[WOW64] Finished skeleton code for PE build (#2542)

* [WOW64] Finished skeleton code for PE build

* move musl to external

26 files changed, 2656 insertions, 0 deletions

diff --git a/external/musl/__cos.c b/external/musl/__cos.c
new file mode 100644
index 00000000..46cefb38
--- /dev/null
+++ b/external/musl/__cos.c
@@ -0,0 +1,71 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_cos.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.
+ * ====================================================
+ */
+/*
+ * __cos( x,  y )
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ *
+ * Algorithm
+ *      1. Since cos(-x) = cos(x), we need only to consider positive x.
+ *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+ *      3. cos(x) is approximated by a polynomial of degree 14 on
+ *         [0,pi/4]
+ *                                       4            14
+ *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+ *         where the remez error is
+ *
+ *      |              2     4     6     8     10    12     14 |     -58
+ *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
+ *      |                                                      |
+ *
+ *                     4     6     8     10    12     14
+ *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
+ *             cos(x) ~ 1 - x*x/2 + r
+ *         since cos(x+y) ~ cos(x) - sin(x)*y
+ *                        ~ cos(x) - x*y,
+ *         a correction term is necessary in cos(x) and hence
+ *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
+ *         For better accuracy, rearrange to
+ *              cos(x+y) ~ w + (tmp + (r-x*y))
+ *         where w = 1 - x*x/2 and tmp is a tiny correction term
+ *         (1 - x*x/2 == w + tmp exactly in infinite precision).
+ *         The exactness of w + tmp in infinite precision depends on w
+ *         and tmp having the same precision as x.  If they have extra
+ *         precision due to compiler bugs, then the extra precision is
+ *         only good provided it is retained in all terms of the final
+ *         expression for cos().  Retention happens in all cases tested
+ *         under FreeBSD, so don't pessimize things by forcibly clipping
+ *         any extra precision in w.
+ */
+
+#include "libm.h"
+
+static const double
+C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
+C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
+C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
+C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
+C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
+C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
+
+double __cos(double x, double y)
+{
+	double_t hz,z,r,w;
+
+	z  = x*x;
+	w  = z*z;
+	r  = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6));
+	hz = 0.5*z;
+	w  = 1.0-hz;
+	return w + (((1.0-w)-hz) + (z*r-x*y));
+}
diff --git a/external/musl/__math_divzero.c b/external/musl/__math_divzero.c
new file mode 100644
index 00000000..59d21350
--- /dev/null
+++ b/external/musl/__math_divzero.c
@@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_divzero(uint32_t sign)
+{
+	return fp_barrier(sign ? -1.0 : 1.0) / 0.0;
+}
diff --git a/external/musl/__math_invalid.c b/external/musl/__math_invalid.c
new file mode 100644
index 00000000..17740490
--- /dev/null
+++ b/external/musl/__math_invalid.c
@@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_invalid(double x)
+{
+	return (x - x) / (x - x);
+}
diff --git a/external/musl/__rem_pio2.c b/external/musl/__rem_pio2.c
new file mode 100644
index 00000000..3addef65
--- /dev/null
+++ b/external/musl/__rem_pio2.c
@@ -0,0 +1,190 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.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.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+/* __rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __rem_pio2_large() for large x
+ */
+
+#include "libm.h"
+
+#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
+#define EPS DBL_EPSILON
+#elif FLT_EVAL_METHOD==2
+#define EPS LDBL_EPSILON
+#endif
+
+/*
+ * invpio2:  53 bits of 2/pi
+ * pio2_1:   first  33 bit of pi/2
+ * pio2_1t:  pi/2 - pio2_1
+ * pio2_2:   second 33 bit of pi/2
+ * pio2_2t:  pi/2 - (pio2_1+pio2_2)
+ * pio2_3:   third  33 bit of pi/2
+ * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+static const double
+toint   = 1.5/EPS,
+pio4    = 0x1.921fb54442d18p-1,
+invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+pio2_1  = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+pio2_2  = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+pio2_3  = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
+int __rem_pio2(double x, double *y)
+{
+	union {double f; uint64_t i;} u = {x};
+	double_t z,w,t,r,fn;
+	double tx[3],ty[2];
+	uint32_t ix;
+	int sign, n, ex, ey, i;
+
+	sign = u.i>>63;
+	ix = u.i>>32 & 0x7fffffff;
+	if (ix <= 0x400f6a7a) {  /* |x| ~<= 5pi/4 */
+		if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
+			goto medium;  /* cancellation -- use medium case */
+		if (ix <= 0x4002d97c) {  /* |x| ~<= 3pi/4 */
+			if (!sign) {
+				z = x - pio2_1;  /* one round good to 85 bits */
+				y[0] = z - pio2_1t;
+				y[1] = (z-y[0]) - pio2_1t;
+				return 1;
+			} else {
+				z = x + pio2_1;
+				y[0] = z + pio2_1t;
+				y[1] = (z-y[0]) + pio2_1t;
+				return -1;
+			}
+		} else {
+			if (!sign) {
+				z = x - 2*pio2_1;
+				y[0] = z - 2*pio2_1t;
+				y[1] = (z-y[0]) - 2*pio2_1t;
+				return 2;
+			} else {
+				z = x + 2*pio2_1;
+				y[0] = z + 2*pio2_1t;
+				y[1] = (z-y[0]) + 2*pio2_1t;
+				return -2;
+			}
+		}
+	}
+	if (ix <= 0x401c463b) {  /* |x| ~<= 9pi/4 */
+		if (ix <= 0x4015fdbc) {  /* |x| ~<= 7pi/4 */
+			if (ix == 0x4012d97c)  /* |x| ~= 3pi/2 */
+				goto medium;
+			if (!sign) {
+				z = x - 3*pio2_1;
+				y[0] = z - 3*pio2_1t;
+				y[1] = (z-y[0]) - 3*pio2_1t;
+				return 3;
+			} else {
+				z = x + 3*pio2_1;
+				y[0] = z + 3*pio2_1t;
+				y[1] = (z-y[0]) + 3*pio2_1t;
+				return -3;
+			}
+		} else {
+			if (ix == 0x401921fb)  /* |x| ~= 4pi/2 */
+				goto medium;
+			if (!sign) {
+				z = x - 4*pio2_1;
+				y[0] = z - 4*pio2_1t;
+				y[1] = (z-y[0]) - 4*pio2_1t;
+				return 4;
+			} else {
+				z = x + 4*pio2_1;
+				y[0] = z + 4*pio2_1t;
+				y[1] = (z-y[0]) + 4*pio2_1t;
+				return -4;
+			}
+		}
+	}
+	if (ix < 0x413921fb) {  /* |x| ~< 2^20*(pi/2), medium size */
+medium:
+		/* rint(x/(pi/2)) */
+		fn = rint(x * invpio2);
+		n = (int32_t)fn;
+		r = x - fn*pio2_1;
+		w = fn*pio2_1t;  /* 1st round, good to 85 bits */
+		/* Matters with directed rounding. */
+		if (predict_false(r - w < -pio4)) {
+			n--;
+			fn--;
+			r = x - fn*pio2_1;
+			w = fn*pio2_1t;
+		} else if (predict_false(r - w > pio4)) {
+			n++;
+			fn++;
+			r = x - fn*pio2_1;
+			w = fn*pio2_1t;
+		}
+		y[0] = r - w;
+		u.f = y[0];
+		ey = u.i>>52 & 0x7ff;
+		ex = ix>>20;
+		if (ex - ey > 16) { /* 2nd round, good to 118 bits */
+			t = r;
+			w = fn*pio2_2;
+			r = t - w;
+			w = fn*pio2_2t - ((t-r)-w);
+			y[0] = r - w;
+			u.f = y[0];
+			ey = u.i>>52 & 0x7ff;
+			if (ex - ey > 49) {  /* 3rd round, good to 151 bits, covers all cases */
+				t = r;
+				w = fn*pio2_3;
+				r = t - w;
+				w = fn*pio2_3t - ((t-r)-w);
+				y[0] = r - w;
+			}
+		}
+		y[1] = (r - y[0]) - w;
+		return n;
+	}
+	/*
+	 * all other (large) arguments
+	 */
+	if (ix >= 0x7ff00000) {  /* x is inf or NaN */
+		y[0] = y[1] = x - x;
+		return 0;
+	}
+	/* set z = scalbn(|x|,-ilogb(x)+23) */
+	u.f = x;
+	u.i &= (uint64_t)-1>>12;
+	u.i |= (uint64_t)(0x3ff + 23)<<52;
+	z = u.f;
+	for (i=0; i < 2; i++) {
+		tx[i] = (double)(int32_t)z;
+		z     = (z-tx[i])*0x1p24;
+	}
+	tx[i] = z;
+	/* skip zero terms, first term is non-zero */
+	while (tx[i] == 0.0)
+		i--;
+	n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
+	if (sign) {
+		y[0] = -ty[0];
+		y[1] = -ty[1];
+		return -n;
+	}
+	y[0] = ty[0];
+	y[1] = ty[1];
+	return n;
+}
diff --git a/external/musl/__rem_pio2_large.c b/external/musl/__rem_pio2_large.c
new file mode 100644
index 00000000..958f28c2
--- /dev/null
+++ b/external/musl/__rem_pio2_large.c
@@ -0,0 +1,442 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.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.
+ * ====================================================
+ */
+/*
+ * __rem_pio2_large(x,y,e0,nx,prec)
+ * double x[],y[]; int e0,nx,prec;
+ *
+ * __rem_pio2_large return the last three digits of N with
+ *              y = x - N*pi/2
+ * so that |y| < pi/2.
+ *
+ * The method is to compute the integer (mod 8) and fraction parts of
+ * (2/pi)*x without doing the full multiplication. In general we
+ * skip the part of the product that are known to be a huge integer (
+ * more accurately, = 0 mod 8 ). Thus the number of operations are
+ * independent of the exponent of the input.
+ *
+ * (2/pi) is represented by an array of 24-bit integers in ipio2[].
+ *
+ * Input parameters:
+ *      x[]     The input value (must be positive) is broken into nx
+ *              pieces of 24-bit integers in double precision format.
+ *              x[i] will be the i-th 24 bit of x. The scaled exponent
+ *              of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
+ *              match x's up to 24 bits.
+ *
+ *              Example of breaking a double positive z into x[0]+x[1]+x[2]:
+ *                      e0 = ilogb(z)-23
+ *                      z  = scalbn(z,-e0)
+ *              for i = 0,1,2
+ *                      x[i] = floor(z)
+ *                      z    = (z-x[i])*2**24
+ *
+ *
+ *      y[]     ouput result in an array of double precision numbers.
