# Transform - Numbers

Transforms which appear in the template list when a numeric field of type float32, float64, int8, int16, int32, int64uint8, uint16, uint32, or uint6, has been picked in the Transform pane.    Operations typically allow choice of numeric type for the Result destination.   For operations on numeric vectors, that is, ordered sets of numbers, see the Transform - Numeric Vectors topic. Previews are computed using full float64 accuracy even if the subject numbers are lower precision data type.  This may lead to slightly different transform template results as compared to the preview if lower precision data types are used.  For exact matches, use float64 data types and not float32 for floating point numbers.

For examples and illustrations of options and available operations, click on the template's link to jump to that template's topic.

 Arithmetic Basic arithmetic operations, automatically providing choice of a second parameter, specified in the Value box and typically allowing a field, a specific value, or an expression, for operations that use an additional parameter.   Save the result into the specified Result destination using the specified numeric type.   absolute value (abs) - Compute the absolute value of the source field number.  Absolute value leaves positive numbers unchanged and converts negative numbers into their positive equivalents.   add (+) - Add the Value to the source field number. cube - Compute the cube of the source field number. cube root (cbrt) - Compute the cube root of the source field number. divide (/) - Divide the source field number by the Value. divide integral (div) - Divide the source field number by the Value and discard any fractional part. divide remainder (mod) - A classic modulo operation (the remainder (of a congruence) function): Divide the source field number by the Value and retain only the fractional part as a non-fractional whole number. error (erf) - Compute the error function (also called erf(z) ) of the source field number.  error complement (erfc) - Compute the complementary error function (also called erfc(z) ) of the source field number. exponent (exp) - The exponential function: Compute e to the power of the source field number.   For anything but relatively small numbers in the source field such exponentiation results in numbers larger than can be represented in most types and thus returns a NULL.    exponent binary (exp2) - Also known as the power of 2: Compute 2 to the power of the source field number.  If the source field has values 1, 2, 3,... the result of a binary exponentiation will be 2, 4, 8,....   For anything but relatively small numbers in the source field such exponentiation results in numbers larger than can be represented in most types and thus returns a NULL.   exponent decimal (exp10) - Also known as the power of 10: Compute 10 to the power of the source field number.  If the source field has values 1, 2, 3,... the result of a decimal exponentiation will be 10, 100, 1000,....   For anything but relatively small numbers in the source field such exponentiation results in numbers larger than can be represented in most types and thus returns a NULL.    gamma (tgamma) - Compute the gamma function of the source field number.   gamma logarithm (lgamma) - Compute the natural logarithm of the gamma function of the source field number.  logarithm (log) - Compute the base e logarithm (also called the natural logarithm) of the source field number. logarithm binary (log2) - Compute the base 2 logarithm (also called the binary logarithm) of the source field number. logarithm decimal (log10) - Compute the base 10 logarithm (also called the common logarithm) of the source field number. multiply (*) - Multiply the source field number by the Value number. power (pow) - Compute the source field to the power of the specified Value.  A power of 1 is the source field number unchanged, a power of 2 is the source field number squared, and a power of 3 is the source field number cubed. reciprocal - One divided by the source field number.  The reciprocal is also the source field number to the power of -1, another way of saying the same thing. The reciprocal of zero is undefined, and thus returns a NULL. sign (sign) - Report if the source field number is positive (return 1) or negative (return -1).   The sign of zero is 0. sign invert - Multiply the source field number by -1, thus inverting the sign of the number.   