--- /dev/null
+/*
+ * Number-to-string and string-to-number conversions.
+ *
+ * Slow path number-to-string and string-to-number conversion is based on
+ * a Dragon4 variant, with fast paths for small integers. Big integer
+ * arithmetic is needed for guaranteeing that the conversion is correct
+ * and uses a minimum number of digits. The big number arithmetic has a
+ * fixed maximum size and does not require dynamic allocations.
+ *
+ * See: doc/number-conversion.rst.
+ */
+
+#include "duk_internal.h"
+
+#define DUK__IEEE_DOUBLE_EXP_BIAS 1023
+#define DUK__IEEE_DOUBLE_EXP_MIN (-1022) /* biased exp == 0 -> denormal, exp -1022 */
+
+#define DUK__DIGITCHAR(x) duk_lc_digits[(x)]
+
+/*
+ * Tables generated with src/gennumdigits.py.
+ *
+ * duk__str2num_digits_for_radix indicates, for each radix, how many input
+ * digits should be considered significant for string-to-number conversion.
+ * The input is also padded to this many digits to give the Dragon4
+ * conversion enough (apparent) precision to work with.
+ *
+ * duk__str2num_exp_limits indicates, for each radix, the radix-specific
+ * minimum/maximum exponent values (for a Dragon4 integer mantissa)
+ * below and above which the number is guaranteed to underflow to zero
+ * or overflow to Infinity. This allows parsing to keep bigint values
+ * bounded.
+ */
+
+DUK_LOCAL const duk_uint8_t duk__str2num_digits_for_radix[] = {
+ 69, 44, 35, 30, 27, 25, 23, 22, 20, 20, /* 2 to 11 */
+ 20, 19, 19, 18, 18, 17, 17, 17, 16, 16, /* 12 to 21 */
+ 16, 16, 16, 15, 15, 15, 15, 15, 15, 14, /* 22 to 31 */
+ 14, 14, 14, 14, 14 /* 31 to 36 */
+};
+
+typedef struct {
+ duk_int16_t upper;
+ duk_int16_t lower;
+} duk__exp_limits;
+
+DUK_LOCAL const duk__exp_limits duk__str2num_exp_limits[] = {
+ { 957, -1147 }, { 605, -725 }, { 479, -575 }, { 414, -496 },
+ { 372, -446 }, { 342, -411 }, { 321, -384 }, { 304, -364 },
+ { 291, -346 }, { 279, -334 }, { 268, -323 }, { 260, -312 },
+ { 252, -304 }, { 247, -296 }, { 240, -289 }, { 236, -283 },
+ { 231, -278 }, { 227, -273 }, { 223, -267 }, { 220, -263 },
+ { 216, -260 }, { 213, -256 }, { 210, -253 }, { 208, -249 },
+ { 205, -246 }, { 203, -244 }, { 201, -241 }, { 198, -239 },
+ { 196, -237 }, { 195, -234 }, { 193, -232 }, { 191, -230 },
+ { 190, -228 }, { 188, -226 }, { 187, -225 },
+};
+
+/*
+ * Limited functionality bigint implementation.
+ *
+ * Restricted to non-negative numbers with less than 32 * DUK__BI_MAX_PARTS bits,
+ * with the caller responsible for ensuring this is never exceeded. No memory
+ * allocation (except stack) is needed for bigint computation. Operations
+ * have been tailored for number conversion needs.
+ *
+ * Argument order is "assignment order", i.e. target first, then arguments:
+ * x <- y * z --> duk__bi_mul(x, y, z);
+ */
+
+/* This upper value has been experimentally determined; debug build will check
+ * bigint size with assertions.
+ */
+#define DUK__BI_MAX_PARTS 37 /* 37x32 = 1184 bits */
+
+#ifdef DUK_USE_DDDPRINT
+#define DUK__BI_PRINT(name,x) duk__bi_print((name),(x))
+#else
+#define DUK__BI_PRINT(name,x)
+#endif
+
+/* Current size is about 152 bytes. */
+typedef struct {
+ duk_small_int_t n;
+ duk_uint32_t v[DUK__BI_MAX_PARTS]; /* low to high */
+} duk__bigint;
+
+#ifdef DUK_USE_DDDPRINT
+DUK_LOCAL void duk__bi_print(const char *name, duk__bigint *x) {
+ /* Overestimate required size; debug code so not critical to be tight. */
+ char buf[DUK__BI_MAX_PARTS * 9 + 64];
+ char *p = buf;
+ duk_small_int_t i;
+
+ /* No NUL term checks in this debug code. */
+ p += DUK_SPRINTF(p, "%p n=%ld", (void *) x, (long) x->n);
+ if (x->n == 0) {
+ p += DUK_SPRINTF(p, " 0");
+ }
+ for (i = x->n - 1; i >= 0; i--) {
+ p += DUK_SPRINTF(p, " %08lx", (unsigned long) x->v[i]);
+ }
+
+ DUK_DDD(DUK_DDDPRINT("%s: %s", (const char *) name, (const char *) buf));
+}
+#endif
+
+#ifdef DUK_USE_ASSERTIONS
+DUK_LOCAL duk_small_int_t duk__bi_is_valid(duk__bigint *x) {
+ return (duk_small_int_t)
+ ( ((x->n >= 0) && (x->n <= DUK__BI_MAX_PARTS)) /* is valid size */ &&
+ ((x->n == 0) || (x->v[x->n - 1] != 0)) /* is normalized */ );
+}
+#endif
+
+DUK_LOCAL void duk__bi_normalize(duk__bigint *x) {
+ duk_small_int_t i;
+
+ for (i = x->n - 1; i >= 0; i--) {
+ if (x->v[i] != 0) {
+ break;
+ }
+ }
+
+ /* Note: if 'x' is zero, x->n becomes 0 here */
+ x->n = i + 1;
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+
+/* x <- y */
+DUK_LOCAL void duk__bi_copy(duk__bigint *x, duk__bigint *y) {
+ duk_small_int_t n;
+
+ n = y->n;
+ x->n = n;
+ if (n == 0) {
+ return;
+ }
+ DUK_MEMCPY((void *) x->v, (const void *) y->v, (size_t) (sizeof(duk_uint32_t) * n));
+}
+
+DUK_LOCAL void duk__bi_set_small(duk__bigint *x, duk_uint32_t v) {
+ if (v == 0U) {
+ x->n = 0;
+ } else {
+ x->n = 1;
+ x->v[0] = v;
+ }
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+
+/* Return value: <0 <=> x < y
+ * 0 <=> x == y
+ * >0 <=> x > y
+ */
+DUK_LOCAL int duk__bi_compare(duk__bigint *x, duk__bigint *y) {
+ duk_small_int_t i, nx, ny;
+ duk_uint32_t tx, ty;
+
+ DUK_ASSERT(duk__bi_is_valid(x));
+ DUK_ASSERT(duk__bi_is_valid(y));
+
+ nx = x->n;
+ ny = y->n;
+ if (nx > ny) {
+ goto ret_gt;
+ }
+ if (nx < ny) {
+ goto ret_lt;
+ }
+ for (i = nx - 1; i >= 0; i--) {
+ tx = x->v[i];
+ ty = y->v[i];
+
+ if (tx > ty) {
+ goto ret_gt;
+ }
+ if (tx < ty) {
+ goto ret_lt;
+ }
+ }
+
+ return 0;
+
+ ret_gt:
+ return 1;
+
+ ret_lt:
+ return -1;
+}
+
+/* x <- y + z */
+#ifdef DUK_USE_64BIT_OPS
+DUK_LOCAL void duk__bi_add(duk__bigint *x, duk__bigint *y, duk__bigint *z) {
+ duk_uint64_t tmp;
+ duk_small_int_t i, ny, nz;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+ DUK_ASSERT(duk__bi_is_valid(z));
+
+ if (z->n > y->n) {
+ duk__bigint *t;
+ t = y; y = z; z = t;
+ }
+ DUK_ASSERT(y->n >= z->n);
+
+ ny = y->n; nz = z->n;
+ tmp = 0U;
+ for (i = 0; i < ny; i++) {
+ DUK_ASSERT(i < DUK__BI_MAX_PARTS);
+ tmp += y->v[i];
+ if (i < nz) {
+ tmp += z->v[i];
+ }
+ x->v[i] = (duk_uint32_t) (tmp & 0xffffffffUL);
+ tmp = tmp >> 32;
+ }
+ if (tmp != 0U) {
+ DUK_ASSERT(i < DUK__BI_MAX_PARTS);
+ x->v[i++] = (duk_uint32_t) tmp;
+ }
+ x->n = i;
+ DUK_ASSERT(x->n <= DUK__BI_MAX_PARTS);
+
+ /* no need to normalize */
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+#else /* DUK_USE_64BIT_OPS */
+DUK_LOCAL void duk__bi_add(duk__bigint *x, duk__bigint *y, duk__bigint *z) {
+ duk_uint32_t carry, tmp1, tmp2;
+ duk_small_int_t i, ny, nz;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+ DUK_ASSERT(duk__bi_is_valid(z));
+
+ if (z->n > y->n) {
+ duk__bigint *t;
+ t = y; y = z; z = t;
+ }
+ DUK_ASSERT(y->n >= z->n);
+
+ ny = y->n; nz = z->n;
+ carry = 0U;
+ for (i = 0; i < ny; i++) {
+ /* Carry is detected based on wrapping which relies on exact 32-bit
+ * types.
+ */
+ DUK_ASSERT(i < DUK__BI_MAX_PARTS);
+ tmp1 = y->v[i];
+ tmp2 = tmp1;
+ if (i < nz) {
+ tmp2 += z->v[i];
+ }
+
+ /* Careful with carry condition:
+ * - If carry not added: 0x12345678 + 0 + 0xffffffff = 0x12345677 (< 0x12345678)
+ * - If carry added: 0x12345678 + 1 + 0xffffffff = 0x12345678 (== 0x12345678)
+ */
+ if (carry) {
+ tmp2++;
+ carry = (tmp2 <= tmp1 ? 1U : 0U);
+ } else {
+ carry = (tmp2 < tmp1 ? 1U : 0U);
+ }
+
+ x->v[i] = tmp2;
+ }
+ if (carry) {
+ DUK_ASSERT(i < DUK__BI_MAX_PARTS);
+ DUK_ASSERT(carry == 1U);
+ x->v[i++] = carry;
+ }
+ x->n = i;
+ DUK_ASSERT(x->n <= DUK__BI_MAX_PARTS);
+
+ /* no need to normalize */
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+#endif /* DUK_USE_64BIT_OPS */
+
+/* x <- y + z */
+DUK_LOCAL void duk__bi_add_small(duk__bigint *x, duk__bigint *y, duk_uint32_t z) {
+ duk__bigint tmp;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+
+ /* XXX: this could be optimized; there is only one call site now though */
+ duk__bi_set_small(&tmp, z);
+ duk__bi_add(x, y, &tmp);
+
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+
+#if 0 /* unused */
+/* x <- x + y, use t as temp */
+DUK_LOCAL void duk__bi_add_copy(duk__bigint *x, duk__bigint *y, duk__bigint *t) {
+ duk__bi_add(t, x, y);
+ duk__bi_copy(x, t);
+}
+#endif
+
+/* x <- y - z, require x >= y => z >= 0, i.e. y >= z */
+#ifdef DUK_USE_64BIT_OPS
+DUK_LOCAL void duk__bi_sub(duk__bigint *x, duk__bigint *y, duk__bigint *z) {
+ duk_small_int_t i, ny, nz;
+ duk_uint32_t ty, tz;
+ duk_int64_t tmp;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+ DUK_ASSERT(duk__bi_is_valid(z));
+ DUK_ASSERT(duk__bi_compare(y, z) >= 0);
+ DUK_ASSERT(y->n >= z->n);
+
+ ny = y->n; nz = z->n;
+ tmp = 0;
+ for (i = 0; i < ny; i++) {
+ ty = y->v[i];
+ if (i < nz) {
+ tz = z->v[i];
+ } else {
+ tz = 0;
+ }
+ tmp = (duk_int64_t) ty - (duk_int64_t) tz + tmp;
+ x->v[i] = (duk_uint32_t) (tmp & 0xffffffffUL);
+ tmp = tmp >> 32; /* 0 or -1 */
+ }
+ DUK_ASSERT(tmp == 0);
+
+ x->n = i;
+ duk__bi_normalize(x); /* need to normalize, may even cancel to 0 */
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+#else
+DUK_LOCAL void duk__bi_sub(duk__bigint *x, duk__bigint *y, duk__bigint *z) {
+ duk_small_int_t i, ny, nz;
+ duk_uint32_t tmp1, tmp2, borrow;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+ DUK_ASSERT(duk__bi_is_valid(z));
+ DUK_ASSERT(duk__bi_compare(y, z) >= 0);
+ DUK_ASSERT(y->n >= z->n);
+
+ ny = y->n; nz = z->n;
+ borrow = 0U;
+ for (i = 0; i < ny; i++) {
+ /* Borrow is detected based on wrapping which relies on exact 32-bit
+ * types.
