# Standard Normal Probability Distribution

magicNum <- 1 / sqrt(2 * pi)

StandardNormalDesicityOriginal <- function(x) {
  result <- exp(-0.5 * (x ^ 2)) / sqrt(2 * pi)
  result
}

StandardNormalDesicity <- function(x) {
  result <- magicNum * (1 / sqrt(exp(x ^ 2)))
  result
}

StandardNormalProbabilityMargin <- function(x) {
  if (x == 0) {
    area <- 0.5
  }
  else {

    if (x < 0) {
      num <- x * 100
      area <- 0.5

      for (s in c(0:num)) {
	area <- area - ((StandardNormalDesicity(s * 0.01) + StandardNormalDesicity(s * 0.01 - 0.01)) * 0.01 * 0.5)
      }
    }
    else {
      num <- x * 100 - 1
      area <- 0.0

      for (s in c(0:num)) {
	area <- area + (StandardNormalDesicity(s * 0.01) + StandardNormalDesicity(s * 0.01 + 0.01)) * 0.01 * 0.5
      }
      
      area <- 0.5 + area
    }
  }

  area
}

StandardNormalProbabilityMargin2 <- function(x) {
  if (x == 0) {
    area <- 0.5
  }
  else {

    if (x < 0) {
      num <- x * 1000
      area <- 0.5

      for (s in c(0:num)) {
	area <- area - ((StandardNormalDesicity(s * 0.001) + StandardNormalDesicity(s * 0.001 - 0.001)) * 0.001 * 0.5)
      }
    }
    else {
      num <- x * 1000 - 1
      area <- 0.0

      for (s in c(0:num)) {
	area <- area + (StandardNormalDesicity(s * 0.001) + StandardNormalDesicity(s * 0.001 + 0.001)) * 0.001 * 0.5
      }
      
      area <- 0.5 + area
    }
  }

  area
}

StandardNormalProbabilityRange <- function(x, y) {
  if (x > y) {
    m <- y
    n <- x
  }
  else {
    m <- x
    n <- y
  }

  area <- StandardNormalProbabilityMargin(n) - StandardNormalProbabilityMargin(m)
  area
}

StandardNormalProbabilityRange2 <- function(x, y) {
  if (x > y) {
    m <- y
    n <- x
  }
  else {
    m <- x
    n <- y
  }

  area <- StandardNormalProbabilityMargin2(n) - StandardNormalProbabilityMargin2(m)
  area
}

###################################################################################

d <- StandardNormalProbabilityMargin(-1.02)
print(d)

d <- StandardNormalProbabilityMargin(1.02)
print(d)

d <- StandardNormalProbabilityRange(0, 1.02)
print(d)