+ *              The dimension of y[] is:
+ *                      24-bit  precision       1
+ *                      53-bit  precision       2
+ *                      64-bit  precision       2
+ *                      113-bit precision       3
+ *              The actual value is the sum of them. Thus for 113-bit
+ *              precison, one may have to do something like:
+ *
+ *              long double t,w,r_head, r_tail;
+ *              t = (long double)y[2] + (long double)y[1];
+ *              w = (long double)y[0];
+ *              r_head = t+w;
+ *              r_tail = w - (r_head - t);
+ *
+ *      e0      The exponent of x[0]. Must be <= 16360 or you need to
+ *              expand the ipio2 table.
+ *
+ *      nx      dimension of x[]
+ *
+ *      prec    an integer indicating the precision:
+ *                      0       24  bits (single)
+ *                      1       53  bits (double)
+ *                      2       64  bits (extended)
+ *                      3       113 bits (quad)
+ *
+ * External function:
+ *      double scalbn(), floor();
+ *
+ *
+ * Here is the description of some local variables:
+ *
+ *      jk      jk+1 is the initial number of terms of ipio2[] needed
+ *              in the computation. The minimum and recommended value
+ *              for jk is 3,4,4,6 for single, double, extended, and quad.
+ *              jk+1 must be 2 larger than you might expect so that our
+ *              recomputation test works. (Up to 24 bits in the integer
+ *              part (the 24 bits of it that we compute) and 23 bits in
+ *              the fraction part may be lost to cancelation before we
+ *              recompute.)
+ *
+ *      jz      local integer variable indicating the number of
+ *              terms of ipio2[] used.
+ *
+ *      jx      nx - 1
+ *
+ *      jv      index for pointing to the suitable ipio2[] for the
+ *              computation. In general, we want
+ *                      ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
+ *              is an integer. Thus
+ *                      e0-3-24*jv >= 0 or (e0-3)/24 >= jv
+ *              Hence jv = max(0,(e0-3)/24).
+ *
+ *      jp      jp+1 is the number of terms in PIo2[] needed, jp = jk.
+ *
+ *      q[]     double array with integral value, representing the
+ *              24-bits chunk of the product of x and 2/pi.
+ *
+ *      q0      the corresponding exponent of q[0]. Note that the
+ *              exponent for q[i] would be q0-24*i.
+ *
+ *      PIo2[]  double precision array, obtained by cutting pi/2
+ *              into 24 bits chunks.
+ *
+ *      f[]     ipio2[] in floating point
+ *
+ *      iq[]    integer array by breaking up q[] in 24-bits chunk.
+ *
+ *      fq[]    final product of x*(2/pi) in fq[0],..,fq[jk]
+ *
+ *      ih      integer. If >0 it indicates q[] is >= 0.5, hence
+ *              it also indicates the *sign* of the result.
+ *
+ */
+/*
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "libm.h"
+
+static const int init_jk[] = {3,4,4,6}; /* initial value for jk */
+
+/*
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+ *
+ *              integer array, contains the (24*i)-th to (24*i+23)-th
+ *              bit of 2/pi after binary point. The corresponding
+ *              floating value is
+ *
+ *                      ipio2[i] * 2^(-24(i+1)).
+ *
+ * NB: This table must have at least (e0-3)/24 + jk terms.
+ *     For quad precision (e0 <= 16360, jk = 6), this is 686.
+ */
+static const int32_t ipio2[] = {
+0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
+0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
+0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
+0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
+0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
+0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
+0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
+0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
+0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
+0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
+0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
+
+#if LDBL_MAX_EXP > 1024
+0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
+0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2,
+0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35,
+0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
+0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C,
+0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4,
+0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
+0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7,
+0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19,
+0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
+0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16,
+0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6,
+0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
+0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48,
+0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3,
+0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
+0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55,
+0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612,
+0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
+0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC,
+0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B,
+0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
+0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4,
+0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB,
+0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
+0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C,
+0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F,
+0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
+0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437,
+0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B,
+0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
+0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD,
+0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3,
+0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
+0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717,
+0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F,
+0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
+0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB,
+0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51,
+0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
+0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C,
+0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6,
+0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
+0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED,
+0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328,
+0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
+0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0,
+0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B,
+0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
+0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3,
+0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F,
+0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
+0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B,
+0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4,
+0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
+0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31,
+0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30,
+0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
+0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E,
+0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1,
+0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
+0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4,
+0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08,
+0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
+0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9,
+0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4,
+0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
+0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C,
+0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0,
+0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
+0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0,
+0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC,
+0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
+0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893,
+0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7,
+0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
+0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F,
+0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4,
+0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
+0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B,
+0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2,
+0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
+0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E,
+0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569,
+0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
+0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9,
+0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D,
+0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
+0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855,
+0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569,
+0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
+0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE,
+0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41,
+0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
+0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F,
+0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110,
+0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
+0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365,
+0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A,
+0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
+0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5,
+0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616,
+0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
+0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0,
+#endif
+};
+
+static const double PIo2[] = {
+  1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
+  7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
+  5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
+  3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
+  1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
+  1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
+  2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
+  2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
+};
+
+int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
+{
+	int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
+	double z,fw,f[20],fq[20],q[20];
+
+	/* initialize jk*/
+	jk = init_jk[prec];
+	jp = jk;
+
+	/* determine jx,jv,q0, note that 3>q0 */
+	jx = nx-1;
+	jv = (e0-3)/24;  if(jv<0) jv=0;
+	q0 = e0-24*(jv+1);
+
+	/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+	j = jv-jx; m = jx+jk;
+	for (i=0; i<=m; i++,j++)
+		f[i] = j<0 ? 0.0 : (double)ipio2[j];
+
+	/* compute q[0],q[1],...q[jk] */
+	for (i=0; i<=jk; i++) {
+		for (j=0,fw=0.0; j<=jx; j++)
+			fw += x[j]*f[jx+i-j];
+		q[i] = fw;
+	}
+
+	jz = jk;
+recompute:
+	/* distill q[] into iq[] reversingly */
+	for (i=0,j=jz,z=q[jz]; j>0; i++,j--) {
+		fw    = (double)(int32_t)(0x1p-24*z);
+		iq[i] = (int32_t)(z - 0x1p24*fw);
+		z     = q[j-1]+fw;
+	}
+
+	/* compute n */
+	z  = scalbn(z,q0);       /* actual value of z */
+	z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
+	n  = (int32_t)z;
+	z -= (double)n;
+	ih = 0;
+	if (q0 > 0) {  /* need iq[jz-1] to determine n */
+		i  = iq[jz-1]>>(24-q0); n += i;
+		iq[jz-1] -= i<<(24-q0);
+		ih = iq[jz-1]>>(23-q0);
+	}
+	else if (q0 == 0) ih = iq[jz-1]>>23;
+	else if (z >= 0.5) ih = 2;
+
+	if (ih > 0) {  /* q > 0.5 */
+		n += 1; carry = 0;
+		for (i=0; i<jz; i++) {  /* compute 1-q */
+			j = iq[i];
+			if (carry == 0) {
+				if (j != 0) {
+					carry = 1;
+					iq[i] = 0x1000000 - j;
+				}
+			} else
+				iq[i] = 0xffffff - j;
+		}
+		if (q0 > 0) {  /* rare case: chance is 1 in 12 */
+			switch(q0) {
+			case 1:
+				iq[jz-1] &= 0x7fffff; break;
+			case 2:
+				iq[jz-1] &= 0x3fffff; break;
+			}
+		}
+		if (ih == 2) {
+			z = 1.0 - z;
+			if (carry != 0)
+				z -= scalbn(1.0,q0);
+		}
+	}
+
+	/* check if recomputation is needed */
+	if (z == 0.0) {
+		j = 0;
+		for (i=jz-1; i>=jk; i--) j |= iq[i];
+		if (j == 0) {  /* need recomputation */
+			for (k=1; iq[jk-k]==0; k++);  /* k = no. of terms needed */
+
+			for (i=jz+1; i<=jz+k; i++) {  /* add q[jz+1] to q[jz+k] */
+				f[jx+i] = (double)ipio2[jv+i];
+				for (j=0,fw=0.0; j<=jx; j++)
+					fw += x[j]*f[jx+i-j];
+				q[i] = fw;
+			}
+			jz += k;
+			goto recompute;
+		}
+	}
+
+	/* chop off zero terms */
+	if (z == 0.0) {
+		jz -= 1;
+		q0 -= 24;
+		while (iq[jz] == 0) {
+			jz--;
+			q0 -= 24;
+		}
+	} else { /* break z into 24-bit if necessary */
+		z = scalbn(z,-q0);
+		if (z >= 0x1p24) {
+			fw = (double)(int32_t)(0x1p-24*z);
+			iq[jz] = (int32_t)(z - 0x1p24*fw);
+			jz += 1;
+			q0 += 24;
+			iq[jz] = (int32_t)fw;
+		} else
+			iq[jz] = (int32_t)z;
+	}
+
+	/* convert integer "bit" chunk to floating-point value */
+	fw = scalbn(1.0,q0);
+	for (i=jz; i>=0; i--) {
+		q[i] = fw*(double)iq[i];
+		fw *= 0x1p-24;
+	}
+
+	/* compute PIo2[0,...,jp]*q[jz,...,0] */
+	for(i=jz; i>=0; i--) {
+		for (fw=0.0,k=0; k<=jp && k<=jz-i; k++)
+			fw += PIo2[k]*q[i+k];
+		fq[jz-i] = fw;
+	}
+
+	/* compress fq[] into y[] */
+	switch(prec) {
+	case 0:
+		fw = 0.0;
+		for (i=jz; i>=0; i--)
+			fw += fq[i];
+		y[0] = ih==0 ? fw : -fw;
+		break;
+	case 1:
+	case 2:
+		fw = 0.0;
+		for (i=jz; i>=0; i--)
+			fw += fq[i];
+		// TODO: drop excess precision here once double_t is used
+		fw = (double)fw;
+		y[0] = ih==0 ? fw : -fw;
+		fw = fq[0]-fw;
+		for (i=1; i<=jz; i++)
+			fw += fq[i];
+		y[1] = ih==0 ? fw : -fw;
+		break;
+	case 3:  /* painful */
+		for (i=jz; i>0; i--) {
+			fw      = fq[i-1]+fq[i];
+			fq[i]  += fq[i-1]-fw;
+			fq[i-1] = fw;
+		}
+		for (i=jz; i>1; i--) {
+			fw      = fq[i-1]+fq[i];
+			fq[i]  += fq[i-1]-fw;
+			fq[i-1] = fw;
+		}
+		for (fw=0.0,i=jz; i>=2; i--)
+			fw += fq[i];
+		if (ih==0) {
+			y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
+		} else {
+			y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
+		}
+	}
+	return n&7;
+}
diff --git a/external/musl/__sin.c b/external/musl/__sin.c
new file mode 100644
index 00000000..40309496
--- /dev/null
+++ b/external/musl/__sin.c
@@ -0,0 +1,64 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_sin.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.
