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Diffstat (limited to 'gcc/config/rs6000/darwin-ldouble-format')
-rw-r--r-- | gcc/config/rs6000/darwin-ldouble-format | 91 |
1 files changed, 91 insertions, 0 deletions
diff --git a/gcc/config/rs6000/darwin-ldouble-format b/gcc/config/rs6000/darwin-ldouble-format new file mode 100644 index 000000000..3d1a06a14 --- /dev/null +++ b/gcc/config/rs6000/darwin-ldouble-format @@ -0,0 +1,91 @@ +Long double format +================== + + Each long double is made up of two IEEE doubles. The value of the +long double is the sum of the values of the two parts (except for +-0.0). The most significant part is required to be the value of the +long double rounded to the nearest double, as specified by IEEE. For +Inf values, the least significant part is required to be one of +0.0 +or -0.0. No other requirements are made; so, for example, 1.0 may be +represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a NaN +is don't-care. + +Classification +-------------- + +A long double can represent any value of the form + s * 2^e * sum(k=0...105: f_k * 2^(-k)) +where 's' is +1 or -1, 'e' is between 1022 and -968 inclusive, f_0 is +1, and f_k for k>0 is 0 or 1. These are the 'normal' long doubles. + +A long double can also represent any value of the form + s * 2^-968 * sum(k=0...105: f_k * 2^(-k)) +where 's' is +1 or -1, f_0 is 0, and f_k for k>0 is 0 or 1. These are +the 'subnormal' long doubles. + +There are four long doubles that represent zero, two that represent ++0.0 and two that represent -0.0. The sign of the high part is the +sign of the long double, and the sign of the low part is ignored. + +Likewise, there are four long doubles that represent infinities, two +for +Inf and two for -Inf. + +Each NaN, quiet or signalling, that can be represented as a 'double' +can be represented as a 'long double'. In fact, there are 2^64 +equivalent representations for each one. + +There are certain other valid long doubles where both parts are +nonzero but the low part represents a value which has a bit set below +2^(e-105). These, together with the subnormal long doubles, make up +the denormal long doubles. + +Many possible long double bit patterns are not valid long doubles. +These do not represent any value. + +Limits +------ + +The maximum representable long double is 2^1024-2^918. The smallest +*normal* positive long double is 2^-968. The smallest denormalised +positive long double is 2^-1074 (this is the same as for 'double'). + +Conversions +----------- + +A double can be converted to a long double by adding a zero low part. + +A long double can be converted to a double by removing the low part. + +Comparisons +----------- + +Two long doubles can be compared by comparing the high parts, and if +those compare equal, comparing the low parts. + +Arithmetic +---------- + +The unary negate operation operates by negating the low and high parts. + +An absolute or absolute-negate operation must be done by comparing +against zero and negating if necessary. + +Addition and subtraction are performed using library routines. They +are not at present performed perfectly accurately, the result produced +will be within 1ulp of the range generated by adding or subtracting +1ulp from the input values, where a 'ulp' is 2^(e-106) given the +exponent 'e'. In the presence of cancellation, this may be +arbitrarily inaccurate. Subtraction is done by negation and addition. + +Multiplication is also performed using a library routine. Its result +will be within 2ulp of the correct result. + +Division is also performed using a library routine. Its result will +be within 3ulp of the correct result. + + +Copyright (C) 2004 Free Software Foundation, Inc. + +Copying and distribution of this file, with or without modification, +are permitted in any medium without royalty provided the copyright +notice and this notice are preserved. |