Use internal implementation for converting FP numbers to strings.

Contributed by Peter Cawley.

src/Makefile

@@ -478,7 +478,7 @@ LJLIB_C= $(LJLIB_O:.o=.c)
 LJCORE_O= lj_gc.o lj_err.o lj_char.o lj_bc.o lj_obj.o lj_buf.o \
 	  lj_str.o lj_tab.o lj_func.o lj_udata.o lj_meta.o lj_debug.o \
 	  lj_state.o lj_dispatch.o lj_vmevent.o lj_vmmath.o lj_strscan.o \
-	  lj_strfmt.o lj_api.o lj_profile.o \
+	  lj_strfmt.o lj_strfmt_num.o lj_api.o lj_profile.o \
 	  lj_lex.o lj_parse.o lj_bcread.o lj_bcwrite.o lj_load.o \
 	  lj_ir.o lj_opt_mem.o lj_opt_fold.o lj_opt_narrow.o \
 	  lj_opt_dce.o lj_opt_loop.o lj_opt_split.o lj_opt_sink.o \

src/Makefile.dep

@@ -94,7 +94,7 @@ lj_crecord.o: lj_crecord.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h \
  lj_crecord.h lj_strfmt.h
 lj_ctype.o: lj_ctype.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h \
  lj_gc.h lj_err.h lj_errmsg.h lj_str.h lj_tab.h lj_strfmt.h lj_ctype.h \
- lj_ccallback.h
+ lj_ccallback.h lj_buf.h
 lj_debug.o: lj_debug.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h \
  lj_err.h lj_errmsg.h lj_debug.h lj_buf.h lj_gc.h lj_str.h lj_tab.h \
  lj_state.h lj_frame.h lj_bc.h lj_strfmt.h lj_jit.h lj_ir.h
@@ -188,6 +188,8 @@ lj_str.o: lj_str.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h lj_gc.h \
  lj_err.h lj_errmsg.h lj_str.h lj_char.h
 lj_strfmt.o: lj_strfmt.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h \
  lj_buf.h lj_gc.h lj_str.h lj_state.h lj_char.h lj_strfmt.h
+lj_strfmt_num.o: lj_strfmt_num.c lj_obj.h lua.h luaconf.h lj_def.h \
+ lj_arch.h lj_buf.h lj_gc.h lj_str.h lj_strfmt.h
 lj_strscan.o: lj_strscan.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h \
  lj_char.h lj_strscan.h
 lj_tab.o: lj_tab.c lj_obj.h lua.h luaconf.h lj_def.h lj_arch.h lj_gc.h \

src/lib_base.c

@@ -495,11 +495,10 @@ LJLIB_CF(print)
   shortcut = (tvisfunc(tv) && funcV(tv)->c.ffid == FF_tostring);
   for (i = 0; i < nargs; i++) {
     cTValue *o = &L->base[i];
-    char buf[STRFMT_MAXBUF_NUM];
     const char *str;
     size_t size;
     MSize len;
-    if (shortcut && (str = lj_strfmt_wstrnum(buf, o, &len)) != NULL) {
+    if (shortcut && (str = lj_strfmt_wstrnum(L, o, &len)) != NULL) {
       size = len;
     } else {
       copyTV(L, L->top+1, o);

src/lib_io.c

@@ -232,9 +232,8 @@ static int io_file_write(lua_State *L, FILE *fp, int start)
   cTValue *tv;
   int status = 1;
   for (tv = L->base+start; tv < L->top; tv++) {
-    char buf[STRFMT_MAXBUF_NUM];
     MSize len;
-    const char *p = lj_strfmt_wstrnum(buf, tv, &len);
+    const char *p = lj_strfmt_wstrnum(L, tv, &len);
     if (!p)
       lj_err_argt(L, (int)(tv - L->base) + 1, LUA_TSTRING);
     status = status && (fwrite(p, 1, len, fp) == len);

src/lj_buf.c

@@ -186,7 +186,7 @@ SBuf *lj_buf_puttab(SBuf *sb, GCtab *t, GCstr *sep, int32_t i, int32_t e)
       } else if (tvisint(o)) {
 	p = lj_strfmt_wint(lj_buf_more(sb, STRFMT_MAXBUF_INT+seplen), intV(o));
       } else if (tvisnum(o)) {
-	p = lj_strfmt_wnum(lj_buf_more(sb, STRFMT_MAXBUF_NUM+seplen), o);
+	p = lj_buf_more(lj_strfmt_putfnum(sb, STRFMT_G14, numV(o)), seplen);
       } else {
 	goto badtype;
       }

src/lj_ctype.c

@@ -14,6 +14,7 @@
 #include "lj_strfmt.h"
 #include "lj_ctype.h"
 #include "lj_ccallback.h"
+#include "lj_buf.h"
 
 /* -- C type definitions -------------------------------------------------- */
 
@@ -571,19 +572,18 @@ GCstr *lj_ctype_repr_int64(lua_State *L, uint64_t n, int isunsigned)
 /* Convert complex to string with 'i' or 'I' suffix. */
 GCstr *lj_ctype_repr_complex(lua_State *L, void *sp, CTSize size)
 {
-  char buf[2*STRFMT_MAXBUF_NUM+2+1], *p = buf;
+  SBuf *sb = lj_buf_tmp_(L);
   TValue re, im;
   if (size == 2*sizeof(double)) {
     re.n = *(double *)sp; im.n = ((double *)sp)[1];
   } else {
     re.n = (double)*(float *)sp; im.n = (double)((float *)sp)[1];
   }
-  p = lj_strfmt_wnum(p, &re);
+  lj_strfmt_putfnum(sb, STRFMT_G14, re.n);
-  if (!(im.u32.hi & 0x80000000u) || im.n != im.n) *p++ = '+';
+  if (!(im.u32.hi & 0x80000000u) || im.n != im.n) lj_buf_putchar(sb, '+');
-  p = lj_strfmt_wnum(p, &im);
+  lj_strfmt_putfnum(sb, STRFMT_G14, im.n);
-  *p = *(p-1) >= 'a' ? 'I' : 'i';
+  lj_buf_putchar(sb, sbufP(sb)[-1] >= 'a' ? 'I' : 'i');
-  p++;
+  return lj_buf_str(L, sb);
-  return lj_str_new(L, buf, p-buf);
 }
 
