Sollya User's Manual

Name:

roundcoefficients rounds the coefficients of a polynomial to classical formats.

Usage:

roundcoefficients(p,L) : (function, list) -> function

Parameters:

p is a function. Usually a polynomial.
L is a list of formats.

Description:

If p is a polynomial and L a list of floating-point formats, roundcoefficients(p,L) rounds each coefficient of p to the corresponding format in L.
If p is not a polynomial, roundcoefficients does not do anything.
If L contains other elements than HP, halfprecision, SG, single, D, double, DE, doubleextended, DD, doubledouble, QD, quad, TD and tripledouble, an error occurs.
The coefficients in p corresponding to X^i is rounded to the format L[i]. If L does not contain enough elements (e.g. if length(L) < degree(p)+1), a warning is displayed. However, the coefficients corresponding to an element of L are rounded. The trailing coefficients (that do not have a corresponding element in L) are kept with their own precision. If L contains too much elements, the trailing useless elements are ignored. In particular L may be end-elliptic in which case roundcoefficients has the natural behavior.

Example 1:

   > p=exp(1) + x*(exp(2) + x*exp(3));
   > display=binary!;
   > roundcoefficients(p,[|DD,D,D|]);
   1.010110111111000010101000101100010100010101110110100101010011010101011111101110001010110001000000010011101_2 * 2^(1) + x * (1.110110001110011001001011100011010100110111011010111_2 * 2^(2) + x * (1.010000010101111001011011111101101111101100010000011_2 * 2^(4)))
   > roundcoefficients(p,[|DD,D...|]);
   1.010110111111000010101000101100010100010101110110100101010011010101011111101110001010110001000000010011101_2 * 2^(1) + x * (1.110110001110011001001011100011010100110111011010111_2 * 2^(2) + x * (1.010000010101111001011011111101101111101100010000011_2 * 2^(4)))

Example 2:

   > f=sin(exp(1)*x);
   > display=binary!;
   > f;
   sin(x * (1.0101101111110000101010001011000101000101011101101001010100110101010111111011100010101100010000000100111001111010011110011110001110110001011100111000101100000111101_2 * 2^(1)))
   > roundcoefficients(f,[|D...|]);
   sin(x * (1.0101101111110000101010001011000101000101011101101001010100110101010111111011100010101100010000000100111001111010011110011110001110110001011100111000101100000111101_2 * 2^(1)))

Example 3:

   > p=exp(1) + x*(exp(2) + x*exp(3));
   > verbosity=1!;
   > display=binary!;
   > roundcoefficients(p,[|DD,D|]);
   Warning: the number of the given formats does not correspond to the degree of the given polynomial.
   Warning: the 0th coefficient of the given polynomial does not evaluate to a floating-point constant without any rounding.
   Will evaluate the coefficient in the current precision in floating-point before rounding to the target format.
   Warning: the 1th coefficient of the given polynomial does not evaluate to a floating-point constant without any rounding.
   Will evaluate the coefficient in the current precision in floating-point before rounding to the target format.
   Warning: rounding may have happened.
   1.010110111111000010101000101100010100010101110110100101010011010101011111101110001010110001000000010011101_2 * 2^(1) + x * (1.110110001110011001001011100011010100110111011010111_2 * 2^(2) + x * (1.01000001010111100101101111110110111110110001000001011111001011010100101111011111110001010011011101000100110000111010001110010000010110000101100000111001011100101001_2 * 2^(4)))

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