+ */
+ tmp1 = y->v[i];
+ tmp2 = tmp1;
+ if (i < nz) {
+ tmp2 -= z->v[i];
+ }
+
+ /* Careful with borrow condition:
+ * - If borrow not subtracted: 0x12345678 - 0 - 0xffffffff = 0x12345679 (> 0x12345678)
+ * - If borrow subtracted: 0x12345678 - 1 - 0xffffffff = 0x12345678 (== 0x12345678)
+ */
+ if (borrow) {
+ tmp2--;
+ borrow = (tmp2 >= tmp1 ? 1U : 0U);
+ } else {
+ borrow = (tmp2 > tmp1 ? 1U : 0U);
+ }
+
+ x->v[i] = tmp2;
+ }
+ DUK_ASSERT(borrow == 0U);
+
+ x->n = i;
+ duk__bi_normalize(x); /* need to normalize, may even cancel to 0 */
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+#endif
+
+#if 0 /* unused */
+/* x <- y - z */
+DUK_LOCAL void duk__bi_sub_small(duk__bigint *x, duk__bigint *y, duk_uint32_t z) {
+ duk__bigint tmp;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+
+ /* XXX: this could be optimized */
+ duk__bi_set_small(&tmp, z);
+ duk__bi_sub(x, y, &tmp);
+
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+#endif
+
+/* x <- x - y, use t as temp */
+DUK_LOCAL void duk__bi_sub_copy(duk__bigint *x, duk__bigint *y, duk__bigint *t) {
+ duk__bi_sub(t, x, y);
+ duk__bi_copy(x, t);
+}
+
+/* x <- y * z */
+DUK_LOCAL void duk__bi_mul(duk__bigint *x, duk__bigint *y, duk__bigint *z) {
+ duk_small_int_t i, j, nx, nz;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+ DUK_ASSERT(duk__bi_is_valid(z));
+
+ nx = y->n + z->n; /* max possible */
+ DUK_ASSERT(nx <= DUK__BI_MAX_PARTS);
+
+ if (nx == 0) {
+ /* Both inputs are zero; cases where only one is zero can go
+ * through main algorithm.
+ */
+ x->n = 0;
+ return;
+ }
+
+ DUK_MEMZERO((void *) x->v, (size_t) (sizeof(duk_uint32_t) * nx));
+ x->n = nx;
+
+ nz = z->n;
+ for (i = 0; i < y->n; i++) {
+#ifdef DUK_USE_64BIT_OPS
+ duk_uint64_t tmp = 0U;
+ for (j = 0; j < nz; j++) {
+ tmp += (duk_uint64_t) y->v[i] * (duk_uint64_t) z->v[j] + x->v[i+j];
+ x->v[i+j] = (duk_uint32_t) (tmp & 0xffffffffUL);
+ tmp = tmp >> 32;
+ }
+ if (tmp > 0) {
+ DUK_ASSERT(i + j < nx);
+ DUK_ASSERT(i + j < DUK__BI_MAX_PARTS);
+ DUK_ASSERT(x->v[i+j] == 0U);
+ x->v[i+j] = (duk_uint32_t) tmp;
+ }
+#else
+ /*
+ * Multiply + add + carry for 32-bit components using only 16x16->32
+ * multiplies and carry detection based on unsigned overflow.
+ *
+ * 1st mult, 32-bit: (A*2^16 + B)
+ * 2nd mult, 32-bit: (C*2^16 + D)
+ * 3rd add, 32-bit: E
+ * 4th add, 32-bit: F
+ *
+ * (AC*2^16 + B) * (C*2^16 + D) + E + F
+ * = AC*2^32 + AD*2^16 + BC*2^16 + BD + E + F
+ * = AC*2^32 + (AD + BC)*2^16 + (BD + E + F)
+ * = AC*2^32 + AD*2^16 + BC*2^16 + (BD + E + F)
+ */
+ duk_uint32_t a, b, c, d, e, f;
+ duk_uint32_t r, s, t;
+
+ a = y->v[i]; b = a & 0xffffUL; a = a >> 16;
+
+ f = 0;
+ for (j = 0; j < nz; j++) {
+ c = z->v[j]; d = c & 0xffffUL; c = c >> 16;
+ e = x->v[i+j];
+
+ /* build result as: (r << 32) + s: start with (BD + E + F) */
+ r = 0;
+ s = b * d;
+
+ /* add E */
+ t = s + e;
+ if (t < s) { r++; } /* carry */
+ s = t;
+
+ /* add F */
+ t = s + f;
+ if (t < s) { r++; } /* carry */
+ s = t;
+
+ /* add BC*2^16 */
+ t = b * c;
+ r += (t >> 16);
+ t = s + ((t & 0xffffUL) << 16);
+ if (t < s) { r++; } /* carry */
+ s = t;
+
+ /* add AD*2^16 */
+ t = a * d;
+ r += (t >> 16);
+ t = s + ((t & 0xffffUL) << 16);
+ if (t < s) { r++; } /* carry */
+ s = t;
+
+ /* add AC*2^32 */
+ t = a * c;
+ r += t;
+
+ DUK_DDD(DUK_DDDPRINT("ab=%08lx cd=%08lx ef=%08lx -> rs=%08lx %08lx",
+ (unsigned long) y->v[i], (unsigned long) z->v[j],
+ (unsigned long) x->v[i+j], (unsigned long) r,
+ (unsigned long) s));
+
+ x->v[i+j] = s;
+ f = r;
+ }
+ if (f > 0U) {
+ DUK_ASSERT(i + j < nx);
+ DUK_ASSERT(i + j < DUK__BI_MAX_PARTS);
+ DUK_ASSERT(x->v[i+j] == 0U);
+ x->v[i+j] = (duk_uint32_t) f;
+ }
+#endif /* DUK_USE_64BIT_OPS */
+ }
+
+ duk__bi_normalize(x);
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+
+/* x <- y * z */
+DUK_LOCAL void duk__bi_mul_small(duk__bigint *x, duk__bigint *y, duk_uint32_t z) {
+ duk__bigint tmp;
+
+ DUK_ASSERT(duk__bi_is_valid(y));
+
+ /* XXX: this could be optimized */
+ duk__bi_set_small(&tmp, z);
+ duk__bi_mul(x, y, &tmp);
+
+ DUK_ASSERT(duk__bi_is_valid(x));
+}
+
+/* x <- x * y, use t as temp */
+DUK_LOCAL void duk__bi_mul_copy(duk__bigint *x, duk__bigint *y, duk__bigint *t) {
+ duk__bi_mul(t, x, y);
+ duk__bi_copy(x, t);
+}
+
+/* x <- x * y, use t as temp */
+DUK_LOCAL void duk__bi_mul_small_copy(duk__bigint *x, duk_uint32_t y, duk__bigint *t) {
+ duk__bi_mul_small(t, x, y);
+ duk__bi_copy(x, t);
+}
+
+DUK_LOCAL int duk__bi_is_even(duk__bigint *x) {
+ DUK_ASSERT(duk__bi_is_valid(x));
+ return (x->n == 0) || ((x->v[0] & 0x01) == 0);
+}
+
+DUK_LOCAL int duk__bi_is_zero(duk__bigint *x) {
+ DUK_ASSERT(duk__bi_is_valid(x));
+ return (x->n == 0); /* this is the case for normalized numbers */
+}
+
+/* Bigint is 2^52. Used to detect normalized IEEE double mantissa values
+ * which are at the lowest edge (next floating point value downwards has
+ * a different exponent). The lowest mantissa has the form:
+ *
+ * 1000........000 (52 zeroes; only "hidden bit" is set)
+ */
+DUK_LOCAL duk_small_int_t duk__bi_is_2to52(duk__bigint *x) {
+ DUK_ASSERT(duk__bi_is_valid(x));
+ return (duk_small_int_t)
+ (x->n == 2) && (x->v[0] == 0U) && (x->v[1] == (1U << (52-32)));
+}
+
+/* x <- (1<<y) */
+DUK_LOCAL void duk__bi_twoexp(duk__bigint *x, duk_small_int_t y) {
+ duk_small_int_t n, r;
+
+ n = (y / 32) + 1;
+ DUK_ASSERT(n > 0);
+ r = y % 32;
+ DUK_MEMZERO((void *) x->v, sizeof(duk_uint32_t) * n);
+ x->n = n;
+ x->v[n - 1] = (((duk_uint32_t) 1) << r);
+}
+
+/* x <- b^y; use t1 and t2 as temps */
+DUK_LOCAL void duk__bi_exp_small(duk__bigint *x, duk_small_int_t b, duk_small_int_t y, duk__bigint *t1, duk__bigint *t2) {
+ /* Fast path the binary case */
+
+ DUK_ASSERT(x != t1 && x != t2 && t1 != t2); /* distinct bignums, easy mistake to make */
+ DUK_ASSERT(b >= 0);
+ DUK_ASSERT(y >= 0);
+
+ if (b == 2) {
+ duk__bi_twoexp(x, y);
+ return;
+ }
+
+ /* http://en.wikipedia.org/wiki/Exponentiation_by_squaring */
+
+ DUK_DDD(DUK_DDDPRINT("exp_small: b=%ld, y=%ld", (long) b, (long) y));
+
+ duk__bi_set_small(x, 1);
+ duk__bi_set_small(t1, b);
+ for (;;) {
+ /* Loop structure ensures that we don't compute t1^2 unnecessarily
+ * on the final round, as that might create a bignum exceeding the
+ * current DUK__BI_MAX_PARTS limit.
+ */
+ if (y & 0x01) {
+ duk__bi_mul_copy(x, t1, t2);
+ }
+ y = y >> 1;
+ if (y == 0) {
+ break;
+ }
+ duk__bi_mul_copy(t1, t1, t2);
+ }
+
+ DUK__BI_PRINT("exp_small result", x);
+}
+
+/*
+ * A Dragon4 number-to-string variant, based on:
+ *
+ * Guy L. Steele Jr., Jon L. White: "How to Print Floating-Point Numbers
+ * Accurately"
+ *
+ * Robert G. Burger, R. Kent Dybvig: "Printing Floating-Point Numbers
+ * Quickly and Accurately"
+ *
+ * The current algorithm is based on Figure 1 of the Burger-Dybvig paper,
+ * i.e. the base implementation without logarithm estimation speedups
+ * (these would increase code footprint considerably). Fixed-format output
+ * does not follow the suggestions in the paper; instead, we generate an
+ * extra digit and round-with-carry.
+ *
+ * The same algorithm is used for number parsing (with b=10 and B=2)
+ * by generating one extra digit and doing rounding manually.
+ *
+ * See doc/number-conversion.rst for limitations.