+ * ====================================================
+ */
+/* __sin( x, y, iy)
+ * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
+ *
+ * Algorithm
+ *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
+ *      2. Callers must return sin(-0) = -0 without calling here since our
+ *         odd polynomial is not evaluated in a way that preserves -0.
+ *         Callers may do the optimization sin(x) ~ x for tiny x.
+ *      3. sin(x) is approximated by a polynomial of degree 13 on
+ *         [0,pi/4]
+ *                               3            13
+ *              sin(x) ~ x + S1*x + ... + S6*x
+ *         where
+ *
+ *      |sin(x)         2     4     6     8     10     12  |     -58
+ *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
+ *      |  x                                               |
+ *
+ *      4. sin(x+y) = sin(x) + sin'(x')*y
+ *                  ~ sin(x) + (1-x*x/2)*y
+ *         For better accuracy, let
+ *                   3      2      2      2      2
+ *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
+ *         then                   3    2
+ *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
+ */
+
+#include "libm.h"
+
+static const double
+S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
+S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
+S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
+S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
+S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
+S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
+
+double __sin(double x, double y, int iy)
+{
+	double_t z,r,v,w;
+
+	z = x*x;
+	w = z*z;
+	r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
+	v = z*x;
+	if (iy == 0)
+		return x + v*(S1 + z*r);
+	else
+		return x - ((z*(0.5*y - v*r) - y) - v*S1);
+}
diff --git a/external/musl/cos.c b/external/musl/cos.c
new file mode 100644
index 00000000..eb5c2a47
--- /dev/null
+++ b/external/musl/cos.c
@@ -0,0 +1,79 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cos.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* cos(x)
+ * Return cosine function of x.
+ *
+ * kernel function:
+ *      __sin           ... sine function on [-pi/4,pi/4]
+ *      __cos           ... cosine function on [-pi/4,pi/4]
+ *      __rem_pio2      ... argument reduction routine
+ *
+ * Method.
+ *      Let S,C and T denote the sin, cos and tan respectively on
+ *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ *      in [-pi/4 , +pi/4], and let n = k mod 4.
+ *      We have
+ *
+ *          n        sin(x)      cos(x)        tan(x)
+ *     ----------------------------------------------------------
+ *          0          S           C             T
+ *          1          C          -S            -1/T
+ *          2         -S          -C             T
+ *          3         -C           S            -1/T
+ *     ----------------------------------------------------------
+ *
+ * Special cases:
+ *      Let trig be any of sin, cos, or tan.
+ *      trig(+-INF)  is NaN, with signals;
+ *      trig(NaN)    is that NaN;
+ *
+ * Accuracy:
+ *      TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "libm.h"
+
+double __cdecl cos(double x)
+{
+	double y[2];
+	uint32_t ix;
+	unsigned n;
+
+	GET_HIGH_WORD(ix, x);
+	ix &= 0x7fffffff;
+
+	/* |x| ~< pi/4 */
+	if (ix <= 0x3fe921fb) {
+		if (ix < 0x3e46a09e) {  /* |x| < 2**-27 * sqrt(2) */
+			/* raise inexact if x!=0 */
+			FORCE_EVAL(x + 0x1p120f);
+			return 1.0;
+		}
+		return __cos(x, 0);
+	}
+
+	/* cos(Inf or NaN) is NaN */
+	if (isinf(x))
+		return math_error(_DOMAIN, "cos", x, 0, x - x);
+	if (ix >= 0x7ff00000)
+		return x-x;
+
+	/* argument reduction */
+	n = __rem_pio2(x, y);
+	switch (n&3) {
+	case 0: return  __cos(y[0], y[1]);
+	case 1: return -__sin(y[0], y[1], 1);
+	case 2: return -__cos(y[0], y[1]);
+	default:
+		return  __sin(y[0], y[1], 1);
+	}
+}
diff --git a/external/musl/exp2.c b/external/musl/exp2.c
new file mode 100644
index 00000000..47c557ce
--- /dev/null
+++ b/external/musl/exp2.c
@@ -0,0 +1,130 @@
+/*
+ * Double-precision 2^x function.
+ *
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "libm.h"
+#include "exp_data.h"
+
+#define N (1 << EXP_TABLE_BITS)
+#define Shift __exp_data.exp2_shift
+#define T __exp_data.tab
+#define C1 __exp_data.exp2_poly[0]
+#define C2 __exp_data.exp2_poly[1]
+#define C3 __exp_data.exp2_poly[2]
+#define C4 __exp_data.exp2_poly[3]
+#define C5 __exp_data.exp2_poly[4]
+
+/* Handle cases that may overflow or underflow when computing the result that
+   is scale*(1+TMP) without intermediate rounding.  The bit representation of
+   scale is in SBITS, however it has a computed exponent that may have
+   overflown into the sign bit so that needs to be adjusted before using it as
+   a double.  (int32_t)KI is the k used in the argument reduction and exponent
+   adjustment of scale, positive k here means the result may overflow and
+   negative k means the result may underflow.  */
+static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
+{
+	double_t scale, y;
+
+	if ((ki & 0x80000000) == 0) {
+		/* k > 0, the exponent of scale might have overflowed by 1.  */
+		sbits -= 1ull << 52;
+		scale = asdouble(sbits);
+		y = 2 * (scale + scale * tmp);
+		return eval_as_double(y);
+	}
+	/* k < 0, need special care in the subnormal range.  */
+	sbits += 1022ull << 52;
+	scale = asdouble(sbits);
+	y = scale + scale * tmp;
+	if (y < 1.0) {
+		/* Round y to the right precision before scaling it into the subnormal
+		   range to avoid double rounding that can cause 0.5+E/2 ulp error where
+		   E is the worst-case ulp error outside the subnormal range.  So this
+		   is only useful if the goal is better than 1 ulp worst-case error.  */
+		double_t hi, lo;
+		lo = scale - y + scale * tmp;
+		hi = 1.0 + y;
+		lo = 1.0 - hi + y + lo;
+		y = eval_as_double(hi + lo) - 1.0;
+		/* Avoid -0.0 with downward rounding.  */
+		if (WANT_ROUNDING && y == 0.0)
+			y = 0.0;
+		/* The underflow exception needs to be signaled explicitly.  */
+		fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022);
+	}
+	y = 0x1p-1022 * y;
+	return eval_as_double(y);
+}
+
+/* Top 12 bits of a double (sign and exponent bits).  */
+static inline uint32_t top12(double x)
+{
+	return asuint64(x) >> 52;
+}
+
+double __cdecl exp2(double x)
+{
+	uint32_t abstop;
+	uint64_t ki, idx, top, sbits;
+	double_t kd, r, r2, scale, tail, tmp;
+
+	abstop = top12(x) & 0x7ff;
+	if (predict_false(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) {
+		if (abstop - top12(0x1p-54) >= 0x80000000)
+			/* Avoid spurious underflow for tiny x.  */
+			/* Note: 0 is common input.  */
+			return WANT_ROUNDING ? 1.0 + x : 1.0;
+		if (abstop >= top12(1024.0)) {
+			if (asuint64(x) == asuint64(-INFINITY))
+				return 0.0;
+			if (abstop >= top12(INFINITY))
+				return 1.0 + x;
+			if (!(asuint64(x) >> 63)) {
+				errno = ERANGE;
+				return fp_barrier(DBL_MAX) * DBL_MAX;
+			}
+			else if (x <= -2147483648.0) {
+				fp_barrier(x + 0x1p120f);
+				return 0;
+			}
+			else if (asuint64(x) >= asuint64(-1075.0)) {
+				errno = ERANGE;
+				fp_barrier(x + 0x1p120f);
+				return 0;
+			}
+		}
+		if (2 * asuint64(x) > 2 * asuint64(928.0))
+			/* Large x is special cased below.  */
+			abstop = 0;
+	}
+
+	/* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)].  */
+	/* x = k/N + r, with int k and r in [-1/2N, 1/2N].  */
+	kd = eval_as_double(x + Shift);
+	ki = asuint64(kd); /* k.  */
+	kd -= Shift; /* k/N for int k.  */
+	r = x - kd;
+	/* 2^(k/N) ~= scale * (1 + tail).  */
+	idx = 2 * (ki % N);
+	top = ki << (52 - EXP_TABLE_BITS);
+	tail = asdouble(T[idx]);
+	/* This is only a valid scale when -1023*N < k < 1024*N.  */
+	sbits = T[idx + 1] + top;
+	/* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1).  */
+	/* Evaluation is optimized assuming superscalar pipelined execution.  */
+	r2 = r * r;
+	/* Without fma the worst case error is 0.5/N ulp larger.  */
+	/* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp.  */
+	tmp = tail + r * C1 + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
+	if (predict_false(abstop == 0))
+		return specialcase(tmp, sbits, ki);
+	scale = asdouble(sbits);
+	/* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there
+	   is no spurious underflow here even without fma.  */
+	return eval_as_double(scale + scale * tmp);
+}
diff --git a/external/musl/exp_data.c b/external/musl/exp_data.c
new file mode 100644
index 00000000..21be0146
--- /dev/null
+++ b/external/musl/exp_data.c
@@ -0,0 +1,182 @@
+/*
+ * Shared data between exp, exp2 and pow.
+ *
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "exp_data.h"
+
+#define N (1 << EXP_TABLE_BITS)
+
+const struct exp_data __exp_data = {
+// N/ln2
+.invln2N = 0x1.71547652b82fep0 * N,
+// -ln2/N
+.negln2hiN = -0x1.62e42fefa0000p-8,
+.negln2loN = -0x1.cf79abc9e3b3ap-47,
+// Used for rounding when !TOINT_INTRINSICS
+#if EXP_USE_TOINT_NARROW
+.shift = 0x1800000000.8p0,
+#else
+.shift = 0x1.8p52,
+#endif
+// exp polynomial coefficients.
