+++ /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;
-}