 /* -- C type state -------------------------------------------------------- */

src/lj_meta.c

@@ -278,25 +278,25 @@ TValue *lj_meta_cat(lua_State *L, TValue *top, int left)
       */
       TValue *e, *o = top;
       uint64_t tlen = tvisstr(o) ? strV(o)->len : STRFMT_MAXBUF_NUM;
-      char *p, *buf;
+      SBuf *sb;
       do {
 	o--; tlen += tvisstr(o) ? strV(o)->len : STRFMT_MAXBUF_NUM;
       } while (--left > 0 && (tvisstr(o-1) || tvisnumber(o-1)));
       if (tlen >= LJ_MAX_STR) lj_err_msg(L, LJ_ERR_STROV);
-      p = buf = lj_buf_tmp(L, (MSize)tlen);
+      sb = lj_buf_tmp_(L);
+      lj_buf_more(sb, (MSize)tlen);
       for (e = top, top = o; o <= e; o++) {
 	if (tvisstr(o)) {
 	  GCstr *s = strV(o);
 	  MSize len = s->len;
-	  p = lj_buf_wmem(p, strdata(s), len);
+	  lj_buf_putmem(sb, strdata(s), len);
 	} else if (tvisint(o)) {
-	  p = lj_strfmt_wint(p, intV(o));
+	  lj_strfmt_putint(sb, intV(o));
 	} else {
-	  lua_assert(tvisnum(o));
+	  lj_strfmt_putfnum(sb, STRFMT_G14, numV(o));
-	  p = lj_strfmt_wnum(p, o);
 	}
       }
-      setstrV(L, top, lj_str_new(L, buf, (size_t)(p-buf)));
+      setstrV(L, top, lj_buf_str(L, sb));
     }
   } while (left >= 1);
   if (LJ_UNLIKELY(G(L)->gc.total >= G(L)->gc.threshold)) {

src/lj_strfmt.c

@@ -18,7 +18,7 @@
 /* -- Format parser ------------------------------------------------------- */
 
 static const uint8_t strfmt_map[('x'-'A')+1] = {
-  STRFMT_A,0,0,0,STRFMT_E,0,STRFMT_G,0,0,0,0,0,0,
+  STRFMT_A,0,0,0,STRFMT_E,STRFMT_F,STRFMT_G,0,0,0,0,0,0,
   0,0,0,0,0,0,0,0,0,0,STRFMT_X,0,0,
   0,0,0,0,0,0,
   STRFMT_A,0,STRFMT_C,STRFMT_D,STRFMT_E,STRFMT_F,STRFMT_G,0,STRFMT_I,0,0,0,0,
@@ -89,24 +89,6 @@ retlit:
 
 /* -- Raw conversions ----------------------------------------------------- */
 
-/* Write number to bufer. */
-char * LJ_FASTCALL lj_strfmt_wnum(char *p, cTValue *o)
-{
-  if (LJ_LIKELY((o->u32.hi << 1) < 0xffe00000)) {  /* Finite? */
-#if __BIONIC__
-    if (tvismzero(o)) { *p++ = '-'; *p++ = '0'; return p; }
-#endif
-    return p + lua_number2str(p, o->n);
-  } else if (((o->u32.hi & 0x000fffff) | o->u32.lo) != 0) {
-    *p++ = 'n'; *p++ = 'a'; *p++ = 'n';
-  } else if ((o->u32.hi & 0x80000000) == 0) {
-    *p++ = 'i'; *p++ = 'n'; *p++ = 'f';
-  } else {
-    *p++ = '-'; *p++ = 'i'; *p++ = 'n'; *p++ = 'f';
-  }
-  return p;
-}
-
 #define WINT_R(x, sh, sc) \
   { uint32_t d = (x*(((1<<sh)+sc-1)/sc))>>sh; x -= d*sc; *p++ = (char)('0'+d); }
 
@@ -168,21 +150,22 @@ char * LJ_FASTCALL lj_strfmt_wuleb128(char *p, uint32_t v)
   return p;
 }
 
-/* Return string or write number to buffer and return pointer to start. */
+/* Return string or write number to tmp buffer and return pointer to start. */
-const char *lj_strfmt_wstrnum(char *buf, cTValue *o, MSize *lenp)
+const char *lj_strfmt_wstrnum(lua_State *L, cTValue *o, MSize *lenp)
 {
+  SBuf *sb;
   if (tvisstr(o)) {
     *lenp = strV(o)->len;
     return strVdata(o);
   } else if (tvisint(o)) {
-    *lenp = (MSize)(lj_strfmt_wint(buf, intV(o)) - buf);
+    sb = lj_strfmt_putint(lj_buf_tmp_(L), intV(o));
-    return buf;
   } else if (tvisnum(o)) {
-    *lenp = (MSize)(lj_strfmt_wnum(buf, o) - buf);
+    sb = lj_strfmt_putfnum(lj_buf_tmp_(L), STRFMT_G14, o->n);
-    return buf;
   } else {
     return NULL;
   }
+  *lenp = sbuflen(sb);
+  return sbufB(sb);
 }
 
 /* -- Unformatted conversions to buffer ----------------------------------- */
@@ -198,8 +181,7 @@ SBuf * LJ_FASTCALL lj_strfmt_putint(SBuf *sb, int32_t k)
 /* Add number to buffer. */
 SBuf * LJ_FASTCALL lj_strfmt_putnum(SBuf *sb, cTValue *o)
 {
-  setsbufP(sb, lj_strfmt_wnum(lj_buf_more(sb, STRFMT_MAXBUF_NUM), o));
+  return lj_strfmt_putfnum(sb, STRFMT_G14, o->n);
-  return sb;
 }
 #endif
 
@@ -360,63 +342,6 @@ SBuf *lj_strfmt_putfnum_uint(SBuf *sb, SFormat sf, lua_Number n)
   return lj_strfmt_putfxint(sb, sf, (uint64_t)k);
 }
 
