ia-32_volume1_basic-arch

Imul mul idiv div fiadd and fisub operate on only one

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Unformatted text preview: n each of these types. Vol. 1 4-5 DATA TYPES Table 4-2. Length, Precision, and Range of Floating-Point Data Types Data Type Single Precision Double Precision Double Extended Precision Length 32 64 80 Precision (Bits) 24 53 64 2 Approximate Normalized Range Binary 126 Decimal 1.18 10 38 to 2 127 to 3.40 1038 21022 to 21023 216382 to 216383 2.23 10308 to 1.79 10308 3.37 104932 to 1.18 104932 NOTE Section 4.8, "Real Numbers and Floating-Point Formats," gives an overview of the IEEE Standard 754 floating-point formats and defines the terms integer bit, QNaN, SNaN, and denormal value. Table 4-3 shows the floating-point encodings for zeros, denormalized finite numbers, normalized finite numbers, infinites, and NaNs for each of the three floating-point data types. It also gives the format for the QNaN floating-point indefinite value. (See Section 4.8.3.7, "QNaN Floating-Point Indefinite," for a discussion of the use of the QNaN floating-point indefinite value.) For the single-precision and double-precision formats, only the fraction part of the significand is encoded. The integer is assumed to be 1 for all numbers except 0 and denormalized finite numbers. For the double extended-precision format, the integer is contained in bit 63, and the most-significant fraction bit is bit 62. Here, the integer is explicitly set to 1 for normalized numbers, infinities, and NaNs, and to 0 for zero and denormalized numbers. 4-6 Vol. 1 DATA TYPES Table 4-3. Floating-Point Number and NaN Encodings Class Positive + +Normals Sign 0 0 . . 0 0 . . 0 0 1 1 . . 1 1 . . 1 1 X X 1 Biased Exponent Integer 11..11 11..10 . . 00..01 00..00 . . 00..00 00..00 00..00 00..00 . . 00..00 00..01 . . 11..10 11..11 11..11 11..11 11..11 1 1 . . 1 0 . . 0 0 0 0 . . 0 1 . . 1 1 1 1 1 Significand 1 Fraction 00..00 11..11 . . 00..00 11.11 . . 00..01 00..00 00..00 00..01 . . 11..11 00..00 . . 11..11 00..00 0X..XX2 1X..XX 10..00 +Denormals +Zero Negative -Zero -Denormals -Normals - NaNs SNaN QNaN QNaN Floating-Point Indefinite Single-Precision: Double-Precision: Double Extended-Precision: 8 Bits 11 Bits 15 Bits 23 Bits 52 Bits 63 Bits NOTES: 1. Integer bit is implied and not stored for single-precision and double-precision formats. 2. The fraction for SNaN encodings must be non-zero with the most-significant bit 0. The exponent of each floating-point data type is encoded in biased format; see Section 4.8.2.2, "Biased Exponent." The biasing constant is 127 for the singleprecision format, 1023 for the double-precision format, and 16,383 for the double extended-precision format. Vol. 1 4-7 DATA TYPES When storing floating-point values in memory, single-precision values are stored in 4 consecutive bytes in memory; double-precision values are stored in 8 consecutive bytes; and double extended-precision values are stored in 10 consecutive bytes. The single-precision and double-precision floating-point data types are operated on by x87 FPU, and SSE/SSE2/SSE3 instructions. The dou...
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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.

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