| /* Originally released by the musl project (http://www.musl-libc.org/) under the |
| * MIT license. Taken from the file src/internal/floatscan.c*/ |
| |
| #include <stdint.h> |
| #include <math.h> |
| #include <limits.h> |
| #include <errno.h> |
| #include <ctype.h> |
| |
| #include "floatscan.h" |
| #include "vfprintf.h" |
| int shgetc(char* input, int *index); |
| void shunget(int *index); |
| int shlim(int a, int b); |
| |
| int shgetc(char* input, int *index){ |
| int res = input[*index]; |
| (*index)++; |
| return res; |
| } |
| |
| void shunget(int *index){ |
| (*index)--; |
| } |
| int shlim(int a, int b){ |
| return '0'; |
| } |
| |
| |
| #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| long double fmodl(long double x, long double y) |
| { |
| return fmod(x, y); |
| } |
| #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 |
| long double fmodl(long double x, long double y) |
| { |
| union ldshape ux = {x}, uy = {y}; |
| int ex = ux.i.se & 0x7fff; |
| int ey = uy.i.se & 0x7fff; |
| int sx = ux.i.se & 0x8000; |
| |
| if (y == 0 || isnan(y) || ex == 0x7fff) |
| return (x*y)/(x*y); |
| ux.i.se = (uint16_t)ex; |
| uy.i.se = (uint16_t)ey; |
| if (ux.f <= uy.f) { |
| if (ux.f == uy.f) |
| return 0*x; |
| return x; |
| } |
| |
| /* normalize x and y */ |
| if (!ex) { |
| ux.f *= 0x1p120f; |
| ex = ux.i.se - 120; |
| } |
| if (!ey) { |
| uy.f *= 0x1p120f; |
| ey = uy.i.se - 120; |
| } |
| |
| /* x mod y */ |
| #if LDBL_MANT_DIG == 64 |
| uint64_t i, mx, my; |
| mx = ux.i.m; |
| my = uy.i.m; |
| for (; ex > ey; ex--) { |
| i = mx - my; |
| if (mx >= my) { |
| if (i == 0) |
| return 0*x; |
| mx = 2*i; |
| } else if (2*mx < mx) { |
| mx = 2*mx - my; |
| } else { |
| mx = 2*mx; |
| } |
| } |
| i = mx - my; |
| if (mx >= my) { |
| if (i == 0) |
| return 0*x; |
| mx = i; |
| } |
| for (; mx >> 63 == 0; mx *= 2, ex--); |
| ux.i.m = mx; |
| #elif LDBL_MANT_DIG == 113 |
| uint64_t hi, lo, xhi, xlo, yhi, ylo; |
| xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48; |
| yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48; |
| xlo = ux.i2.lo; |
| ylo = uy.i2.lo; |
| for (; ex > ey; ex--) { |
| hi = xhi - yhi; |
| lo = xlo - ylo; |
| if (xlo < ylo) |
| hi -= 1; |
| if (hi >> 63 == 0) { |
| if ((hi|lo) == 0) |
| return 0*x; |
| xhi = 2*hi + (lo>>63); |
| xlo = 2*lo; |
| } else { |
| xhi = 2*xhi + (xlo>>63); |
| xlo = 2*xlo; |
| } |
| } |
| hi = xhi - yhi; |
| lo = xlo - ylo; |
| if (xlo < ylo) |
| hi -= 1; |
| if (hi >> 63 == 0) { |
| if ((hi|lo) == 0) |
| return 0*x; |
| xhi = hi; |
| xlo = lo; |
| } |
| for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--); |
| ux.i2.hi = xhi; |
| ux.i2.lo = xlo; |
| #endif |
| |
| /* scale result */ |
| if (ex <= 0) { |
| ux.i.se = (uint16_t)((ex+120)|sx); |
