// Code ported from musl libc 8f12c4e110acb3bbbdc8abfb3a552c3ced718039 // and then modified to use softfloat and to assume f128 for everything #include "parse_f128.h" #include "softfloat.h" #include #include #include #include #include #include #define shcnt(f) ((f)->shcnt + ((f)->rpos - (f)->buf)) #define shlim(f, lim) __shlim((f), (lim)) #define shgetc(f) (((f)->rpos != (f)->shend) ? *(f)->rpos++ : __shgetc(f)) #define shunget(f) ((f)->shlim>=0 ? (void)(f)->rpos-- : (void)0) #define sh_fromstring(f, s) \ ((f)->buf = (f)->rpos = (void *)(s), (f)->rend = (void*)-1) #define LD_B1B_DIG 4 #define LD_B1B_MAX 10384593, 717069655, 257060992, 658440191 #define KMAX 2048 #define MASK (KMAX-1) #define CONCAT2(x,y) x ## y #define CONCAT(x,y) CONCAT2(x,y) #define F_PERM 1 #define F_NORD 4 #define F_NOWR 8 #define F_EOF 16 #define F_ERR 32 #define F_SVB 64 #define F_APP 128 #define EOF (-1) #define LDBL_MANT_DIG 113 #define LDBL_MIN_EXP (-16381) #define LDBL_MAX_EXP 16384 #define LDBL_DIG 33 #define LDBL_MIN_10_EXP (-4931) #define LDBL_MAX_10_EXP 4932 #define DECIMAL_DIG 36 #if __BYTE_ORDER == __LITTLE_ENDIAN union ldshape { float128_t f; struct { uint64_t lo; uint32_t mid; uint16_t top; uint16_t se; } i; struct { uint64_t lo; uint64_t hi; } i2; }; #elif __BYTE_ORDER == __BIG_ENDIAN union ldshape { float128_t f; struct { uint16_t se; uint16_t top; uint32_t mid; uint64_t lo; } i; struct { uint64_t hi; uint64_t lo; } i2; }; #error Unsupported endian #endif struct MuslFILE { unsigned flags; unsigned char *rpos, *rend; int (*close)(struct MuslFILE *); unsigned char *wend, *wpos; unsigned char *mustbezero_1; unsigned char *wbase; size_t (*read)(struct MuslFILE *, unsigned char *, size_t); size_t (*write)(struct MuslFILE *, const unsigned char *, size_t); off_t (*seek)(struct MuslFILE *, off_t, int); unsigned char *buf; size_t buf_size; struct MuslFILE *prev, *next; int fd; int pipe_pid; long lockcount; int mode; volatile int lock; int lbf; void *cookie; off_t off; char *getln_buf; void *mustbezero_2; unsigned char *shend; off_t shlim, shcnt; struct MuslFILE *prev_locked, *next_locked; struct __locale_struct *locale; }; static void __shlim(struct MuslFILE *f, off_t lim) { f->shlim = lim; f->shcnt = f->buf - f->rpos; /* If lim is nonzero, rend must be a valid pointer. */ if (lim && f->rend - f->rpos > lim) f->shend = f->rpos + lim; else f->shend = f->rend; } static int __toread(struct MuslFILE *f) { f->mode |= f->mode-1; if (f->wpos != f->wbase) f->write(f, 0, 0); f->wpos = f->wbase = f->wend = 0; if (f->flags & F_NORD) { f->flags |= F_ERR; return EOF; } f->rpos = f->rend = f->buf + f->buf_size; return (f->flags & F_EOF) ? EOF : 0; } static int __uflow(struct MuslFILE *f) { unsigned char c; if (!