Changeset 2040 for trunk/docsrc/d-floating-point.dd
- Timestamp:
- 09/19/10 02:11:27 (2 years ago)
- Files:
-
- trunk/docsrc/d-floating-point.dd (modified) (4 diffs)
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trunk/docsrc/d-floating-point.dd
r1322 r2040 66 66 $(P Since $(INFIN) can be produced by overflow, both +$(INFIN) and -$(INFIN) are required. Both +0 and -0 are required in order to preserve identities such as: if $(D x>0), then $(D 1/(1/x) > 0). In almost all other cases, however, there is no difference between +0 and -0.) 67 67 68 $(P It's worth noting that these "special values"are usually not very efficient. On x86 machines, for example, a multiplication involving a NaN, an infinity, or a subnormal can be twenty to fifty times slower than an operation on normal numbers. If your numerical code is unexpectedly slow, it's possible that you are inadvertently creating many of these special values. Enabling floating-point exception trapping, described later, is a quick way to confirm this.)68 $(P It's worth noting that these $(SINGLEQUOTE special values) are usually not very efficient. On x86 machines, for example, a multiplication involving a NaN, an infinity, or a subnormal can be twenty to fifty times slower than an operation on normal numbers. If your numerical code is unexpectedly slow, it's possible that you are inadvertently creating many of these special values. Enabling floating-point exception trapping, described later, is a quick way to confirm this.) 69 69 70 70 $(P One of the biggest factor obscuring what the machine is doing is in the conversion between binary and decimal. You can eliminate this by using the $(D "%a") format when displaying results. This is an invaluable debugging tool, and an enormously helpful aid when developing floating-point algorithms. The $(D 0x1.23Ap+6) hexadecimal floating-point format can also be used in source code for ensuring that your input data is $(I exactly) what you intended.) … … 132 132 $(P A key design goal is: it should be possible to write code such that, regardless of the processor which is used, the accuracy is never worse than would be obtained on a system which only supports the $(D double) type.) 133 133 134 $(P (Footnote: $(D real) is close to 'indigenous'in the Borneo proposal for the Java programming language[Ref Borneo]).)134 $(P (Footnote: $(D real) is close to $(SINGLEQUOTE indigenous) in the Borneo proposal for the Java programming language[Ref Borneo]).) 135 135 136 136 $(P Consider evaluating $(D x*y + z*w), where $(D x, y, z) and $(D w) are double.) … … 235 235 $(H2 NaN payloads) 236 236 237 $(P According to the IEEE 754 standard, a 'payload'can be stored in the mantissa of a NaN. This payload can contain information about how or why it was generated. Historically, almost no programming languages have ever made use of this potentially powerful feature. In D, this payload consists of a positive integer.)237 $(P According to the IEEE 754 standard, a $(SINGLEQUOTE payload) can be stored in the mantissa of a NaN. This payload can contain information about how or why it was generated. Historically, almost no programming languages have ever made use of this potentially powerful feature. In D, this payload consists of a positive integer.) 238 238 239 239 $(UL … … 305 305 ) 306 306 307 $(H2 Floating point and 'pure nothrow')307 $(H2 Floating point and $(SINGLEQUOTE pure nothrow)) 308 308 309 309 $(P Every floating point operation, even the most trivial, is affected by the floating-point rounding state, and writes to the sticky flags. The status flags and control state are thus 'hidden variables', potentially affecting every $(D pure) function; and if the floating point traps are enabled, any floating point operation can generate a hardware exception.