Sollya User's Manual

Name:

round rounds a number to a floating-point format.

Usage:

round(x,n,mode) : (constant, integer, RN|RZ|RU|RD) -> constant round(x,format,mode) : (constant, HP|halfprecision|SG|single|D|double|DE|doubleextended|DD|doubledouble|QD|quad|TD|tripledouble, RN|RZ|RU|RD) -> constant

Parameters:

x is a constant to be rounded.
n is the precision of the target format.
format is the name of a supported floating-point format.
mode is the desired rounding mode.

Description:

If used with an integer parameter n, round(x,n,mode) rounds x to a floating-point number with precision n, according to rounding-mode mode.
If used with a format parameter format, round(x,format,mode) rounds x to a floating-point number in the floating-point format format, according to rounding-mode mode.
Subnormal numbers are handled for the case when format is one of halfprecision, single, double, doubleextended, doubledouble, quad or tripledouble. Otherwise, when format is an integer, round does not take any exponent range into consideration, i.e. typically uses the full exponent range of the underlying MPFR library.

Example 1:

   > display=binary!;
   > round(Pi,20,RN);
   1.100100100001111111_2 * 2^(1)

Example 2:

   > printdouble(round(exp(17),53,RU));
   0x417709348c0ea4f9
   > printdouble(D(exp(17)));
   0x417709348c0ea4f9

Example 3:

   > display=binary!;
   > a=2^(-1100);
   > round(a,53,RN);
   1_2 * 2^(-1100)
   > round(a,D,RN);
   0
   > double(a);
   0

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