| ux.f *= (uint16_t)(0x1p-120f); |
| } else |
| ux.i.se = (uint16_t)(ex|sx); |
| return ux.f; |
| } |
| #endif |
| |
| |
| #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| long double copysignl(long double x, long double y) |
| { |
| return copysign(x, y); |
| } |
| #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 |
| long double copysignl(long double x, long double y) |
| { |
| union ldshape ux = {x}, uy = {y}; |
| ux.i.se &= 0x7fff; |
| ux.i.se = (uint16_t)(ux.i.se | (uy.i.se & 0x8000)); |
| return ux.f; |
| } |
| #endif |
| |
| double scalbn(double x, int n) |
| { |
| union {double f; uint64_t i;} u; |
| double_t y = x; |
| |
| if (n > 1023) { |
| y *= 0x1p1023; |
| n -= 1023; |
| if (n > 1023) { |
| y *= 0x1p1023; |
| n -= 1023; |
| if (n > 1023) |
| n = 1023; |
| } |
| } else if (n < -1022) { |
| /* make sure final n < -53 to avoid double |
| rounding in the subnormal range */ |
| y *= 0x1p-1022 * 0x1p53; |
| n += 1022 - 53; |
| if (n < -1022) { |
| y *= 0x1p-1022 * 0x1p53; |
| n += 1022 - 53; |
| if (n < -1022) |
| n = -1022; |
| } |
| } |
| u.i = (uint64_t)(0x3ff+n)<<52; |
| x = y * u.f; |
| return x; |
| } |
| |
| #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| |
| #define LD_B1B_DIG 2 |
| #define LD_B1B_MAX 9007199, 254740991 |
| #define KMAX 128 |
| |
| #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 |
| |
| #define LD_B1B_DIG 3 |
| #define LD_B1B_MAX 18, 446744073, 709551615 |
| #define KMAX 2048 |
| |
| #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 |
| |
| #define LD_B1B_DIG 4 |
| #define LD_B1B_MAX 10384593, 717069655, 257060992, 658440191 |
| #define KMAX 2048 |
| |
| #else |
| #error Unsupported long double representation |
| #endif |
| |
| #define MASK (KMAX-1) |
| |
| #define CONCAT2(x,y) x ## y |
| #define CONCAT(x,y) CONCAT2(x,y) |
| |
| |
| #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| long double scalbnl(long double x, int n) |
| { |
| return scalbn(x, n); |
| } |
| #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 |
| long double scalbnl(long double x, int n) |
| { |
| union ldshape u; |
| |
| if (n > 16383) { |
| x *= 0x1p16383L; |
| n -= 16383; |
| if (n > 16383) { |
| x *= 0x1p16383L; |
| n -= 16383; |
| if (n > 16383) |
| n = 16383; |
| } |
| } else if (n < -16382) { |
| x *= 0x1p-16382L * 0x1p113L; |
| n += 16382 - 113; |
| if (n < -16382) { |
| x *= 0x1p-16382L * 0x1p113L; |
| n += 16382 - 113; |
| if (n < -16382) |
| n = -16382; |
| } |
| } |
| u.f = 1.0; |
| u.i.se = (uint16_t)(0x3fff + n); |
| return x * u.f; |
| } |
| #endif |
| |
| static long long scanexp(char* input, int *index, int pok) |
| { |
| int c; |
| int x; |
| long long y; |
| int neg = 0; |
| |
| c = shgetc(input, index); |
| if (c=='+' || c=='-') { |
| neg = (c=='-'); |
