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Unformatted text preview: er P,U,O,Z,D,I unsigned int exception_cause; //exception cause unsigned int status_flag_inexact; //inexact status flag unsigned int status_flag_underflow; //underflow status flag unsigned int status_flag_overflow; //overflow status flag unsigned int status_flag_divide_by_zero; //divide by zero status flag unsigned int status_flag_denormal_operand; //denormal operand status flag unsigned int status_flag_invalid_operation; //invalid operation status flag unsigned int ftz; // flush-to-zero flag unsigned int daz; // denormals-are-zeros flag } EXC_ENV; Vol. 1 E-21 GUIDELINES FOR WRITING SIMD FLOATING-POINT EXCEPTION HANDLERS The arithmetic operations exemplified are emulated as follows: 1. If the denormals-are-zeros mode is enabled (the DAZ bit in MXCSR is set to 1), replace all the denormal inputs with zeroes of the same sign (the denormal flag is not affected by this change). 2. Perform the operation using x87 FPU instructions, with exceptions disabled, the original user rounding mode, and single precision. This reveals invalid, denormal, or divide-by-zero exceptions (if there are any) and stores the result in memory as a double precision value (whose exponent range is large enough to look like "unbounded" to the result of the single precision computation). 3. If no unmasked exceptions were detected, determine if the result is less than the smallest normal number (tiny) that can be represented in single precision format, or greater than the largest normal number that can be represented in single precision format (huge). If an unmasked overflow or underflow occurs, calculate the scaled result that will be handed to the user exception handler, as specified by IEEE Standard 754. 4. If no exception was raised, calculate the result with a "bounded" exponent. If the result is tiny, it requires denormalization (shifting the significand right while incrementing the exponent to bring it into the admissible range of [-126,+127] for single precision floating-point numbers). The result obtained in step 2 cannot be used because it might incur a double rounding error (it was rounded to 24 bits in step 2, and might have to be rounded again in the denormalization process). To overcome this is, calculate the result as a double precision value, and store it to memory in single precision format. Rounding first to 53 bits in the significand, and then to 24 never causes a double rounding error (exact properties exist that state when double-rounding error occurs, but for the elementary arithmetic operations, the rule of thumb is that if an infinitely precise result is rounded to 2p+1 bits and then again to p bits, the result is the same as when rounding directly to p bits, which means that no double-rounding error occurs). 5. If the result is inexact and the inexact exceptions are unmasked, the calculated result will be delivered to the user floating-point exception handler. 6. The flush-to-zero case is dealt with if the result is tiny. 7. The emulati...
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This note was uploaded on 10/01/2013 for the course CPE 103 taught by Professor Watlins during the Winter '11 term at Mississippi State.
- Winter '11