+ */
+
+/* Maximum number of digits generated. */
+#define DUK__MAX_OUTPUT_DIGITS 1040 /* (Number.MAX_VALUE).toString(2).length == 1024, + spare */
+
+/* Maximum number of characters in formatted value. */
+#define DUK__MAX_FORMATTED_LENGTH 1040 /* (-Number.MAX_VALUE).toString(2).length == 1025, + spare */
+
+/* Number and (minimum) size of bigints in the nc_ctx structure. */
+#define DUK__NUMCONV_CTX_NUM_BIGINTS 7
+#define DUK__NUMCONV_CTX_BIGINTS_SIZE (sizeof(duk__bigint) * DUK__NUMCONV_CTX_NUM_BIGINTS)
+
+typedef struct {
+ /* Currently about 7*152 = 1064 bytes. The space for these
+ * duk__bigints is used also as a temporary buffer for generating
+ * the final string. This is a bit awkard; a union would be
+ * more correct.
+ */
+ duk__bigint f, r, s, mp, mm, t1, t2;
+
+ duk_small_int_t is_s2n; /* if 1, doing a string-to-number; else doing a number-to-string */
+ duk_small_int_t is_fixed; /* if 1, doing a fixed format output (not free format) */
+ duk_small_int_t req_digits; /* requested number of output digits; 0 = free-format */
+ duk_small_int_t abs_pos; /* digit position is absolute, not relative */
+ duk_small_int_t e; /* exponent for 'f' */
+ duk_small_int_t b; /* input radix */
+ duk_small_int_t B; /* output radix */
+ duk_small_int_t k; /* see algorithm */
+ duk_small_int_t low_ok; /* see algorithm */
+ duk_small_int_t high_ok; /* see algorithm */
+ duk_small_int_t unequal_gaps; /* m+ != m- (very rarely) */
+
+ /* Buffer used for generated digits, values are in the range [0,B-1]. */
+ duk_uint8_t digits[DUK__MAX_OUTPUT_DIGITS];
+ duk_small_int_t count; /* digit count */
+} duk__numconv_stringify_ctx;
+
+/* Note: computes with 'idx' in assertions, so caller beware.
+ * 'idx' is preincremented, i.e. '1' on first call, because it
+ * is more convenient for the caller.
+ */
+#define DUK__DRAGON4_OUTPUT_PREINC(nc_ctx,preinc_idx,x) do { \
+ DUK_ASSERT((preinc_idx) - 1 >= 0); \
+ DUK_ASSERT((preinc_idx) - 1 < DUK__MAX_OUTPUT_DIGITS); \
+ ((nc_ctx)->digits[(preinc_idx) - 1]) = (duk_uint8_t) (x); \
+ } while (0)
+
+DUK_LOCAL duk_size_t duk__dragon4_format_uint32(duk_uint8_t *buf, duk_uint32_t x, duk_small_int_t radix) {
+ duk_uint8_t *p;
+ duk_size_t len;
+ duk_small_int_t dig;
+ duk_small_int_t t;
+
+ DUK_ASSERT(radix >= 2 && radix <= 36);
+
+ /* A 32-bit unsigned integer formats to at most 32 digits (the
+ * worst case happens with radix == 2). Output the digits backwards,
+ * and use a memmove() to get them in the right place.
+ */
+
+ p = buf + 32;
+ for (;;) {
+ t = x / radix;
+ dig = x - t * radix;
+ x = t;
+
+ DUK_ASSERT(dig >= 0 && dig < 36);
+ *(--p) = DUK__DIGITCHAR(dig);
+
+ if (x == 0) {
+ break;
+ }
+ }
+ len = (duk_size_t) ((buf + 32) - p);
+
+ DUK_MEMMOVE((void *) buf, (const void *) p, (size_t) len);
+
+ return len;
+}
+
+DUK_LOCAL void duk__dragon4_prepare(duk__numconv_stringify_ctx *nc_ctx) {
+ duk_small_int_t lowest_mantissa;
+
+#if 1
+ /* Assume IEEE round-to-even, so that shorter encoding can be used
+ * when round-to-even would produce correct result. By removing
+ * this check (and having low_ok == high_ok == 0) the results would
+ * still be accurate but in some cases longer than necessary.
+ */
+ if (duk__bi_is_even(&nc_ctx->f)) {
+ DUK_DDD(DUK_DDDPRINT("f is even"));
+ nc_ctx->low_ok = 1;
+ nc_ctx->high_ok = 1;
+ } else {
+ DUK_DDD(DUK_DDDPRINT("f is odd"));
+ nc_ctx->low_ok = 0;
+ nc_ctx->high_ok = 0;
+ }
+#else
+ /* Note: not honoring round-to-even should work but now generates incorrect
+ * results. For instance, 1e23 serializes to "a000...", i.e. the first digit
+ * equals the radix (10). Scaling stops one step too early in this case.
+ * Don't know why this is the case, but since this code path is unused, it
+ * doesn't matter.
+ */
+ nc_ctx->low_ok = 0;
+ nc_ctx->high_ok = 0;
+#endif
+
+ /* For string-to-number, pretend we never have the lowest mantissa as there
+ * is no natural "precision" for inputs. Having lowest_mantissa == 0, we'll
+ * fall into the base cases for both e >= 0 and e < 0.
+ */
+ if (nc_ctx->is_s2n) {
+ lowest_mantissa = 0;
+ } else {
+ lowest_mantissa = duk__bi_is_2to52(&nc_ctx->f);
+ }
+
+ nc_ctx->unequal_gaps = 0;
+ if (nc_ctx->e >= 0) {
+ /* exponent non-negative (and thus not minimum exponent) */
+
+ if (lowest_mantissa) {
+ /* (>= e 0) AND (= f (expt b (- p 1)))
+ *
+ * be <- (expt b e) == b^e
+ * be1 <- (* be b) == (expt b (+ e 1)) == b^(e+1)
+ * r <- (* f be1 2) == 2 * f * b^(e+1) [if b==2 -> f * b^(e+2)]
+ * s <- (* b 2) [if b==2 -> 4]
+ * m+ <- be1 == b^(e+1)
+ * m- <- be == b^e
+ * k <- 0
+ * B <- B
+ * low_ok <- round
+ * high_ok <- round
+ */
+
+ DUK_DDD(DUK_DDDPRINT("non-negative exponent (not smallest exponent); "
+ "lowest mantissa value for this exponent -> "
+ "unequal gaps"));
+
+ duk__bi_exp_small(&nc_ctx->mm, nc_ctx->b, nc_ctx->e, &nc_ctx->t1, &nc_ctx->t2); /* mm <- b^e */
+ duk__bi_mul_small(&nc_ctx->mp, &nc_ctx->mm, nc_ctx->b); /* mp <- b^(e+1) */
+ duk__bi_mul_small(&nc_ctx->t1, &nc_ctx->f, 2);
+ duk__bi_mul(&nc_ctx->r, &nc_ctx->t1, &nc_ctx->mp); /* r <- (2 * f) * b^(e+1) */
+ duk__bi_set_small(&nc_ctx->s, nc_ctx->b * 2); /* s <- 2 * b */
+ nc_ctx->unequal_gaps = 1;
+ } else {
+ /* (>= e 0) AND (not (= f (expt b (- p 1))))
+ *
+ * be <- (expt b e) == b^e
+ * r <- (* f be 2) == 2 * f * b^e [if b==2 -> f * b^(e+1)]
+ * s <- 2
+ * m+ <- be == b^e
+ * m- <- be == b^e
+ * k <- 0
+ * B <- B
+ * low_ok <- round
+ * high_ok <- round
+ */
+
+ DUK_DDD(DUK_DDDPRINT("non-negative exponent (not smallest exponent); "
+ "not lowest mantissa for this exponent -> "
+ "equal gaps"));
+
+ duk__bi_exp_small(&nc_ctx->mm, nc_ctx->b, nc_ctx->e, &nc_ctx->t1, &nc_ctx->t2); /* mm <- b^e */
+ duk__bi_copy(&nc_ctx->mp, &nc_ctx->mm); /* mp <- b^e */
+ duk__bi_mul_small(&nc_ctx->t1, &nc_ctx->f, 2);
+ duk__bi_mul(&nc_ctx->r, &nc_ctx->t1, &nc_ctx->mp); /* r <- (2 * f) * b^e */
+ duk__bi_set_small(&nc_ctx->s, 2); /* s <- 2 */
+ }
+ } else {
+ /* When doing string-to-number, lowest_mantissa is always 0 so
+ * the exponent check, while incorrect, won't matter.
+ */
+ if (nc_ctx->e > DUK__IEEE_DOUBLE_EXP_MIN /*not minimum exponent*/ &&
+ lowest_mantissa /* lowest mantissa for this exponent*/) {
+ /* r <- (* f b 2) [if b==2 -> (* f 4)]
+ * s <- (* (expt b (- 1 e)) 2) == b^(1-e) * 2 [if b==2 -> b^(2-e)]
+ * m+ <- b == 2
+ * m- <- 1
+ * k <- 0
+ * B <- B
+ * low_ok <- round
+ * high_ok <- round
+ */
+
+ DUK_DDD(DUK_DDDPRINT("negative exponent; not minimum exponent and "
+ "lowest mantissa for this exponent -> "
+ "unequal gaps"));
+
+ duk__bi_mul_small(&nc_ctx->r, &nc_ctx->f, nc_ctx->b * 2); /* r <- (2 * b) * f */
+ duk__bi_exp_small(&nc_ctx->t1, nc_ctx->b, 1 - nc_ctx->e, &nc_ctx->s, &nc_ctx->t2); /* NB: use 's' as temp on purpose */
+ duk__bi_mul_small(&nc_ctx->s, &nc_ctx->t1, 2); /* s <- b^(1-e) * 2 */
+ duk__bi_set_small(&nc_ctx->mp, 2);
+ duk__bi_set_small(&nc_ctx->mm, 1);
+ nc_ctx->unequal_gaps = 1;
+ } else {
+ /* r <- (* f 2)
+ * s <- (* (expt b (- e)) 2) == b^(-e) * 2 [if b==2 -> b^(1-e)]
+ * m+ <- 1
+ * m- <- 1
+ * k <- 0
+ * B <- B
+ * low_ok <- round
+ * high_ok <- round
+ */
+
+ DUK_DDD(DUK_DDDPRINT("negative exponent; minimum exponent or not "
+ "lowest mantissa for this exponent -> "
+ "equal gaps"));
+
+ duk__bi_mul_small(&nc_ctx->r, &nc_ctx->f, 2); /* r <- 2 * f */
+ duk__bi_exp_small(&nc_ctx->t1, nc_ctx->b, -nc_ctx->e, &nc_ctx->s, &nc_ctx->t2); /* NB: use 's' as temp on purpose */
+ duk__bi_mul_small(&nc_ctx->s, &nc_ctx->t1, 2); /* s <- b^(-e) * 2 */
+ duk__bi_set_small(&nc_ctx->mp, 1);
+ duk__bi_set_small(&nc_ctx->mm, 1);
+ }
+ }
+}
+
+DUK_LOCAL void duk__dragon4_scale(duk__numconv_stringify_ctx *nc_ctx) {
+ duk_small_int_t k = 0;
+
+ /* This is essentially the 'scale' algorithm, with recursion removed.
+ * Note that 'k' is either correct immediately, or will move in one
+ * direction in the loop. There's no need to do the low/high checks
+ * on every round (like the Scheme algorithm does).
+ *
+ * The scheme algorithm finds 'k' and updates 's' simultaneously,
+ * while the logical algorithm finds 'k' with 's' having its initial
+ * value, after which 's' is updated separately (see the Burger-Dybvig
+ * paper, Section 3.1, steps 2 and 3).
+ *
+ * The case where m+ == m- (almost always) is optimized for, because
+ * it reduces the bigint operations considerably and almost always
+ * applies. The scale loop only needs to work with m+, so this works.