+.poly = {
+// abs error: 1.555*2^-66
+// ulp error: 0.509 (0.511 without fma)
+// if |x| < ln2/256+eps
+// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65
+// abs error if |x| < ln2/128: 1.7145*2^-56
+0x1.ffffffffffdbdp-2,
+0x1.555555555543cp-3,
+0x1.55555cf172b91p-5,
+0x1.1111167a4d017p-7,
+},
+.exp2_shift = 0x1.8p52 / N,
+// exp2 polynomial coefficients.
+.exp2_poly = {
+// abs error: 1.2195*2^-65
+// ulp error: 0.507 (0.511 without fma)
+// if |x| < 1/256
+// abs error if |x| < 1/128: 1.9941*2^-56
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c424p-3,
+0x1.c6b08d70cf4b5p-5,
+0x1.3b2abd24650ccp-7,
+0x1.5d7e09b4e3a84p-10,
+},
+// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
+// tab[2*k] = asuint64(T[k])
+// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
+.tab = {
+0x0, 0x3ff0000000000000,
+0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0xbc905e7a108766d1, 0x3fefe315e86e7f85,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc6a033489906e0b, 0x3fef9b66affed31b,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0xbc96d99c7611eb26, 0x3fef5be084045cd4,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c864201e2ac744c, 0x3fef0170fc4cd831,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc9907f81b512d8e, 0x3feeecae6d05d866,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc9312607a28698a, 0x3feeda4504ac801c,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0x3c9666093b0664ef, 0x3feeca41ed1d0057,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0x3c34c7855019c6ea, 0x3feea9268a5946b7,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0xbc845378892be9ae, 0x3feea34634ccc320,
+0xbc93cedd78565858, 0x3feea23882552225,
+0x3c5710aa807e1964, 0x3feea155d44ca973,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0xbc6a12ad8734b982, 0x3feea012750bdabf,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc80dc3d54e08851, 0x3fee9f7df9519484,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0x3c6dd235e10a73bb, 0x3feec86319e32323,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c90cc319cee31d2, 0x3feed99e1330b358,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc90a40e3da6f640, 0x3feef9728de5593a,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0xbc91eee26b588a35, 0x3fef05b030a1064a,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0xbc900dae3875a949, 0x3fef4f87080d89f2,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0xbc82919e2040220f, 0x3fef60e316c98398,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0x3c843a59ac016b4b, 0x3fef7321f301b460,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0xbc892ab93b470dc9, 0x3fef864614f5a129,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
+},
+};
diff --git a/external/musl/exp_data.h b/external/musl/exp_data.h
new file mode 100644
index 00000000..3e24bac5
--- /dev/null
+++ b/external/musl/exp_data.h
@@ -0,0 +1,26 @@
+/*
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+#ifndef _EXP_DATA_H
+#define _EXP_DATA_H
+
+#include <features.h>
+#include <stdint.h>
+
+#define EXP_TABLE_BITS 7
+#define EXP_POLY_ORDER 5
+#define EXP_USE_TOINT_NARROW 0
+#define EXP2_POLY_ORDER 5
+extern hidden const struct exp_data {
+	double invln2N;
+	double shift;
+	double negln2hiN;
+	double negln2loN;
+	double poly[4]; /* Last four coefficients.  */
+	double exp2_shift;
+	double exp2_poly[EXP2_POLY_ORDER];
+	uint64_t tab[2*(1 << EXP_TABLE_BITS)];
+} __exp_data;
+
+#endif
diff --git a/external/musl/expm1.c b/external/musl/expm1.c
new file mode 100644
index 00000000..d29f73fa
--- /dev/null
+++ b/external/musl/expm1.c
@@ -0,0 +1,202 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* expm1(x)
+ * Returns exp(x)-1, the exponential of x minus 1.
+ *
+ * Method
+ *   1. Argument reduction:
+ *      Given x, find r and integer k such that
+ *
+ *               x = k*ln2 + r,  |r| <= 0.5*ln2 ~ 0.34658
+ *
+ *      Here a correction term c will be computed to compensate
+ *      the error in r when rounded to a floating-point number.
+ *
+ *   2. Approximating expm1(r) by a special rational function on
+ *      the interval [0,0.34658]:
+ *      Since
+ *          r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
+ *      we define R1(r*r) by
+ *          r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
+ *      That is,
+ *          R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
+ *                   = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
+ *                   = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
+ *      We use a special Remez algorithm on [0,0.347] to generate
+ *      a polynomial of degree 5 in r*r to approximate R1. The
+ *      maximum error of this polynomial approximation is bounded
+ *      by 2**-61. In other words,
+ *          R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
+ *      where   Q1  =  -1.6666666666666567384E-2,
+ *              Q2  =   3.9682539681370365873E-4,
+ *              Q3  =  -9.9206344733435987357E-6,
+ *              Q4  =   2.5051361420808517002E-7,
+ *              Q5  =  -6.2843505682382617102E-9;
+ *              z   =  r*r,
+ *      with error bounded by
+ *          |                  5           |     -61
+ *          | 1.0+Q1*z+...+Q5*z   -  R1(z) | <= 2
+ *          |                              |
+ *
+ *      expm1(r) = exp(r)-1 is then computed by the following
+ *      specific way which minimize the accumulation rounding error:
+ *                             2     3
+ *                            r     r    [ 3 - (R1 + R1*r/2)  ]
+ *            expm1(r) = r + --- + --- * [--------------------]
+ *                            2     2    [ 6 - r*(3 - R1*r/2) ]
+ *
+ *      To compensate the error in the argument reduction, we use
+ *              expm1(r+c) = expm1(r) + c + expm1(r)*c
+ *                         ~ expm1(r) + c + r*c
+ *      Thus c+r*c will be added in as the correction terms for
+ *      expm1(r+c). Now rearrange the term to avoid optimization
+ *      screw up:
+ *                      (      2                                    2 )
+ *                      ({  ( r    [ R1 -  (3 - R1*r/2) ]  )  }    r  )
+ *       expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
+ *                      ({  ( 2    [ 6 - r*(3 - R1*r/2) ]  )  }    2  )
+ *                      (                                             )
+ *
+ *                 = r - E
+ *   3. Scale back to obtain expm1(x):
+ *      From step 1, we have
+ *         expm1(x) = either 2^k*[expm1(r)+1] - 1
+ *                  = or     2^k*[expm1(r) + (1-2^-k)]
+ *   4. Implementation notes:
+ *      (A). To save one multiplication, we scale the coefficient Qi
+ *           to Qi*2^i, and replace z by (x^2)/2.
+ *      (B). To achieve maximum accuracy, we compute expm1(x) by
+ *        (i)   if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
+ *        (ii)  if k=0, return r-E
+ *        (iii) if k=-1, return 0.5*(r-E)-0.5
+ *        (iv)  if k=1 if r < -0.25, return 2*((r+0.5)- E)
+ *                     else          return  1.0+2.0*(r-E);
+ *        (v)   if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
+ *        (vi)  if k <= 20, return 2^k((1-2^-k)-(E-r)), else
+ *        (vii) return 2^k(1-((E+2^-k)-r))
+ *
+ * Special cases:
+ *      expm1(INF) is INF, expm1(NaN) is NaN;
+ *      expm1(-INF) is -1, and
+ *      for finite argument, only expm1(0)=0 is exact.
+ *
+ * Accuracy:
+ *      according to an error analysis, the error is always less than
+ *      1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ *      For IEEE double
+ *          if x >  7.09782712893383973096e+02 then expm1(x) overflow
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "libm.h"
+
+static const double
+o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+ln2_hi      = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ln2_lo      = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+invln2      = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
+Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
+Q2 =  1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
+Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
+Q4 =  4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
+Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+double __cdecl expm1(double x)
+{
+	double_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
+	union {double f; uint64_t i;} u = {x};
+	uint32_t hx = u.i>>32 & 0x7fffffff;
+	int k, sign = u.i>>63;
+
+	/* filter out huge and non-finite argument */
+	if (hx >= 0x4043687A) {  /* if |x|>=56*ln2 */
+		if (isnan(x))
+			return x;
+		if (isinf(x))
+			return sign ? -1 : x;
+		if (sign)
+			return math_error(_UNDERFLOW, "exp", x, 0, -1);
+		if (x > o_threshold) {
+			return math_error(_OVERFLOW, "exp", x, 0, x * 0x1p1023);
+		}
+	}
+
+	/* argument reduction */
+	if (hx > 0x3fd62e42) {  /* if  |x| > 0.5 ln2 */
+		if (hx < 0x3FF0A2B2) {  /* and |x| < 1.5 ln2 */
+			if (!sign) {
+				hi = x - ln2_hi;
+				lo = ln2_lo;
+				k =  1;
+			} else {
+				hi = x + ln2_hi;
+				lo = -ln2_lo;
+				k = -1;
+			}
+		} else {
+			k  = invln2*x + (sign ? -0.5 : 0.5);
+			t  = k;
+			hi = x - t*ln2_hi;  /* t*ln2_hi is exact here */
+			lo = t*ln2_lo;
+		}
+		x = hi-lo;
+		c = (hi-x)-lo;
+	} else if (hx < 0x3c900000) {  /* |x| < 2**-54, return x */
+		if (hx < 0x00100000)
+			FORCE_EVAL((float)x);
+		return x;
+	} else
+		k = 0;
+
+	/* x is now in primary range */
+	hfx = 0.5*x;
+	hxs = x*hfx;
+	r1 = 1.0+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
+	t  = 3.0-r1*hfx;
+	e  = hxs*((r1-t)/(6.0 - x*t));
+	if (k == 0)   /* c is 0 */
+		return x - (x*e-hxs);
+	e  = x*(e-c) - c;
+	e -= hxs;
+	/* exp(x) ~ 2^k (x_reduced - e + 1) */
+	if (k == -1)
+		return 0.5*(x-e) - 0.5;
+	if (k == 1) {
+		if (x < -0.25)
+			return -2.0*(e-(x+0.5));
+		return 1.0+2.0*(x-e);
+	}
+	u.i = (uint64_t)(0x3ff + k)<<52;  /* 2^k */
+	twopk = u.f;
+	if (k < 0 || k > 56) {  /* suffice to return exp(x)-1 */
+		y = x - e + 1.0;
+		if (k == 1024)
+			y = y*2.0*0x1p1023;
+		else
+			y = y*twopk;
+		return y - 1.0;
+	}
