py/formatfloat: Format all whole-number floats exactly.

Formerly, py/formatfloat would print whole numbers inaccurately with
nonzero digits beyond the decimal place.  This resulted from its strategy
of successive scaling of the argument by 0.1 which cannot be exactly
represented in floating point.  The change in this commit avoids scaling
until the value is smaller than 1, so all whole numbers print with zero
fractional part.

Fixes issue #4212.

Signed-off-by: Dan Ellis dan.ellis@gmail.com

py/formatfloat.c

@@ -25,6 +25,7 @@
  */
 
 #include "py/mpconfig.h"
+#include "py/misc.h"
 #if MICROPY_FLOAT_IMPL != MICROPY_FLOAT_IMPL_NONE
 
 #include <assert.h>
@@ -96,7 +97,16 @@ static inline int fp_isless1(float x) {
 #define fp_iszero(x) (x == 0)
 #define fp_isless1(x) (x < 1.0)
 
-#endif
+#endif // MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT/DOUBLE
+
+static inline int fp_ge_eps(FPTYPE x, FPTYPE y) {
+    mp_float_union_t fb_y = {y};
+    // Back off 2 eps.
+    // This is valid for almost all values, but in practice
+    // it's only used when y = 1eX for X>=0.
+    fb_y.i -= 2;
+    return x >= fb_y.f;
+}
 
 static const FPTYPE g_pos_pow[] = {
     #if FPDECEXP > 32
@@ -173,6 +183,7 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
     int num_digits = 0;
     const FPTYPE *pos_pow = g_pos_pow;
     const FPTYPE *neg_pow = g_neg_pow;
+    int signed_e = 0;
 
     if (fp_iszero(f)) {
         e = 0;
@@ -192,31 +203,24 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
             }
         }
     } else if (fp_isless1(f)) {
-        // We need to figure out what an integer digit will be used
+        FPTYPE f_mod = f;
-        // in case 'f' is used (or we revert other format to it below).
-        // As we just tested number to be <1, this is obviously 0,
-        // but we can round it up to 1 below.
-        char first_dig = '0';
-        if (f >= FPROUND_TO_ONE) {
-            first_dig = '1';
-        }
-
         // Build negative exponent
         for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
-            if (*neg_pow > f) {
+            if (*neg_pow > f_mod) {
                 e += e1;
-                f *= *pos_pow;
+                f_mod *= *pos_pow;
             }
         }
+
         char e_sign_char = '-';
-        if (fp_isless1(f) && f >= FPROUND_TO_ONE) {
+        if (fp_isless1(f_mod) && f_mod >= FPROUND_TO_ONE) {
-            f = FPCONST(1.0);
+            f_mod = FPCONST(1.0);
             if (e == 0) {
                 e_sign_char = '+';
             }
-        } else if (fp_isless1(f)) {
+        } else if (fp_isless1(f_mod)) {
             e++;
-            f *= FPCONST(10.0);
+            f_mod *= FPCONST(10.0);
         }
 
         // If the user specified 'g' format, and e is <= 4, then we'll switch
@@ -224,8 +228,7 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
 
         if (fmt == 'f' || (fmt == 'g' && e <= 4)) {
             fmt = 'f';
-            dec = -1;
+            dec = 0;
-            *s++ = first_dig;
 
             if (org_fmt == 'g') {
                 prec += (e - 1);
@@ -237,13 +240,8 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
             }
 
             num_digits = prec;
-            if (num_digits) {
+            signed_e = 0;
-                *s++ = '.';
+            ++num_digits;
-                while (--e && num_digits) {
-                    *s++ = '0';
-                    num_digits--;
-                }
-            }
         } else {
             // For e & g formats, we'll be printing the exponent, so set the
             // sign.
@@ -256,22 +254,29 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
                     prec++;
                 }
             }
+            signed_e = -e;
         }
     } else {
-        // Build positive exponent
+        // Build positive exponent.
-        for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++, neg_pow++) {
+        // We don't modify f at this point to avoid innaccuracies from
-            if (*pos_pow <= f) {
+        // scaling it.  Instead, we find the product of powers of 10
+        // that is not greater than it, and use that to start the
+        // mantissa.
+        FPTYPE u_base = FPCONST(1.0);
+        for (e = 0, e1 = FPDECEXP; e1; e1 >>= 1, pos_pow++) {
+            FPTYPE next_u = u_base * *pos_pow;
+            // fp_ge_eps performs "f >= (next_u - 2eps)" so that if, for
+            // numerical reasons, f is very close to a power of ten but
+            // not strictly equal, we still treat it as that power of 10.
+            // The comparison was failing for maybe 10% of 1eX values, but
+            // although rounding fixed many of them, there were still some
+            // rendering as 9.99999998e(X-1).
+            if (fp_ge_eps(f, next_u)) {
+                u_base = next_u;
                 e += e1;
-                f *= *neg_pow;
             }
         }
 
