| /* |
| * 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; |
| } |