rray (version 0.0.0.9000)

remainder: Remainders

Description

• rray_fmod() computes the element-wise remainder of the floating point division of x / y.

• rray_remainder() computes the IEEE element-wise remainder of the floating point division of x / y.

Usage

rray_fmod(x, y)
rray_remainder(x, y)

Arguments

x, y

A vector, matrix, array or rray.

Details

• rray_fmod() - The floating-point remainder of the division operation x / y calculated by this function is exactly the value x - n * y, where n is x / y with its fractional part truncated.

• rray_remainder() - The IEEE floating-point remainder of the division operation x / y calculated by this function is exactly the value x - n * y, where the value n is the integral value nearest the exact value x / y. When |n - x / y| = 1/2, the value n is chosen to be even. In contrast to rray_fmod(), the returned value is not guaranteed to have the same sign as x.

See Also

Other math functions: rray_abs, rray_clip, rray_maximum, rray_multiply_add, rray_sign

Examples

# NOT RUN {
rray_fmod(1, 2)
rray_remainder(1, 2)

# Always same sign as `x`
# 2 / 3 = 0.667 -> n = 0
# (2 - 0 * 3) = 2
rray_fmod(2, 3)

# No guarantee of same sign as `x`
# 2 / 3 = 0.667 -> n = 1
# (2 - 1 * 3) = -1
rray_remainder(2, 3)

# 12 / 8 = 1.5 -> n = 2 or 1?
# This is the `|n - x / y| = 1/2` case
# Chosen to be n = 2, i.e. even, by convention.
# (12 - 2 * 8) = -4
rray_remainder(12, 8)

# Broadcasts appropriately
x <- matrix(1:5)
rray_remainder(x, t(x))

# Be aware of the limits of floating
# point arithmetic!
# 1 / .2 = 5 -> n = 5
# (1 - 5 * .2) = 0
# I get -5.551115e-17
rray_remainder(1, .2)

# More serious limitations with rray_fmod()
# 1 / .1 = 10 -> n = 10
# (1 - 10 * .1) = 0
# I get 0.1
rray_fmod(1, .1)

# ^ is due to the implementation of `std::fmod()`
# in C++. It is basically the following, which
# gives the incorrect 0.1:
x <- 1
y <- 0.1
x_abs <- abs(x)
y_abs <- abs(y)
# I get -5.551115e-17
result <- rray_remainder(x_abs, y_abs)
if (sign(result)) result <- result + y_abs
rray_abs(result) * sign(x)

# }