py and libm: Add asinf,acosf; print higher precision for float.

Also use less stack space when printing single precision float.

Addition of asinf and acosf addresses issue #851.

lib/libm/asinfacosf.c

+/*****************************************************************************/
+/*****************************************************************************/
+// asinf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asinf.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 "libm.h"
+
+// dpgeorge: pio2 was double in original implementation of asinf
+static const float
+pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
+pio2_lo = 7.5497894159e-08; /* 0x33a22168 */
+
+static const float
+/* coefficients for R(x^2) */
+pS0 =  1.6666586697e-01,
+pS1 = -4.2743422091e-02,
+pS2 = -8.6563630030e-03,
+qS1 = -7.0662963390e-01;
+
+static float R(float z)
+{
+	float_t p, q;
+	p = z*(pS0+z*(pS1+z*pS2));
+	q = 1.0f+z*qS1;
+	return p/q;
+}
+
+float asinf(float x)
+{
+	// dpgeorge: s was double in original implementation
+	float s,z;
+	uint32_t hx,ix;
+
+	GET_FLOAT_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+	if (ix >= 0x3f800000) {  /* |x| >= 1 */
+		if (ix == 0x3f800000)  /* |x| == 1 */
+			return x*pio2_hi + 0x1p-120f;  /* asin(+-1) = +-pi/2 with inexact */
+		return 0/(x-x);  /* asin(|x|>1) is NaN */
+	}
+	if (ix < 0x3f000000) {  /* |x| < 0.5 */
+		/* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
+		if (ix < 0x39800000 && ix >= 0x00800000)
+			return x;
+		return x + x*R(x*x);
+	}
+	/* 1 > |x| >= 0.5 */
+	z = (1 - fabsf(x))*0.5f;
+	s = sqrtf(z);
+	x = pio2_hi - (2*(s+s*R(z)) - pio2_lo); // dpgeorge: use pio2_hi and pio2_lo
+	if (hx >> 31)
+		return -x;
+	return x;
+}
+
+/*****************************************************************************/
+/*****************************************************************************/
+// acosf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.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.
+ * ====================================================
+ */
+
+float acosf(float x)
+{
+	float z,w,s,c,df;
+	uint32_t hx,ix;
+
+	GET_FLOAT_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+	/* |x| >= 1 or nan */
+	if (ix >= 0x3f800000) {
+		if (ix == 0x3f800000) {
+			if (hx >> 31)
+				return 2*pio2_hi + 0x1p-120f;
+			return 0;
+		}
+		return 0/(x-x);
+	}
+	/* |x| < 0.5 */
+	if (ix < 0x3f000000) {
+		if (ix <= 0x32800000) /* |x| < 2**-26 */
+			return pio2_hi + 0x1p-120f;
+		return pio2_hi - (x - (pio2_lo-x*R(x*x)));
+	}
+	/* x < -0.5 */
+	if (hx >> 31) {
+		z = (1+x)*0.5f;
+		s = sqrtf(z);
+		w = R(z)*s-pio2_lo;
+		return 2*(pio2_hi - (s+w));
+	}
+	/* x > 0.5 */
+	z = (1-x)*0.5f;
+	s = sqrtf(z);
+	GET_FLOAT_WORD(hx,s);
+	SET_FLOAT_WORD(df,hx&0xfffff000);
+	c = (z-df*df)/(s+df);
+	w = R(z)*s+c;
+	return 2*(df+w);
+}

lib/libm/math.c

@@ -117,8 +117,6 @@ float acoshf(float x) { return 0.0; }
 float asinhf(float x) { return 0.0; }
 float atanhf(float x) { return 0.0; }
 float tanf(float x) { return 0.0; }
-float acosf(float x) { return 0.0; }
-float asinf(float x) { return 0.0; }
 float fmodf(float x, float y) { return 0.0; }
 float tgammaf(float x) { return 0.0; }
 float lgammaf(float x) { return 0.0; }

py/objcomplex.c

@@ -25,6 +25,7 @@
  */
 
 #include <stdlib.h>
+#include <stdio.h>
 #include <assert.h>
 
 #include "mpconfig.h"
@@ -55,21 +56,26 @@ mp_obj_t mp_obj_new_complex(mp_float_t real, mp_float_t imag);
 STATIC void complex_print(void (*print)(void *env, const char *fmt, ...), void *env, mp_obj_t o_in, mp_print_kind_t kind) {
     mp_obj_complex_t *o = o_in;
 #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
-    char buf[32];
+    char buf[16];
     if (o->real == 0) {
-        format_float(o->imag, buf, sizeof(buf), 'g', 6, '\0');
+        format_float(o->imag, buf, sizeof(buf), 'g', 7, '\0');
         print(env, "%sj", buf);
     } else {
-        format_float(o->real, buf, sizeof(buf), 'g', 6, '\0');
+        format_float(o->real, buf, sizeof(buf), 'g', 7, '\0');
         print(env, "(%s+", buf);
-        format_float(o->imag, buf, sizeof(buf), 'g', 6, '\0');
+        format_float(o->imag, buf, sizeof(buf), 'g', 7, '\0');
         print(env, "%sj)", buf);
     }
 #else
+    char buf[32];
     if (o->real == 0) {
-        print(env, "%.8gj",  (double) o->imag);
+        sprintf(buf, "%.16g", (double)o->imag);
+        print(env, "%sj", buf);
     } else {
-        print(env, "(%.8g+%.8gj)", (double) o->real, (double) o->imag);
+        sprintf(buf, "%.16g", (double)o->real);
+        print(env, "(%s+", buf);
+        sprintf(buf, "%.16g", (double)o->imag);
+        print(env, "%sj)", buf);
     }
 #endif
 }

py/objfloat.c

@@ -48,18 +48,18 @@
 STATIC void float_print(void (*print)(void *env, const char *fmt, ...), void *env, mp_obj_t o_in, mp_print_kind_t kind) {
     mp_obj_float_t *o = o_in;
 #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
-    char buf[32];
-    format_float(o->value, buf, sizeof(buf), 'g', 6, '\0');
+    char buf[16];
+    format_float(o->value, buf, sizeof(buf), 'g', 7, '\0');
     print(env, "%s", buf);
-    if (strchr(buf, '.') == NULL) {
+    if (strchr(buf, '.') == NULL && strchr(buf, 'e') == NULL) {
         // Python floats always have decimal point
         print(env, ".0");
     }
 #else
     char buf[32];
-    sprintf(buf, "%.17g", (double) o->value);
+    sprintf(buf, "%.16g", (double) o->value);
     print(env, buf);
-    if (strchr(buf, '.') == NULL) {
+    if (strchr(buf, '.') == NULL && strchr(buf, 'e') == NULL) {
         // Python floats always have decimal point
         print(env, ".0");
     }

stmhal/Makefile

@@ -64,6 +64,7 @@ endif
 SRC_LIB = $(addprefix lib/,\
 	libm/math.c \
 	libm/mathsincos.c \
+	libm/asinfacosf.c \
 	libm/atanf.c \
 	libm/atan2f.c \
 	)