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//
// GENERATED FILE
//
use super::*;
use f2rust_std::*;
const SMALL: f64 = 0.00000001;
struct SaveVars {
INVUB: f64,
FIRST: bool,
}
impl SaveInit for SaveVars {
fn new() -> Self {
let mut INVUB: f64 = 0.0;
let mut FIRST: bool = false;
FIRST = true;
INVUB = -1.0;
Self { INVUB, FIRST }
}
}
//$Procedure ZZCNQUAD ( Solve quadratic equation for cone intercept )
pub fn ZZCNQUAD(
A: f64,
B: f64,
C: f64,
UB: f64,
N: &mut i32,
R1: &mut f64,
R2: &mut f64,
ctx: &mut Context,
) -> f2rust_std::Result<()> {
let save = ctx.get_vars::<SaveVars>();
let save = &mut *save.borrow_mut();
let mut COEFFS = StackArray::<f64, 3>::new(1..=3);
let mut INV1: f64 = 0.0;
let mut INV2: f64 = 0.0;
let mut MAXMAG: f64 = 0.0;
let mut MAXIX: i32 = 0;
let mut NX: i32 = 0;
//
// SPICELIB functions
//
//
// Local parameters
//
//
// Local variables
//
//
// Saved values
//
//
// Initial values
//
if RETURN(ctx) {
return Ok(());
}
CHKIN(b"ZZCNQUAD", ctx)?;
//
// On the first pass, set the upper bound for the reciprocal
// solution.
//
if save.FIRST {
save.INVUB = (f64::sqrt(DPMAX()) / 200.0);
save.FIRST = false;
}
//
// Handle the degenerate cases first.
//
if ((A == 0.0) && (B == 0.0)) {
*R1 = 0.0;
*R2 = 0.0;
if (C == 0.0) {
*N = -1;
} else {
*N = -2;
}
CHKOUT(b"ZZCNQUAD", ctx)?;
return Ok(());
}
//
// Scale the input coefficients.
//
MAXMAG = intrinsics::DMAX1(&[f64::abs(A), f64::abs(B), f64::abs(C)]);
COEFFS[1] = TOUCHD((A / MAXMAG));
COEFFS[2] = TOUCHD((B / MAXMAG));
COEFFS[3] = TOUCHD((C / MAXMAG));
//
// Identify the coefficient of largest magnitude.
//
MAXIX = 1;
for I in 2..=3 {
if (f64::abs(COEFFS[I]) > f64::abs(COEFFS[MAXIX])) {
//
// Record the index of the maximum magnitude.
//
MAXIX = I;
}
}
//
// Make sure the value of maximum magnitude is +/- 1.
//
COEFFS[MAXIX] = f64::copysign(1.0, COEFFS[MAXIX]);
//
// Find roots in a manner suited to the coefficients we have.
//
if ((f64::abs(COEFFS[1]) >= SMALL) || (COEFFS[1] == 0.0)) {
//
// This is a numerically well-behaved case. Delegate the
// job to ZZBQUAD.
//
ZZBQUAD(COEFFS[1], COEFFS[2], COEFFS[3], UB, N, &mut NX, R1, R2, ctx)?;
} else if (f64::abs(COEFFS[3]) >= SMALL) {
//
// The zero-order coefficient has magnitude >= SMALL.
//
// The original equation
//
// 2
// a x + b x + c = 0
//
// can be replaced by
//
// 2
// c y + b y + a = 0
//
// where
//
// y = 1/x
//
// Here
//
// |c| >= SMALL
// |c| <= 1
//
// |a| < SMALL
//
//
// Because the quadratic coefficient is bounded away from zero,
// the roots of the reciprocal equation are not in danger of
// overflowing. So we can safely solve for 1/x. We might have
// complex roots; these are rejected.
//
// The roots of the transformed equation don't have a maximum
// magnitude restriction imposed by UB. We set the upper bound
// to a value that ZZBQUAD will allow.