| c = shgetc(input, index); |
| if ((unsigned)(c-'0')>=10U && pok) shunget(index); |
| } |
| if ((unsigned)(c-'0')>=10U) { |
| shunget(index); |
| return LLONG_MIN; |
| } |
| for (x=0; (unsigned)(c-'0')<10U && x<INT_MAX/10; c = shgetc(input, index)) |
| x = 10*x + c-'0'; |
| for (y=x; (unsigned)(c-'0')<10U && y<LLONG_MAX/100; c = shgetc(input, index)) |
| y = 10*y + c-'0'; |
| for (; (unsigned)(c-'0')<10U; c = shgetc(input, index)); |
| shunget(index); |
| return neg ? -y : y; |
| } |
| |
| |
| static long double decfloat(char *input, int *index, int c, int bits, int emin, int sign, int pok) |
| { |
| uint32_t x[KMAX]; |
| static const uint32_t th[] = { LD_B1B_MAX }; |
| int i, j, k, a, z; |
| long long lrp=0, dc=0; |
| long long e10=0; |
| int lnz = 0; |
| int gotdig = 0, gotrad = 0; |
| int rp; |
| int e2; |
| int emax = -emin-bits+3; |
| int denormal = 0; |
| long double y; |
| long double frac=0; |
| long double bias=0; |
| static const int p10s[] = { 10, 100, 1000, 10000, |
| 100000, 1000000, 10000000, 100000000 }; |
| |
| j=0; |
| k=0; |
| |
| /* Don't let leading zeros consume buffer space */ |
| for (; c=='0'; c = shgetc(input, index)) gotdig=1; |
| if (c=='.') { |
| gotrad = 1; |
| for (c = shgetc(input, index); c=='0'; c = shgetc(input, index)) gotdig=1, lrp--; |
| } |
| |
| x[0] = 0; |
| for (; (unsigned)(c-'0')<10U || c=='.'; c = shgetc(input, index)) { |
| if (c == '.') { |
| if (gotrad) break; |
| gotrad = 1; |
| lrp = dc; |
| } else if (k < KMAX-3) { |
| dc++; |
| if (c!='0') lnz = (int)dc; |
| if (j) x[k] = (x[k]*10 + (uint32_t)(c-'0')); |
| else x[k] = (uint32_t)(c-'0'); |
| if (++j==9) { |
| k++; |
| j=0; |
| } |
| gotdig=1; |
| } else { |
| dc++; |
| if (c!='0') { |
| lnz = (KMAX-4)*9; |
| x[KMAX-4] |= 1; |
| } |
| } |
| } |
| if (!gotrad) lrp=dc; |
| |
| if (gotdig && (c|32)=='e') { |
| e10 = scanexp(input, index, pok); |
| if (e10 == LLONG_MIN) { |
| if (pok) { |
| shunget(index); |
| } else { |
| //shlim(f, 0); |
| return 0; |
| } |
| e10 = 0; |
| } |
| lrp += e10; |
| } else if (c>=0) { |
| shunget(index); |
| } |
| if (!gotdig) { |
| errno = EINVAL; |
| //shlim(f, 0); |
| return 0; |
| } |
| |
| /* Handle zero specially to avoid nasty special cases later */ |
| if (!x[0]) return sign * 0.0; |
| |
| /* Optimize small integers (w/no exponent) and over/under-flow */ |
| if (lrp==dc && dc<10 && (bits>30 || x[0]>>bits==0)) |
| return sign * (long double)x[0]; |
| if (lrp > -emin/2) { |
| errno = ERANGE; |
| return sign * LDBL_MAX * LDBL_MAX; |
| } |
| if (lrp < emin-2*LDBL_MANT_DIG) { |
| errno = ERANGE; |
| return sign * LDBL_MIN * LDBL_MIN; |
| } |
| |
| /* Align incomplete final B1B digit */ |
| if (j) { |
| for (; j<9; j++) x[k]*=10; |
| k++; |
| //j=0; |
| } |
| |
| a = 0; |
| z = k; |