+ */
+
+ /* XXX: this algorithm could be optimized quite a lot by using e.g.
+ * a logarithm based estimator for 'k' and performing B^n multiplication
+ * using a lookup table or using some bit-representation based exp
+ * algorithm. Currently we just loop, with significant performance
+ * impact for very large and very small numbers.
+ */
+
+ DUK_DDD(DUK_DDDPRINT("scale: B=%ld, low_ok=%ld, high_ok=%ld",
+ (long) nc_ctx->B, (long) nc_ctx->low_ok, (long) nc_ctx->high_ok));
+ DUK__BI_PRINT("r(init)", &nc_ctx->r);
+ DUK__BI_PRINT("s(init)", &nc_ctx->s);
+ DUK__BI_PRINT("mp(init)", &nc_ctx->mp);
+ DUK__BI_PRINT("mm(init)", &nc_ctx->mm);
+
+ for (;;) {
+ DUK_DDD(DUK_DDDPRINT("scale loop (inc k), k=%ld", (long) k));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("m+", &nc_ctx->mp);
+ DUK__BI_PRINT("m-", &nc_ctx->mm);
+
+ duk__bi_add(&nc_ctx->t1, &nc_ctx->r, &nc_ctx->mp); /* t1 = (+ r m+) */
+ if (duk__bi_compare(&nc_ctx->t1, &nc_ctx->s) >= (nc_ctx->high_ok ? 0 : 1)) {
+ DUK_DDD(DUK_DDDPRINT("k is too low"));
+ /* r <- r
+ * s <- (* s B)
+ * m+ <- m+
+ * m- <- m-
+ * k <- (+ k 1)
+ */
+
+ duk__bi_mul_small_copy(&nc_ctx->s, nc_ctx->B, &nc_ctx->t1);
+ k++;
+ } else {
+ break;
+ }
+ }
+
+ /* k > 0 -> k was too low, and cannot be too high */
+ if (k > 0) {
+ goto skip_dec_k;
+ }
+
+ for (;;) {
+ DUK_DDD(DUK_DDDPRINT("scale loop (dec k), k=%ld", (long) k));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("m+", &nc_ctx->mp);
+ DUK__BI_PRINT("m-", &nc_ctx->mm);
+
+ duk__bi_add(&nc_ctx->t1, &nc_ctx->r, &nc_ctx->mp); /* t1 = (+ r m+) */
+ duk__bi_mul_small(&nc_ctx->t2, &nc_ctx->t1, nc_ctx->B); /* t2 = (* (+ r m+) B) */
+ if (duk__bi_compare(&nc_ctx->t2, &nc_ctx->s) <= (nc_ctx->high_ok ? -1 : 0)) {
+ DUK_DDD(DUK_DDDPRINT("k is too high"));
+ /* r <- (* r B)
+ * s <- s
+ * m+ <- (* m+ B)
+ * m- <- (* m- B)
+ * k <- (- k 1)
+ */
+ duk__bi_mul_small_copy(&nc_ctx->r, nc_ctx->B, &nc_ctx->t1);
+ duk__bi_mul_small_copy(&nc_ctx->mp, nc_ctx->B, &nc_ctx->t1);
+ if (nc_ctx->unequal_gaps) {
+ DUK_DDD(DUK_DDDPRINT("m+ != m- -> need to update m- too"));
+ duk__bi_mul_small_copy(&nc_ctx->mm, nc_ctx->B, &nc_ctx->t1);
+ }
+ k--;
+ } else {
+ break;
+ }
+ }
+
+ skip_dec_k:
+
+ if (!nc_ctx->unequal_gaps) {
+ DUK_DDD(DUK_DDDPRINT("equal gaps, copy m- from m+"));
+ duk__bi_copy(&nc_ctx->mm, &nc_ctx->mp); /* mm <- mp */
+ }
+ nc_ctx->k = k;
+
+ DUK_DDD(DUK_DDDPRINT("final k: %ld", (long) k));
+ DUK__BI_PRINT("r(final)", &nc_ctx->r);
+ DUK__BI_PRINT("s(final)", &nc_ctx->s);
+ DUK__BI_PRINT("mp(final)", &nc_ctx->mp);
+ DUK__BI_PRINT("mm(final)", &nc_ctx->mm);
+}
+
+DUK_LOCAL void duk__dragon4_generate(duk__numconv_stringify_ctx *nc_ctx) {
+ duk_small_int_t tc1, tc2; /* terminating conditions */
+ duk_small_int_t d; /* current digit */
+ duk_small_int_t count = 0; /* digit count */
+
+ /*
+ * Digit generation loop.
+ *
+ * Different termination conditions:
+ *
+ * 1. Free format output. Terminate when shortest accurate
+ * representation found.
+ *
+ * 2. Fixed format output, with specific number of digits.
+ * Ignore termination conditions, terminate when digits
+ * generated. Caller requests an extra digit and rounds.
+ *
+ * 3. Fixed format output, with a specific absolute cut-off
+ * position (e.g. 10 digits after decimal point). Note
+ * that we always generate at least one digit, even if
+ * the digit is below the cut-off point already.
+ */
+
+ for (;;) {
+ DUK_DDD(DUK_DDDPRINT("generate loop, count=%ld, k=%ld, B=%ld, low_ok=%ld, high_ok=%ld",
+ (long) count, (long) nc_ctx->k, (long) nc_ctx->B,
+ (long) nc_ctx->low_ok, (long) nc_ctx->high_ok));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("m+", &nc_ctx->mp);
+ DUK__BI_PRINT("m-", &nc_ctx->mm);
+
+ /* (quotient-remainder (* r B) s) using a dummy subtraction loop */
+ duk__bi_mul_small(&nc_ctx->t1, &nc_ctx->r, nc_ctx->B); /* t1 <- (* r B) */
+ d = 0;
+ for (;;) {
+ if (duk__bi_compare(&nc_ctx->t1, &nc_ctx->s) < 0) {
+ break;
+ }
+ duk__bi_sub_copy(&nc_ctx->t1, &nc_ctx->s, &nc_ctx->t2); /* t1 <- t1 - s */
+ d++;
+ }
+ duk__bi_copy(&nc_ctx->r, &nc_ctx->t1); /* r <- (remainder (* r B) s) */
+ /* d <- (quotient (* r B) s) (in range 0...B-1) */
+ DUK_DDD(DUK_DDDPRINT("-> d(quot)=%ld", (long) d));
+ DUK__BI_PRINT("r(rem)", &nc_ctx->r);
+
+ duk__bi_mul_small_copy(&nc_ctx->mp, nc_ctx->B, &nc_ctx->t2); /* m+ <- (* m+ B) */
+ duk__bi_mul_small_copy(&nc_ctx->mm, nc_ctx->B, &nc_ctx->t2); /* m- <- (* m- B) */
+ DUK__BI_PRINT("mp(upd)", &nc_ctx->mp);
+ DUK__BI_PRINT("mm(upd)", &nc_ctx->mm);
+
+ /* Terminating conditions. For fixed width output, we just ignore the
+ * terminating conditions (and pretend that tc1 == tc2 == false). The
+ * the current shortcut for fixed-format output is to generate a few
+ * extra digits and use rounding (with carry) to finish the output.
+ */
+
+ if (nc_ctx->is_fixed == 0) {
+ /* free-form */
+ tc1 = (duk__bi_compare(&nc_ctx->r, &nc_ctx->mm) <= (nc_ctx->low_ok ? 0 : -1));
+
+ duk__bi_add(&nc_ctx->t1, &nc_ctx->r, &nc_ctx->mp); /* t1 <- (+ r m+) */
+ tc2 = (duk__bi_compare(&nc_ctx->t1, &nc_ctx->s) >= (nc_ctx->high_ok ? 0 : 1));
+
+ DUK_DDD(DUK_DDDPRINT("tc1=%ld, tc2=%ld", (long) tc1, (long) tc2));
+ } else {
+ /* fixed-format */
+ tc1 = 0;
+ tc2 = 0;
+ }
+
+ /* Count is incremented before DUK__DRAGON4_OUTPUT_PREINC() call
+ * on purpose, which is taken into account by the macro.
+ */
+ count++;
+
+ if (tc1) {
+ if (tc2) {
+ /* tc1 = true, tc2 = true */
+ duk__bi_mul_small(&nc_ctx->t1, &nc_ctx->r, 2);
+ if (duk__bi_compare(&nc_ctx->t1, &nc_ctx->s) < 0) { /* (< (* r 2) s) */
+ DUK_DDD(DUK_DDDPRINT("tc1=true, tc2=true, 2r > s: output d --> %ld (k=%ld)",
+ (long) d, (long) nc_ctx->k));
+ DUK__DRAGON4_OUTPUT_PREINC(nc_ctx, count, d);
+ } else {
+ DUK_DDD(DUK_DDDPRINT("tc1=true, tc2=true, 2r <= s: output d+1 --> %ld (k=%ld)",
+ (long) (d + 1), (long) nc_ctx->k));
+ DUK__DRAGON4_OUTPUT_PREINC(nc_ctx, count, d + 1);
+ }
+ break;
+ } else {
+ /* tc1 = true, tc2 = false */
+ DUK_DDD(DUK_DDDPRINT("tc1=true, tc2=false: output d --> %ld (k=%ld)",
+ (long) d, (long) nc_ctx->k));
+ DUK__DRAGON4_OUTPUT_PREINC(nc_ctx, count, d);
+ break;
+ }
+ } else {
+ if (tc2) {
+ /* tc1 = false, tc2 = true */
+ DUK_DDD(DUK_DDDPRINT("tc1=false, tc2=true: output d+1 --> %ld (k=%ld)",
+ (long) (d + 1), (long) nc_ctx->k));
+ DUK__DRAGON4_OUTPUT_PREINC(nc_ctx, count, d + 1);
+ break;
+ } else {
+ /* tc1 = false, tc2 = false */
+ DUK_DDD(DUK_DDDPRINT("tc1=false, tc2=false: output d --> %ld (k=%ld)",
+ (long) d, (long) nc_ctx->k));
+ DUK__DRAGON4_OUTPUT_PREINC(nc_ctx, count, d);
+
+ /* r <- r (updated above: r <- (remainder (* r B) s)
+ * s <- s
+ * m+ <- m+ (updated above: m+ <- (* m+ B)
+ * m- <- m- (updated above: m- <- (* m- B)
+ * B, low_ok, high_ok are fixed
+ */
+
+ /* fall through and continue for-loop */
+ }
+ }
+
+ /* fixed-format termination conditions */
+ if (nc_ctx->is_fixed) {
+ if (nc_ctx->abs_pos) {
+ int pos = nc_ctx->k - count + 1; /* count is already incremented, take into account */
+ DUK_DDD(DUK_DDDPRINT("fixed format, absolute: abs pos=%ld, k=%ld, count=%ld, req=%ld",
+ (long) pos, (long) nc_ctx->k, (long) count, (long) nc_ctx->req_digits));
+ if (pos <= nc_ctx->req_digits) {
+ DUK_DDD(DUK_DDDPRINT("digit position reached req_digits, end generate loop"));
+ break;
+ }
+ } else {
+ DUK_DDD(DUK_DDDPRINT("fixed format, relative: k=%ld, count=%ld, req=%ld",
+ (long) nc_ctx->k, (long) count, (long) nc_ctx->req_digits));
+ if (count >= nc_ctx->req_digits) {
+ DUK_DDD(DUK_DDDPRINT("digit count reached req_digits, end generate loop"));
+ break;
+ }
+ }
+ }
+ } /* for */
+
+ nc_ctx->count = count;
+
+ DUK_DDD(DUK_DDDPRINT("generate finished"));
+
+#ifdef DUK_USE_DDDPRINT
+ {
+ duk_uint8_t buf[2048];
+ duk_small_int_t i, t;
+ DUK_MEMZERO(buf, sizeof(buf));
+ for (i = 0; i < nc_ctx->count; i++) {
+ t = nc_ctx->digits[i];
+ if (t < 0 || t > 36) {
+ buf[i] = (duk_uint8_t) '?';
+ } else {
+ buf[i] = (duk_uint8_t) DUK__DIGITCHAR(t);
+ }
+ }
+ DUK_DDD(DUK_DDDPRINT("-> generated digits; k=%ld, digits='%s'",
+ (long) nc_ctx->k, (const char *) buf));
+ }
+#endif
+}
+
+/* Round up digits to a given position. If position is out-of-bounds,
+ * does nothing. If carry propagates over the first digit, a '1' is
+ * prepended to digits and 'k' will be updated. Return value indicates
+ * whether carry propagated over the first digit.
