#include #include #include #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) >> 52u; 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 <<= 1u; fp->exp--; } const unsigned 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 << 1u) + 1u; upper->exp = fp->exp - 1u; while ((upper->frac & (hiddenbit << 1u)) == 0) { upper->frac <<= 1u; upper->exp--; } const unsigned int u_shift = 64 - 52 - 2; upper->frac <<= u_shift; upper->exp = upper->exp - u_shift; unsigned int l_shift = fp->frac == hiddenbit ? 2u : 1u; 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 = 0x00000000FFFFFFFFu; uint64_t ah_bl = (a->frac >> 32u) * (b->frac & lomask); uint64_t al_bh = (a->frac & lomask) * (b->frac >> 32u); uint64_t al_bl = (a->frac & lomask) * (b->frac & lomask); uint64_t ah_bh = (a->frac >> 32u) * (b->frac >> 32u); uint64_t tmp = (ah_bl & lomask) + (al_bh & lomask) + (al_bl >> 32u); /* round up */ tmp += 1U << 31u; Fp fp = { ah_bh + (ah_bl >> 32u) + (al_bh >> 32u) + (tmp >> 32u), a->exp + b->exp + 64u }; 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 inline int emit_integer (char *digits, int ndigits, char *dest, int K, bool neg, unsigned precision) { char *d = dest; memcpy (d, digits, ndigits); d += ndigits; memset (d, '0', K); d += K; precision = MIN(precision, FPCONV_BUFLEN - (ndigits + K + 1)); if (precision) { *d++ = '.'; memset (d, '0', precision); d += precision; } return d - dest; } static inline int emit_scientific_digits (char *digits, int ndigits, char *dest, int K, bool neg, unsigned precision, int exp) { /* 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, 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 inline int emit_fixed_digits (char *digits, int ndigits, char *dest, int K, bool neg, unsigned precision, int exp) { int offset = ndigits - absv(K), to_print; /* fp < 1.0 -> write leading zero */ if (K < 0) { if (offset <= 0) { if (precision) { if (-offset >= precision) { /* Just print 0.[0]{precision} */ dest[0] = '0'; dest[1] = '.'; memset(dest + 2, '0', precision); return precision + 2; } to_print = MAX(ndigits - offset, precision); } else { to_print = ndigits - offset; } if (to_print <= FPCONV_BUFLEN - 3) { offset = -offset; dest[0] = '0'; dest[1] = '.'; memset(dest + 2, '0', offset); if (precision) { /* The case where offset > precision is covered previously */ precision -= offset; if (precision <= ndigits) { /* Truncate or leave as is */ memcpy(dest + offset + 2, digits, precision); return precision + 2 + offset; } else { /* Expand */ memcpy(dest + offset + 2, digits, ndigits); precision -= ndigits; memset(dest + offset + 2 + ndigits, '0', precision); return ndigits + 2 + offset + precision; } } else { memcpy(dest + offset + 2, digits, ndigits); } return ndigits + 2 + offset; } else { return emit_scientific_digits (digits, ndigits, dest, K, neg, precision, exp); } } else { /* * fp > 1.0, if offset > 0 then we have less digits than * fp exponent, so we need to switch to scientific notation to * display number at least more or less precisely */ if (offset > 0 && ndigits <= FPCONV_BUFLEN - 3) { char *d = dest; memcpy(d, digits, offset); d += offset; *d++ = '.'; ndigits -= offset; if (precision) { if (ndigits >= precision) { /* Truncate or leave as is */ memcpy(d, digits + offset, precision); d += precision; } else { /* Expand */ memcpy(d, digits + offset, ndigits); precision -= ndigits; d += ndigits; /* Check if we have enough bufspace */ if ((d - dest) + precision <= FPCONV_BUFLEN) { memset (d, '0', precision); d += precision; } else { memset (d, '0', FPCONV_BUFLEN - (d - dest)); d += FPCONV_BUFLEN - (d - dest); } } } else { memcpy(d, digits + offset, ndigits); d += ndigits; } return d - dest; } } } return emit_scientific_digits (digits, ndigits, dest, K, neg, precision, exp); } static int emit_digits (char *digits, int ndigits, char *dest, int K, bool neg, unsigned precision, bool scientific) { int exp = absv(K + ndigits - 1); /* write plain integer */ if (K >= 0 && (exp < (ndigits + 7))) { return emit_integer (digits, ndigits, dest, K, neg, precision); } /* write decimal w/o scientific notation */ if (!scientific || (K < 0 && (K > -7 || exp < 4))) { return emit_fixed_digits (digits, ndigits, dest, K, neg, precision, exp); } return emit_scientific_digits (digits, ndigits, dest, K, neg, precision, exp); } static int filter_special (double fp, char *dest, unsigned precision) { int nchars = 3; char *d = dest; if (fp == 0.0) { if (get_dbits (fp) & signmask) { *d++ = '-'; *d++ = '0'; } else { *d++ = '0'; } if (precision) { *d ++ = '.'; memset (d, '0', precision); } return d - dest + precision; } 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 { if (get_dbits (fp) & signmask) { dest[0] = '-'; dest[1] = 'i'; dest[2] = 'n'; dest[3] = 'f'; nchars = 4; } else { dest[0] = 'i'; dest[1] = 'n'; dest[2] = 'f'; } } return nchars; } int fpconv_dtoa (double d, char dest[FPCONV_BUFLEN], unsigned precision, bool scientific) { char digits[18]; int str_len = 0; bool neg = false; if (precision > FPCONV_BUFLEN - 5) { precision = FPCONV_BUFLEN - 5; } int spec = filter_special (d, dest, precision); if (spec) { return spec; } if (get_dbits (d) & signmask) { dest[0] = '-'; str_len++; neg = true; } int K = 0; int ndigits = grisu2 (d, digits, &K); str_len += emit_digits (digits, ndigits, dest + str_len, K, neg, precision, scientific); return str_len; }