| e2 = 0; |
| rp = (int)lrp; |
| |
| /* Optimize small to mid-size integers (even in exp. notation) */ |
| if (lnz<9 && lnz<=rp && rp < 18) { |
| if (rp == 9) return sign * (long double)x[0]; |
| if (rp < 9) return sign * (long double)x[0] / p10s[8-rp]; |
| int bitlim = bits-3*(int)(rp-9); |
| if (bitlim>30 || x[0]>>bitlim==0) |
| return sign * (long double)x[0] * p10s[rp-10]; |
| } |
| |
| /* Drop trailing zeros */ |
| for (; !x[z-1]; z--); |
| |
| /* Align radix point to B1B digit boundary */ |
| if (rp % 9) { |
| int rpm9 = rp>=0 ? rp%9 : rp%9+9; |
| int p10 = p10s[8-rpm9]; |
| uint32_t carry = 0; |
| for (k=a; k!=z; k++) { |
| uint32_t tmp = (x[k] % (uint32_t)p10); |
| x[k] = x[k]/(uint32_t)p10 + carry; |
| carry = 1000000000/(uint32_t)p10 * tmp; |
| if (k==a && !x[k]) { |
| a = ((a+1) & MASK); |
| rp -= 9; |
| } |
| } |
| if (carry) x[z++] = carry; |
| rp += 9-rpm9; |
| } |
| |
| /* Upscale until desired number of bits are left of radix point */ |
| while (rp < 9*LD_B1B_DIG || (rp == 9*LD_B1B_DIG && x[a]<th[0])) { |
| uint32_t carry = 0; |
| e2 -= 29; |
| for (k=((z-1) & MASK); ; k=((k-1) & MASK)) { |
| uint64_t tmp = ((uint64_t)x[k] << 29) + carry; |
| if (tmp > 1000000000) { |
| carry = (uint32_t)(tmp / 1000000000); |
| x[k] = (uint32_t)(tmp % 1000000000); |
| } else { |
| carry = 0; |
| x[k] = (uint32_t)tmp; |
| } |
| if (k==((z-1) & MASK) && k!=a && !x[k]) z = k; |
| if (k==a) break; |
| } |
| if (carry) { |
| rp += 9; |
| a = ((a-1) & MASK); |
| if (a == z) { |
| z = ((z-1) & MASK); |
| x[(z-1) & MASK] |= x[z]; |
| } |
| x[a] = carry; |
| } |
| } |
| |
| /* Downscale until exactly number of bits are left of radix point */ |
| for (;;) { |
| uint32_t carry = 0; |
| int sh = 1; |
| for (i=0; i<LD_B1B_DIG; i++) { |
| k = ((a+i) & MASK); |
| if (k == z || x[k] < th[i]) { |
| i=LD_B1B_DIG; |
| break; |
| } |
| if (x[(a+i) & MASK] > th[i]) break; |
| } |
| if (i==LD_B1B_DIG && rp==9*LD_B1B_DIG) break; |
| /* FIXME: find a way to compute optimal sh */ |
| if (rp > 9+9*LD_B1B_DIG) sh = 9; |
| e2 += sh; |
| for (k=a; k!=z; k=((k+1) & MASK)) { |
| uint32_t tmp = (x[k] & (uint32_t)((1<<sh)-1)); |
| x[k] = (x[k]>>sh) + carry; |
| carry = ((uint32_t)(1000000000>>sh) * tmp); |
| if (k==a && !x[k]) { |
| a = ((a+1) & MASK); |
| i--; |
| rp -= 9; |
| } |
| } |
| if (carry) { |
| if (((z+1) & MASK) != a) { |
| x[z] = carry; |
| z = ((z+1) & MASK); |
| } else x[(z-1) & MASK] |= 1; |
| } |
| } |
| |
| /* Assemble desired bits into floating point variable */ |
| for (y=i=0; i<LD_B1B_DIG; i++) { |
| if (((a+i) & MASK)==z) x[(z=((z+1) & MASK))-1] = 0; |
| y = 1000000000.0L * y + x[(a+i) & MASK]; |
| } |
| |
| y *= sign; |
| |
| /* Limit precision for denormal results */ |
| if (bits > LDBL_MANT_DIG+e2-emin) { |
| bits = LDBL_MANT_DIG+e2-emin; |