__toread(f) && f->read(f, &c, 1)==1) return c; return EOF; } static int __shgetc(struct MuslFILE *f) { int c; off_t cnt = shcnt(f); if ((f->shlim && cnt >= f->shlim) || (c=__uflow(f)) < 0) { f->shcnt = f->buf - f->rpos + cnt; f->shend = f->rpos; f->shlim = -1; return EOF; } cnt++; if (f->shlim && f->rend - f->rpos > f->shlim - cnt) f->shend = f->rpos + (f->shlim - cnt); else f->shend = f->rend; f->shcnt = f->buf - f->rpos + cnt; if (f->rpos[-1] != c) f->rpos[-1] = c; return c; } static long long scanexp(struct MuslFILE *f, int pok) { int c; int x; long long y; int neg = 0; c = shgetc(f); if (c=='+' || c=='-') { neg = (c=='-'); c = shgetc(f); if (c-'0'>=10U && pok) shunget(f); } if (c-'0'>=10U) { shunget(f); return LLONG_MIN; } for (x=0; c-'0'<10U && x>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; float128_t result; f128M_mul(&zero, &x, &result); return result; } 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; float128_t result; f128M_mul(&zero, &x, &result); return result; } 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; /* scale result */ if (ex <= 0) { ux.i.se = (ex+120)|sx; //ux.f *= 0x1p-120f; mul_eq_f128_float(&ux.f, 0x1p-120f); } else ux.i.se = ex|sx; return ux.f; } static float128_t int_mul_f128_cast_u32(int sign, uint32_t x0) { float128_t x0_f128; ui32_to_f128M(x0, &x0_f128); float128_t sign_f128; i32_to_f128M(sign, &sign_f128); float128_t result; f128M_mul(&sign_f128, &x0_f128, &result); return result; } static float128_t triple_divide(int sign, uint32_t x0, int p10s) { float128_t part1 = int_mul_f128_cast_u32(sign, x0); float128_t p10s_f128; i32_to_f128M(p10s, &p10s_f128); float128_t result; f128M_div(&part1, &p10s_f128, &result); return result; } static float128_t triple_multiply(int sign, uint32_t x0, int p10s) { float128_t part1 = int_mul_f128_cast_u32(sign, x0); float128_t p10s_f128; i32_to_f128M(p10s, &p10s_f128); float128_t result; f128M_mul(&part1, &p10s_f128, &result); return result; } static void mul_eq_f128_int(float128_t *y, int sign) { float128_t sign_f128; i32_to_f128M(sign, &sign_f128); float128_t new_value; f128M_mul(y, &sign_f128, &new_value); *y = new_value; } static float128_t make_f128(uint64_t hi, uint64_t lo) { union ldshape ux; ux.i2.hi = hi; ux.i2.lo = lo; return ux.f; } static void mul_eq_f128_f128(float128_t *a, float128_t b) { float128_t new_value; f128M_mul(a, &b, &new_value); *a = new_value; } static void add_eq_f128_dbl(float128_t *a, double b) { float64_t b_f64; memcpy(&b_f64, &b, sizeof(double)); float128_t b_f128; f64_to_f128M(b_f64, &b_f128); float128_t new_value; f128M_add(a, &b_f128, &new_value); *a = new_value; } static float128_t scalbnf128(float128_t x, int n) { union ldshape u; if (n > 16383) { //x *= 0x1p16383q; mul_eq_f128_f128(&x, make_f128(0x7ffe000000000000, 0x0000000000000000)); n -= 16383; if (n > 16383) { //x *= 0x1p16383q; mul_eq_f128_f128(&x, make_f128(0x7ffe000000000000, 0x0000000000000000)); n -= 16383; if (n > 16383) n = 16383; } } else if (n < -16382) { //x *= 0x1p-16382q * 0x1p113q; { float128_t mul_result; float128_t a = make_f128(0x0001000000000000, 0x0000000000000000); float128_t b = make_f128(0x4070000000000000, 0x0000000000000000); f128M_mul(&a, &b, &mul_result); mul_eq_f128_f128(&x, mul_result); } n += 16382 - 113; if (n < -16382) { //x *= 0x1p-16382q * 0x1p113q; { float128_t mul_result; float128_t a = make_f128(0x0001000000000000, 0x0000000000000000); float128_t b = make_f128(0x4070000000000000, 0x0000000000000000); f128M_mul(&a, &b, &mul_result); mul_eq_f128_f128(&x, mul_result); } n += 16382 - 113; if (n < -16382) n = -16382; } } //u.f = 1.0; ui32_to_f128M(1, &u.f); u.i.se = 0x3fff + n; mul_eq_f128_f128(&x, u.f); return x; } static float128_t fabsf128(float128_t x) { union ldshape u = {x}; u.i.se &= 0x7fff; return u.f; } static float128_t decfloat(struct MuslFILE *f, 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; float128_t y; float128_t zero; ui32_to_f128M(0, &zero); float128_t frac=zero; float128_t bias=zero; 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(f)) gotdig=1; if (c=='.') { gotrad = 1; for (c = shgetc(f); c=='0'; c = shgetc(f)) gotdig=1, lrp--; } x[0] = 0; for (; c-'0'<10U || c=='.'; c = shgetc(f)) { if (c == '.') { if (gotrad) break; gotrad = 1; lrp = dc; } else if (k < KMAX-3) { dc++; if (c!='0') lnz = dc; if (j) x[k] = x[k]*10 + c-'0'; else x[k] = 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(f, pok); if (e10 == LLONG_MIN) { if (pok) { shunget(f); } else { shlim(f, 0); return zero; } e10 = 0; } lrp += e10; } else if (c>=0) { shunget(f); } if (!gotdig) { errno = EINVAL; shlim(f, 0); return zero; } /* Handle zero specially to avoid nasty special cases later */ if (!x[0]) { //return sign * 0.0; return dbl_to_f128(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 * (float128_t)x[0]; float128_t sign_f128; i32_to_f128M(sign, &sign_f128); float128_t x0_f128; ui32_to_f128M(x[0], &x0_f128); float128_t result; f128M_mul(&sign_f128, &x0_f128, &result); return result; } if (lrp > -emin/2) { errno = ERANGE; //return sign * LDBL_MAX * LDBL_MAX; return zero; } if (lrp < emin-2*LDBL_MANT_DIG) { errno = ERANGE; //return sign * LDBL_MIN * LDBL_MIN; return zero; } /* Align incomplete final B1B digit */ if (j) { for (; j<9; j++) x[k]*=10; k++; j=0; } a = 0; z = k; e2 = 0; rp = lrp; /* Optimize small to mid-size integers (even in exp. notation) */ if (lnz<9 && lnz<=rp && rp < 18) { if (rp == 9) { //return sign * (float128_t)(x[0]); return int_mul_f128_cast_u32(sign, x[0]); } if (rp < 9) { //return sign * (float128_t)(x[0]) / p10s[8-rp]; return triple_divide(sign, x[0], p10s[8-rp]); } int bitlim = bits-3*(int)(rp-9); if (bitlim>30 || x[0]>>bitlim==0) //return sign * (float128_t)(x[0]) * p10s[rp-10]; return triple_multiply(sign, 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] % p10; x[k] = x[k]/p10 + carry; carry = 1000000000/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] 1000000000) { carry = tmp / 1000000000; x[k] = tmp % 1000000000; } else { carry = 0; x[k] = 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 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] & (1<>sh) + carry; carry = (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=zero,i=0; i 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 = copysignf128(dbl_to_f128(scalbn(1, 2*LDBL_MANT_DIG-bits-1)), y); frac = fmodf128(y, dbl_to_f128(scalbn(1, LDBL_MANT_DIG-bits))); //y -= frac; { float128_t new_value; f128M_sub(&y, &frac, &new_value); y = new_value; } //y += bias; { float128_t new_value; f128M_add(&y, &frac, &new_value); y = new_value; } } /* 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; add_eq_f128_dbl(&frac, 