summaryrefslogtreecommitdiffstats
path: root/vendor/libm-0.1.4/src/math/jn.rs
diff options
context:
space:
mode:
Diffstat (limited to 'vendor/libm-0.1.4/src/math/jn.rs')
-rw-r--r--vendor/libm-0.1.4/src/math/jn.rs343
1 files changed, 343 insertions, 0 deletions
diff --git a/vendor/libm-0.1.4/src/math/jn.rs b/vendor/libm-0.1.4/src/math/jn.rs
new file mode 100644
index 000000000..1be167f84
--- /dev/null
+++ b/vendor/libm-0.1.4/src/math/jn.rs
@@ -0,0 +1,343 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/*
+ * jn(n, x), yn(n, x)
+ * floating point Bessel's function of the 1st and 2nd kind
+ * of order n
+ *
+ * Special cases:
+ * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
+ * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
+ * Note 2. About jn(n,x), yn(n,x)
+ * For n=0, j0(x) is called,
+ * for n=1, j1(x) is called,
+ * for n<=x, forward recursion is used starting
+ * from values of j0(x) and j1(x).
+ * for n>x, a continued fraction approximation to
+ * j(n,x)/j(n-1,x) is evaluated and then backward
+ * recursion is used starting from a supposed value
+ * for j(n,x). The resulting value of j(0,x) is
+ * compared with the actual value to correct the
+ * supposed value of j(n,x).
+ *
+ * yn(n,x) is similar in all respects, except
+ * that forward recursion is used for all
+ * values of n>1.
+ */
+
+use super::{cos, fabs, get_high_word, get_low_word, j0, j1, log, sin, sqrt, y0, y1};
+
+const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+
+pub fn jn(n: i32, mut x: f64) -> f64 {
+ let mut ix: u32;
+ let lx: u32;
+ let nm1: i32;
+ let mut i: i32;
+ let mut sign: bool;
+ let mut a: f64;
+ let mut b: f64;
+ let mut temp: f64;
+
+ ix = get_high_word(x);
+ lx = get_low_word(x);
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ // -lx == !lx + 1
+ if (ix | (lx | ((!lx).wrapping_add(1))) >> 31) > 0x7ff00000 {
+ /* nan */
+ return x;
+ }
+
+ /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+ * Thus, J(-n,x) = J(n,-x)
+ */
+ /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
+ if n == 0 {
+ return j0(x);
+ }
+ if n < 0 {
+ nm1 = -(n + 1);
+ x = -x;
+ sign = !sign;
+ } else {
+ nm1 = n - 1;
+ }
+ if nm1 == 0 {
+ return j1(x);
+ }
+
+ sign &= (n & 1) != 0; /* even n: 0, odd n: signbit(x) */
+ x = fabs(x);
+ if (ix | lx) == 0 || ix == 0x7ff00000 {
+ /* if x is 0 or inf */
+ b = 0.0;
+ } else if (nm1 as f64) < x {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if ix >= 0x52d00000 {
+ /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ temp = match nm1 & 3 {
+ 0 => -cos(x) + sin(x),
+ 1 => -cos(x) - sin(x),
+ 2 => cos(x) - sin(x),
+ 3 | _ => cos(x) + sin(x),
+ };
+ b = INVSQRTPI * temp / sqrt(x);
+ } else {
+ a = j0(x);
+ b = j1(x);
+ i = 0;
+ while i < nm1 {
+ i += 1;
+ temp = b;
+ b = b * (2.0 * (i as f64) / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ } else {
+ if ix < 0x3e100000 {
+ /* x < 2**-29 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if nm1 > 32 {
+ /* underflow */
+ b = 0.0;
+ } else {
+ temp = x * 0.5;
+ b = temp;
+ a = 1.0;
+ i = 2;
+ while i <= nm1 + 1 {
+ a *= i as f64; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ i += 1;
+ }
+ b = b / a;
+ }
+ } else {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ let mut t: f64;
+ let mut q0: f64;
+ let mut q1: f64;
+ let mut w: f64;
+ let h: f64;
+ let mut z: f64;
+ let mut tmp: f64;
+ let nf: f64;
+
+ let mut k: i32;
+
+ nf = (nm1 as f64) + 1.0;
+ w = 2.0 * nf / x;
+ h = 2.0 / x;
+ z = w + h;
+ q0 = w;
+ q1 = w * z - 1.0;
+ k = 1;
+ while q1 < 1.0e9 {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ t = 0.0;
+ i = k;
+ while i >= 0 {
+ t = 1.0 / (2.0 * ((i as f64) + nf) / x - t);
+ i -= 1;
+ }
+ a = t;
+ b = 1.0;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = nf * log(fabs(w));
+ if tmp < 7.09782712893383973096e+02 {
+ i = nm1;
+ while i > 0 {
+ temp = b;
+ b = b * (2.0 * (i as f64)) / x - a;
+ a = temp;
+ i -= 1;
+ }
+ } else {
+ i = nm1;
+ while i > 0 {
+ temp = b;
+ b = b * (2.0 * (i as f64)) / x - a;
+ a = temp;
+ /* scale b to avoid spurious overflow */
+ let x1p500 = f64::from_bits(0x5f30000000000000); // 0x1p500 == 2^500
+ if b > x1p500 {
+ a /= b;
+ t /= b;
+ b = 1.0;
+ }
+ i -= 1;
+ }
+ }
+ z = j0(x);
+ w = j1(x);
+ if fabs(z) >= fabs(w) {
+ b = t * z / b;
+ } else {
+ b = t * w / a;
+ }
+ }
+ }
+
+ if sign {
+ -b
+ } else {
+ b
+ }
+}
+
+pub fn yn(n: i32, x: f64) -> f64 {
+ let mut ix: u32;
+ let lx: u32;
+ let mut ib: u32;
+ let nm1: i32;
+ let mut sign: bool;
+ let mut i: i32;
+ let mut a: f64;
+ let mut b: f64;
+ let mut temp: f64;
+
+ ix = get_high_word(x);
+ lx = get_low_word(x);
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ // -lx == !lx + 1
+ if (ix | (lx | ((!lx).wrapping_add(1))) >> 31) > 0x7ff00000 {
+ /* nan */
+ return x;
+ }
+ if sign && (ix | lx) != 0 {
+ /* x < 0 */
+ return 0.0 / 0.0;
+ }
+ if ix == 0x7ff00000 {
+ return 0.0;
+ }
+
+ if n == 0 {
+ return y0(x);
+ }
+ if n < 0 {
+ nm1 = -(n + 1);
+ sign = (n & 1) != 0;
+ } else {
+ nm1 = n - 1;
+ sign = false;
+ }
+ if nm1 == 0 {
+ if sign {
+ return -y1(x);
+ } else {
+ return y1(x);
+ }
+ }
+
+ if ix >= 0x52d00000 {
+ /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ temp = match nm1 & 3 {
+ 0 => -sin(x) - cos(x),
+ 1 => -sin(x) + cos(x),
+ 2 => sin(x) + cos(x),
+ 3 | _ => sin(x) - cos(x),
+ };
+ b = INVSQRTPI * temp / sqrt(x);
+ } else {
+ a = y0(x);
+ b = y1(x);
+ /* quit if b is -inf */
+ ib = get_high_word(b);
+ i = 0;
+ while i < nm1 && ib != 0xfff00000 {
+ i += 1;
+ temp = b;
+ b = (2.0 * (i as f64) / x) * b - a;
+ ib = get_high_word(b);
+ a = temp;
+ }
+ }
+
+ if sign {
+ -b
+ } else {
+ b
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2025-02-25 00:21:59 +0000