieee_mantissa; return(value); #endif } /**********************************************************************/