-/* Max. sprintf buffer size needed. At least #string.format("%.99f", -1e308). */
-#define STRFMT_FMTNUMBUF	512
-
-/* Add formatted floating-point number to buffer. */
-SBuf *lj_strfmt_putfnum(SBuf *sb, SFormat sf, lua_Number n)
-{
-  TValue tv;
-  tv.n = n;
-  if (LJ_UNLIKELY((tv.u32.hi << 1) >= 0xffe00000)) {
-    /* Canonicalize output of non-finite values. */
-    MSize width = STRFMT_WIDTH(sf), len = 3;
-    int prefix = 0, ch = (sf & STRFMT_F_UPPER) ? 0x202020 : 0;
-    char *p;
-    if (((tv.u32.hi & 0x000fffff) | tv.u32.lo) != 0) {
-      ch ^= ('n' << 16) | ('a' << 8) | 'n';
-      if ((sf & STRFMT_F_SPACE)) prefix = ' ';
-    } else {
-      ch ^= ('i' << 16) | ('n' << 8) | 'f';
-      if ((tv.u32.hi & 0x80000000)) prefix = '-';
-      else if ((sf & STRFMT_F_PLUS)) prefix = '+';
-      else if ((sf & STRFMT_F_SPACE)) prefix = ' ';
-    }
-    if (prefix) len = 4;
-    p = lj_buf_more(sb, width > len ? width : len);
-    if (!(sf & STRFMT_F_LEFT)) while (width-- > len) *p++ = ' ';
-    if (prefix) *p++ = prefix;
-    *p++ = (char)(ch >> 16); *p++ = (char)(ch >> 8); *p++ = (char)ch;
-    if ((sf & STRFMT_F_LEFT)) while (width-- > len) *p++ = ' ';
-    setsbufP(sb, p);
-  } else {  /* Delegate to sprintf() for now. */
-    uint8_t width = (uint8_t)STRFMT_WIDTH(sf), prec = (uint8_t)STRFMT_PREC(sf);
-    char fmt[1+5+2+3+1+1], *p = fmt;
-    *p++ = '%';
-    if ((sf & STRFMT_F_LEFT)) *p++ = '-';
-    if ((sf & STRFMT_F_PLUS)) *p++ = '+';
-    if ((sf & STRFMT_F_ZERO)) *p++ = '0';
-    if ((sf & STRFMT_F_SPACE)) *p++ = ' ';
-    if ((sf & STRFMT_F_ALT)) *p++ = '#';
-    if (width) {
-      uint8_t x = width / 10, y = width % 10;
-      if (x) *p++ = '0' + x;
-      *p++ = '0' + y;
-    }
-    if (prec != 255) {
-      uint8_t x = prec / 10, y = prec % 10;
-      *p++ = '.';
-      if (x) *p++ = '0' + x;
-      *p++ = '0' + y;
-    }
-    *p++ = (0x67666561 >> (STRFMT_FP(sf)<<3)) ^ ((sf & STRFMT_F_UPPER)?0x20:0);
-    *p = '\0';
-    p = lj_buf_more(sb, STRFMT_FMTNUMBUF);
-    setsbufP(sb, p + sprintf(p, fmt, n));
-  }
-  return sb;
-}
-
 /* -- Conversions to strings ---------------------------------------------- */
 
 /* Convert integer to string. */
@@ -427,14 +352,6 @@ GCstr * LJ_FASTCALL lj_strfmt_int(lua_State *L, int32_t k)
   return lj_str_new(L, buf, len);
 }
 
-/* Convert number to string. */
-GCstr * LJ_FASTCALL lj_strfmt_num(lua_State *L, cTValue *o)
-{
-  char buf[STRFMT_MAXBUF_NUM];
-  MSize len = (MSize)(lj_strfmt_wnum(buf, o) - buf);
-  return lj_str_new(L, buf, len);
-}
-
 /* Convert integer or number to string. */
 GCstr * LJ_FASTCALL lj_strfmt_number(lua_State *L, cTValue *o)
 {
@@ -510,12 +427,9 @@ const char *lj_strfmt_pushvf(lua_State *L, const char *fmt, va_list argp)
     case STRFMT_UINT:
       lj_strfmt_putfxint(sb, sf, va_arg(argp, uint32_t));
       break;
-    case STRFMT_NUM: {
+    case STRFMT_NUM:
-      TValue tv;
+      lj_strfmt_putfnum(sb, STRFMT_G14, va_arg(argp, lua_Number));
-      tv.n = va_arg(argp, lua_Number);
-      setsbufP(sb, lj_strfmt_wnum(lj_buf_more(sb, STRFMT_MAXBUF_NUM), &tv));
       break;
-      }
     case STRFMT_STR: {
       const char *s = va_arg(argp, char *);
       if (s == NULL) s = "(null)";

src/lj_strfmt.h

@@ -64,11 +64,12 @@ typedef enum FormatType {
 #define STRFMT_S	(STRFMT_STR)
 #define STRFMT_U	(STRFMT_UINT)
 #define STRFMT_X	(STRFMT_UINT|STRFMT_T_HEX)
+#define STRFMT_G14	(STRFMT_G | ((14+1) << STRFMT_SH_PREC))
 
 /* Maximum buffer sizes for conversions. */
 #define STRFMT_MAXBUF_XINT	(1+22)  /* '0' prefix + uint64_t in octal. */
 #define STRFMT_MAXBUF_INT	(1+10)  /* Sign + int32_t in decimal. */
-#define STRFMT_MAXBUF_NUM	LUAI_MAXNUMBER2STR
+#define STRFMT_MAXBUF_NUM	32  /* Must correspond with STRFMT_G14. */
 #define STRFMT_MAXBUF_PTR	(2+2*sizeof(ptrdiff_t))  /* "0x" + hex ptr. */
 
 /* Format parser. */
@@ -83,10 +84,9 @@ static LJ_AINLINE void lj_strfmt_init(FormatState *fs, const char *p, MSize len)
 
 /* Raw conversions. */
 LJ_FUNC char * LJ_FASTCALL lj_strfmt_wint(char *p, int32_t k);
-LJ_FUNC char * LJ_FASTCALL lj_strfmt_wnum(char *p, cTValue *o);
 LJ_FUNC char * LJ_FASTCALL lj_strfmt_wptr(char *p, const void *v);
 LJ_FUNC char * LJ_FASTCALL lj_strfmt_wuleb128(char *p, uint32_t v);
-LJ_FUNC const char *lj_strfmt_wstrnum(char *buf, cTValue *o, MSize *lenp);
+LJ_FUNC const char *lj_strfmt_wstrnum(lua_State *L, cTValue *o, MSize *lenp);
 