-        // It can be that f was right on the edge of an entry in pos_pow needs to be reduced
-        if ((int)f >= 10) {
-            e += 1;
-            f *= FPCONST(0.1);
-        }
-
         // If the user specified fixed format (fmt == 'f') and e makes the
         // number too big to fit into the available buffer, then we'll
         // switch to the 'e' format.
@@ -310,15 +315,15 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
         } else {
             e_sign = '+';
         }
+        signed_e = e;
     }
     if (prec < 0) {
         // This can happen when the prec is trimmed to prevent buffer overflow
         prec = 0;
     }
 
-    // We now have num.f as a floating point number between >= 1 and < 10
+    // At this point e contains the absolute value of the power of 10 exponent.
-    // (or equal to zero), and e contains the absolute value of the power of
+    // (dec + 1) == the number of dgits before the decimal.
-    // 10 exponent. and (dec + 1) == the number of dgits before the decimal.
 
     // For e, prec is # digits after the decimal
     // For f, prec is # digits after the decimal
@@ -336,25 +341,63 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
         num_digits = prec;
     }
 
-    // Print the digits of the mantissa
+    if (signed_e < 0) {
-    for (int i = 0; i < num_digits; ++i, --dec) {
+        // The algorithm below treats numbers smaller than 1 by scaling them
-        int32_t d = (int32_t)f;
+        // repeatedly by 10 to bring the new digit to the top.  Our input number
-        if (d < 0) {
+        // was smaller than 1, so scale it up to be 1 <= f < 10.
-            *s++ = '0';
+        FPTYPE u_base = FPCONST(1.0);
-        } else {
+        const FPTYPE *pow_u = g_pos_pow;
-            *s++ = '0' + d;
+        for (int m = FPDECEXP; m; m >>= 1, pow_u++) {
+            if (m & e) {
+                u_base *= *pow_u;
+            }
         }
-        if (dec == 0 && prec > 0) {
+        f *= u_base;
-            *s++ = '.';
-        }
-        f -= (FPTYPE)d;
-        f *= FPCONST(10.0);
     }
 
-    // Round
+    int d = 0;
-    // If we print non-exponential format (i.e. 'f'), but a digit we're going
+    int num_digits_left = num_digits;
-    // to round by (e) is too far away, then there's nothing to round.
+    for (int digit_index = signed_e; num_digits_left >= 0; --digit_index) {
-    if ((org_fmt != 'f' || e <= num_digits) && f >= FPCONST(5.0)) {
+        FPTYPE u_base = FPCONST(1.0);
+        if (digit_index > 0) {
+            // Generate 10^digit_index for positive digit_index.
+            const FPTYPE *pow_u = g_pos_pow;
+            int target_index = digit_index;
+            for (int m = FPDECEXP; m; m >>= 1, pow_u++) {
+                if (m & target_index) {
+                    u_base *= *pow_u;
+                }
+            }
+        }
+        for (d = 0; d < 9; ++d) {
+            // This is essentially "if (f < u_base)", but with 2eps margin
+            // so that if f is just a tiny bit smaller, we treat it as
+            // equal (and accept the additional digit value).
+            if (!fp_ge_eps(f, u_base)) {
+                break;
+            }
+            f -= u_base;
+        }
+        // We calculate one more digit than we display, to use in rounding
+        // below.  So only emit the digit if it's one that we display.
+        if (num_digits_left > 0) {
+            // Emit this number (the leading digit).
+            *s++ = '0' + d;
+            if (dec == 0 && prec > 0) {
+                *s++ = '.';
+            }
+        }
+        --dec;
+        --num_digits_left;
+        if (digit_index <= 0) {
+            // Once we get below 1.0, we scale up f instead of calculting
+            // negative powers of 10 in u_base.  This provides better
+            // renditions of exact decimals like 1/16 etc.
+            f *= FPCONST(10.0);
+        }
+    }
+    // Rounding.  If the next digit to print is >= 5, round up.
+    if (d >= 5) {
         char *rs = s;
         rs--;
         while (1) {
@@ -394,7 +437,10 @@ int mp_format_float(FPTYPE f, char *buf, size_t buf_size, char fmt, int prec, ch
                 }
             } else {
                 // Need at extra digit at the end to make room for the leading '1'
-                s++;
+                // but if we're at the buffer size limit, just drop the final digit.
+                if ((size_t)(s + 1 - buf) < buf_size) {
+                    s++;
+                }
             }
             char *ss = s;
             while (ss > rs) {

