When a floating-point operation underflows, always return zero, even if the result would be in the range of subnormal numbers.
A measure of how well one number approximates another. For example, the accuracy of a computed result often reflects the extent to which errors in the computation cause it to differ from the mathematically exact result. Accuracy can be expressed in terms of significant digits (e.g., “The result is accurate to six digits”) or more generally in terms of the preservation of relevant mathematical properties (e.g., “The result has the correct algebraic sign”).
The sum of the base-2 exponent and a constant (bias) chosen to make the stored exponent's range non-negative. For example, the exponent of 2-100 is stored in IEEE single precision format as (-100) + (single precision bias of 127) = 27.
A hardware feature of some pipeline architectures that allows the result of an operation to be used immediately as an operand for a second operation, simultaneously with the writing of the result to its destination register. The total cycle time of two chained operations is less than the sum of the stand-alone cycle times for the instructions. For example, the TI 8847 supports chaining of consecutive fadd, fsub, and fmul (of the same precision). Chained faddd/fmuld requires 12 cycles, while consecutive unchained faddd/fmuld requires 17 cycles.
The three floating point exceptions overflow, invalid, and division-by-zero are collectively referred to as the common exceptions for the purposes of ieee_flags(3m) and ieee_handler(3m). They are called common exceptions because they are commonly trapped as errors.
In multitasking operating systems, such as the Oracle Solaris operating system, processes run for a fixed time quantum. At the end of the time quantum, the CPU receives a signal from the timer, interrupts the currently running process, and prepares to run a new process. The CPU saves the registers for the old process, and then loads the registers for the new process. Switching from the old process state to the new is known as a context switch. Time spent switching contexts is system overhead; the time required depends on the number of registers, and on whether there are special instructions to save the registers associated with a process.
The value that is delivered as the result of a floating-point operation that caused an exception when no other handling has been specified for that exception.
Using two words to represent a number in order to keep or increase precision. On SPARC® workstations, double precision is the 64-bit IEEE double precision.
An arithmetic exception arises when an attempted atomic arithmetic operation has no result that is acceptable universally. The meanings of atomic and acceptable vary with time and place.
The component of a floating-point number that signifies the integer power to which the base is raised in determining the value of the represented number.
A system for representing a subset of real numbers in which the spacing between representable numbers is not a fixed, absolute constant. Such a system is characterized by a base, a sign, a significand, and an exponent (usually biased). The value of the number is the signed product of its significand and the base raised to the power of the unbiased exponent.
When a floating-point operation underflows into the range of subnormal numbers, return a subnormal number instead of zero. This method of handling underflow minimizes the loss of accuracy in floating-point calculations on small numbers.
Extra bits used by hardware to ensure correct rounding, not accessible by software. For example, IEEE double precision operations use three hidden bits to compute a 56-bit result that is then rounded to 53 bits.
The standard for binary floating-point arithmetic developed by the Institute of Electrical and Electronics Engineers, published in 1985, revised in 2008.
A fragment of assembly language code that is substituted for the function call it defines, during the inlining pass of Oracle Developer Studio compilers. Used (for example) by the math library in in-line template files (libm.il) in order to access hardware implementations of trigonometric functions and other elementary functions from C programs.
In IEEE arithmetic, a number with a biased exponent that is neither zero nor maximal (all ones), representing a subset of the normal range of real numbers with a bounded small relative error.
A hardware feature where operations are reduced to multiple stages, each of which takes (typically) one cycle to complete. The pipeline is filled when new operations can be issued each cycle. If there are no dependencies among instructions in the pipe, new results can be delivered each cycle. Chaining implies pipelining of dependent instructions. If dependent instructions cannot be chained, when the hardware does not support chaining of those particular instructions, then the pipeline stalls.
A quantitative measure of the density of representable numbers. For example, in a binary floating point format that has a precision of 53 significant bits, there are 253 representable numbers between any two adjacent powers of two (within the range of normal numbers). Do not confuse precision with accuracy, which expresses how closely one number approximates another.
A NaN (not a number) that propagates through almost every arithmetic operation without raising new exceptions.
The base number of any system of numbers. For example, 2 is the radix of a binary system, and 10 is the radix of the decimal system of numeration. SPARC workstations use radix-2 arithmetic; IEEE Std 754 is a radix-2 arithmetic standard.
Inexact results must be rounded up or down to obtain representable values. When a result is rounded up, it is increased to the next representable value. When rounded down, it is reduced to the preceding representable value.
The error introduced when a real number is rounded to a machine-representable number. Most floating-point calculations incur roundoff error. For any one floating-point operation, IEEE Std 754 specifies that the result shall not incur more than one rounding error.
A NaN (not a number) that raises the invalid operation exception whenever it appears as an operand.
The component of a floating-point number that is multiplied by a signed power of the base to determine the value of the number. In a normalized number, the significand consists of a single nonzero digit to the left of the radix point and a fraction to the right.
Standard Error is the Unix file pointer to standard error output. This file is opened when a program is started.
In IEEE arithmetic, a nonzero floating point number with a biased exponent of zero. The subnormal numbers are those between zero and the smallest normal number.
The radix complement of a binary numeral, formed by subtracting each digit from 1, then adding 1 to the least significant digit and executing any required carries. For example, the two's complement of 1101 is 0011.
Stands for unit in last place. In binary formats, the least significant bit of the significand, bit 0, is the unit in the last place.
A condition that occurs when the result of a floating-point arithmetic operation is so small that it cannot be represented as a normal number in the destination floating-point format with only normal roundoff.