 /* Unformatted conversions to buffer. */
 LJ_FUNC SBuf * LJ_FASTCALL lj_strfmt_putint(SBuf *sb, int32_t k);

src/lj_strfmt_num.c

@@ -0,0 +1,591 @@
+/*
+** String formatting for floating-point numbers.
+** Copyright (C) 2005-2015 Mike Pall. See Copyright Notice in luajit.h
+** Contributed by Peter Cawley.
+*/
+
+#include <stdio.h>
+
+#define lj_strfmt_num_c
+#define LUA_CORE
+
+#include "lj_obj.h"
+#include "lj_buf.h"
+#include "lj_str.h"
+#include "lj_strfmt.h"
+
+/* -- Precomputed tables -------------------------------------------------- */
+
+/* Rescale factors to push the exponent of a number towards zero. */
+#define RESCALE_EXPONENTS(P, N) \
+  P(308), P(289), P(270), P(250), P(231), P(212), P(193), P(173), P(154), \
+  P(135), P(115), P(96), P(77), P(58), P(38), P(0), P(0), P(0), N(39), N(58), \
+  N(77), N(96), N(116), N(135), N(154), N(174), N(193), N(212), N(231), \
+  N(251), N(270), N(289)
+
+#define ONE_E_P(X) 1e+0 ## X
+#define ONE_E_N(X) 1e-0 ## X
+static const int16_t rescale_e[] = { RESCALE_EXPONENTS(-, +) };
+static const double rescale_n[] = { RESCALE_EXPONENTS(ONE_E_P, ONE_E_N) };
+#undef ONE_E_N
+#undef ONE_E_P
+
+/*
+** For p in range -70 through 57, this table encodes pairs (m, e) such that
+** 4*2^p <= (uint8_t)m*10^e, and is the smallest value for which this holds.
+*/
+static const int8_t four_ulp_m_e[] = {
+  34, -21, 68, -21, 14, -20, 28, -20, 55, -20, 2, -19, 3, -19, 5, -19, 9, -19,
+  -82, -18, 35, -18, 7, -17, -117, -17, 28, -17, 56, -17, 112, -16, -33, -16,
+  45, -16, 89, -16, -78, -15, 36, -15, 72, -15, -113, -14, 29, -14, 57, -14,
+  114, -13, -28, -13, 46, -13, 91, -12, -74, -12, 37, -12, 73, -12, 15, -11, 3,
+  -11, 59, -11, 2, -10, 3, -10, 5, -10, 1, -9, -69, -9, 38, -9, 75, -9, 15, -7,
+  3, -7, 6, -7, 12, -6, -17, -7, 48, -7, 96, -7, -65, -6, 39, -6, 77, -6, -103,
+  -5, 31, -5, 62, -5, 123, -4, -11, -4, 49, -4, 98, -4, -60, -3, 4, -2, 79, -3,
+  16, -2, 32, -2, 63, -2, 2, -1, 25, 0, 5, 1, 1, 2, 2, 2, 4, 2, 8, 2, 16, 2,
+  32, 2, 64, 2, -128, 2, 26, 2, 52, 2, 103, 3, -51, 3, 41, 4, 82, 4, -92, 4,
+  33, 4, 66, 4, -124, 5, 27, 5, 53, 5, 105, 6, 21, 6, 42, 6, 84, 6, 17, 7, 34,
+  7, 68, 7, 2, 8, 3, 8, 6, 8, 108, 9, -41, 9, 43, 10, 86, 9, -84, 10, 35, 10,
+  69, 10, -118, 11, 28, 11, 55, 12, 11, 13, 22, 13, 44, 13, 88, 13, -80, 13,
+  36, 13, 71, 13, -115, 14, 29, 14, 57, 14, 113, 15, -30, 15, 46, 15, 91, 15,
+  19, 16, 37, 16, 73, 16, 2, 17, 3, 17, 6, 17
+};
+
+/* min(2^32-1, 10^e-1) for e in range 0 through 10 */
+static uint32_t ndigits_dec_threshold[] = {
+  0, 9U, 99U, 999U, 9999U, 99999U, 999999U,
+  9999999U, 99999999U, 999999999U, 0xffffffffU
+};
+
+/* -- Helper functions ---------------------------------------------------- */
+
+/* Compute the number of digits in the decimal representation of x. */
+static MSize ndigits_dec(uint32_t x)
+{
+  MSize t = ((lj_fls(x | 1) * 77) >> 8) + 1; /* 2^8/77 is roughly log2(10) */
+  return t + (x > ndigits_dec_threshold[t]);
+}
+
+#define WINT_R(x, sh, sc) \
+  { uint32_t d = (x*(((1<<sh)+sc-1)/sc))>>sh; x -= d*sc; *p++ = (char)('0'+d); }
+
+/* Write 9-digit unsigned integer to buffer. */
+static char *lj_strfmt_wuint9(char *p, uint32_t u)
+{
+  uint32_t v = u / 10000, w;
+  u -= v * 10000;
+  w = v / 10000;
+  v -= w * 10000;
+  *p++ = (char)('0'+w);
+  WINT_R(v, 23, 1000)
+  WINT_R(v, 12, 100)
+  WINT_R(v, 10, 10)
+  *p++ = (char)('0'+v);
+  WINT_R(u, 23, 1000)
+  WINT_R(u, 12, 100)
+  WINT_R(u, 10, 10)
+  *p++ = (char)('0'+u);
+  return p;
+}
+#undef WINT_R
+
+/* -- Extended precision arithmetic --------------------------------------- */
+
+/*
+** The "nd" format is a fixed-precision decimal representation for numbers. It
+** consists of up to 64 uint32_t values, with each uint32_t storing a value
+** in the range [0, 1e9). A number in "nd" format consists of three variables:
+**
+**  uint32_t nd[64];
+**  uint32_t ndlo;
+**  uint32_t ndhi;
+**
+** The integral part of the number is stored in nd[0 ... ndhi], the value of
+** which is sum{i in [0, ndhi] | nd[i] * 10^(9*i)}. If the fractional part of
+** the number is zero, ndlo is zero. Otherwise, the fractional part is stored
+** in nd[ndlo ... 63], the value of which is taken to be
+** sum{i in [ndlo, 63] | nd[i] * 10^(9*(i-64))}.
+**
