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79 lines
2.2 KiB
Plaintext
79 lines
2.2 KiB
Plaintext
NAME
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quo - compute integer quotient of a value by a real number
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SYNOPSIS
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quo(x, y, rnd) or x // y
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TYPES
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If x is a matrix or list, the returned value is a matrix or list v of
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the same structure for which each element v[[i]] = quo(x[[i]], y, rnd).
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If x is an xx-object or x is not an object and y is an xx-object,
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this function calls the user-defined function xx_quo(x, y, rnd);
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the types of arguments and returned value are as required by the
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definition of xx_quo().
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If neither x nor y is an object, and x is not a matrix or list:
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x number (real or complex)
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y real
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rnd integer, defaults to config("quo")
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return number
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DESCRIPTION
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If x is real or complex and y is zero, quo(x, y, rnd) returns zero.
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If x is complex, quo(x, y, rnd) returns
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quo(re(x), y, rnd) + quo(im(x), y, rnd) * 1i.
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In the following it is assumed that x is real and y is nonzero.
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If x/y is an integer quo(x, y, rnd) returns x/y.
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If x is real, y nonzero and x/y is not an integer, x // y returns
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one of the two integers v for which abs(x/y - v) < 1. Which
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integer is returned is controlled by rnd as follows:
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rnd sign of x/y - v Description of rounding
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0 + down, towards minus infinity
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1 - up, towards infinity
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2 sgn(x/y) towards zero
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3 -sgn(x/y) from zero
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4 sgn(y)
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5 -sgn(y)
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6 sgn(x)
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7 -sgn(x)
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8 to nearest even integer
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9 to nearest odd integer
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10 even if x/y > 0, otherwise odd
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11 odd if x/y > 0, otherwise even
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12 even if y > 0, otherwise odd
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13 odd if y > 0, otherwise even
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14 even if x > 0, otherwise odd
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15 odd if x > 0, otherwise even
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16-31 to nearest integer when this
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is uniquely determined;
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otherwise, when x/y is a
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half-integer, as if
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rnd replaced by rnd & 15
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EXAMPLE
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print quo(11,5,0), quo(11,5,1), quo(-11,5,2), quo(-11,-5,3)
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2 3 -2 3
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print quo(12.5,5,16), quo(12.5,5,17), quo(12.5,5,24), quo(-7.5,-5,24)
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2 3 2 2
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LIMITS
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none
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LIBRARY
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void quovalue(VALUE *x, VALUE *y, VALUE *rnd, VALUE *result)
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NUMBER *qquo(NUMBER *x, NUMBER *y, long rnd)
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SEE ALSO
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mod, quomod, //, %
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