TAILIEUCHUNG - Marketing versus Mathematics and other Ruminations on the Design of Floating-Point Arithmetic

Diamonds serve two main functions today: jewelry and industrial uses. Slightly more than 50 percent of the volume of diamonds extracted becomes gemstones for jewelry, yet they account for more than 95 percent of the total value. Polished diamonds have always been considered among the world’s most precious gemstones. They account for about 40 percent of all jewelry manufacturing; engagement rings are the largest category of diamond jewelry. Jewelers usually set the diamonds in precious metals such as gold or platinum to emphasize the sparkle of the stones. Stones not suited for jewelry, called “bort,” are used for industrial purposes. Key characteristics. | Prof. W. Kahan August 27 2000 6 44 pm Marketing versus Mathematics and other Ruminations on the Design of Floating-Point Arithmetic Prof. W. Kahan Math. Dept. and Elect. Eng. Computer Sci. Univ. of Calif. @ Berkeley . upon receiving the IEEE s Emanuel R. Piore Award 15 Aug. 2000 Abstract No that is not my message. Rather in so far as our technological activities have become ever more mathematical as well as market-oriented mathematics and marketing have come to depend upon each other and therefore must appreciate each other s needs more than ever. This growing interdependence is illustrated in what follows by the design and implementation of floating-point arithmetic. This document is at http wkahan The title Marketing versus Mathematics was chosen by Prof. Alan Jay Smith. MktgMath Page 1 Prof. W. Kahan August 27 2000 6 44 pm Contents Mathematics for Marketing and vice-versa page 3 A Good Example The Intimidation Factor 5 Good and Bad in Marketing and in Mathematics 7 A Good Example HP-92 . HP-12C Financial Calculators 9 Market-motivated Mathematics is a Gamble 12 A Bad Example QPRO and QPRO for Windows 13 Why is Floating-Point almost all Binary nowadays 18 Example . literal constant what s its nationality 19 What is worth learning from the story about . 23 Besides its massive size what distinguishes today s market for floating-point . 24 Case study Kernighan-Ritchie C vs. ANSI C Java 26 Example Find the nearest point . 27 Old Kernighan-Ritchie C works better than ANSI C or Java 28 The Intel 8087 Numeric Coprocessor s Marketing Vicissitudes 29 Floating-Point Arithmetic for a Mass Market . What was Best 30 How do Errors get Amplified By Singularities Near the Data. . 33 Testing floating-point software . A Frightening Example 36 What else should we remember about the foregoing examples 42 A Bad Example of a Programming Language Ostensibly for a Mass Market 43 Appendix How Directed Roundings May Help Locate Numerical .

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