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Diffstat (limited to 'src/stdlib/fpconv.c')
| -rw-r--r-- | src/stdlib/fpconv.c | 341 |
1 files changed, 341 insertions, 0 deletions
diff --git a/src/stdlib/fpconv.c b/src/stdlib/fpconv.c new file mode 100644 index 00000000..97699784 --- /dev/null +++ b/src/stdlib/fpconv.c @@ -0,0 +1,341 @@ +// This file defines a function to convert floating point numbers to strings. +// For license, see: fpconv_license.txt +#include <stdbool.h> +#include <string.h> + +#include "fpconv.h" +#include "powers.h" + +#define fracmask 0x000FFFFFFFFFFFFFU +#define expmask 0x7FF0000000000000U +#define hiddenbit 0x0010000000000000U +#define signmask 0x8000000000000000U +#define expbias (1023 + 52) + +#define absv(n) ((n) < 0 ? -(n) : (n)) +#define minv(a, b) ((a) < (b) ? (a) : (b)) + +static uint64_t tens[] = { + 10000000000000000000U, 1000000000000000000U, 100000000000000000U, + 10000000000000000U, 1000000000000000U, 100000000000000U, + 10000000000000U, 1000000000000U, 100000000000U, + 10000000000U, 1000000000U, 100000000U, + 10000000U, 1000000U, 100000U, + 10000U, 1000U, 100U, + 10U, 1U +}; + +static inline uint64_t get_dbits(double d) +{ + union { + double dbl; + uint64_t i; + } dbl_bits = { d }; + + return dbl_bits.i; +} + +static Fp build_fp(double d) +{ + uint64_t bits = get_dbits(d); + + Fp fp; + fp.frac = bits & fracmask; + fp.exp = (bits & expmask) >> 52; + + if (fp.exp) { + fp.frac += hiddenbit; + fp.exp -= expbias; + + } else { + fp.exp = -expbias + 1; + } + + return fp; +} + +static void normalize(Fp* fp) +{ + while ((fp->frac & hiddenbit) == 0) { + fp->frac <<= 1; + fp->exp--; + } + + int shift = 64 - 52 - 1; + fp->frac <<= shift; + fp->exp -= shift; +} + +static void get_normalized_boundaries(Fp* fp, Fp* lower, Fp* upper) +{ + upper->frac = (fp->frac << 1) + 1; + upper->exp = fp->exp - 1; + + while ((upper->frac & (hiddenbit << 1)) == 0) { + upper->frac <<= 1; + upper->exp--; + } + + int u_shift = 64 - 52 - 2; + + upper->frac <<= u_shift; + upper->exp = upper->exp - u_shift; + + + int l_shift = fp->frac == hiddenbit ? 2 : 1; + + lower->frac = (fp->frac << l_shift) - 1; + lower->exp = fp->exp - l_shift; + + + lower->frac <<= lower->exp - upper->exp; + lower->exp = upper->exp; +} + +static Fp multiply(Fp* a, Fp* b) +{ + const uint64_t lomask = 0x00000000FFFFFFFF; + + uint64_t ah_bl = (a->frac >> 32) * (b->frac & lomask); + uint64_t al_bh = (a->frac & lomask) * (b->frac >> 32); + uint64_t al_bl = (a->frac & lomask) * (b->frac & lomask); + uint64_t ah_bh = (a->frac >> 32) * (b->frac >> 32); + + uint64_t tmp = (ah_bl & lomask) + (al_bh & lomask) + (al_bl >> 32); + /* round up */ + tmp += 1U << 31; + + Fp fp = { + ah_bh + (ah_bl >> 32) + (al_bh >> 32) + (tmp >> 32), + a->exp + b->exp + 64 + }; + + return fp; +} + +static void round_digit(char* digits, int ndigits, uint64_t delta, uint64_t rem, uint64_t kappa, uint64_t frac) +{ + while (rem < frac && delta - rem >= kappa && + (rem + kappa < frac || frac - rem > rem + kappa - frac)) { + + digits[ndigits - 1]--; + rem += kappa; + } +} + +static int generate_digits(Fp* fp, Fp* upper, Fp* lower, char* digits, int* K) +{ + uint64_t wfrac = upper->frac - fp->frac; + uint64_t delta = upper->frac - lower->frac; + + Fp one; + one.frac = 1ULL << -upper->exp; + one.exp = upper->exp; + + uint64_t part1 = upper->frac >> -one.exp; + uint64_t part2 = upper->frac & (one.frac - 1); + + int idx = 0, kappa = 10; + uint64_t* divp; + /* 1000000000 */ + for(divp = tens + 10; kappa > 0; divp++) { + + uint64_t