| if (bits<0) bits=0; |
| denormal = 1; |
| } |
| |
| /* Calculate bias term to force rounding, move out lower bits */ |
| if (bits < LDBL_MANT_DIG) { |
| bias = copysignl(scalbn(1, 2*LDBL_MANT_DIG-bits-1), y); |
| frac = fmodl(y, scalbn(1, LDBL_MANT_DIG-bits)); |
| y -= frac; |
| y += bias; |
| } |
| |
| /* Process tail of decimal input so it can affect rounding */ |
| if (((a+i) & MASK) != z) { |
| uint32_t t = x[(a+i) & MASK]; |
| if (t < 500000000 && (t || ((a+i+1) & MASK) != z)) |
| frac += 0.25*sign; |
| else if (t > 500000000) |
| frac += 0.75*sign; |
| else if (t == 500000000) { |
| if (((a+i+1) & MASK) == z) |
| frac += 0.5*sign; |
| else |
| frac += 0.75*sign; |
| } |
| //if (LDBL_MANT_DIG-bits >= 2 && !fmodl(frac, 1)) implicit conversion turns floating-point number into integer: |
| if (LDBL_MANT_DIG-bits >= 2 && !((_Bool)fmodl(frac, 1))) |
| frac++; |
| } |
| |
| y += frac; |
| y -= bias; |
| |
| if (((e2+LDBL_MANT_DIG) & INT_MAX) > emax-5) { |
| if (fabs((double)y) >= CONCAT(0x1p, LDBL_MANT_DIG)) { |
| if (denormal && bits==LDBL_MANT_DIG+e2-emin) |
| denormal = 0; |
| y *= 0.5; |
| e2++; |
| } |
| //if (e2+LDBL_MANT_DIG>emax || (denormal && frac)) implicit conversion turns floating-point number into integer: |
| if (e2+LDBL_MANT_DIG>emax || ((_Bool)denormal && (_Bool)frac)) |
| errno = ERANGE; |
| } |
| |
| return scalbnl(y, e2); |
| } |
| |
| static long double hexfloat(char *input, int *index, int bits, int emin, int sign, int pok) |
| { |
| uint32_t x = 0; |
| long double y = 0; |
| long double scale = 1; |
| long double bias = 0; |
| int gottail = 0, gotrad = 0, gotdig = 0; |
| long long rp = 0; |
| long long dc = 0; |
| long long e2 = 0; |
| int d; |
| int c; |
| |
| c = shgetc(input, index); |
| |
| /* Skip leading zeros */ |
| for (; c=='0'; c = shgetc(input, index)) gotdig = 1; |
| |
| if (c=='.') { |
| gotrad = 1; |
| c = shgetc(input, index); |
| /* Count zeros after the radix point before significand */ |
| for (rp=0; c=='0'; c = shgetc(input, index), rp--) gotdig = 1; |
| } |
| |
| for (; (unsigned)(c-'0')<10U || (unsigned)((c|32)-'a')<6U || c=='.'; c = shgetc(input, index)) { |
| if (c=='.') { |
| if (gotrad) break; |
| rp = dc; |
| gotrad = 1; |
| } else { |
| gotdig = 1; |
| if (c > '9') d = (c|32)+10-'a'; |
| else d = c-'0'; |
| if (dc<8) { |
| x = (x*16 + (uint32_t)d); |
| } else if (dc < LDBL_MANT_DIG/4+1) { |
| y += d*(scale/=16); |
| } else if (d && !gottail) { |
| y += 0.5*scale; |
| gottail = 1; |
| } |
| dc++; |
| } |
| } |
| if (!gotdig) { |
| shunget(index); |
| if (pok) { |
| shunget(index); |
| if (gotrad) shunget(index); |
| } else { |
| //shlim(f, 0); |
| } |
| return sign * 0.0; |
| } |
| if (!gotrad) rp = dc; |
| while (dc<8) x *= 16, dc++; |
| if ((c|32)=='p') { |