tests/float/float_format_ftoe.py

@@ -0,0 +1,4 @@
+# check a case where rounding was suppressed inappropriately when "f" was
+# promoted to "e" for large numbers.
+v = 8.888e32
+print("%.2f" % v)  # '%.2f' format with e32 becomes '%.2e', expect 8.89e+32.

tests/float/float_format_ftoe.py.exp

@@ -0,0 +1 @@
+8.89e+32

tests/float/float_format_ints.py

@@ -0,0 +1,31 @@
+# Test that integers format to exact values.
+
+for b in [13, 123, 457, 23456]:
+    for r in range(1, 10):
+        e_fmt = "{:." + str(r) + "e}"
+        f_fmt = "{:." + str(r) + "f}"
+        g_fmt = "{:." + str(r) + "g}"
+        for e in range(0, 5):
+            f = b * (10**e)
+            title = str(b) + " x 10^" + str(e)
+            print(title, "with format", e_fmt, "gives", e_fmt.format(f))
+            print(title, "with format", f_fmt, "gives", f_fmt.format(f))
+            print(title, "with format", g_fmt, "gives", g_fmt.format(f))
+
+# Check that powers of 10 (that fit in float32) format correctly.
+for i in range(31):
+    # It works to 12 digits on all platforms *except* qemu-arm, where
+    # 10^11 comes out as 10000000820 or something.
+    print("{:.7g}".format(float("1e" + str(i))))
+
+# 16777215 is 2^24 - 1, the largest integer that can be completely held
+# in a float32.
+print("{:f}".format(16777215))
+# 4294967040 = 16777215 * 128 is the largest integer that is exactly
+# represented by a float32 and that will also fit within a (signed) int32.
+# The upper bound of our integer-handling code is actually double this,
+# but that constant might cause trouble on systems using 32 bit ints.
+print("{:f}".format(2147483520))
+# Very large positive integers can be a test for precision and resolution.
+# This is a weird way to represent 1e38 (largest power of 10 for float32).
+print("{:.6e}".format(float("9" * 30 + "e8")))

tests/float/float_format_ints_doubleprec.py

@@ -0,0 +1,15 @@
+# Test formatting of very large ints.
+# Relies on double-precision floats.
+
+import array
+import sys
+
+# Challenging way to express 1e200 and 1e100.
+print("{:.12e}".format(float("9" * 400 + "e-200")))
+print("{:.12e}".format(float("9" * 400 + "e-300")))
+
+# These correspond to the binary representation of 1e200 in float64s:
+v1 = 0x54B249AD2594C37D  # 1e100
+v2 = 0x6974E718D7D7625A  # 1e200
+print("{:.12e}".format(array.array("d", v1.to_bytes(8, sys.byteorder))[0]))
+print("{:.12e}".format(array.array("d", v2.to_bytes(8, sys.byteorder))[0]))

tests/run-tests.py

@@ -426,6 +426,7 @@ def run_tests(pyb, tests, args, result_dir, num_threads=1):
     if upy_float_precision < 64:
         skip_tests.add("float/float_divmod.py")  # tested by float/float_divmod_relaxed.py instead
         skip_tests.add("float/float2int_doubleprec_intbig.py")
+        skip_tests.add("float/float_format_ints_doubleprec.py")
         skip_tests.add("float/float_parse_doubleprec.py")
 
     if not has_complex:

tools/tinytest-codegen.py

@@ -100,6 +100,7 @@ exclude_tests = (
     "float/float_divmod.py",
     # requires double precision floating point to work
     "float/float2int_doubleprec_intbig.py",
+    "float/float_format_ints_doubleprec.py",
     "float/float_parse_doubleprec.py",
     # inline asm FP tests (require Cortex-M4)
     "inlineasm/asmfpaddsub.py",