+	u.i = (uint64_t)(0x3ff - k)<<52;  /* 2^-k */
+	if (k < 20)
+		y = (x-e+(1-u.f))*twopk;
+	else
+		y = (x-(e+u.f)+1)*twopk;
+	return y;
+}
diff --git a/external/musl/frexp.c b/external/musl/frexp.c
new file mode 100644
index 00000000..5eb5114e
--- /dev/null
+++ b/external/musl/frexp.c
@@ -0,0 +1,23 @@
+#include <math.h>
+#include <stdint.h>
+
+double __cdecl frexp(double x, int *e)
+{
+	union { double d; uint64_t i; } y = { x };
+	int ee = y.i>>52 & 0x7ff;
+
+	if (!ee) {
+		if (x) {
+			x = frexp(x*0x1p64, e);
+			*e -= 64;
+		} else *e = 0;
+		return x;
+	} else if (ee == 0x7ff) {
+		return x;
+	}
+
+	*e = ee - 0x3fe;
+	y.i &= 0x800fffffffffffffull;
+	y.i |= 0x3fe0000000000000ull;
+	return y.d;
+}
diff --git a/external/musl/internal/features.h b/external/musl/internal/features.h
new file mode 100644
index 00000000..a984ae94
--- /dev/null
+++ b/external/musl/internal/features.h
@@ -0,0 +1,8 @@
+#ifndef FEATURES_H
+#define FEATURES_H
+
+#define weak
+#define hidden
+#define weak_alias(old, new)
+
+#endif
diff --git a/external/musl/internal/libm.h b/external/musl/internal/libm.h
new file mode 100644
index 00000000..fa3ec4bd
--- /dev/null
+++ b/external/musl/internal/libm.h
@@ -0,0 +1,282 @@
+#ifndef _LIBM_H
+#define _LIBM_H
+
+#include <stdint.h>
+#include <float.h>
+#include <math.h>
+#include <errno.h>
+#include <features.h>
+
+typedef float float_t;
+typedef double double_t;
+
+hidden double math_error(int type, const char *name, double arg1, double arg2, double retval);
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
+union ldshape {
+	long double f;
+	struct {
+		uint64_t m;
+		uint16_t se;
+	} i;
+};
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
+/* This is the m68k variant of 80-bit long double, and this definition only works
+ * on archs where the alignment requirement of uint64_t is <= 4. */
+union ldshape {
+	long double f;
+	struct {
+		uint16_t se;
+		uint16_t pad;
+		uint64_t m;
+	} i;
+};
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
+union ldshape {
+	long double f;
+	struct {
+		uint64_t lo;
+		uint32_t mid;
+		uint16_t top;
+		uint16_t se;
+	} i;
+	struct {
+		uint64_t lo;
+		uint64_t hi;
+	} i2;
+};
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
+union ldshape {
+	long double f;
+	struct {
+		uint16_t se;
+		uint16_t top;
+		uint32_t mid;
+		uint64_t lo;
+	} i;
+	struct {
+		uint64_t hi;
+		uint64_t lo;
+	} i2;
+};
+#else
+#error Unsupported long double representation
+#endif
+
+/* Support non-nearest rounding mode.  */
+#define WANT_ROUNDING 1
+/* Support signaling NaNs.  */
+#define WANT_SNAN 0
+
+#if WANT_SNAN
+#error SNaN is unsupported
+#else
+#define issignalingf_inline(x) 0
+#define issignaling_inline(x) 0
+#endif
+
+#ifndef TOINT_INTRINSICS
+#define TOINT_INTRINSICS 0
+#endif
+
+#if TOINT_INTRINSICS
+/* Round x to nearest int in all rounding modes, ties have to be rounded
+   consistently with converttoint so the results match.  If the result
+   would be outside of [-2^31, 2^31-1] then the semantics is unspecified.  */
+static double_t roundtoint(double_t);
+
+/* Convert x to nearest int in all rounding modes, ties have to be rounded
+   consistently with roundtoint.  If the result is not representible in an
+   int32_t then the semantics is unspecified.  */
+static int32_t converttoint(double_t);
+#endif
+
+/* Helps static branch prediction so hot path can be better optimized.  */
+#ifdef __GNUC__
+#define predict_true(x) __builtin_expect(!!(x), 1)
+#define predict_false(x) __builtin_expect(x, 0)
+#else
+#define predict_true(x) (x)
+#define predict_false(x) (x)
+#endif
+
+/* Evaluate an expression as the specified type. With standard excess
+   precision handling a type cast or assignment is enough (with
+   -ffloat-store an assignment is required, in old compilers argument
+   passing and return statement may not drop excess precision).
+
+   If compiled without -ffloat-store or -fexcess-precision=standard,
+   an extra volatile qualifier here will force limiting the precision.  */
+
+static inline float eval_as_float(float x)
+{
+	volatile float y = x;
+	return y;
+}
+
+static inline double eval_as_double(double x)
+{
+	volatile double y = x;
+	return y;
+}
+
+/* fp_barrier returns its input, but limits code transformations
+   as if it had a side-effect (e.g. observable io) and returned
+   an arbitrary value.  */
+
+#ifndef fp_barrierf
+#define fp_barrierf fp_barrierf
+static inline float fp_barrierf(float x)
+{
+	volatile float y = x;
+	return y;
+}
+#endif
+
+#ifndef fp_barrier
+#define fp_barrier fp_barrier
+static inline double fp_barrier(double x)
+{
+	volatile double y = x;
+	return y;
+}
+#endif
+
+#ifndef fp_barrierl
+#define fp_barrierl fp_barrierl
+static inline long double fp_barrierl(long double x)
+{
+	volatile long double y = x;
+	return y;
+}
+#endif
+
+/* fp_force_eval ensures that the input value is computed when that's
+   otherwise unused.  To prevent the constant folding of the input
+   expression, an additional fp_barrier may be needed or a compilation
+   mode that does so (e.g. -frounding-math in gcc). Then it can be
+   used to evaluate an expression for its fenv side-effects only.   */
+
+#ifndef fp_force_evalf
+#define fp_force_evalf fp_force_evalf
+static inline void fp_force_evalf(float x)
+{
+	volatile float y;
+	y = x;
+}
+#endif
+
+#ifndef fp_force_eval
+#define fp_force_eval fp_force_eval
+static inline void fp_force_eval(double x)
+{
+	volatile double y;
+	y = x;
+}
+#endif
+
+#ifndef fp_force_evall
+#define fp_force_evall fp_force_evall
+static inline void fp_force_evall(long double x)
+{
+	volatile long double y;
+	y = x;
+}
+#endif
+
+#define FORCE_EVAL(x) do {                        \
+	if (sizeof(x) == sizeof(float)) {         \
+		fp_force_evalf(x);                \
+	} else if (sizeof(x) == sizeof(double)) { \
+		fp_force_eval(x);                 \
+	} else {                                  \
+		fp_force_evall(x);                \
+	}                                         \
+} while(0)
+
+#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
+#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
+#define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
+#define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
+
+#define EXTRACT_WORDS(hi,lo,d)                    \
+do {                                              \
+  uint64_t __u = asuint64(d);                     \
+  (hi) = __u >> 32;                               \
+  (lo) = (uint32_t)__u;                           \
+} while (0)
+
+#define GET_HIGH_WORD(hi,d)                       \
+do {                                              \
+  (hi) = asuint64(d) >> 32;                       \
+} while (0)
+
+#define GET_LOW_WORD(lo,d)                        \
+do {                                              \
+  (lo) = (uint32_t)asuint64(d);                   \
+} while (0)
+
+#define INSERT_WORDS(d,hi,lo)                     \
+do {                                              \
+  (d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
+} while (0)
+
+#define SET_HIGH_WORD(d,hi)                       \
+  INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
+
+#define SET_LOW_WORD(d,lo)                        \
+  INSERT_WORDS(d, asuint64(d)>>32, lo)
+
+#define GET_FLOAT_WORD(w,d)                       \
+do {                                              \
+  (w) = asuint(d);                                \
+} while (0)
+
+#define SET_FLOAT_WORD(d,w)                       \
+do {                                              \
+  (d) = asfloat(w);                               \
+} while (0)
+
+hidden int    __rem_pio2_large(double*,double*,int,int,int);
+
+hidden int    __rem_pio2(double,double*);
+hidden double __sin(double,double,int);
+hidden double __cos(double,double);
+hidden double __tan(double,double,int);
+hidden double __expo2(double,double);
+
+hidden int    __rem_pio2f(float,double*);
+hidden float  __sindf(double);
+hidden float  __cosdf(double);
+hidden float  __tandf(double,int);
+hidden float  __expo2f(float,float);
+
+hidden int __rem_pio2l(long double, long double *);
+hidden long double __sinl(long double, long double, int);
+hidden long double __cosl(long double, long double);
+hidden long double __tanl(long double, long double, int);
+
+hidden long double __polevll(long double, const long double *, int);
+hidden long double __p1evll(long double, const long double *, int);
+
+extern int __signgam;
+hidden double __lgamma_r(double, int *);
+hidden float __lgammaf_r(float, int *);
+
+/* error handling functions */
+hidden float __math_xflowf(uint32_t, float);
+hidden float __math_uflowf(uint32_t);
+hidden float __math_oflowf(uint32_t);
+hidden float __math_divzerof(uint32_t);
+hidden float __math_invalidf(float);
+hidden double __math_xflow(uint32_t, double);
+hidden double __math_uflow(uint32_t);
+hidden double __math_oflow(uint32_t);
+hidden double __math_divzero(uint32_t);
+hidden double __math_invalid(double);
+#if LDBL_MANT_DIG != DBL_MANT_DIG
+hidden long double __math_invalidl(long double);
+#endif
+
+#endif
diff --git a/external/musl/ldexp.c b/external/musl/ldexp.c
new file mode 100644
index 00000000..2b49bd96
--- /dev/null
+++ b/external/musl/ldexp.c
@@ -0,0 +1,6 @@
+#include <math.h>
+
+double __cdecl ldexp(double x, int n)
+{
+	return scalbn(x, n);
+}
diff --git a/external/musl/log1p.c b/external/musl/log1p.c
new file mode 100644
index 00000000..e206f17a
--- /dev/null
+++ b/external/musl/log1p.c
@@ -0,0 +1,126 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* double log1p(double x)
+ * Return the natural logarithm of 1+x.
+ *
+ * Method :
+ *   1. Argument Reduction: find k and f such that
+ *                      1+x = 2^k * (1+f),
+ *         where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *      Note. If k=0, then f=x is exact. However, if k!=0, then f
+ *      may not be representable exactly. In that case, a correction
+ *      term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+ *      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+ *      and add back the correction term c/u.