| e2 = scanexp(input, index, pok); |
| if (e2 == LLONG_MIN) { |
| if (pok) { |
| shunget(index); |
| } else { |
| //shlim(f, 0); |
| return 0; |
| } |
| e2 = 0; |
| } |
| } else { |
| shunget(index); |
| } |
| e2 += 4*rp - 32; |
| |
| if (!x) return sign * 0.0; |
| if (e2 > -emin) { |
| errno = ERANGE; |
| return sign * LDBL_MAX * LDBL_MAX; |
| } |
| if (e2 < emin-2*LDBL_MANT_DIG) { |
| errno = ERANGE; |
| return sign * LDBL_MIN * LDBL_MIN; |
| } |
| |
| while (x < 0x80000000) { |
| if (y>=0.5) { |
| x += x + 1; |
| y += y - 1; |
| } else { |
| x += x; |
| y += y; |
| } |
| e2--; |
| } |
| |
| if (bits > 32+e2-emin) { |
| bits =(int)(32+e2-emin); |
| if (bits<0) bits=0; |
| } |
| |
| if (bits < LDBL_MANT_DIG) |
| bias = copysignl(scalbn(1, 32+LDBL_MANT_DIG-bits-1), sign); |
| |
| if (bits<32 && (_Bool)y && !(x&1)) x++, y=0; |
| |
| y = bias + sign*(long double)x + sign*y; |
| y -= bias; |
| |
| if (!((_Bool)y)) errno = ERANGE; |
| |
| return scalbnl(y, (int)e2); |
| } |
| |
| long double __floatscan(char* input, int prec, int pok) |
| { |
| int index = 0; |
| int sign = 1; |
| //size_t i; |
| int i; |
| int bits; |
| int emin; |
| int c; |
| |
| switch (prec) { |
| case 0: |
| bits = FLT_MANT_DIG; |
| emin = FLT_MIN_EXP-bits; |
| break; |
| case 1: |
| bits = DBL_MANT_DIG; |
| emin = DBL_MIN_EXP-bits; |
| break; |
| case 2: |
| bits = LDBL_MANT_DIG; |
| emin = LDBL_MIN_EXP-bits; |
| break; |
| default: |
| return 0; |
| } |
| |
| while (isspace((c=shgetc(input, &index)))); |
| |
| if (c=='+' || c=='-') { |
| sign -= 2*(c=='-'); |
| c = shgetc(input, &index); |
| } |
| |
| for (i=0; i<8 && (c|32)=="infinity"[i]; i++) |
| if (i<7) c = shgetc(input, &index); |
| if (i==3 || i==8 || (i>3 && pok)) { |
| if (i!=8) { |
| shunget(&index); |
| if (pok) for (; i>3; i--) shunget(&index); |
| } |
| return ((float)sign * INFINITY); |
| } |
| if (!i) for (i=0; i<3 && (c|32)=="nan"[i]; i++) |
| if (i<2) c = shgetc(input, &index); |
| if (i==3) { |
| if (shgetc(input, &index) != '(') { |
| shunget(&index); |
| return NAN; |
| } |
| for (i=1; ; i++) { |
| c = shgetc(input, &index); |
| if ((unsigned)(c-'0')<10U || (unsigned)(c-'A')<26U || (unsigned)(c-'a')<26U || c=='_') |
| continue; |
| if (c==')') return NAN; |
| shunget(&index); |
| if (!pok) { |
| errno = EINVAL; |
| //shlim(0, 0); |
| return 0; |
| } |
| while (i--) shunget(&index); |
| return NAN; |
| } |
| return NAN; |
| } |
| |
| if (i) { |
| shunget(&index); |
| errno = EINVAL; |
| //shlim(0, 0); |
| return 0; |
| } |
| |
| if (c=='0') { |
| c = shgetc(input, &index); |
| if ((c|32) == 'x') |
| return hexfloat(input, &index, bits, emin, sign, pok); |
| shunget(&index); |
| c = '0'; |
| } |
| |
| return decfloat(input, &index, c, bits, emin, sign, pok); |
| } |