0.25*sign); } else if (t > 500000000) { //frac += 0.75*sign; add_eq_f128_dbl(&frac, 0.75*sign); } else if (t == 500000000) { if ((a+i+1 & MASK) == z) { //frac += 0.5*sign; add_eq_f128_dbl(&frac, 0.5*sign); } else { //frac += 0.75*sign; add_eq_f128_dbl(&frac, 0.75*sign); } } //if (LDBL_MANT_DIG-bits >= 2 && !fmodf128(frac, 1)) if (LDBL_MANT_DIG-bits >= 2) { float128_t one; ui32_to_f128M(1, &one); float128_t mod_result = fmodf128(frac, one); if (f128M_eq(&mod_result, &zero)) { //frac++; add_eq_f128_dbl(&frac, 1.0); } } } //y += frac; { float128_t new_value; f128M_add(&y, &frac, &new_value); y = new_value; } //y -= bias; { float128_t new_value; f128M_sub(&y, &bias, &new_value); y = new_value; } if ((e2+LDBL_MANT_DIG & INT_MAX) > emax-5) { //if (fabsf128(y) >= 0x1p113) float128_t abs_y = fabsf128(y); float128_t mant_f128 = make_f128(0x4070000000000000, 0x0000000000000000); if (!f128M_lt(&abs_y, &mant_f128)) { if (denormal && bits==LDBL_MANT_DIG+e2-emin) denormal = 0; //y *= 0.5; { float128_t point_5 = dbl_to_f128(0.5); float128_t new_value; f128M_mul(&y, &point_5, &new_value); y = new_value; } e2++; } if (e2+LDBL_MANT_DIG>emax || (denormal && !f128M_eq(&frac, &zero))) errno = ERANGE; } return scalbnf128(y, e2); } static float128_t hexfloat(struct MuslFILE *f, int bits, int emin, int sign, int pok) { float128_t zero; ui32_to_f128M(0, &zero); float128_t one; ui32_to_f128M(1, &one); float128_t sixteen; ui32_to_f128M(16, &sixteen); float128_t point_5 = dbl_to_f128(0.5); uint32_t x = 0; float128_t y = zero; float128_t scale = one; float128_t bias = zero; 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(f); /* Skip leading zeros */ for (; c=='0'; c = shgetc(f)) gotdig = 1; if (c=='.') { gotrad = 1; c = shgetc(f); /* Count zeros after the radix point before significand */ for (rp=0; c=='0'; c = shgetc(f), rp--) gotdig = 1; } for (; c-'0'<10U || (c|32)-'a'<6U || c=='.'; c = shgetc(f)) { 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 + d; } else if (dc < LDBL_MANT_DIG/4+1) { //y += d*(scale/=16); { float128_t divided; f128M_div(&scale, &sixteen, ÷d); scale = divided; float128_t d_f128; i32_to_f128M(d, &d_f128); float128_t add_op; f128M_mul(&d_f128, &scale, &add_op); float128_t new_y; f128M_add(&y, &add_op, &new_y); y = new_y; } } else if (d && !gottail) { //y += 0.5*scale; { float128_t add_op; f128M_mul(&point_5, &scale, &add_op); float128_t new_y; f128M_add(&y, &add_op, &new_y); y = new_y; } gottail = 1; } dc++; } } if (!gotdig) { shunget(f); if (pok) { shunget(f); if (gotrad) shunget(f); } else { shlim(f, 0); } //return sign * 0.0; return dbl_to_f128(sign * 0.0); } if (!gotrad) rp = dc; while (dc<8) x *= 16, dc++; if ((c|32)=='p') { e2 = scanexp(f, pok); if (e2 == LLONG_MIN) { if (pok) { shunget(f); } else { shlim(f, 0); return zero; } e2 = 0; } } else { shunget(f); } e2 += 4*rp - 32; if (!x) { //return sign * 0.0; return dbl_to_f128(sign * 0.0); } if (e2 > -emin) { errno = ERANGE; //return sign * LDBL_MAX * LDBL_MAX; return zero; } if (e2 < emin-2*LDBL_MANT_DIG) { errno = ERANGE; //return sign * LDBL_MIN * LDBL_MIN; return zero; } while (x < 