+ *      (Note: when x > 2**53, one can simply return log(x))
+ *
+ *   2. Approximation of log(1+f): See log.c
+ *
+ *   3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
+ *
+ * Special cases:
+ *      log1p(x) is NaN with signal if x < -1 (including -INF) ;
+ *      log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+ *      log1p(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ *      according to an error analysis, the error is always less than
+ *      1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ *
+ * Note: Assuming log() return accurate answer, the following
+ *       algorithm can be used to compute log1p(x) to within a few ULP:
+ *
+ *              u = 1+x;
+ *              if(u==1.0) return x ; else
+ *                         return log(u)*(x/(u-1.0));
+ *
+ *       See HP-15C Advanced Functions Handbook, p.193.
+ */
+
+#include "libm.h"
+
+static const double
+ln2_hi = 6.93147180369123816490e-01,  /* 3fe62e42 fee00000 */
+ln2_lo = 1.90821492927058770002e-10,  /* 3dea39ef 35793c76 */
+Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
+
+double __cdecl log1p(double x)
+{
+	union {double f; uint64_t i;} u = {x};
+	double_t hfsq,f,c,s,z,R,w,t1,t2,dk;
+	uint32_t hx,hu;
+	int k;
+
+	hx = u.i>>32;
+	k = 1;
+	if (hx < 0x3fda827a || hx>>31) {  /* 1+x < sqrt(2)+ */
+		if (hx >= 0xbff00000) {  /* x <= -1.0 */
+			if (x == -1) {
+				errno = ERANGE;
+				return x/0.0; /* log1p(-1) = -inf */
+			}
+			errno = EDOM;
+			return (x-x)/0.0;     /* log1p(x<-1) = NaN */
+		}
+		if (hx<<1 < 0x3ca00000<<1) {  /* |x| < 2**-53 */
+			fp_barrier(x + 0x1p120f);
+			/* underflow if subnormal */
+			if ((hx&0x7ff00000) == 0)
+				FORCE_EVAL((float)x);
+			return x;
+		}
+		if (hx <= 0xbfd2bec4) {  /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+			k = 0;
+			c = 0;
+			f = x;
+		}
+	} else if (hx >= 0x7ff00000)
+		return x;
+	if (k) {
+		u.f = 1 + x;
+		hu = u.i>>32;
+		hu += 0x3ff00000 - 0x3fe6a09e;
+		k = (int)(hu>>20) - 0x3ff;
+		/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+		if (k < 54) {
+			c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
+			c /= u.f;
+		} else
+			c = 0;
+		/* reduce u into [sqrt(2)/2, sqrt(2)] */
+		hu = (hu&0x000fffff) + 0x3fe6a09e;
+		u.i = (uint64_t)hu<<32 | (u.i&0xffffffff);
+		f = u.f - 1;
+	}
+	hfsq = 0.5*f*f;
+	s = f/(2.0+f);
+	z = s*s;
+	w = z*z;
+	t1 = w*(Lg2+w*(Lg4+w*Lg6));
+	t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+	R = t2 + t1;
+	dk = k;
+	return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
+}
diff --git a/external/musl/log2.c b/external/musl/log2.c
new file mode 100644
index 00000000..988d97bb
--- /dev/null
+++ b/external/musl/log2.c
@@ -0,0 +1,128 @@
+/*
+ * Double-precision log2(x) function.
+ *
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "libm.h"
+#include "log2_data.h"
+
+#define T __log2_data.tab
+#define T2 __log2_data.tab2
+#define B __log2_data.poly1
+#define A __log2_data.poly
+#define InvLn2hi __log2_data.invln2hi
+#define InvLn2lo __log2_data.invln2lo
+#define N (1 << LOG2_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+/* Top 16 bits of a double.  */
+static inline uint32_t top16(double x)
+{
+	return asuint64(x) >> 48;
+}
+
+double __cdecl log2(double x)
+{
+	double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
+	uint64_t ix, iz, tmp;
+	uint32_t top;
+	int k, i;
+
+	ix = asuint64(x);
+	top = top16(x);
+#define LO asuint64(1.0 - 0x1.5b51p-5)
+#define HI asuint64(1.0 + 0x1.6ab2p-5)
+	if (predict_false(ix - LO < HI - LO)) {
+		/* Handle close to 1.0 inputs separately.  */
+		/* Fix sign of zero with downward rounding when x==1.  */
+		if (WANT_ROUNDING && predict_false(ix == asuint64(1.0)))
+			return 0;
+		r = x - 1.0;
+#if __FP_FAST_FMA
+		hi = r * InvLn2hi;
+		lo = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -hi);
+#else
+		double_t rhi, rlo;
+		rhi = asdouble(asuint64(r) & -1ULL << 32);
+		rlo = r - rhi;
+		hi = rhi * InvLn2hi;
+		lo = rlo * InvLn2hi + r * InvLn2lo;
+#endif
+		r2 = r * r; /* rounding error: 0x1p-62.  */
+		r4 = r2 * r2;
+		/* Worst-case error is less than 0.54 ULP (0.55 ULP without fma).  */
+		p = r2 * (B[0] + r * B[1]);
+		y = hi + p;
+		lo += hi - y + p;
+		lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5]) +
+			    r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
+		y += lo;
+		return eval_as_double(y);
+	}
+	if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) {
+		/* x < 0x1p-1022 or inf or nan.  */
+		if (ix * 2 == 0) {
+			errno = ERANGE;
+			return __math_divzero(1);
+		}
+		if (ix == asuint64(INFINITY)) /* log(inf) == inf.  */
+			return x;
+		if ((top & 0x7ff0) == 0x7ff0 && (ix & 0xfffffffffffffULL))
+			return x;
+		if (top & 0x8000) {
+			errno = EDOM;
+			return __math_invalid(x);
+		}
+		/* x is subnormal, normalize it.  */
+		ix = asuint64(x * 0x1p52);
+		ix -= 52ULL << 52;
+	}
+
+	/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+	   The range is split into N subintervals.
+	   The ith subinterval contains z and c is near its center.  */
+	tmp = ix - OFF;
+	i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
+	k = (int64_t)tmp >> 52; /* arithmetic shift */
+	iz = ix - (tmp & 0xfffULL << 52);
+	invc = T[i].invc;
+	logc = T[i].logc;
+	z = asdouble(iz);
+	kd = (double_t)k;
+
+	/* log2(x) = log2(z/c) + log2(c) + k.  */
+	/* r ~= z/c - 1, |r| < 1/(2*N).  */
+#if __FP_FAST_FMA
+	/* rounding error: 0x1p-55/N.  */
+	r = __builtin_fma(z, invc, -1.0);
+	t1 = r * InvLn2hi;
+	t2 = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -t1);
+#else
+	double_t rhi, rlo;
+	/* rounding error: 0x1p-55/N + 0x1p-65.  */
+	r = (z - T2[i].chi - T2[i].clo) * invc;
+	rhi = asdouble(asuint64(r) & -1ULL << 32);
+	rlo = r - rhi;
+	t1 = rhi * InvLn2hi;
+	t2 = rlo * InvLn2hi + r * InvLn2lo;
+#endif
+
+	/* hi + lo = r/ln2 + log2(c) + k.  */
+	t3 = kd + logc;
+	hi = t3 + t1;
+	lo = t3 - hi + t1 + t2;
+
+	/* log2(r+1) = r/ln2 + r^2*poly(r).  */
+	/* Evaluation is optimized assuming superscalar pipelined execution.  */
+	r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
+	r4 = r2 * r2;
+	/* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
+	   ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma).  */
+	p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
+	y = lo + r2 * p + hi;
+	return eval_as_double(y);
+}
diff --git a/external/musl/log2_data.c b/external/musl/log2_data.c
new file mode 100644
index 00000000..3dd1ca51
--- /dev/null
+++ b/external/musl/log2_data.c
@@ -0,0 +1,201 @@
+/*
+ * Data for log2.
+ *
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "log2_data.h"
+
+#define N (1 << LOG2_TABLE_BITS)
+
+const struct log2_data __log2_data = {
+// First coefficient: 0x1.71547652b82fe1777d0ffda0d24p0
+.invln2hi = 0x1.7154765200000p+0,
+.invln2lo = 0x1.705fc2eefa200p-33,
+.poly1 = {
+// relative error: 0x1.2fad8188p-63
+// in -0x1.5b51p-5 0x1.6ab2p-5
+-0x1.71547652b82fep-1,
+0x1.ec709dc3a03f7p-2,
+-0x1.71547652b7c3fp-2,
+0x1.2776c50f05be4p-2,
+-0x1.ec709dd768fe5p-3,
+0x1.a61761ec4e736p-3,
+-0x1.7153fbc64a79bp-3,
+0x1.484d154f01b4ap-3,
+-0x1.289e4a72c383cp-3,
+0x1.0b32f285aee66p-3,
+},
+.poly = {
+// relative error: 0x1.a72c2bf8p-58
+// abs error: 0x1.67a552c8p-66
+// in -0x1.f45p-8 0x1.f45p-8
+-0x1.71547652b8339p-1,
+0x1.ec709dc3a04bep-2,
+-0x1.7154764702ffbp-2,
+0x1.2776c50034c48p-2,
+-0x1.ec7b328ea92bcp-3,
+0x1.a6225e117f92ep-3,
+},
+/* Algorithm:
+
+	x = 2^k z
+	log2(x) = k + log2(c) + log2(z/c)
+	log2(z/c) = poly(z/c - 1)
+
+where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls
+into the ith one, then table entries are computed as
+
+	tab[i].invc = 1/c
+	tab[i].logc = (double)log2(c)
+	tab2[i].chi = (double)c
+	tab2[i].clo = (double)(c - (double)c)
+
+where c is near the center of the subinterval and is chosen by trying +-2^29
+floating point invc candidates around 1/center and selecting one for which
+
+	1) the rounding error in 0x1.8p10 + logc is 0,
+	2) the rounding error in z - chi - clo is < 0x1p-64 and
+	3) the rounding error in (double)log2(c) is minimized (< 0x1p-68).