+ *
+ * Note that nc_ctx->count is NOT updated based on the rounding position
+ * (it is updated only if carry overflows over the first digit and an
+ * extra digit is prepended).
+ */
+DUK_LOCAL duk_small_int_t duk__dragon4_fixed_format_round(duk__numconv_stringify_ctx *nc_ctx, duk_small_int_t round_idx) {
+ duk_small_int_t t;
+ duk_uint8_t *p;
+ duk_uint8_t roundup_limit;
+ duk_small_int_t ret = 0;
+
+ /*
+ * round_idx points to the digit which is considered for rounding; the
+ * digit to its left is the final digit of the rounded value. If round_idx
+ * is zero, rounding will be performed; the result will either be an empty
+ * rounded value or if carry happens a '1' digit is generated.
+ */
+
+ if (round_idx >= nc_ctx->count) {
+ DUK_DDD(DUK_DDDPRINT("round_idx out of bounds (%ld >= %ld (count)) -> no rounding",
+ (long) round_idx, (long) nc_ctx->count));
+ return 0;
+ } else if (round_idx < 0) {
+ DUK_DDD(DUK_DDDPRINT("round_idx out of bounds (%ld < 0) -> no rounding",
+ (long) round_idx));
+ return 0;
+ }
+
+ /*
+ * Round-up limit.
+ *
+ * For even values, divides evenly, e.g. 10 -> roundup_limit=5.
+ *
+ * For odd values, rounds up, e.g. 3 -> roundup_limit=2.
+ * If radix is 3, 0/3 -> down, 1/3 -> down, 2/3 -> up.
+ */
+ roundup_limit = (duk_uint8_t) ((nc_ctx->B + 1) / 2);
+
+ p = &nc_ctx->digits[round_idx];
+ if (*p >= roundup_limit) {
+ DUK_DDD(DUK_DDDPRINT("fixed-format rounding carry required"));
+ /* carry */
+ for (;;) {
+ *p = 0;
+ if (p == &nc_ctx->digits[0]) {
+ DUK_DDD(DUK_DDDPRINT("carry propagated to first digit -> special case handling"));
+ DUK_MEMMOVE((void *) (&nc_ctx->digits[1]),
+ (const void *) (&nc_ctx->digits[0]),
+ (size_t) (sizeof(char) * nc_ctx->count));
+ nc_ctx->digits[0] = 1; /* don't increase 'count' */
+ nc_ctx->k++; /* position of highest digit changed */
+ nc_ctx->count++; /* number of digits changed */
+ ret = 1;
+ break;
+ }
+
+ DUK_DDD(DUK_DDDPRINT("fixed-format rounding carry: B=%ld, roundup_limit=%ld, p=%p, digits=%p",
+ (long) nc_ctx->B, (long) roundup_limit, (void *) p, (void *) nc_ctx->digits));
+ p--;
+ t = *p;
+ DUK_DDD(DUK_DDDPRINT("digit before carry: %ld", (long) t));
+ if (++t < nc_ctx->B) {
+ DUK_DDD(DUK_DDDPRINT("rounding carry terminated"));
+ *p = (duk_uint8_t) t;
+ break;
+ }
+
+ DUK_DDD(DUK_DDDPRINT("wraps, carry to next digit"));
+ }
+ }
+
+ return ret;
+}
+
+#define DUK__NO_EXP (65536) /* arbitrary marker, outside valid exp range */
+
+DUK_LOCAL void duk__dragon4_convert_and_push(duk__numconv_stringify_ctx *nc_ctx,
+ duk_context *ctx,
+ duk_small_int_t radix,
+ duk_small_int_t digits,
+ duk_small_uint_t flags,
+ duk_small_int_t neg) {
+ duk_small_int_t k;
+ duk_small_int_t pos, pos_end;
+ duk_small_int_t expt;
+ duk_small_int_t dig;
+ duk_uint8_t *q;
+ duk_uint8_t *buf;
+
+ /*
+ * The string conversion here incorporates all the necessary Ecmascript
+ * semantics without attempting to be generic. nc_ctx->digits contains
+ * nc_ctx->count digits (>= 1), with the topmost digit's 'position'
+ * indicated by nc_ctx->k as follows:
+ *
+ * digits="123" count=3 k=0 --> 0.123
+ * digits="123" count=3 k=1 --> 1.23
+ * digits="123" count=3 k=5 --> 12300
+ * digits="123" count=3 k=-1 --> 0.0123
+ *
+ * Note that the identifier names used for format selection are different
+ * in Burger-Dybvig paper and Ecmascript specification (quite confusingly
+ * so, because e.g. 'k' has a totally different meaning in each). See
+ * documentation for discussion.
+ *
+ * Ecmascript doesn't specify any specific behavior for format selection
+ * (e.g. when to use exponent notation) for non-base-10 numbers.
+ *
+ * The bigint space in the context is reused for string output, as there
+ * is more than enough space for that (>1kB at the moment), and we avoid
+ * allocating even more stack.
+ */
+
+ DUK_ASSERT(DUK__NUMCONV_CTX_BIGINTS_SIZE >= DUK__MAX_FORMATTED_LENGTH);
+ DUK_ASSERT(nc_ctx->count >= 1);
+
+ k = nc_ctx->k;
+ buf = (duk_uint8_t *) &nc_ctx->f; /* XXX: union would be more correct */
+ q = buf;
+
+ /* Exponent handling: if exponent format is used, record exponent value and
+ * fake k such that one leading digit is generated (e.g. digits=123 -> "1.23").
+ *
+ * toFixed() prevents exponent use; otherwise apply a set of criteria to
+ * match the other API calls (toString(), toPrecision, etc).
+ */
+
+ expt = DUK__NO_EXP;
+ if (!nc_ctx->abs_pos /* toFixed() */) {
+ if ((flags & DUK_N2S_FLAG_FORCE_EXP) || /* exponential notation forced */
+ ((flags & DUK_N2S_FLAG_NO_ZERO_PAD) && /* fixed precision and zero padding would be required */
+ (k - digits >= 1)) || /* (e.g. k=3, digits=2 -> "12X") */
+ ((k > 21 || k <= -6) && (radix == 10))) { /* toString() conditions */
+ DUK_DDD(DUK_DDDPRINT("use exponential notation: k=%ld -> expt=%ld",
+ (long) k, (long) (k - 1)));
+ expt = k - 1; /* e.g. 12.3 -> digits="123" k=2 -> 1.23e1 */
+ k = 1; /* generate mantissa with a single leading whole number digit */
+ }
+ }
+
+ if (neg) {
+ *q++ = '-';
+ }
+
+ /* Start position (inclusive) and end position (exclusive) */
+ pos = (k >= 1 ? k : 1);
+ if (nc_ctx->is_fixed) {
+ if (nc_ctx->abs_pos) {
+ /* toFixed() */
+ pos_end = -digits;
+ } else {
+ pos_end = k - digits;
+ }
+ } else {
+ pos_end = k - nc_ctx->count;
+ }
+ if (pos_end > 0) {
+ pos_end = 0;
+ }
+
+ DUK_DDD(DUK_DDDPRINT("expt=%ld, k=%ld, count=%ld, pos=%ld, pos_end=%ld, is_fixed=%ld, "
+ "digits=%ld, abs_pos=%ld",
+ (long) expt, (long) k, (long) nc_ctx->count, (long) pos, (long) pos_end,
+ (long) nc_ctx->is_fixed, (long) digits, (long) nc_ctx->abs_pos));
+
+ /* Digit generation */
+ while (pos > pos_end) {
+ DUK_DDD(DUK_DDDPRINT("digit generation: pos=%ld, pos_end=%ld",
+ (long) pos, (long) pos_end));
+ if (pos == 0) {
+ *q++ = (duk_uint8_t) '.';
+ }
+ if (pos > k) {
+ *q++ = (duk_uint8_t) '0';
+ } else if (pos <= k - nc_ctx->count) {
+ *q++ = (duk_uint8_t) '0';
+ } else {
+ dig = nc_ctx->digits[k - pos];
+ DUK_ASSERT(dig >= 0 && dig < nc_ctx->B);
+ *q++ = (duk_uint8_t) DUK__DIGITCHAR(dig);
+ }
+
+ pos--;
+ }
+ DUK_ASSERT(pos <= 1);
+
+ /* Exponent */
+ if (expt != DUK__NO_EXP) {
+ /*
+ * Exponent notation for non-base-10 numbers isn't specified in Ecmascript
+ * specification, as it never explicitly turns up: non-decimal numbers can
+ * only be formatted with Number.prototype.toString([radix]) and for that,
+ * behavior is not explicitly specified.
+ *
+ * Logical choices include formatting the exponent as decimal (e.g. binary
+ * 100000 as 1e+5) or in current radix (e.g. binary 100000 as 1e+101).
+ * The Dragon4 algorithm (in the original paper) prints the exponent value
+ * in the target radix B. However, for radix values 15 and above, the
+ * exponent separator 'e' is no longer easily parseable. Consider, for
+ * instance, the number "1.faecee+1c".
+ */
+
+ duk_size_t len;
+ char expt_sign;
+
+ *q++ = 'e';
+ if (expt >= 0) {
+ expt_sign = '+';
+ } else {
+ expt_sign = '-';
+ expt = -expt;
+ }
+ *q++ = (duk_uint8_t) expt_sign;
+ len = duk__dragon4_format_uint32(q, (duk_uint32_t) expt, radix);
+ q += len;
+ }
+
+ duk_push_lstring(ctx, (const char *) buf, (size_t) (q - buf));
+}
+
+/*
+ * Conversion helpers
+ */
+
+DUK_LOCAL void duk__dragon4_double_to_ctx(duk__numconv_stringify_ctx *nc_ctx, duk_double_t x) {
+ duk_double_union u;
+ duk_uint32_t tmp;
+ duk_small_int_t expt;
+
+ /*
+ * seeeeeee eeeeffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff
+ * A B C D E F G H
+ *
+ * s sign bit
+ * eee... exponent field
+ * fff... fraction
+ *
+ * ieee value = 1.ffff... * 2^(e - 1023) (normal)
+ * = 0.ffff... * 2^(-1022) (denormal)
+ *
+ * algorithm v = f * b^e
+ */
+
+ DUK_DBLUNION_SET_DOUBLE(&u, x);
+
+ nc_ctx->f.n = 2;
+
+ tmp = DUK_DBLUNION_GET_LOW32(&u);
+ nc_ctx->f.v[0] = tmp;
+ tmp = DUK_DBLUNION_GET_HIGH32(&u);
+ nc_ctx->f.v[1] = tmp & 0x000fffffUL;
+ expt = (duk_small_int_t) ((tmp >> 20) & 0x07ffUL);
+
+ if (expt == 0) {
+ /* denormal */
+ expt = DUK__IEEE_DOUBLE_EXP_MIN - 52;
+ duk__bi_normalize(&nc_ctx->f);
+ } else {
+ /* normal: implicit leading 1-bit */
+ nc_ctx->f.v[1] |= 0x00100000UL;
+ expt = expt - DUK__IEEE_DOUBLE_EXP_BIAS - 52;
+ DUK_ASSERT(duk__bi_is_valid(&nc_ctx->f)); /* true, because v[1] has at least one bit set */
+ }
+
+ DUK_ASSERT(duk__bi_is_valid(&nc_ctx->f));
+
+ nc_ctx->e = expt;
+}
+
+DUK_LOCAL void duk__dragon4_ctx_to_double(duk__numconv_stringify_ctx *nc_ctx, duk_double_t *x) {
+ duk_double_union u;
+ duk_small_int_t expt;
+ duk_small_int_t i;
+ duk_small_int_t bitstart;
+ duk_small_int_t bitround;
+ duk_small_int_t bitidx;
+ duk_small_int_t skip_round;
+ duk_uint32_t t, v;
+
+ DUK_ASSERT(nc_ctx->count == 53 + 1);
+
+ /* Sometimes this assert is not true right now; it will be true after
+ * rounding. See: test-bug-numconv-mantissa-assert.js.
