diff options
Diffstat (limited to 'src/civetweb/src/third_party/duktape-1.8.0/src-separate/duk_numconv.c')
| -rw-r--r-- | src/civetweb/src/third_party/duktape-1.8.0/src-separate/duk_numconv.c | 2266 |
1 files changed, 2266 insertions, 0 deletions
diff --git a/src/civetweb/src/third_party/duktape-1.8.0/src-separate/duk_numconv.c b/src/civetweb/src/third_party/duktape-1.8.0/src-separate/duk_numconv.c new file mode 100644 index 000000000..de9a4744d --- /dev/null +++ b/src/civetweb/src/third_party/duktape-1.8.0/src-separate/duk_numconv.c @@ -0,0 +1,2266 @@ +/* + * 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; +} |