+
+Note: 1) ensures that k + logc can be computed without rounding error, 2)
+ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to a
+single rounding error when there is no fast fma for z*invc - 1, 3) ensures
+that logc + poly(z/c - 1) has small error, however near x == 1 when
+|log2(x)| < 0x1p-4, this is not enough so that is special cased.  */
+.tab = {
+{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1},
+{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1},
+{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1},
+{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2},
+{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2},
+{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2},
+{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2},
+{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2},
+{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2},
+{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2},
+{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2},
+{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2},
+{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2},
+{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2},
+{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2},
+{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2},
+{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2},
+{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2},
+{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2},
+{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2},
+{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3},
+{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3},
+{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3},
+{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3},
+{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3},
+{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3},
+{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3},
+{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3},
+{0x1.19453847f2200p+0, -0x1.162595afdc000p-3},
+{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4},
+{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4},
+{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4},
+{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4},
+{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4},
+{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4},
+{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5},
+{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5},
+{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6},
+{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6},
+{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8},
+{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7},
+{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5},
+{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5},
+{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4},
+{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4},
+{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4},
+{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3},
+{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3},
+{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3},
+{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3},
+{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3},
+{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3},
+{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2},
+{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2},
+{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2},
+{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2},
+{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2},
+{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2},
+{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2},
+{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2},
+{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2},
+{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2},
+{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2},
+{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2},
+},
+#if !__FP_FAST_FMA
+.tab2 = {
+{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55},
+{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57},
+{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55},
+{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55},
+{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55},
+{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56},
+{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56},
+{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57},
+{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55},
+{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57},
+{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55},
+{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55},
+{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56},
+{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56},
+{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56},
+{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55},
+{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57},
+{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55},
+{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55},
+{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58},
+{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55},
+{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58},
+{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56},
+{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56},
+{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57},
+{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56},
+{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56},
+{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55},
+{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58},
+{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56},
+{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55},
+{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56},
+{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55},
+{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56},
+{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55},
+{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55},
+{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55},
+{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59},
+{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58},
+{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55},
+{0x1.0200004292367p+0, 0x1.b7ff365324681p-54},
+{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55},
+{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58},
+{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54},
+{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55},
+{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54},
+{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54},
+{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54},
+{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55},
+{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55},
+{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56},
+{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54},
+{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56},
+{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54},
+{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56},
+{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54},
+{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56},
+{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55},
+{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55},
+{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56},
+{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54},
+{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55},
+{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55},
+{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54},
+},
+#endif
+};
diff --git a/external/musl/log2_data.h b/external/musl/log2_data.h
new file mode 100644
index 00000000..276a786d
--- /dev/null
+++ b/external/musl/log2_data.h
@@ -0,0 +1,28 @@
+/*
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+#ifndef _LOG2_DATA_H
+#define _LOG2_DATA_H
+
+#include <features.h>
+
+#define LOG2_TABLE_BITS 6
+#define LOG2_POLY_ORDER 7
+#define LOG2_POLY1_ORDER 11
+extern hidden const struct log2_data {
+	double invln2hi;
+	double invln2lo;
+	double poly[LOG2_POLY_ORDER - 1];
+	double poly1[LOG2_POLY1_ORDER - 1];
+	struct {
+		double invc, logc;
+	} tab[1 << LOG2_TABLE_BITS];
+#if !__FP_FAST_FMA
+	struct {
+		double chi, clo;
+	} tab2[1 << LOG2_TABLE_BITS];
+#endif
+} __log2_data;
+
+#endif
diff --git a/external/musl/scalbn.c b/external/musl/scalbn.c
new file mode 100644
index 00000000..20f71167
--- /dev/null
+++ b/external/musl/scalbn.c
@@ -0,0 +1,34 @@
+#include <math.h>
+#include <stdint.h>
+#include "libm.h"
+
+double __cdecl scalbn(double x, int n)
+{
+	union {double f; uint64_t i;} u;
+	double_t y = x;
+
+	if (n > 1023) {
+		y *= 0x1p1023;
+		n -= 1023;
+		if (n > 1023) {
+			y *= 0x1p1023;
+			n -= 1023;
+			if (n > 1023)
+				n = 1023;
+		}
+	} else if (n < -1022) {
+		/* make sure final n < -53 to avoid double
+		   rounding in the subnormal range */
+		y *= 0x1p-1022 * 0x1p53;
+		n += 1022 - 53;
+		if (n < -1022) {
+			y *= 0x1p-1022 * 0x1p53;
+			n += 1022 - 53;
+			if (n < -1022)
+				n = -1022;
+		}
+	}
+	u.i = (uint64_t)(0x3ff+n)<<52;
+	x = y * u.f;
+	return x;
+}
diff --git a/external/musl/sin.c b/external/musl/sin.c
new file mode 100644
index 00000000..4bbc2ee6
--- /dev/null
+++ b/external/musl/sin.c
@@ -0,0 +1,80 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* sin(x)
+ * Return sine function of x.
+ *
+ * kernel function:
+ *      __sin            ... sine function on [-pi/4,pi/4]
+ *      __cos            ... cose function on [-pi/4,pi/4]
+ *      __rem_pio2       ... argument reduction routine
+ *
+ * Method.
+ *      Let S,C and T denote the sin, cos and tan respectively on
+ *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ *      in [-pi/4 , +pi/4], and let n = k mod 4.
+ *      We have
+ *
+ *          n        sin(x)      cos(x)        tan(x)
+ *     ----------------------------------------------------------
+ *          0          S           C             T
+ *          1          C          -S            -1/T
+ *          2         -S          -C             T
+ *          3         -C           S            -1/T
+ *     ----------------------------------------------------------
+ *
+ * Special cases:
+ *      Let trig be any of sin, cos, or tan.
+ *      trig(+-INF)  is NaN, with signals;
+ *      trig(NaN)    is that NaN;
+ *
+ * Accuracy:
+ *      TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "libm.h"
+
+double __cdecl sin(double x)
+{
+	double y[2];
+	uint32_t ix;
+	unsigned n;
+
+	/* High word of x. */
+	GET_HIGH_WORD(ix, x);
+	ix &= 0x7fffffff;
+
+	/* |x| ~< pi/4 */
+	if (ix <= 0x3fe921fb) {
+		if (ix < 0x3e500000) {  /* |x| < 2**-26 */
+			/* raise inexact if x != 0 and underflow if subnormal*/
+			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
+			return x;
+		}
+		return __sin(x, 0.0, 0);
+	}
+
+	/* sin(Inf or NaN) is NaN */
+	if (isinf(x))
+		return math_error(_DOMAIN, "sin", x, 0, x - x);
+	if (ix >= 0x7ff00000)
+		return x - x;
+
+	/* argument reduction needed */
+	n = __rem_pio2(x, y);
+	switch (n&3) {
+	case 0: return  __sin(y[0], y[1], 1);
+	case 1: return  __cos(y[0], y[1]);
+	case 2: return -__sin(y[0], y[1], 1);
+	default:
+		return -__cos(y[0], y[1]);
+	}
+}
diff --git a/external/musl/sincos.c b/external/musl/sincos.c
new file mode 100644
index 00000000..c8d866ba
--- /dev/null
+++ b/external/musl/sincos.c
@@ -0,0 +1,69 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
+/*
+ * ====================================================
+ * 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"
+
+void __cdecl sincos(double x, double *sin, double *cos)
+{
+	double y[2], s, c;
+	uint32_t ix;
+	unsigned n;
+
+	GET_HIGH_WORD(ix, x);
+	ix &= 0x7fffffff;
+
+	/* |x| ~< pi/4 */
+	if (ix <= 0x3fe921fb) {
+		/* if |x| < 2**-27 * sqrt(2) */
+		if (ix < 0x3e46a09e) {
+			/* raise inexact if x!=0 and underflow if subnormal */
+			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
+			*sin = x;
+			*cos = 1.0;
+			return;
+		}
+		*sin = __sin(x, 0.0, 0);
+		*cos = __cos(x, 0.0);
+		return;
+	}
+
+	/* sincos(Inf or NaN) is NaN */
+	if (ix >= 0x7ff00000) {
+		*sin = *cos = x - x;
+		return;
+	}
+
+	/* argument reduction needed */
+	n = __rem_pio2(x, y);
+	s = __sin(y[0], y[1], 1);
+	c = __cos(y[0], y[1]);
+	switch (n&3) {
+	case 0:
+		*sin = s;
+		*cos = c;
+		break;
+	case 1:
+		*sin = c;
+		*cos = -s;
+		break;
+	case 2:
+		*sin = -s;
+		*cos = -c;
+		break;
+	case 3:
+	default:
+		*sin = -c;
+		*cos = s;
+		break;
+	}
+}
diff --git a/external/musl/sqrt.c b/external/musl/sqrt.c
new file mode 100644
index 00000000..beee70a4
--- /dev/null
+++ b/external/musl/sqrt.c
@@ -0,0 +1,158 @@
+#include <stdint.h>
+#include <math.h>
+#include "libm.h"
+#include "sqrt_data.h"
+
+#define FENV_SUPPORT 1
+
+/* returns a*b*2^-32 - e, with error 0 <= e < 1.  */
+static inline uint32_t mul32(uint32_t a, uint32_t b)
+{
+	return (uint64_t)a*b >> 32;
+}
+
+/* returns a*b*2^-64 - e, with error 0 <= e < 3.  */
+static inline uint64_t mul64(uint64_t a, uint64_t b)
+{
+	uint64_t ahi = a>>32;
+	uint64_t alo = a&0xffffffff;
+	uint64_t bhi = b>>32;
+	uint64_t blo = b&0xffffffff;
+	return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32);
+}
+
+double __cdecl sqrt(double x)
+{
+	uint64_t ix, top, m;
+
+	/* special case handling.  */
+	ix = asuint64(x);
+	top = ix >> 52;
+	if (predict_false(top - 0x001 >= 0x7ff - 0x001)) {
+		/* x < 0x1p-1022 or inf or nan.  */
+		if (ix * 2 == 0)
+			return x;
+		if (ix == 0x7ff0000000000000)
+			return x;
+		if (ix > 0x7ff0000000000000)
+			return math_error(_DOMAIN, "sqrt", x, 0, (x - x) / (x - x));
+		/* x is subnormal, normalize it.  */
+		ix = asuint64(x * 0x1p52);
+		top = ix >> 52;
+		top -= 52;
+	}
+
+	/* argument reduction:
+	   x = 4^e m; with integer e, and m in [1, 4)
+	   m: fixed point representation [2.62]
+	   2^e is the exponent part of the result.  */
+	int even = top & 1;
+	m = (ix << 11) | 0x8000000000000000;
+	if (even) m >>= 1;
+	top = (top + 0x3ff) >> 1;
+
+	/* approximate r ~ 1/sqrt(m) and s ~ sqrt(m) when m in [1,4)
+
+	   initial estimate:
+	   7bit table lookup (1bit exponent and 6bit significand).
+
+	   iterative approximation:
+	   using 2 goldschmidt iterations with 32bit int arithmetics
+	   and a final iteration with 64bit int arithmetics.