+** If the array part had 128 elements rather than 64, then every double would
+** have an exact representation in "nd" format. With 64 elements, all integral
+** doubles have an exact representation, and all non-integral doubles have
+** enough digits to make both %.99e and %.99f do the right thing.
+*/
+
+#if LJ_64
+#define ND_MUL2K_MAX_SHIFT	29
+#define ND_MUL2K_DIV1E9(val)	((uint32_t)((val) / 1000000000))
+#else
+#define ND_MUL2K_MAX_SHIFT	11
+#define ND_MUL2K_DIV1E9(val)	((uint32_t)((val) >> 9) / 1953125)
+#endif
+
+/* Multiply nd by 2^k and add carry_in (ndlo is assumed to be zero). */
+static uint32_t nd_mul2k(uint32_t* nd, uint32_t ndhi, uint32_t k,
+			 uint32_t carry_in, SFormat sf)
+{
+  uint32_t i, ndlo = 0, start = 1;
+  /* Performance hacks. */
+  if (k > ND_MUL2K_MAX_SHIFT*2 && STRFMT_FP(sf) != STRFMT_FP(STRFMT_T_FP_F)) {
+    start = ndhi - (STRFMT_PREC(sf) + 17) / 8;
+  }
+  /* Real logic. */
+  while (k >= ND_MUL2K_MAX_SHIFT) {
+    for (i = ndlo; i <= ndhi; i++) {
+      uint64_t val = ((uint64_t)nd[i] << ND_MUL2K_MAX_SHIFT) | carry_in;
+      carry_in = ND_MUL2K_DIV1E9(val);
+      nd[i] = (uint32_t)val - carry_in * 1000000000;
+    }
+    if (carry_in) {
+      nd[++ndhi] = carry_in; carry_in = 0;
+      if(start++ == ndlo) ++ndlo;
+    }
+    k -= ND_MUL2K_MAX_SHIFT;
+  }
+  if (k) {
+    for (i = ndlo; i <= ndhi; i++) {
+      uint64_t val = ((uint64_t)nd[i] << k) | carry_in;
+      carry_in = ND_MUL2K_DIV1E9(val);
+      nd[i] = (uint32_t)val - carry_in * 1000000000;
+    }
+    if (carry_in) nd[++ndhi] = carry_in;
+  }
+  return ndhi;
+}
+
+/* Divide nd by 2^k (ndlo is assumed to be zero). */
+static uint32_t nd_div2k(uint32_t* nd, uint32_t ndhi, uint32_t k, SFormat sf)
+{
+  uint32_t ndlo = 0, stop1 = ~0, stop2 = ~0;
+  /* Performance hacks. */
+  if (!ndhi) {
+    if (!nd[0]) {
+      return 0;
+    } else {
+      uint32_t s = lj_ffs(nd[0]);
+      if (s >= k) { nd[0] >>= k; return 0; }
+      nd[0] >>= s; k -= s;
+    }
+  }
+  if (k > 18) {
+    if (STRFMT_FP(sf) == STRFMT_FP(STRFMT_T_FP_F)) {
+      stop1 = 63 - (int32_t)STRFMT_PREC(sf) / 9;
+    } else {
+      int32_t floorlog2 = ndhi * 29 + lj_fls(nd[ndhi]) - k;
+      int32_t floorlog10 = (int32_t)(floorlog2 * 0.30102999566398114);
+      stop1 = 62 + (floorlog10 - (int32_t)STRFMT_PREC(sf)) / 9;
+      stop2 = 61 + ndhi - (int32_t)STRFMT_PREC(sf) / 8;
+    }
+  }
+  /* Real logic. */
+  while (k >= 9) {
+    uint32_t i = ndhi, carry = 0;
+    for (;;) {
+      uint32_t val = nd[i];
+      nd[i] = (val >> 9) + carry;
+      carry = (val & 0x1ff) * 1953125;
+      if (i == ndlo) break;
+      i = (i - 1) & 0x3f;
+    }
+    if (ndlo != stop1 && ndlo != stop2) {
+      if (carry) { ndlo = (ndlo - 1) & 0x3f; nd[ndlo] = carry; }
+      if (!nd[ndhi]) { ndhi = (ndhi - 1) & 0x3f; stop2--; }
+    } else if (!nd[ndhi]) {
+      if (ndhi != ndlo) { ndhi = (ndhi - 1) & 0x3f; stop2--; }
+      else return ndlo;
+    }
+    k -= 9;
+  }
+  if (k) {
+    uint32_t mask = (1U << k) - 1, mul = 1000000000 >> k, i = ndhi, carry = 0;
+    for (;;) {
+      uint32_t val = nd[i];
+      nd[i] = (val >> k) + carry;
+      carry = (val & mask) * mul;
+      if (i == ndlo) break;
+      i = (i - 1) & 0x3f;
+    }
+    if (carry) { ndlo = (ndlo - 1) & 0x3f; nd[ndlo] = carry; }
+  }
+  return ndlo;
+}
+
+/* Add m*10^e to nd (assumes ndlo <= e/9 <= ndhi and 0 <= m <= 9). */
+static uint32_t nd_add_m10e(uint32_t* nd, uint32_t ndhi, uint8_t m, int32_t e)
+{
+  uint32_t i, carry;
+  if (e >= 0) {
+    i = (uint32_t)e/9;
+    carry = m * (ndigits_dec_threshold[e - (int32_t)i*9] + 1);
+  } else {
+    int32_t f = (e-8)/9;
+    i = (uint32_t)(64 + f);
+    carry = m * (ndigits_dec_threshold[e - f*9] + 1);
+  }
+  for (;;) {
+    uint32_t val = nd[i] + carry;
+    if (LJ_UNLIKELY(val >= 1000000000)) {
+      val -= 1000000000;
+      nd[i] = val;
+      if (LJ_UNLIKELY(i == ndhi)) {
+	ndhi = (ndhi + 1) & 0x3f;
+	nd[ndhi] = 1;
+	break;
+      }
+      carry = 1;
+      i = (i + 1) & 0x3f;
+    } else {
+      nd[i] = val;
+      break;
+    }
+  }
+  return ndhi;
+}
+
+/* Test whether two "nd" values are equal in their most significant digits. */
+static int nd_similar(uint32_t* nd, uint32_t ndhi, uint32_t* ref, MSize hilen,