0x80000000) { //if (y>=0.5) if (!f128M_lt(&y, &point_5)) { x += x + 1; //y += y - 1; { float128_t minus_one; f128M_sub(&y, &one, &minus_one); float128_t new_y; f128M_add(&y, &minus_one, &new_y); y = new_y; } } else { x += x; //y += y; { float128_t new_y; f128M_add(&y, &y, &new_y); y = new_y; } } e2--; } if (bits > 32+e2-emin) { bits = 32+e2-emin; if (bits<0) bits=0; } if (bits < LDBL_MANT_DIG) { float128_t sign_f128; i32_to_f128M(sign, &sign_f128); bias = copysignf128(dbl_to_f128(scalbn(1, 32+LDBL_MANT_DIG-bits-1)), sign_f128); } //if (bits<32 && y && !(x&1)) x++, y=0; if (bits<32 && !f128M_eq(&y, &zero) && !(x&1)) x++, y=zero; //y = bias + sign*(float128_t)x + sign*y; { float128_t x_f128; ui32_to_f128M(x, &x_f128); float128_t sign_f128; i32_to_f128M(sign, &sign_f128); float128_t sign_mul_x; f128M_mul(&sign_f128, &x_f128, &sign_mul_x); float128_t sign_mul_y; f128M_mul(&sign_f128, &y, &sign_mul_y); float128_t bias_op; f128M_add(&bias, &sign_mul_x, &bias_op); float128_t new_y; f128M_add(&bias_op, &sign_mul_y, &new_y); y = new_y; } //y -= bias; { float128_t new_y; f128M_sub(&y, &bias, &new_y); y = new_y; } if (f128M_eq(&y, &zero)) errno = ERANGE; return scalbnf128(y, e2); } static int isspace(int c) { return c == ' ' || (unsigned)c-'\t' < 5; } static inline float128_t makeInf128() { union ldshape ux; ux.i2.hi = 0x7fff000000000000UL; ux.i2.lo = 0x0UL; return ux.f; } static inline float128_t makeNaN128() { uint64_t rand = 0UL; union ldshape ux; ux.i2.hi = 0x7fff000000000000UL | (rand & 0xffffffffffffUL); ux.i2.lo = 0x0UL; return ux.f; } float128_t __floatscan(struct MuslFILE *f, int prec, int pok) { int sign = 1; size_t i; int bits = LDBL_MANT_DIG; int emin = LDBL_MIN_EXP-bits; int c; while (isspace((c=shgetc(f)))); if (c=='+' || c=='-') { sign -= 2*(c=='-'); c = shgetc(f); } for (i=0; i<8 && (c|32)=="infinity"[i]; i++) if (i<7) c = shgetc(f); if (i==3 || i==8 || (i>3 && pok)) { if (i!=8) { shunget(f); if (pok) for (; i>3; i--) shunget(f); } //return sign * INFINITY; float128_t sign_f128; i32_to_f128M(sign, &sign_f128); float128_t infinity_f128 = makeInf128(); float128_t result; f128M_mul(&sign_f128, &infinity_f128, &result); return result; } if (!i) for (i=0; i<3 && (c|32)=="nan"[i]; i++) if (i<2) c = shgetc(f); if (i==3) { if (shgetc(f) != '(') { shunget(f); return makeNaN128(); } for (i=1; ; i++) { c = shgetc(f); if (c-'0'<10U || c-'A'<26U || c-'a'<26U || c=='_') continue; if (c==')') return makeNaN128(); shunget(f); if (!pok) { errno = EINVAL; shlim(f, 0); float128_t zero; ui32_to_f128M(0, &zero); return zero; } while (i--) shunget(f); return makeNaN128(); } return makeNaN128(); } if (i) { shunget(f); errno = EINVAL; shlim(f, 0); float128_t zero; ui32_to_f128M(0, &zero); return zero; } if (c=='0') { c = shgetc(f); if ((c|32) == 'x') return hexfloat(f, bits, emin, sign, pok); shunget(f); c = '0'; } return decfloat(f, c, bits, emin, sign, pok); } float128_t parse_f128(const char *s, char **p) { struct MuslFILE f; sh_fromstring(&f, s); shlim(&f, 0); float128_t y = __floatscan(&f, 2, 1); off_t cnt = shcnt(&f); if (p) *p = cnt ? (char *)s + cnt : (char *)s; return y; }