div = *divp; + unsigned digit = part1 / div; + + if (digit || idx) { + digits[idx++] = digit + '0'; + } + + part1 -= digit * div; + kappa--; + + uint64_t tmp = (part1 <<-one.exp) + part2; + if (tmp <= delta) { + *K += kappa; + round_digit(digits, idx, delta, tmp, div << -one.exp, wfrac); + + return idx; + } + } + + /* 10 */ + uint64_t* unit = tens + 18; + + while (true) { + part2 *= 10; + delta *= 10; + kappa--; + + unsigned digit = part2 >> -one.exp; + if (digit || idx) { + digits[idx++] = digit + '0'; + } + + part2 &= one.frac - 1; + if (part2 < delta) { + *K += kappa; + round_digit(digits, idx, delta, part2, one.frac, wfrac * *unit); + + return idx; + } + + unit--; + } +} + +static int grisu2(double d, char* digits, int* K) +{ + Fp w = build_fp(d); + + Fp lower, upper; + get_normalized_boundaries(&w, &lower, &upper); + + normalize(&w); + + int k; + Fp cp = find_cachedpow10(upper.exp, &k); + + w = multiply(&w, &cp); + upper = multiply(&upper, &cp); + lower = multiply(&lower, &cp); + + lower.frac++; + upper.frac--; + + *K = -k; + + return generate_digits(&w, &upper, &lower, digits, K); +} + +static int emit_digits(char* digits, int ndigits, char* dest, int K, bool neg) +{ + int exp = absv(K + ndigits - 1); + + int max_trailing_zeros = 7; + + if (neg) { + max_trailing_zeros -= 1; + } + + /* write plain integer */ + if (K >= 0 && (exp < (ndigits + max_trailing_zeros))) { + + memcpy(dest, digits, (size_t)ndigits); + memset(dest + ndigits, '0', (size_t)K); + + return ndigits + K; + } + + /* write decimal w/o scientific notation */ + if (K < 0 && (K > -7 || exp < 4)) { + int offset = ndigits - absv(K); + /* fp < 1.0 -> write leading zero */ + if (offset <= 0) { + offset = -offset; + dest[0] = '0'; + dest[1] = '.'; + memset(dest + 2, '0', (size_t)offset); + memcpy(dest + offset + 2, digits, (size_t)ndigits); + + return ndigits + 2 + offset; + + /* fp > 1.0 */ + } else { + memcpy(dest, digits, (size_t)offset); + dest[offset] = '.'; + memcpy(dest + offset + 1, digits + offset, (size_t)(ndigits - offset)); + + return ndigits + 1; + } + } + + /* write decimal w/ scientific notation */ + ndigits = minv(ndigits, 18 - neg); + + int idx = 0; + dest[idx++] = digits[0]; + + if (ndigits > 1) { + dest[idx++] = '.'; + memcpy(dest + idx, digits + 1, (size_t)ndigits - 1); + idx += ndigits - 1; + } + + dest[idx++] = 'e'; + + char sign = K + ndigits - 1 < 0 ? '-' : '+'; + dest[idx++] = sign; + + int cent = 0; + + if (exp > 99) { + cent = exp / 100; + dest[idx++] = cent + '0'; + exp -= cent * 100; + } + if (exp > 9) { + int dec = exp / 10; + dest[idx++] = dec + '0'; + exp -= dec * 10; + + } else if (cent) { + dest[idx++] = '0'; + } + + dest[idx++] = exp % 10 + '0'; + + return idx; +} + +static int filter_special(double fp, char* dest) +{ + if (fp == 0.0) { + dest[0] = '0'; + return 1; + } + + uint64_t bits = get_dbits(fp); + + bool nan = (bits & expmask) == expmask; + + if (!nan) { + return 0; + } + + if (bits & fracmask) { + dest[0] = 'n'; dest[1] = 'a'; dest[2] = 'n'; + + } else { + dest[0] = 'i'; dest[1] = 'n'; dest[2] = 'f'; + } + + return 3; +} + +int fpconv_dtoa(double d, char dest[24]) +{ + char digits[18]; + + int str_len = 0; + bool neg = false; + + if (get_dbits(d) & signmask) { + dest[0] = '-'; + str_len++; + neg = true; + } + + int spec = filter_special(d, dest + str_len); + + if (spec) { + return str_len + spec; + } + + int K = 0; + int ndigits = grisu2(d, digits, &K); + + str_len += emit_digits(digits, ndigits, dest + str_len, K, neg); + + return str_len; +} |