+		      MSize prec)
+{
+  char nd9[9], ref9[9];
+  if (hilen <= prec) {
+    if (LJ_UNLIKELY(nd[ndhi] != *ref)) return 0;
+    prec -= hilen; ref--; ndhi = (ndhi - 1) & 0x3f;
+    if (prec >= 9) {
+      if (LJ_UNLIKELY(nd[ndhi] != *ref)) return 0;
+      prec -= 9; ref--; ndhi = (ndhi - 1) & 0x3f;
+    }
+  } else {
+    prec -= hilen - 9;
+  }
+  lua_assert(prec < 9);
+  lj_strfmt_wuint9(nd9, nd[ndhi]);
+  lj_strfmt_wuint9(ref9, *ref);
+  return !memcmp(nd9, ref9, prec) && (nd9[prec] < '5') == (ref9[prec] < '5');
+}
+
+/* -- Formatted conversions to buffer ------------------------------------- */
+
+/* Write formatted floating-point number to either sb or p. */
+static char *lj_strfmt_wfnum(SBuf *sb, SFormat sf, lua_Number n, char *p)
+{
+  MSize width = STRFMT_WIDTH(sf), prec = STRFMT_PREC(sf), len;
+  TValue t;
+  t.n = n;
+  if (LJ_UNLIKELY((t.u32.hi << 1) >= 0xffe00000)) {
+    /* Handle non-finite values uniformly for %a, %e, %f, %g. */
+    int prefix = 0, ch = (sf & STRFMT_F_UPPER) ? 0x202020 : 0;
+    if (((t.u32.hi & 0x000fffff) | t.u32.lo) != 0) {
+      ch ^= ('n' << 16) | ('a' << 8) | 'n';
+      if ((sf & STRFMT_F_SPACE)) prefix = ' ';
+    } else {
+      ch ^= ('i' << 16) | ('n' << 8) | 'f';
+      if ((t.u32.hi & 0x80000000)) prefix = '-';
+      else if ((sf & STRFMT_F_PLUS)) prefix = '+';
+      else if ((sf & STRFMT_F_SPACE)) prefix = ' ';
+    }
+    len = 3 + (prefix != 0);
+    if (!p) p = lj_buf_more(sb, width > len ? width : len);
+    if (!(sf & STRFMT_F_LEFT)) while (width-- > len) *p++ = ' ';
+    if (prefix) *p++ = prefix;
+    *p++ = (char)(ch >> 16); *p++ = (char)(ch >> 8); *p++ = (char)ch;
+  } else if (STRFMT_FP(sf) == STRFMT_FP(STRFMT_T_FP_A)) {
+    /* %a */
+    const char *hexdig = (sf & STRFMT_F_UPPER) ? "0123456789ABCDEFPX"
+					       : "0123456789abcdefpx";
+    int32_t e = (t.u32.hi >> 20) & 0x7ff;
+    char prefix = 0, eprefix = '+';
+    if (t.u32.hi & 0x80000000) prefix = '-';
+    else if ((sf & STRFMT_F_PLUS)) prefix = '+';
+    else if ((sf & STRFMT_F_SPACE)) prefix = ' ';
+    t.u32.hi &= 0xfffff;
+    if (e) {
+      t.u32.hi |= 0x100000;
+      e -= 1023;
+    } else if (t.u32.lo | t.u32.hi) {
+      /* Non-zero denormal - normalise it. */
+      uint32_t shift = t.u32.hi ? 20-lj_fls(t.u32.hi) : 52-lj_fls(t.u32.lo);
+      e = -1022 - shift;
+      t.u64 <<= shift;
+    }
+    /* abs(n) == t.u64 * 2^(e - 52) */
+    /* If n != 0, bit 52 of t.u64 is set, and is the highest set bit. */
+    if ((int32_t)prec < 0) {
+      /* Default precision: use smallest precision giving exact result. */
+      prec = t.u32.lo ? 13-lj_ffs(t.u32.lo)/4 : 5-lj_ffs(t.u32.hi|0x100000)/4;
+    } else if (prec < 13) {
+      /* Precision is sufficiently low as to maybe require rounding. */
+      t.u64 += (((uint64_t)1) << (51 - prec*4));
+    }
+    if (e < 0) {
+      eprefix = '-';
+      e = -e;
+    }
+    len = 5 + ndigits_dec((uint32_t)e) + prec + (prefix != 0)
+	    + ((prec | (sf & STRFMT_F_ALT)) != 0);
+    if (!p) p = lj_buf_more(sb, width > len ? width : len);
+    if (!(sf & (STRFMT_F_LEFT | STRFMT_F_ZERO))) {
+      while (width-- > len) *p++ = ' ';
+    }
+    if (prefix) *p++ = prefix;
+    *p++ = '0';
+    *p++ = hexdig[17]; /* x or X */
+    if ((sf & (STRFMT_F_LEFT | STRFMT_F_ZERO)) == STRFMT_F_ZERO) {
+      while (width-- > len) *p++ = '0';
+    }
+    *p++ = '0' + (t.u32.hi >> 20); /* Usually '1', sometimes '0' or '2'. */
+    if ((prec | (sf & STRFMT_F_ALT))) {
+      /* Emit fractional part. */
+      char *q = p + 1 + prec;
+      *p = '.';
+      if (prec < 13) t.u64 >>= (52 - prec*4);
+      else while (prec > 13) p[prec--] = '0';
+      while (prec) { p[prec--] = hexdig[t.u64 & 15]; t.u64 >>= 4; }
+      p = q;
+    }
+    *p++ = hexdig[16]; /* p or P */
+    *p++ = eprefix; /* + or - */
+    p = lj_strfmt_wint(p, e);
+  } else {
+    /* %e or %f or %g - begin by converting n to "nd" format. */
+    uint32_t nd[64];
+    uint32_t ndhi = 0, ndlo, i;
+    int32_t e = (t.u32.hi >> 20) & 0x7ff, ndebias = 0;
+    char prefix = 0, *q;
+    if (t.u32.hi & 0x80000000) prefix = '-';
+    else if ((sf & STRFMT_F_PLUS)) prefix = '+';
+    else if ((sf & STRFMT_F_SPACE)) prefix = ' ';