+ */
+ DUK_ASSERT_DISABLE(nc_ctx->digits[0] == 1); /* zero handled by caller */
+
+ /* Should not be required because the code below always sets both high
+ * and low parts, but at least gcc-4.4.5 fails to deduce this correctly
+ * (perhaps because the low part is set (seemingly) conditionally in a
+ * loop), so this is here to avoid the bogus warning.
+ */
+ DUK_MEMZERO((void *) &u, sizeof(u));
+
+ /*
+ * Figure out how generated digits match up with the mantissa,
+ * and then perform rounding. If mantissa overflows, need to
+ * recompute the exponent (it is bumped and may overflow to
+ * infinity).
+ *
+ * For normal numbers the leading '1' is hidden and ignored,
+ * and the last bit is used for rounding:
+ *
+ * rounding pt
+ * <--------52------->|
+ * 1 x x x x ... x x x x|y ==> x x x x ... x x x x
+ *
+ * For denormals, the leading '1' is included in the number,
+ * and the rounding point is different:
+ *
+ * rounding pt
+ * <--52 or less--->|
+ * 1 x x x x ... x x|x x y ==> 0 0 ... 1 x x ... x x
+ *
+ * The largest denormals will have a mantissa beginning with
+ * a '1' (the explicit leading bit); smaller denormals will
+ * have leading zero bits.
+ *
+ * If the exponent would become too high, the result becomes
+ * Infinity. If the exponent is so small that the entire
+ * mantissa becomes zero, the result becomes zero.
+ *
+ * Note: the Dragon4 'k' is off-by-one with respect to the IEEE
+ * exponent. For instance, k==0 indicates that the leading '1'
+ * digit is at the first binary fraction position (0.1xxx...);
+ * the corresponding IEEE exponent would be -1.
+ */
+
+ skip_round = 0;
+
+ recheck_exp:
+
+ expt = nc_ctx->k - 1; /* IEEE exp without bias */
+ if (expt > 1023) {
+ /* Infinity */
+ bitstart = -255; /* needed for inf: causes mantissa to become zero,
+ * and rounding to be skipped.
+ */
+ expt = 2047;
+ } else if (expt >= -1022) {
+ /* normal */
+ bitstart = 1; /* skip leading digit */
+ expt += DUK__IEEE_DOUBLE_EXP_BIAS;
+ DUK_ASSERT(expt >= 1 && expt <= 2046);
+ } else {
+ /* denormal or zero */
+ bitstart = 1023 + expt; /* expt==-1023 -> bitstart=0 (leading 1);
+ * expt==-1024 -> bitstart=-1 (one left of leading 1), etc
+ */
+ expt = 0;
+ }
+ bitround = bitstart + 52;
+
+ DUK_DDD(DUK_DDDPRINT("ieee expt=%ld, bitstart=%ld, bitround=%ld",
+ (long) expt, (long) bitstart, (long) bitround));
+
+ if (!skip_round) {
+ if (duk__dragon4_fixed_format_round(nc_ctx, bitround)) {
+ /* Corner case: see test-numconv-parse-mant-carry.js. We could
+ * just bump the exponent and update bitstart, but it's more robust
+ * to recompute (but avoid rounding twice).
+ */
+ DUK_DDD(DUK_DDDPRINT("rounding caused exponent to be bumped, recheck exponent"));
+ skip_round = 1;
+ goto recheck_exp;
+ }
+ }
+
+ /*
+ * Create mantissa
+ */
+
+ t = 0;
+ for (i = 0; i < 52; i++) {
+ bitidx = bitstart + 52 - 1 - i;
+ if (bitidx >= nc_ctx->count) {
+ v = 0;
+ } else if (bitidx < 0) {
+ v = 0;
+ } else {
+ v = nc_ctx->digits[bitidx];
+ }
+ DUK_ASSERT(v == 0 || v == 1);
+ t += v << (i % 32);
+ if (i == 31) {
+ /* low 32 bits is complete */
+ DUK_DBLUNION_SET_LOW32(&u, t);
+ t = 0;
+ }
+ }
+ /* t has high mantissa */
+
+ DUK_DDD(DUK_DDDPRINT("mantissa is complete: %08lx %08lx",
+ (unsigned long) t,
+ (unsigned long) DUK_DBLUNION_GET_LOW32(&u)));
+
+ DUK_ASSERT(expt >= 0 && expt <= 0x7ffL);
+ t += expt << 20;
+#if 0 /* caller handles sign change */
+ if (negative) {
+ t |= 0x80000000U;
+ }
+#endif
+ DUK_DBLUNION_SET_HIGH32(&u, t);
+
+ DUK_DDD(DUK_DDDPRINT("number is complete: %08lx %08lx",
+ (unsigned long) DUK_DBLUNION_GET_HIGH32(&u),
+ (unsigned long) DUK_DBLUNION_GET_LOW32(&u)));
+
+ *x = DUK_DBLUNION_GET_DOUBLE(&u);
+}
+
+/*
+ * Exposed number-to-string API
+ *
+ * Input: [ number ]
+ * Output: [ string ]
+ */
+
+DUK_INTERNAL void duk_numconv_stringify(duk_context *ctx, duk_small_int_t radix, duk_small_int_t digits, duk_small_uint_t flags) {
+ duk_double_t x;
+ duk_small_int_t c;
+ duk_small_int_t neg;
+ duk_uint32_t uval;
+ duk__numconv_stringify_ctx nc_ctx_alloc; /* large context; around 2kB now */
+ duk__numconv_stringify_ctx *nc_ctx = &nc_ctx_alloc;
+
+ x = (duk_double_t) duk_require_number(ctx, -1);
+ duk_pop(ctx);
+
+ /*
+ * Handle special cases (NaN, infinity, zero).
+ */
+
+ c = (duk_small_int_t) DUK_FPCLASSIFY(x);
+ if (DUK_SIGNBIT((double) x)) {
+ x = -x;
+ neg = 1;
+ } else {
+ neg = 0;
+ }
+
+ /* NaN sign bit is platform specific with unpacked, un-normalized NaNs */
+ DUK_ASSERT(c == DUK_FP_NAN || DUK_SIGNBIT((double) x) == 0);
+
+ if (c == DUK_FP_NAN) {
+ duk_push_hstring_stridx(ctx, DUK_STRIDX_NAN);
+ return;
+ } else if (c == DUK_FP_INFINITE) {
+ if (neg) {
+ /* -Infinity */
+ duk_push_hstring_stridx(ctx, DUK_STRIDX_MINUS_INFINITY);
+ } else {
+ /* Infinity */
+ duk_push_hstring_stridx(ctx, DUK_STRIDX_INFINITY);
+ }
+ return;
+ } else if (c == DUK_FP_ZERO) {
+ /* We can't shortcut zero here if it goes through special formatting
+ * (such as forced exponential notation).
+ */
+ ;
+ }
+
+ /*
+ * Handle integers in 32-bit range (that is, [-(2**32-1),2**32-1])
+ * specially, as they're very likely for embedded programs. This
+ * is now done for all radix values. We must be careful not to use
+ * the fast path when special formatting (e.g. forced exponential)
+ * is in force.
+ *
+ * XXX: could save space by supporting radix 10 only and using
+ * sprintf "%lu" for the fast path and for exponent formatting.
+ */
+
+ uval = (unsigned int) x;
+ if (((double) uval) == x && /* integer number in range */
+ flags == 0) { /* no special formatting */
+ /* use bigint area as a temp */
+ duk_uint8_t *buf = (duk_uint8_t *) (&nc_ctx->f);
+ duk_uint8_t *p = buf;
+
+ DUK_ASSERT(DUK__NUMCONV_CTX_BIGINTS_SIZE >= 32 + 1); /* max size: radix=2 + sign */
+ if (neg && uval != 0) {
+ /* no negative sign for zero */
+ *p++ = (duk_uint8_t) '-';
+ }
+ p += duk__dragon4_format_uint32(p, uval, radix);
+ duk_push_lstring(ctx, (const char *) buf, (duk_size_t) (p - buf));
+ return;
+ }
+
+ /*
+ * Dragon4 setup.
+ *
+ * Convert double from IEEE representation for conversion;
+ * normal finite values have an implicit leading 1-bit. The
+ * slow path algorithm doesn't handle zero, so zero is special
+ * cased here but still creates a valid nc_ctx, and goes
+ * through normal formatting in case special formatting has
+ * been requested (e.g. forced exponential format: 0 -> "0e+0").
+ */
+
+ /* Would be nice to bulk clear the allocation, but the context
+ * is 1-2 kilobytes and nothing should rely on it being zeroed.
+ */
+#if 0
+ DUK_MEMZERO((void *) nc_ctx, sizeof(*nc_ctx)); /* slow init, do only for slow path cases */
+#endif
+
+ nc_ctx->is_s2n = 0;
+ nc_ctx->b = 2;
+ nc_ctx->B = radix;
+ nc_ctx->abs_pos = 0;
+ if (flags & DUK_N2S_FLAG_FIXED_FORMAT) {
+ nc_ctx->is_fixed = 1;
+ if (flags & DUK_N2S_FLAG_FRACTION_DIGITS) {
+ /* absolute req_digits; e.g. digits = 1 -> last digit is 0,
+ * but add an extra digit for rounding.
+ */
+ nc_ctx->abs_pos = 1;
+ nc_ctx->req_digits = (-digits + 1) - 1;
+ } else {
+ nc_ctx->req_digits = digits + 1;
+ }
+ } else {
+ nc_ctx->is_fixed = 0;
+ nc_ctx->req_digits = 0;
+ }
+
+ if (c == DUK_FP_ZERO) {
+ /* Zero special case: fake requested number of zero digits; ensure
+ * no sign bit is printed. Relative and absolute fixed format
+ * require separate handling.
+ */
+ duk_small_int_t count;
+ if (nc_ctx->is_fixed) {
+ if (nc_ctx->abs_pos) {
+ count = digits + 2; /* lead zero + 'digits' fractions + 1 for rounding */
+ } else {
+ count = digits + 1; /* + 1 for rounding */
+ }
+ } else {
+ count = 1;
+ }
+ DUK_DDD(DUK_DDDPRINT("count=%ld", (long) count));
+ DUK_ASSERT(count >= 1);
+ DUK_MEMZERO((void *) nc_ctx->digits, count);
+ nc_ctx->count = count;
+ nc_ctx->k = 1; /* 0.000... */
+ neg = 0;
+ goto zero_skip;
+ }
+
+ duk__dragon4_double_to_ctx(nc_ctx, x); /* -> sets 'f' and 'e' */
+ DUK__BI_PRINT("f", &nc_ctx->f);
+ DUK_DDD(DUK_DDDPRINT("e=%ld", (long) nc_ctx->e));
+
+ /*
+ * Dragon4 slow path digit generation.
