Add a "fork" of musl as //fusl.

fusl/src/math/jnf.c

Index: fusl/src/math/jnf.c
diff --git a/fusl/src/math/jnf.c b/fusl/src/math/jnf.c
new file mode 100644
index 0000000000000000000000000000000000000000..f63c062f32caf74b724f11e0ac97ece8da4d75b9
--- /dev/null
+++ b/fusl/src/math/jnf.c
@@ -0,0 +1,202 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#define _GNU_SOURCE
+#include "libm.h"
+
+float jnf(int n, float x)
+{
+	uint32_t ix;
+	int nm1, sign, i;
+	float a, b, temp;
+
+	GET_FLOAT_WORD(ix, x);
+	sign = ix>>31;
+	ix &= 0x7fffffff;
+	if (ix > 0x7f800000) /* nan */
+		return x;
+
+	/* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
+	if (n == 0)
+		return j0f(x);
+	if (n < 0) {
+		nm1 = -(n+1);
+		x = -x;
+		sign ^= 1;
+	} else
+		nm1 = n-1;
+	if (nm1 == 0)
+		return j1f(x);
+
+	sign &= n;  /* even n: 0, odd n: signbit(x) */
+	x = fabsf(x);
+	if (ix == 0 || ix == 0x7f800000)  /* if x is 0 or inf */
+		b = 0.0f;
+	else if (nm1 < x) {
+		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+		a = j0f(x);
+		b = j1f(x);
+		for (i=0; i<nm1; ){
+			i++;
+			temp = b;
+			b = b*(2.0f*i/x) - a;
+			a = temp;
+		}
+	} else {
+		if (ix < 0x35800000) { /* x < 2**-20 */
+			/* x is tiny, return the first Taylor expansion of J(n,x)
+			 * J(n,x) = 1/n!*(x/2)^n  - ...
+			 */
+			if (nm1 > 8)  /* underflow */
+				nm1 = 8;
+			temp = 0.5f * x;
+			b = temp;
+			a = 1.0f;
+			for (i=2; i<=nm1+1; i++) {
+				a *= (float)i;    /* a = n! */
+				b *= temp;        /* b = (x/2)^n */
+			}
+			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 */
+			float t,q0,q1,w,h,z,tmp,nf;
+			int k;
+
+			nf = nm1+1.0f;
+			w = 2*nf/x;
+			h = 2/x;
+			z = w+h;
+			q0 = w;
+			q1 = w*z - 1.0f;
+			k = 1;
+			while (q1 < 1.0e4f) {
+				k += 1;
+				z += h;
+				tmp = z*q1 - q0;
+				q0 = q1;
+				q1 = tmp;
+			}
+			for (t=0.0f, i=k; i>=0; i--)
+				t = 1.0f/(2*(i+nf)/x-t);
+			a = t;
+			b = 1.0f;
+			/*  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*logf(fabsf(w));
+			if (tmp < 88.721679688f) {
+				for (i=nm1; i>0; i--) {
+					temp = b;
+					b = 2.0f*i*b/x - a;
+					a = temp;
+				}
+			} else {
+				for (i=nm1; i>0; i--){
+					temp = b;
+					b = 2.0f*i*b/x - a;
+					a = temp;
+					/* scale b to avoid spurious overflow */
+					if (b > 0x1p60f) {
+						a /= b;
+						t /= b;
+						b = 1.0f;
+					}
+				}
+			}
+			z = j0f(x);
+			w = j1f(x);
+			if (fabsf(z) >= fabsf(w))
+				b = t*z/b;
+			else
+				b = t*w/a;
+		}
+	}
+	return sign ? -b : b;
+}
+
+float ynf(int n, float x)
+{
+	uint32_t ix, ib;
+	int nm1, sign, i;
+	float a, b, temp;
+
+	GET_FLOAT_WORD(ix, x);
+	sign = ix>>31;
+	ix &= 0x7fffffff;
+	if (ix > 0x7f800000) /* nan */
+		return x;
+	if (sign && ix != 0) /* x < 0 */
+		return 0/0.0f;
+	if (ix == 0x7f800000)
+		return 0.0f;
+
+	if (n == 0)
+		return y0f(x);
+	if (n < 0) {
+		nm1 = -(n+1);
+		sign = n&1;
+	} else {
+		nm1 = n-1;
+		sign = 0;
+	}
+	if (nm1 == 0)
+		return sign ? -y1f(x) : y1f(x);
+
+	a = y0f(x);
+	b = y1f(x);
+	/* quit if b is -inf */
+	GET_FLOAT_WORD(ib,b);
+	for (i = 0; i < nm1 && ib != 0xff800000; ) {
+		i++;
+		temp = b;
+		b = (2.0f*i/x)*b - a;
+		GET_FLOAT_WORD(ib, b);
+		a = temp;
+	}
+	return sign ? -b : b;
+}