Fujitsu Fujitsu SPARC64 V manual Denormalized number, eres is less than zero

Implementation Note – Detecting the exact boundary conditions requires a large amount of hardware. SPARC64 V detects approximate boundary conditions by calculating the exponent intermediate result (the exponent before rounding) from input operands, to avoid the hardware cost. Since the computation of the boundary conditions is approximate, the detection of a zero result or an overflow result shall be pessimistic. SPARC64 V generates an unfinished_FPop exception pessimistically.

The equations to calculate the result exponent to detect the boundary conditions from the input exponents are presented in TABLE B-1, where Er is the approximation of the biased result exponent before rounding and is calculated only from the input exponents (esrc1, esrc2). Er is to be used for detecting the boundary condition for an unfinished_FPop.

TABLE B-1Result Exponent Approximation for Detecting unfinished_FPop Boundary Conditions

		Operation	Formula
		fmuls	Er = esrc1 + esrc2 −	126
		fmuld	Er = esrc1 + esrc2 −	1022
		fdivs	Er = esrc1 - esrc2 + 126
		fdivd	Er = esrc1 - esrc2 + 1022
		esrc1 and esrc2 are the biased exponents of the input operands. When the
		corresponding input operand is a denormalized number, the value is 0.
		From Er, eres is calculated. eres is a biased result exponent, after mantissa alignment
		and before rounding, where the appropriate adjustment of the exponent is applied to
		the result mantissa: left-shifting or right-shifting the mantissa to the implicit 1 at the
		left of the binary point, subtracting or adding the shift-amount to the exponent. The
		result mantissa is assumed to be 1.xxxx in calculating eres. If the result is a
		denormalized number, eres is less than zero.
		TABLE B-2describes the boundary condition of each floating-point instruction that
		generates an unfinished_FPop exception.
TABLE B-2	unfinished_FPop Boundary Conditions
Operation		Boundary Conditions
FdTOs		− 25 < eres < 1 and TEM.UFM = 0.
FsTOd		Second operand (rs2) is a denormalized number.
FADDs, FSUBs,		1. One of the operands is a denormalized number, and the other operand is a normal,
FADDd, FSUBd			nonzero floating-point number (except for a NaN and an infinity)1.

2.Both operands are denormalized numbers.

3.Both operands are normal nonzero floating-point numbers (except for a NaN and an infinity), eres < 1, and TEM.UFM = 0.

Release 1.0, 1 July 2002 F. Chapter B IEEE Std 754-1985 Requirements for SPARC V9 63