+    prec += ((int32_t)prec >> 31) & 7; /* Default precision is 6. */
+    if (STRFMT_FP(sf) == STRFMT_FP(STRFMT_T_FP_G)) {
+      /* %g - decrement precision if non-zero (to make it like %e). */
+      prec--;
+      prec ^= (uint32_t)((int32_t)prec >> 31);
+    }
+    if ((sf & STRFMT_T_FP_E) && prec < 14 && n != 0) {
+      /* Precision is sufficiently low that rescaling will probably work. */
+      if ((ndebias = rescale_e[e >> 6])) {
+	t.n = n * rescale_n[e >> 6];
+	t.u64 -= 2; /* Convert 2ulp below (later we convert 2ulp above). */
+	nd[0] = 0x100000 | (t.u32.hi & 0xfffff);
+	e = ((t.u32.hi >> 20) & 0x7ff) - 1075 - (ND_MUL2K_MAX_SHIFT < 29);
+	goto load_t_lo; rescale_failed:
+	t.n = n;
+	e = (t.u32.hi >> 20) & 0x7ff;
+	ndebias = ndhi = 0;
+      }
+    }
+    nd[0] = t.u32.hi & 0xfffff;
+    if (e == 0) e++; else nd[0] |= 0x100000;
+    e -= 1043;
+    if (t.u32.lo) {
+      e -= 32 + (ND_MUL2K_MAX_SHIFT < 29); load_t_lo:
+#if ND_MUL2K_MAX_SHIFT >= 29
+      nd[0] = (nd[0] << 3) | (t.u32.lo >> 29);
+      ndhi = nd_mul2k(nd, ndhi, 29, t.u32.lo & 0x1fffffff, sf);
+#elif ND_MUL2K_MAX_SHIFT >= 11
+      ndhi = nd_mul2k(nd, ndhi, 11, t.u32.lo >> 21, sf);
+      ndhi = nd_mul2k(nd, ndhi, 11, (t.u32.lo >> 10) & 0x7ff, sf);
+      ndhi = nd_mul2k(nd, ndhi, 11, (t.u32.lo <<  1) & 0x7ff, sf);
+#else
+#error "ND_MUL2K_MAX_SHIFT too small"
+#endif
+    }
+    if (e >= 0) {
+      ndhi = nd_mul2k(nd, ndhi, (uint32_t)e, 0, sf);
+      ndlo = 0;
+    } else {
+      ndlo = nd_div2k(nd, ndhi, (uint32_t)-e, sf);
+      if (ndhi && !nd[ndhi]) ndhi--;
+    }
+    /* abs(n) == nd * 10^ndebias (for slightly loose interpretation of ==) */
+    if ((sf & STRFMT_T_FP_E)) {
+      /* %e or %g - assume %e and start by calculating nd's exponent (nde). */
+      char eprefix = '+';
+      int32_t nde = -1;
+      MSize hilen;
+      if (ndlo && !nd[ndhi]) {
+	ndhi = 64; do {} while (!nd[--ndhi]);
+	nde -= 64 * 9;
+      }
+      hilen = ndigits_dec(nd[ndhi]);
+      nde += ndhi * 9 + hilen;
+      if (ndebias) {
+	/*
+	** Rescaling was performed, but this introduced some error, and might
+	** have pushed us across a rounding boundary. We check whether this
+	** error affected the result by introducing even more error (2ulp in
+	** either direction), and seeing whether a roundary boundary was
+	** crossed. Having already converted the -2ulp case, we save off its
+	** most significant digits, convert the +2ulp case, and compare them.
+	*/
+	int32_t eidx = e + 70 + (ND_MUL2K_MAX_SHIFT < 29)
+			 + (t.u32.lo >= 0xfffffffe && !(~t.u32.hi << 12));
+	const int8_t *m_e = four_ulp_m_e + eidx * 2;
+	lua_assert(0 <= eidx && eidx < 128);
+	nd[33] = nd[ndhi];
+	nd[32] = nd[(ndhi - 1) & 0x3f];
+	nd[31] = nd[(ndhi - 2) & 0x3f];
+	nd_add_m10e(nd, ndhi, (uint8_t)*m_e, m_e[1]);
+	if (LJ_UNLIKELY(!nd_similar(nd, ndhi, nd + 33, hilen, prec + 1))) {
+	  goto rescale_failed;
+	}
+      }
+      if ((int32_t)(prec - nde) < (0x3f & -(int32_t)ndlo) * 9) {
+	/* Precision is sufficiently low as to maybe require rounding. */
+	ndhi = nd_add_m10e(nd, ndhi, 5, nde - prec - 1);
+	nde += (hilen != ndigits_dec(nd[ndhi]));
+      }
+      nde += ndebias;
+      if ((sf & STRFMT_T_FP_F)) {
+	/* %g */
+	if ((int32_t)prec >= nde && nde >= -4) {
+	  if (nde < 0) ndhi = 0;
+	  prec -= nde;
+	  goto g_format_like_f;
+	} else if (!(sf & STRFMT_F_ALT) && prec && width > 5) {
+	  /* Decrease precision in order to strip trailing zeroes. */
+	  char tail[9];
+	  uint32_t maxprec = hilen - 1 + ((ndhi - ndlo) & 0x3f) * 9;
+	  if (prec >= maxprec) prec = maxprec;
+	  else ndlo = (ndhi - (((int32_t)(prec - hilen) + 9) / 9)) & 0x3f;
+	  i = prec - hilen - (((ndhi - ndlo) & 0x3f) * 9) + 10;
+	  lj_strfmt_wuint9(tail, nd[ndlo]);
+	  while (prec && tail[--i] == '0') {
+	    prec--;
+	    if (!i) {
+	      if (ndlo == ndhi) { prec = 0; break; }
+	      lj_strfmt_wuint9(tail, nd[++ndlo]);
+	      i = 9;
+	    }
+	  }
+	}
+      }
+      if (nde < 0) {
+	/* Make nde non-negative. */
+	eprefix = '-';
+	nde = -nde;
+      }
+      len = 3 + prec + (prefix != 0) + ndigits_dec((uint32_t)nde) + (nde < 10)
+	      + ((prec | (sf & STRFMT_F_ALT)) != 0);
+      if (!p) p = lj_buf_more(sb, (width > len ? width : len) + 5);
+      if (!(sf & (STRFMT_F_LEFT | STRFMT_F_ZERO))) {
