lib/libm: Allow math funcs to be used by non-Thumb archs.

Requires addition of software implementation of sqrtf function.

lib/libm/ef_sqrt.c

+/*
+ * This file is part of the MicroPython project, http://micropython.org/
+ *
+ * These math functions are taken from newlib-nano-2, the newlib/libm/math
+ * directory, available from https://github.com/32bitmicro/newlib-nano-2.
+ *
+ * Appropriate copyright headers are reproduced below.
+ */
+
+/* ef_sqrtf.c -- float version of e_sqrt.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.
+ * ====================================================
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+static	const float	one	= 1.0, tiny=1.0e-30;
+#else
+static	float	one	= 1.0, tiny=1.0e-30;
+#endif
+
+// sqrtf is exactly __ieee754_sqrtf when _IEEE_LIBM defined
+float sqrtf(float x)
+/*
+#ifdef __STDC__
+	float __ieee754_sqrtf(float x)
+#else
+	float __ieee754_sqrtf(x)
+	float x;
+#endif
+*/
+{
+	float z;
+	__uint32_t r,hx;
+	__int32_t ix,s,q,m,t,i;
+
+	GET_FLOAT_WORD(ix,x);
+	hx = ix&0x7fffffff;
+
+    /* take care of Inf and NaN */
+	if(!FLT_UWORD_IS_FINITE(hx))
+	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+					   sqrt(-inf)=sNaN */
+    /* take care of zero and -ves */
+	if(FLT_UWORD_IS_ZERO(hx)) return x;/* sqrt(+-0) = +-0 */
+	if(ix<0) return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
+
+    /* normalize x */
+	m = (ix>>23);
+	if(FLT_UWORD_IS_SUBNORMAL(hx)) {		/* subnormal x */
+	    for(i=0;(ix&0x00800000L)==0;i++) ix<<=1;
+	    m -= i-1;
+	}
+	m -= 127;	/* unbias exponent */
+	ix = (ix&0x007fffffL)|0x00800000L;
+	if(m&1)	/* odd m, double x to make it even */
+	    ix += ix;
+	m >>= 1;	/* m = [m/2] */
+
+    /* generate sqrt(x) bit by bit */
+	ix += ix;
+	q = s = 0;		/* q = sqrt(x) */
+	r = 0x01000000L;		/* r = moving bit from right to left */
+
+	while(r!=0) {
+	    t = s+r; 
+	    if(t<=ix) { 
+		s    = t+r; 
+		ix  -= t; 
+		q   += r; 
+	    } 
+	    ix += ix;
+	    r>>=1;
+	}
+
+    /* use floating add to find out rounding direction */
+	if(ix!=0) {
+	    z = one-tiny; /* trigger inexact flag */
+	    if (z>=one) {
+	        z = one+tiny;
+		if (z>one)
+		    q += 2;
+		else
+		    q += (q&1);
+	    }
+	}
+	ix = (q>>1)+0x3f000000L;
+	ix += (m <<23);
+	SET_FLOAT_WORD(z,ix);
+	return z;
+}

lib/libm/math.c

@@ -45,6 +45,8 @@ typedef union {
     };
 } double_s_t;
 
+#if defined(__thumb__)
+
 double __attribute__((pcs("aapcs"))) __aeabi_i2d(int32_t x) {
     return (float)x;
 }
@@ -82,6 +84,11 @@ double __aeabi_dmul(double x , double y) {
 
 }
 
+#endif // defined(__thumb__)
+
+// TODO this needs a better way of testing for Thumb2 FP hardware
+#if defined(__thumb2__)
+
 float sqrtf(float x) {
     asm volatile (
             "vsqrt.f32  %[r], %[x]\n"
@@ -90,6 +97,8 @@ float sqrtf(float x) {
     return x;
 }
 
+#endif
+
 #ifndef NDEBUG
 float copysignf(float x, float y) {
     float_s_t fx={.f = x};