+ */
+
+ duk__dragon4_prepare(nc_ctx); /* setup many variables in nc_ctx */
+
+ DUK_DDD(DUK_DDDPRINT("after prepare:"));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("mp", &nc_ctx->mp);
+ DUK__BI_PRINT("mm", &nc_ctx->mm);
+
+ duk__dragon4_scale(nc_ctx);
+
+ DUK_DDD(DUK_DDDPRINT("after scale; k=%ld", (long) nc_ctx->k));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("mp", &nc_ctx->mp);
+ DUK__BI_PRINT("mm", &nc_ctx->mm);
+
+ duk__dragon4_generate(nc_ctx);
+
+ /*
+ * Convert and push final string.
+ */
+
+ zero_skip:
+
+ if (flags & DUK_N2S_FLAG_FIXED_FORMAT) {
+ /* Perform fixed-format rounding. */
+ duk_small_int_t roundpos;
+ if (flags & DUK_N2S_FLAG_FRACTION_DIGITS) {
+ /* 'roundpos' is relative to nc_ctx->k and increases to the right
+ * (opposite of how 'k' changes).
+ */
+ roundpos = -digits; /* absolute position for digit considered for rounding */
+ roundpos = nc_ctx->k - roundpos;
+ } else {
+ roundpos = digits;
+ }
+ DUK_DDD(DUK_DDDPRINT("rounding: k=%ld, count=%ld, digits=%ld, roundpos=%ld",
+ (long) nc_ctx->k, (long) nc_ctx->count, (long) digits, (long) roundpos));
+ (void) duk__dragon4_fixed_format_round(nc_ctx, roundpos);
+
+ /* Note: 'count' is currently not adjusted by rounding (i.e. the
+ * digits are not "chopped off". That shouldn't matter because
+ * the digit position (absolute or relative) is passed on to the
+ * convert-and-push function.
+ */
+ }
+
+ duk__dragon4_convert_and_push(nc_ctx, ctx, radix, digits, flags, neg);
+}
+
+/*
+ * Exposed string-to-number API
+ *
+ * Input: [ string ]
+ * Output: [ number ]
+ *
+ * If number parsing fails, a NaN is pushed as the result. If number parsing
+ * fails due to an internal error, an InternalError is thrown.
+ */
+
+DUK_INTERNAL void duk_numconv_parse(duk_context *ctx, duk_small_int_t radix, duk_small_uint_t flags) {
+ duk_hthread *thr = (duk_hthread *) ctx;
+ duk__numconv_stringify_ctx nc_ctx_alloc; /* large context; around 2kB now */
+ duk__numconv_stringify_ctx *nc_ctx = &nc_ctx_alloc;
+ duk_double_t res;
+ duk_hstring *h_str;
+ duk_small_int_t expt;
+ duk_small_int_t expt_neg;
+ duk_small_int_t expt_adj;
+ duk_small_int_t neg;
+ duk_small_int_t dig;
+ duk_small_int_t dig_whole;
+ duk_small_int_t dig_lzero;
+ duk_small_int_t dig_frac;
+ duk_small_int_t dig_expt;
+ duk_small_int_t dig_prec;
+ const duk__exp_limits *explim;
+ const duk_uint8_t *p;
+ duk_small_int_t ch;
+
+ /* This seems to waste a lot of stack frame entries, but good compilers
+ * will compute these as needed below. Some of these initial flags are
+ * also modified in the code below, so they can't all be removed.
+ */
+ duk_small_int_t trim_white = (flags & DUK_S2N_FLAG_TRIM_WHITE);
+ duk_small_int_t allow_expt = (flags & DUK_S2N_FLAG_ALLOW_EXP);
+ duk_small_int_t allow_garbage = (flags & DUK_S2N_FLAG_ALLOW_GARBAGE);
+ duk_small_int_t allow_plus = (flags & DUK_S2N_FLAG_ALLOW_PLUS);
+ duk_small_int_t allow_minus = (flags & DUK_S2N_FLAG_ALLOW_MINUS);
+ duk_small_int_t allow_infinity = (flags & DUK_S2N_FLAG_ALLOW_INF);
+ duk_small_int_t allow_frac = (flags & DUK_S2N_FLAG_ALLOW_FRAC);
+ duk_small_int_t allow_naked_frac = (flags & DUK_S2N_FLAG_ALLOW_NAKED_FRAC);
+ duk_small_int_t allow_empty_frac = (flags & DUK_S2N_FLAG_ALLOW_EMPTY_FRAC);
+ duk_small_int_t allow_empty = (flags & DUK_S2N_FLAG_ALLOW_EMPTY_AS_ZERO);
+ duk_small_int_t allow_leading_zero = (flags & DUK_S2N_FLAG_ALLOW_LEADING_ZERO);
+ duk_small_int_t allow_auto_hex_int = (flags & DUK_S2N_FLAG_ALLOW_AUTO_HEX_INT);
+ duk_small_int_t allow_auto_oct_int = (flags & DUK_S2N_FLAG_ALLOW_AUTO_OCT_INT);
+
+ DUK_DDD(DUK_DDDPRINT("parse number: %!T, radix=%ld, flags=0x%08lx",
+ (duk_tval *) duk_get_tval(ctx, -1),
+ (long) radix, (unsigned long) flags));
+
+ DUK_ASSERT(radix >= 2 && radix <= 36);
+ DUK_ASSERT(radix - 2 < (duk_small_int_t) sizeof(duk__str2num_digits_for_radix));
+
+ /*
+ * Preliminaries: trim, sign, Infinity check
+ *
+ * We rely on the interned string having a NUL terminator, which will
+ * cause a parse failure wherever it is encountered. As a result, we
+ * don't need separate pointer checks.
+ *
+ * There is no special parsing for 'NaN' in the specification although
+ * 'Infinity' (with an optional sign) is allowed in some contexts.
+ * Some contexts allow plus/minus sign, while others only allow the
+ * minus sign (like JSON.parse()).
+ *
+ * Automatic hex number detection (leading '0x' or '0X') and octal
+ * number detection (leading '0' followed by at least one octal digit)
+ * is done here too.
+ */
+
+ if (trim_white) {
+ /* Leading / trailing whitespace is sometimes accepted and
+ * sometimes not. After white space trimming, all valid input
+ * characters are pure ASCII.
+ */
+ duk_trim(ctx, -1);
+ }
+ h_str = duk_require_hstring(ctx, -1);
+ DUK_ASSERT(h_str != NULL);
+ p = (const duk_uint8_t *) DUK_HSTRING_GET_DATA(h_str);
+
+ neg = 0;
+ ch = *p;
+ if (ch == (duk_small_int_t) '+') {
+ if (!allow_plus) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: leading plus sign not allowed"));
+ goto parse_fail;
+ }
+ p++;
+ } else if (ch == (duk_small_int_t) '-') {
+ if (!allow_minus) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: leading minus sign not allowed"));
+ goto parse_fail;
+ }
+ p++;
+ neg = 1;
+ }
+
+ ch = *p;
+ if (allow_infinity && ch == (duk_small_int_t) 'I') {
+ /* Don't check for Infinity unless the context allows it.
+ * 'Infinity' is a valid integer literal in e.g. base-36:
+ *
+ * parseInt('Infinity', 36)
+ * 1461559270678
+ */
+
+ const duk_uint8_t *q;
+
+ /* borrow literal Infinity from builtin string */
+ q = (const duk_uint8_t *) DUK_HSTRING_GET_DATA(DUK_HTHREAD_STRING_INFINITY(thr));
+ if (DUK_STRNCMP((const char *) p, (const char *) q, 8) == 0) {
+ if (!allow_garbage && (p[8] != (duk_uint8_t) 0)) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: trailing garbage after matching 'Infinity' not allowed"));
+ goto parse_fail;
+ } else {
+ res = DUK_DOUBLE_INFINITY;
+ goto negcheck_and_ret;
+ }
+ }
+ }
+ if (ch == (duk_small_int_t) '0') {
+ duk_small_int_t detect_radix = 0;
+ ch = p[1];
+ if (allow_auto_hex_int && (ch == (duk_small_int_t) 'x' || ch == (duk_small_int_t) 'X')) {
+ DUK_DDD(DUK_DDDPRINT("detected 0x/0X hex prefix, changing radix and preventing fractions and exponent"));
+ detect_radix = 16;
+ allow_empty = 0; /* interpret e.g. '0x' and '0xg' as a NaN (= parse error) */
+ p += 2;
+ } else if (allow_auto_oct_int && (ch >= (duk_small_int_t) '0' && ch <= (duk_small_int_t) '9')) {
+ DUK_DDD(DUK_DDDPRINT("detected 0n oct prefix, changing radix and preventing fractions and exponent"));
+ detect_radix = 8;
+ allow_empty = 1; /* interpret e.g. '09' as '0', not NaN */
+ p += 1;
+ }
+ if (detect_radix > 0) {
+ radix = detect_radix;
+ allow_expt = 0;
+ allow_frac = 0;
+ allow_naked_frac = 0;
+ allow_empty_frac = 0;
+ allow_leading_zero = 1; /* allow e.g. '0x0009' and '00077' */
+ }
+ }
+
+ /*
+ * Scan number and setup for Dragon4.
+ *
+ * The fast path case is detected during setup: an integer which
+ * can be converted without rounding, no net exponent. The fast
+ * path could be implemented as a separate scan, but may not really
+ * be worth it: the multiplications for building 'f' are not
+ * expensive when 'f' is small.
+ *
+ * The significand ('f') must contain enough bits of (apparent)
+ * accuracy, so that Dragon4 will generate enough binary output digits.
+ * For decimal numbers, this means generating a 20-digit significand,
+ * which should yield enough practical accuracy to parse IEEE doubles.
+ * In fact, the Ecmascript specification explicitly allows an
+ * implementation to treat digits beyond 20 as zeroes (and even
+ * to round the 20th digit upwards). For non-decimal numbers, the
+ * appropriate number of digits has been precomputed for comparable
+ * accuracy.
+ *
+ * Digit counts:
+ *
+ * [ dig_lzero ]
+ * |
+ * .+-..---[ dig_prec ]----.
+ * | || |
+ * 0000123.456789012345678901234567890e+123456
+ * | | | | | |
+ * `--+--' `------[ dig_frac ]-------' `-+--'
+ * | |
+ * [ dig_whole ] [ dig_expt ]
+ *
+ * dig_frac and dig_expt are -1 if not present
+ * dig_lzero is only computed for whole number part
+ *
+ * Parsing state
+ *
+ * Parsing whole part dig_frac < 0 AND dig_expt < 0
+ * Parsing fraction part dig_frac >= 0 AND dig_expt < 0
+ * Parsing exponent part dig_expt >= 0 (dig_frac may be < 0 or >= 0)
+ *
+ * Note: in case we hit an implementation limit (like exponent range),
+ * we should throw an error, NOT return NaN or Infinity. Even with
+ * very large exponent (or significand) values the final result may be
+ * finite, so NaN/Infinity would be incorrect.
+ */
+
+ duk__bi_set_small(&nc_ctx->f, 0);
+ dig_prec = 0;
+ dig_lzero = 0;
+ dig_whole = 0;
+ dig_frac = -1;
+ dig_expt = -1;
+ expt = 0;
+ expt_adj = 0; /* essentially tracks digit position of lowest 'f' digit */
+ expt_neg = 0;
+ for (;;) {
+ ch = *p++;
+
+ DUK_DDD(DUK_DDDPRINT("parse digits: p=%p, ch='%c' (%ld), expt=%ld, expt_adj=%ld, "
+ "dig_whole=%ld, dig_frac=%ld, dig_expt=%ld, dig_lzero=%ld, dig_prec=%ld",
+ (const void *) p, (int) ((ch >= 0x20 && ch <= 0x7e) ? ch : '?'), (long) ch,
+ (long) expt, (long) expt_adj, (long) dig_whole, (long) dig_frac,
+ (long) dig_expt, (long) dig_lzero, (long) dig_prec));
+ DUK__BI_PRINT("f", &nc_ctx->f);
+
+ /* Most common cases first. */
+ if (ch >= (duk_small_int_t) '0' && ch <= (duk_small_int_t) '9') {
+ dig = (int) ch - '0' + 0;
+ } else if (ch == (duk_small_int_t) '.') {
+ /* A leading digit is not required in some cases, e.g. accept ".123".