square - Compute the square of the source field number (the number multiplied by itself). square root (sqrt) - Compute the square root of the source field number. subtract (-) -  Subtract the Value from the source field number. subtract from (-) - Subtract the source field number from the Value. Bit Logic Perform a bitwise logical operation on the source field, using the specified field, value, or expression for and, or, and xor operations,  and save the result into the specified Result destination using the specified numeric type.   and - Bitwise logical AND operation between the source field and the second specified field, value or expression result. not - Bitwise logical inversion changing bits from 1 to 0 and from 0 to 1. or - Bitwise logical OR operation between the source field and the second specified field, value or expression result. xor - Bitwise logical XOR operation between the source field and the second specified field, value or expression result. Copy Copy into the specified numeric Result destination the values in the source field,  using the specified numeric type. Expression Save the numeric result of the given expression into the specified numeric Result destination, creating new fields using the specified numeric type. Hyperbolic Basic hyperbolic trigonometric operations, allowing choice of radial unit from Arc Minute, Arc Second, Degree or Radian.    Save the result into the specified Result destination using the specified numeric type.   hyperbolic arc cosine (acosh) - Compute the hyperbolic arc cosine of the source field number. hyperbolic arc sine (asinh) - Compute the hyperbolic arc sine of the source field number. hyperbolic arc tangent (atanh) - Compute the hyperbolic arc tangent of the source field number. hyperbolic cosine (cosh) - Compute the hyperbolic cosine of the source field number. hyperbolic sine (sinh) - Compute the hyperbolic sine of the source field number. hyperbolic tangent (tanh) - Compute the hyperbolic tangent of the source field number. Limit Limit values within a numeric field:   limit both - Limit values to a range between the At least and At most values specified.   limit maximum - Limit values to no greater than the At most value specified. limit minimum - Limit values to no less than the At least value specified. Round Rounding operations.   Save the result into the specified Result destination using the specified numeric type.  The Round to box allows choosing the decimal position for rounding, for example, rounding to decimal fractions like 0.001 or rounding to whole decimal positions like 10000.   down (floor) - Round down to the next lowest Round to position value. 400.7 would round down to 400.   -400.7 would round down to -401 (which is a smaller amount, and thus "down," from 400). to nearest (round) - Round up or down to the nearest Round to position value. When rounding to 1, a value of 400.5 or greater fraction will get rounded up to 401 while fractional parts less than .5 will get rounded down to 400. to zero (trunc) - Rounding towards zero: Equivalent to rounding down for positive numbers, and rounding up for negative numbers. up (ceil) - Round up to the next highest Round to position value. 400.2 would round up to 401.   -400.2 would round up to -400 (which is a large amount, and thus "up," from 400). Special Bessel function operations, with specification of Order. Order may be taken from a field, or specified by a value or by an expression.  Save the result into the specified Result destination using the specified numeric type.   Bessel 1st kind (jn) - The nth Bessel function of the first kind: Compute  the Bessel function Jn(x) for Order n using the source field number as x.  Specifying 2 for Order uses a J2(x) Bessel function.  Using 0 or 1 for the Order is equivalent to using J0(x) or J1(x), respectively. Bessel 2nd kind (yn) - The nth Bessel function of the second kind: Compute the Bessel Function Yn(x) for Order n using the source field number as x.  Specifying 2 for Order uses a Y2(x) Bessel function.  Using 0 or 1 for the Order is equivalent to using Y0(x) or Y1(x), respectively. Trigonometric Basic hyperbolic trigonometric operations, allowing choice of radial unit from Arc Minute, Arc Second, Degree or Radian.    Save the result into the specified Result destination using the specified numeric type.   arc cosine (acos) - Compute the arc cosine of the source field number. arc sine (asin) - Compute the arc sine of the source field number. arc tangent (atan) - Compute the arc tangent of the source field number. cosine (cos) - Compute the cosine of the source field number. sine (sin) - Compute the sine of the source field number. tangent (tan) - Compute the tangent of the source field number.

## Notes

Everything Math - For a handy reference to anything in mathematics, see the Wolfram MathWorld site.   Thank you, Wolfram!

Drinks - A guy walks into a bar and asks for 1.014 root beers.  The bartender says, “I’ll have to charge you extra, that’s a root beer float”.  So the guy says, “In that case, better make it a double.”

Holidays - Why do programmers confuse Halloween with Christmas?  Because OCT 31 = DEC 25.

Transform Pane

Transform Reference

Transform - Expression

Transform - Numeric Vectors

Transform - Numbers: Arithmetic

Transform - Numbers: Bit Logic

Transform - Numbers: Copy

Transform - Numbers: Expression

Transform - Numbers: Hyperbolic

Transform - Numbers: Limit

Transform - Numbers: Round

Transform - Numbers: Special

Transform - Numbers: Trigonometric