//
ZZBQUAD(
COEFFS[3], COEFFS[2], COEFFS[1], save.INVUB, N, &mut NX, &mut INV1, &mut INV2, ctx,
)?;
if (*N == 1) {
//
// We have one real root. Make sure we can invert it.
//
if (f64::abs((INV1 * UB)) >= 1.0) {
//
//
// |1/INV1| <= UB
//
//
*R1 = (1.0 / INV1);
} else {
//
// There are no real roots having magnitude within the
// bound.
//
*N = 0;
}
//
// There is no second root.
//
*R2 = 0.0;
} else if (*N == 2) {
//
// We have two real roots. The one of larger magnitude is
// the second one. The reciprocal of this root will be
// the smaller root of the original equation, as long
// as the reciprocal is within bounds.
//
if (f64::abs((INV2 * UB)) >= 1.0) {
//
//
// |1/INV2| <= UB
//
//
*R1 = (1.0 / INV2);
//
// Proceed to the first root of the transformed equation.
//
if (f64::abs((INV1 * UB)) >= 1.0) {
//
//
// |1/INV1| <= UB
//
//
*R2 = (1.0 / INV1);
} else {
//
// Only the second root qualifies for inversion.
//
*N = 1;
*R2 = 0.0;
}
} else {
//
// The reciprocal of the larger root is too big; the
// reciprocal of the smaller root will be even larger.
// There are no real roots having magnitude within the
// bound.
//
*N = 0;
*R1 = 0.0;
*R2 = 0.0;
}
} else {
//
// We have no viable roots of the transformed equation, so
// we have no viable roots of the original one.
//
*N = 0;
*R1 = 0.0;
*R2 = 0.0;
}
} else {
//
// The linear coefficient B has the greatest magnitude, which
// is 1. The quadratic coefficient A is "small": 0 < |A| < 1.D-8.
// The zero-order coefficient is "small" as well.
//
// It will be convenient to make B equal to 1; do this now.
//
if (B < 0.0) {
COEFFS[1] = -COEFFS[1];
COEFFS[2] = -COEFFS[2];
COEFFS[3] = -COEFFS[3];
}
//
// In this case we use a low-order Taylor expansion about
// x = 0 for the square root term of the formula for the roots:
//
// inf
// __
// 1/2 \ (k) k
// T(x) = ( 1 + x ) = /_ f (0) x / (k!)
//
// k=0
//
//
// 2 3 4
// = 1 + x/2 - x /8 + x /16 + O(x )
//
//
// Apply this formula to that for the solution having the
// positive square root term. Here let `x' be
//
//
// 2
// -4ac / b
//
// which equals
//
// -4ac
//
// since we've set b = 1.
//
//
// Then the root is
//
//
// -1 + sqrt( 1 - 4ac )
// x = --------------------
// 1 2a
//
//
// 2 2 3
// -1 + ( 1 - 2ac - 16a c /8 + O((ac)) )
// = -------------------------------------
// 2a
//
// Discarding the high-order terms in a, we have
//
//
// x ~= ( -1 + 1 - 2ac ) / 2a = -c
// 1
//
// Similarly, we have
//
//
// x ~= ( -1 - 1 + 2ac ) / 2a = ( ac - 1 )/a = c - 1/a
// 2
//
//
// Based on the conditions that got us here, we know
//
// |c| < 1
//
// |c - 1/a| ~= |1/a| > 1.e8
//
*N = 0;
*R1 = 0.0;
*R2 = 0.0;
if (f64::abs(COEFFS[3]) <= UB) {
*R1 = -COEFFS[3];
*N = 1;
if (f64::abs(((COEFFS[1] * COEFFS[3]) - 1.0)) < f64::abs((COEFFS[1] * UB))) {
*R2 = (COEFFS[3] - (1.0 / COEFFS[1]));
*N = 2;
}
}
}
CHKOUT(b"ZZCNQUAD", ctx)?;
Ok(())
}