+ * In other cases (JSON.parse()) a leading digit is required. This
+ * is checked for after the loop.
+ */
+ if (dig_frac >= 0 || dig_expt >= 0) {
+ if (allow_garbage) {
+ DUK_DDD(DUK_DDDPRINT("garbage termination (invalid period)"));
+ break;
+ } else {
+ DUK_DDD(DUK_DDDPRINT("parse failed: period not allowed"));
+ goto parse_fail;
+ }
+ }
+
+ if (!allow_frac) {
+ /* Some contexts don't allow fractions at all; this can't be a
+ * post-check because the state ('f' and expt) would be incorrect.
+ */
+ if (allow_garbage) {
+ DUK_DDD(DUK_DDDPRINT("garbage termination (invalid first period)"));
+ break;
+ } else {
+ DUK_DDD(DUK_DDDPRINT("parse failed: fraction part not allowed"));
+ }
+ }
+
+ DUK_DDD(DUK_DDDPRINT("start fraction part"));
+ dig_frac = 0;
+ continue;
+ } else if (ch == (duk_small_int_t) 0) {
+ DUK_DDD(DUK_DDDPRINT("NUL termination"));
+ break;
+ } else if (allow_expt && dig_expt < 0 && (ch == (duk_small_int_t) 'e' || ch == (duk_small_int_t) 'E')) {
+ /* Note: we don't parse back exponent notation for anything else
+ * than radix 10, so this is not an ambiguous check (e.g. hex
+ * exponent values may have 'e' either as a significand digit
+ * or as an exponent separator).
+ *
+ * If the exponent separator occurs twice, 'e' will be interpreted
+ * as a digit (= 14) and will be rejected as an invalid decimal
+ * digit.
+ */
+
+ DUK_DDD(DUK_DDDPRINT("start exponent part"));
+
+ /* Exponent without a sign or with a +/- sign is accepted
+ * by all call sites (even JSON.parse()).
+ */
+ ch = *p;
+ if (ch == (duk_small_int_t) '-') {
+ expt_neg = 1;
+ p++;
+ } else if (ch == (duk_small_int_t) '+') {
+ p++;
+ }
+ dig_expt = 0;
+ continue;
+ } else if (ch >= (duk_small_int_t) 'a' && ch <= (duk_small_int_t) 'z') {
+ dig = (duk_small_int_t) (ch - (duk_small_int_t) 'a' + 0x0a);
+ } else if (ch >= (duk_small_int_t) 'A' && ch <= (duk_small_int_t) 'Z') {
+ dig = (duk_small_int_t) (ch - (duk_small_int_t) 'A' + 0x0a);
+ } else {
+ dig = 255; /* triggers garbage digit check below */
+ }
+ DUK_ASSERT((dig >= 0 && dig <= 35) || dig == 255);
+
+ if (dig >= radix) {
+ if (allow_garbage) {
+ DUK_DDD(DUK_DDDPRINT("garbage termination"));
+ break;
+ } else {
+ DUK_DDD(DUK_DDDPRINT("parse failed: trailing garbage or invalid digit"));
+ goto parse_fail;
+ }
+ }
+
+ if (dig_expt < 0) {
+ /* whole or fraction digit */
+
+ if (dig_prec < duk__str2num_digits_for_radix[radix - 2]) {
+ /* significant from precision perspective */
+
+ duk_small_int_t f_zero = duk__bi_is_zero(&nc_ctx->f);
+ if (f_zero && dig == 0) {
+ /* Leading zero is not counted towards precision digits; not
+ * in the integer part, nor in the fraction part.
+ */
+ if (dig_frac < 0) {
+ dig_lzero++;
+ }
+ } else {
+ /* XXX: join these ops (multiply-accumulate), but only if
+ * code footprint decreases.
+ */
+ duk__bi_mul_small(&nc_ctx->t1, &nc_ctx->f, radix);
+ duk__bi_add_small(&nc_ctx->f, &nc_ctx->t1, dig);
+ dig_prec++;
+ }
+ } else {
+ /* Ignore digits beyond a radix-specific limit, but note them
+ * in expt_adj.
+ */
+ expt_adj++;
+ }
+
+ if (dig_frac >= 0) {
+ dig_frac++;
+ expt_adj--;
+ } else {
+ dig_whole++;
+ }
+ } else {
+ /* exponent digit */
+
+ expt = expt * radix + dig;
+ if (expt > DUK_S2N_MAX_EXPONENT) {
+ /* impose a reasonable exponent limit, so that exp
+ * doesn't need to get tracked using a bigint.
+ */
+ DUK_DDD(DUK_DDDPRINT("parse failed: exponent too large"));
+ goto parse_explimit_error;
+ }
+ dig_expt++;
+ }
+ }
+
+ /* Leading zero. */
+
+ if (dig_lzero > 0 && dig_whole > 1) {
+ if (!allow_leading_zero) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: leading zeroes not allowed in integer part"));
+ goto parse_fail;
+ }
+ }
+
+ /* Validity checks for various fraction formats ("0.1", ".1", "1.", "."). */
+
+ if (dig_whole == 0) {
+ if (dig_frac == 0) {
+ /* "." is not accepted in any format */
+ DUK_DDD(DUK_DDDPRINT("parse failed: plain period without leading or trailing digits"));
+ goto parse_fail;
+ } else if (dig_frac > 0) {
+ /* ".123" */
+ if (!allow_naked_frac) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: fraction part not allowed without "
+ "leading integer digit(s)"));
+ goto parse_fail;
+ }
+ } else {
+ /* empty ("") is allowed in some formats (e.g. Number(''), as zero */
+ if (!allow_empty) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: empty string not allowed (as zero)"));
+ goto parse_fail;
+ }
+ }
+ } else {
+ if (dig_frac == 0) {
+ /* "123." is allowed in some formats */
+ if (!allow_empty_frac) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: empty fractions"));
+ goto parse_fail;
+ }
+ } else if (dig_frac > 0) {
+ /* "123.456" */
+ ;
+ } else {
+ /* "123" */
+ ;
+ }
+ }
+
+ /* Exponent without digits (e.g. "1e" or "1e+"). If trailing garbage is
+ * allowed, ignore exponent part as garbage (= parse as "1", i.e. exp 0).
+ */
+
+ if (dig_expt == 0) {
+ if (!allow_garbage) {
+ DUK_DDD(DUK_DDDPRINT("parse failed: empty exponent"));
+ goto parse_fail;
+ }
+ DUK_ASSERT(expt == 0);
+ }
+
+ if (expt_neg) {
+ expt = -expt;
+ }
+ DUK_DDD(DUK_DDDPRINT("expt=%ld, expt_adj=%ld, net exponent -> %ld",
+ (long) expt, (long) expt_adj, (long) (expt + expt_adj)));
+ expt += expt_adj;
+
+ /* Fast path check. */
+
+ if (nc_ctx->f.n <= 1 && /* 32-bit value */
+ expt == 0 /* no net exponent */) {
+ /* Fast path is triggered for no exponent and also for balanced exponent
+ * and fraction parts, e.g. for "1.23e2" == "123". Remember to respect
+ * zero sign.
+ */
+
+ /* XXX: could accept numbers larger than 32 bits, e.g. up to 53 bits? */
+ DUK_DDD(DUK_DDDPRINT("fast path number parse"));
+ if (nc_ctx->f.n == 1) {
+ res = (double) nc_ctx->f.v[0];
+ } else {
+ res = 0.0;
+ }
+ goto negcheck_and_ret;
+ }
+
+ /* Significand ('f') padding. */
+
+ while (dig_prec < duk__str2num_digits_for_radix[radix - 2]) {
+ /* Pad significand with "virtual" zero digits so that Dragon4 will
+ * have enough (apparent) precision to work with.
+ */
+ DUK_DDD(DUK_DDDPRINT("dig_prec=%ld, pad significand with zero", (long) dig_prec));
+ duk__bi_mul_small_copy(&nc_ctx->f, radix, &nc_ctx->t1);
+ DUK__BI_PRINT("f", &nc_ctx->f);
+ expt--;
+ dig_prec++;
+ }
+
+ DUK_DDD(DUK_DDDPRINT("final exponent: %ld", (long) expt));
+
+ /* Detect zero special case. */
+
+ if (nc_ctx->f.n == 0) {
+ /* This may happen even after the fast path check, if exponent is
+ * not balanced (e.g. "0e1"). Remember to respect zero sign.
+ */
+ DUK_DDD(DUK_DDDPRINT("significand is zero"));
+ res = 0.0;
+ goto negcheck_and_ret;
+ }
+
+
+ /* Quick reject of too large or too small exponents. This check
+ * would be incorrect for zero (e.g. "0e1000" is zero, not Infinity)
+ * so zero check must be above.
+ */
+
+ explim = &duk__str2num_exp_limits[radix - 2];
+ if (expt > explim->upper) {
+ DUK_DDD(DUK_DDDPRINT("exponent too large -> infinite"));
+ res = (duk_double_t) DUK_DOUBLE_INFINITY;
+ goto negcheck_and_ret;
+ } else if (expt < explim->lower) {
+ DUK_DDD(DUK_DDDPRINT("exponent too small -> zero"));
+ res = (duk_double_t) 0.0;
+ goto negcheck_and_ret;
+ }
+
+ nc_ctx->is_s2n = 1;
+ nc_ctx->e = expt;
+ nc_ctx->b = radix;
+ nc_ctx->B = 2;
+ nc_ctx->is_fixed = 1;
+ nc_ctx->abs_pos = 0;
+ nc_ctx->req_digits = 53 + 1;
+
+ DUK__BI_PRINT("f", &nc_ctx->f);
+ DUK_DDD(DUK_DDDPRINT("e=%ld", (long) nc_ctx->e));
+
+ /*
+ * Dragon4 slow path (binary) digit generation.
+ * An extra digit is generated for rounding.
+ */
+
+ duk__dragon4_prepare(nc_ctx); /* setup many variables in nc_ctx */
+
+ DUK_DDD(DUK_DDDPRINT("after prepare:"));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("mp", &nc_ctx->mp);
+ DUK__BI_PRINT("mm", &nc_ctx->mm);
+
+ duk__dragon4_scale(nc_ctx);
+
+ DUK_DDD(DUK_DDDPRINT("after scale; k=%ld", (long) nc_ctx->k));
+ DUK__BI_PRINT("r", &nc_ctx->r);
+ DUK__BI_PRINT("s", &nc_ctx->s);
+ DUK__BI_PRINT("mp", &nc_ctx->mp);
+ DUK__BI_PRINT("mm", &nc_ctx->mm);
+
+ duk__dragon4_generate(nc_ctx);
+
+ DUK_ASSERT(nc_ctx->count == 53 + 1);
+
+ /*
+ * Convert binary digits into an IEEE double. Need to handle
+ * denormals and rounding correctly.
+ */
+
+ duk__dragon4_ctx_to_double(nc_ctx, &res);
+ goto negcheck_and_ret;
+
+ negcheck_and_ret:
+ if (neg) {
+ res = -res;
+ }
+ duk_pop(ctx);
+ duk_push_number(ctx, (double) res);
+ DUK_DDD(DUK_DDDPRINT("result: %!T", (duk_tval *) duk_get_tval(ctx, -1)));
+ return;
+
+ parse_fail:
+ DUK_DDD(DUK_DDDPRINT("parse failed"));
+ duk_pop(ctx);
+ duk_push_nan(ctx);
+ return;
+
+ parse_explimit_error:
+ DUK_DDD(DUK_DDDPRINT("parse failed, internal error, can't return a value"));
+ DUK_ERROR_RANGE(thr, "exponent too large");
+ return;
+}
projects / ceph.git / blobdiff