+	while (width-- > len) *p++ = ' ';
+      }
+      if (prefix) *p++ = prefix;
+      if ((sf & (STRFMT_F_LEFT | STRFMT_F_ZERO)) == STRFMT_F_ZERO) {
+	while (width-- > len) *p++ = '0';
+      }
+      q = lj_strfmt_wint(p + 1, nd[ndhi]);
+      p[0] = p[1]; /* Put leading digit in the correct place. */
+      if ((prec | (sf & STRFMT_F_ALT))) {
+	/* Emit fractional part. */
+	p[1] = '.'; p += 2;
+	prec -= (q - p); p = q; /* Account for the digits already emitted. */
+	/* Then emit chunks of 9 digits (this may emit 8 digits too many). */
+	for (i = ndhi; (int32_t)prec > 0 && i != ndlo; prec -= 9) {
+	  i = (i - 1) & 0x3f;
+	  p = lj_strfmt_wuint9(p, nd[i]);
+	}
+	if ((sf & STRFMT_T_FP_F) && !(sf & STRFMT_F_ALT)) {
+	  /* %g (and not %#g) - strip trailing zeroes. */
+	  p += (int32_t)prec & ((int32_t)prec >> 31);
+	  while (p[-1] == '0') p--;
+	  if (p[-1] == '.') p--;
+	} else {
+	  /* %e (or %#g) - emit trailing zeroes. */
+	  while ((int32_t)prec > 0) { *p++ = '0'; prec--; }
+	  p += (int32_t)prec;
+	}
+      } else {
+	p++;
+      }
+      *p++ = (sf & STRFMT_F_UPPER) ? 'E' : 'e';
+      *p++ = eprefix; /* + or - */
+      if (nde < 10) *p++ = '0'; /* Always at least two digits of exponent. */
+      p = lj_strfmt_wint(p, nde);
+    } else {
+      /* %f (or, shortly, %g in %f style) */
+      if (prec < (MSize)(0x3f & -(int32_t)ndlo) * 9) {
+	/* Precision is sufficiently low as to maybe require rounding. */
+	ndhi = nd_add_m10e(nd, ndhi, 5, 0 - prec - 1);
+      }
+      g_format_like_f:
+      if ((sf & STRFMT_T_FP_E) && !(sf & STRFMT_F_ALT) && prec && width) {
+	/* Decrease precision in order to strip trailing zeroes. */
+	if (ndlo) {
+	  /* nd has a fractional part; we need to look at its digits. */
+	  char tail[9];
+	  uint32_t maxprec = (64 - ndlo) * 9;
+	  if (prec >= maxprec) prec = maxprec;
+	  else ndlo = 64 - (prec + 8) / 9;
+	  i = prec - ((63 - ndlo) * 9);
+	  lj_strfmt_wuint9(tail, nd[ndlo]);
+	  while (prec && tail[--i] == '0') {
+	    prec--;
+	    if (!i) {
+	      if (ndlo == 63) { prec = 0; break; }
+	      lj_strfmt_wuint9(tail, nd[++ndlo]);
+	      i = 9;
+	    }
+	  }
+	} else {
+	  /* nd has no fractional part, so precision goes straight to zero. */
+	  prec = 0;
+	}
+      }
+      len = ndhi * 9 + ndigits_dec(nd[ndhi]) + prec + (prefix != 0)
+		     + ((prec | (sf & STRFMT_F_ALT)) != 0);
+      if (!p) p = lj_buf_more(sb, (width > len ? width : len) + 8);
+      if (!(sf & (STRFMT_F_LEFT | STRFMT_F_ZERO))) {
+	while (width-- > len) *p++ = ' ';
+      }
+      if (prefix) *p++ = prefix;
+      if ((sf & (STRFMT_F_LEFT | STRFMT_F_ZERO)) == STRFMT_F_ZERO) {
+	while (width-- > len) *p++ = '0';
+      }
+      /* Emit integer part. */
+      p = lj_strfmt_wint(p, nd[ndhi]);
+      i = ndhi;
+      while (i) p = lj_strfmt_wuint9(p, nd[--i]);
+      if ((prec | (sf & STRFMT_F_ALT))) {
+	/* Emit fractional part. */
+	*p++ = '.';
+	/* Emit chunks of 9 digits (this may emit 8 digits too many). */
+	while ((int32_t)prec > 0 && i != ndlo) {
+	  i = (i - 1) & 0x3f;
+	  p = lj_strfmt_wuint9(p, nd[i]);
+	  prec -= 9;
+	}
+	if ((sf & STRFMT_T_FP_E) && !(sf & STRFMT_F_ALT)) {
+	  /* %g (and not %#g) - strip trailing zeroes. */
+	  p += (int32_t)prec & ((int32_t)prec >> 31);
+	  while (p[-1] == '0') p--;
+	  if (p[-1] == '.') p--;
+	} else {
+	  /* %f (or %#g) - emit trailing zeroes. */
+	  while ((int32_t)prec > 0) { *p++ = '0'; prec--; }
+	  p += (int32_t)prec;
+	}
+      }
+    }
+  }
+  if ((sf & STRFMT_F_LEFT)) while (width-- > len) *p++ = ' ';
+  return p;
+}
+
+/* Add formatted floating-point number to buffer. */
+SBuf *lj_strfmt_putfnum(SBuf *sb, SFormat sf, lua_Number n)
+{
+  setsbufP(sb, lj_strfmt_wfnum(sb, sf, n, NULL));
+  return sb;
+}
+
+/* -- Conversions to strings ---------------------------------------------- */
+
+/* Convert number to string. */
+GCstr * LJ_FASTCALL lj_strfmt_num(lua_State *L, cTValue *o)
+{
+  char buf[STRFMT_MAXBUF_NUM];
+  MSize len = (MSize)(lj_strfmt_wfnum(NULL, STRFMT_G14, o->n, buf) - buf);
+  return lj_str_new(L, buf, len);
+}
+

src/ljamalg.c

@@ -46,6 +46,7 @@
 #include "lj_vmmath.c"
 #include "lj_strscan.c"
 #include "lj_strfmt.c"
+#include "lj_strfmt_num.c"
 #include "lj_api.c"
 #include "lj_profile.c"
 #include "lj_lex.c"