+
+	   details:
+
+	   the relative error (e = r0 sqrt(m)-1) of a linear estimate
+	   (r0 = a m + b) is |e| < 0.085955 ~ 0x1.6p-4 at best,
+	   a table lookup is faster and needs one less iteration
+	   6 bit lookup table (128b) gives |e| < 0x1.f9p-8
+	   7 bit lookup table (256b) gives |e| < 0x1.fdp-9
+	   for single and double prec 6bit is enough but for quad
+	   prec 7bit is needed (or modified iterations). to avoid
+	   one more iteration >=13bit table would be needed (16k).
+
+	   a newton-raphson iteration for r is
+	     w = r*r
+	     u = 3 - m*w
+	     r = r*u/2
+	   can use a goldschmidt iteration for s at the end or
+	     s = m*r
+
+	   first goldschmidt iteration is
+	     s = m*r
+	     u = 3 - s*r
+	     r = r*u/2
+	     s = s*u/2
+	   next goldschmidt iteration is
+	     u = 3 - s*r
+	     r = r*u/2
+	     s = s*u/2
+	   and at the end r is not computed only s.
+
+	   they use the same amount of operations and converge at the
+	   same quadratic rate, i.e. if
+	     r1 sqrt(m) - 1 = e, then
+	     r2 sqrt(m) - 1 = -3/2 e^2 - 1/2 e^3
+	   the advantage of goldschmidt is that the mul for s and r
+	   are independent (computed in parallel), however it is not
+	   "self synchronizing": it only uses the input m in the
+	   first iteration so rounding errors accumulate. at the end
+	   or when switching to larger precision arithmetics rounding
+	   errors dominate so the first iteration should be used.
+
+	   the fixed point representations are
+	     m: 2.30 r: 0.32, s: 2.30, d: 2.30, u: 2.30, three: 2.30
+	   and after switching to 64 bit
+	     m: 2.62 r: 0.64, s: 2.62, d: 2.62, u: 2.62, three: 2.62  */
+
+	static const uint64_t three = 0xc0000000;
+	uint64_t r, s, d, u, i;
+
+	i = (ix >> 46) % 128;
+	r = (uint32_t)__rsqrt_tab[i] << 16;
+	/* |r sqrt(m) - 1| < 0x1.fdp-9 */
+	s = mul32(m>>32, r);
+	/* |s/sqrt(m) - 1| < 0x1.fdp-9 */
+	d = mul32(s, r);
+	u = three - d;
+	r = mul32(r, u) << 1;
+	/* |r sqrt(m) - 1| < 0x1.7bp-16 */
+	s = mul32(s, u) << 1;
+	/* |s/sqrt(m) - 1| < 0x1.7bp-16 */
+	d = mul32(s, r);
+	u = three - d;
+	r = mul32(r, u) << 1;
+	/* |r sqrt(m) - 1| < 0x1.3704p-29 (measured worst-case) */
+	r = r << 32;
+	s = mul64(m, r);
+	d = mul64(s, r);
+	u = (three<<32) - d;
+	s = mul64(s, u);  /* repr: 3.61 */
+	/* -0x1p-57 < s - sqrt(m) < 0x1.8001p-61 */
+	s = (s - 2) >> 9; /* repr: 12.52 */
+	/* -0x1.09p-52 < s - sqrt(m) < -0x1.fffcp-63 */
+
+	/* s < sqrt(m) < s + 0x1.09p-52,
+	   compute nearest rounded result:
+	   the nearest result to 52 bits is either s or s+0x1p-52,
+	   we can decide by comparing (2^52 s + 0.5)^2 to 2^104 m.  */
+	uint64_t d0, d1, d2;
+	double y, t;
+	d0 = (m << 42) - s*s;
+	d1 = s - d0;
+	d2 = d1 + s + 1;
+	s += d1 >> 63;
+	s &= 0x000fffffffffffff;
+	s |= top << 52;
+	y = asdouble(s);
+	if (FENV_SUPPORT) {
+		/* handle rounding modes and inexact exception:
+		   only (s+1)^2 == 2^42 m case is exact otherwise
+		   add a tiny value to cause the fenv effects.  */
+		uint64_t tiny = predict_false(d2==0) ? 0 : 0x0010000000000000;
+		tiny |= (d1^d2) & 0x8000000000000000;
+		t = asdouble(tiny);
+		y = eval_as_double(y + t);
+	}
+	return y;
+}
diff --git a/external/musl/sqrt_data.c b/external/musl/sqrt_data.c
new file mode 100644
index 00000000..61bc22f4
--- /dev/null
+++ b/external/musl/sqrt_data.c
@@ -0,0 +1,19 @@
+#include "sqrt_data.h"
+const uint16_t __rsqrt_tab[128] = {
+0xb451,0xb2f0,0xb196,0xb044,0xaef9,0xadb6,0xac79,0xab43,
+0xaa14,0xa8eb,0xa7c8,0xa6aa,0xa592,0xa480,0xa373,0xa26b,
+0xa168,0xa06a,0x9f70,0x9e7b,0x9d8a,0x9c9d,0x9bb5,0x9ad1,
+0x99f0,0x9913,0x983a,0x9765,0x9693,0x95c4,0x94f8,0x9430,
+0x936b,0x92a9,0x91ea,0x912e,0x9075,0x8fbe,0x8f0a,0x8e59,
+0x8daa,0x8cfe,0x8c54,0x8bac,0x8b07,0x8a64,0x89c4,0x8925,
+0x8889,0x87ee,0x8756,0x86c0,0x862b,0x8599,0x8508,0x8479,
+0x83ec,0x8361,0x82d8,0x8250,0x81c9,0x8145,0x80c2,0x8040,
+0xff02,0xfd0e,0xfb25,0xf947,0xf773,0xf5aa,0xf3ea,0xf234,
+0xf087,0xeee3,0xed47,0xebb3,0xea27,0xe8a3,0xe727,0xe5b2,
+0xe443,0xe2dc,0xe17a,0xe020,0xdecb,0xdd7d,0xdc34,0xdaf1,
+0xd9b3,0xd87b,0xd748,0xd61a,0xd4f1,0xd3cd,0xd2ad,0xd192,
+0xd07b,0xcf69,0xce5b,0xcd51,0xcc4a,0xcb48,0xca4a,0xc94f,
+0xc858,0xc764,0xc674,0xc587,0xc49d,0xc3b7,0xc2d4,0xc1f4,
+0xc116,0xc03c,0xbf65,0xbe90,0xbdbe,0xbcef,0xbc23,0xbb59,
+0xba91,0xb9cc,0xb90a,0xb84a,0xb78c,0xb6d0,0xb617,0xb560,
+};
diff --git a/external/musl/sqrt_data.h b/external/musl/sqrt_data.h
new file mode 100644
index 00000000..260c7f9c
--- /dev/null
+++ b/external/musl/sqrt_data.h
@@ -0,0 +1,13 @@
+#ifndef _SQRT_DATA_H
+#define _SQRT_DATA_H
+
+#include <features.h>
+#include <stdint.h>
+
+/* if x in [1,2): i = (int)(64*x);
+   if x in [2,4): i = (int)(32*x-64);
+   __rsqrt_tab[i]*2^-16 is estimating 1/sqrt(x) with small relative error:
+   |__rsqrt_tab[i]*0x1p-16*sqrt(x) - 1| < -0x1.fdp-9 < 2^-8 */
+extern hidden const uint16_t __rsqrt_tab[128];
+
+#endif
diff --git a/external/musl/sqrtf.c b/external/musl/sqrtf.c
new file mode 100644
index 00000000..45559f0b
--- /dev/null
+++ b/external/musl/sqrtf.c
@@ -0,0 +1,83 @@
+#include <stdint.h>
+#include <math.h>
+#include "libm.h"
+#include "sqrt_data.h"
+
+#define FENV_SUPPORT 1
+
+static inline uint32_t mul32(uint32_t a, uint32_t b)
+{
+	return (uint64_t)a*b >> 32;
+}
+
+/* see sqrt.c for more detailed comments.  */
+
+float __cdecl sqrtf(float x)
+{
+	uint32_t ix, m, m1, m0, even, ey;
+
+	ix = asuint(x);
+	if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
+		/* x < 0x1p-126 or inf or nan.  */
+		if (ix * 2 == 0)
+			return x;
+		if (ix == 0x7f800000)
+			return x;
+		if (ix > 0x7f800000)
+			return math_error(_DOMAIN, "sqrtf", x, 0, (x - x) / (x - x));
+		/* x is subnormal, normalize it.  */
+		ix = asuint(x * 0x1p23f);
+		ix -= 23 << 23;
+	}
+
+	/* x = 4^e m; with int e and m in [1, 4).  */
+	even = ix & 0x00800000;
+	m1 = (ix << 8) | 0x80000000;
+	m0 = (ix << 7) & 0x7fffffff;
+	m = even ? m0 : m1;
+
+	/* 2^e is the exponent part of the return value.  */
+	ey = ix >> 1;
+	ey += 0x3f800000 >> 1;
+	ey &= 0x7f800000;
+
+	/* compute r ~ 1/sqrt(m), s ~ sqrt(m) with 2 goldschmidt iterations.  */
+	static const uint32_t three = 0xc0000000;
+	uint32_t r, s, d, u, i;
+	i = (ix >> 17) % 128;
+	r = (uint32_t)__rsqrt_tab[i] << 16;
+	/* |r*sqrt(m) - 1| < 0x1p-8 */
+	s = mul32(m, r);
+	/* |s/sqrt(m) - 1| < 0x1p-8 */
+	d = mul32(s, r);
+	u = three - d;
+	r = mul32(r, u) << 1;
+	/* |r*sqrt(m) - 1| < 0x1.7bp-16 */
+	s = mul32(s, u) << 1;
+	/* |s/sqrt(m) - 1| < 0x1.7bp-16 */
+	d = mul32(s, r);
+	u = three - d;
+	s = mul32(s, u);
+	/* -0x1.03p-28 < s/sqrt(m) - 1 < 0x1.fp-31 */
+	s = (s - 1)>>6;
+	/* s < sqrt(m) < s + 0x1.08p-23 */
+
+	/* compute nearest rounded result.  */
+	uint32_t d0, d1, d2;
+	float y, t;
+	d0 = (m << 16) - s*s;
+	d1 = s - d0;
+	d2 = d1 + s + 1;
+	s += d1 >> 31;
+	s &= 0x007fffff;
+	s |= ey;
+	y = asfloat(s);
+	if (FENV_SUPPORT) {
+		/* handle rounding and inexact exception. */
+		uint32_t tiny = predict_false(d2==0) ? 0 : 0x01000000;
+		tiny |= (d1^d2) & 0x80000000;
+		t = asfloat(tiny);
+		y = eval_as_float(y + t);
+	}
+	return y;
+}