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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
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Meet the people whose lives, choices and achievements shaped the journey.
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Moments that changed communities, movements, institutions and the nation.
In 1968 Shirley Chisholm became the first Black woman elected to the United States Congress. In 1972 she launched a campaign for the Democratic presidential nomination, breaking another political barrier.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
Floating-point error mitigation is the minimization of errors caused by the fact that real numbers cannot, in general, be accurately represented in a fixed space. By definition, floating-point error cannot be eliminated, and, at best, can only be managed. Huberto M. Sierra noted in his 1956 patent "Floating Decimal Point Arithmetic Control Means for Calculator": Thus under some conditions, the major portion of the significant data digits may lie beyond the capacity of the registers. Therefore, the result obtained may have little meaning if not totally erroneous. The Z1, developed by Konrad Zuse in 1936, was the first computer with floating-point arithmetic and was thus susceptible to floating-point error. Early computers, however, with operation times measured in milliseconds, could not solve large, complex problems and thus were seldom plagued with floating-point error. Today, however, with supercomputer system performance measured in petaflops, floating-point error is a major concern for computational problem solvers. The following sections describe the strengths and weaknesses of various means of mitigating floating-point error.
RapidCAD is a specially packaged Intel 486DX and a dummy floating-point unit (FPU) designed as pin-compatible replacements for an Intel 80386 processor and 80387 FPU. Because the i486DX has a working on-chip FPU, a dummy FPU package (the "RapidCAD-2") is supplied to go in the Intel 387 FPU socket. The dummy FPU is used to provide the FERR (Floating-point ERRor) signal, necessary for compatibility purposes. Despite being able to execute instructions in the same number of cycles as an i486DX, integer performance on RapidCAD suffers due to the absence of level 1 cache and the bottleneck of the 386 bus. RapidCAD offers minimal improvement in integer performance over a 386DX (typically 10%, at most 35%), but provides substantial improvement in floating-point operations (up to 80% faster) for which it was marketed, primarily for computer-aided design (hence the name). Floating-point performance is mostly improved by moving the FPU onto the CPU core. Other source reports that the performance boost ranged from 20 to 170 percent faster than the regular 386DX based motherboards. It was available at manufacturer's suggested list price of US$499.
As with other spreadsheets, Microsoft Excel works only to limited accuracy because it retains only a certain number of figures to describe numbers (it has limited precision). With some exceptions regarding erroneous values, infinities, and denormalized numbers, Excel calculates in double-precision floating-point format from the IEEE 754 specification (besides numbers, Excel uses a few other data types). Although Excel allows display of up to 30 decimal places, its precision for any specific number is no more than 15 significant figures, and calculations may have an accuracy that is even less due to five issues: round off, truncation, and binary storage, accumulation of the deviations of the operands in calculations, and worst, "catastrophic cancellation" at subtraction of values with similar magnitude. Standard floating-point error mitigation techniques apply.
Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base-2) fractions. The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with 8 decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on. This wider range can dramatically slow the accumulation of rounding errors during successive calculations; for example, the Kahan summation algorithm can be used in floating point to add many numbers with no asymptotic accumulation of rounding error.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →The Greenwood District.
