gists/c-programming/experiments/floatscan-experiment.c

/*
 * This was an experiment to learn about how libc turn floating point strings
 * into actual values.
 *
 * The original code is licensed to and was taken from musl libc, originally
 * stored at src/internal/floatscan.c
 *
 * musl libc is licensed under MIT license:
 *     musl as a whole is licensed under the following standard MIT license:
 *
 *     ----------------------------------------------------------------------
 *     Copyright © 2005-2020 Rich Felker, et al.
 *
 *     Permission is hereby granted, free of charge, to any person obtaining
 *     a copy of this software and associated documentation files (the
 *     "Software"), to deal in the Software without restriction, including
 *     without limitation the rights to use, copy, modify, merge, publish,
 *     distribute, sublicense, and/or sell copies of the Software, and to
 *     permit persons to whom the Software is furnished to do so, subject to
 *     the following conditions:
 *
 *     The above copyright notice and this permission notice shall be
 *     included in all copies or substantial portions of the Software.
 *
 *     THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 *     EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 *     MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 *     IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 *     CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 *     TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 *     SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * The license information of the added code and this modification:
 *     Author: Intel A80486DX2-66
 *     License: Creative Commons Zero 1.0 Universal
 */

#include <ctype.h>
#include <errno.h>
#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdint.h>
#include <stdio.h>

/* wrapping code --- beginning */
const char* fgetc_ptr = NULL;

int __shgetc(void);
long double floatscan(const char* s, int prec);

#define shgetc(f) __shgetc()
#define shlim(...)
#define shunget(...)

#define FLOAT_TYPE 0
#define DOUBLE_TYPE 1
#define LONG_DOUBLE_TYPE 2

static long long scanexp(FILE *f, int pok);
static long double decfloat(FILE *f, int c, int bits, int emin, int sign, int pok);
static long double hexfloat(FILE *f, int bits, int emin, int sign, int pok);
long double __floatscan(FILE *f, int prec, int pok);
/* wrapping code --- end */

/* the original musl libc code --- beginning */
#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)

static long long scanexp(FILE *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<INT_MAX/10; c = shgetc(f))
		x = 10*x + c-'0';
	for (y=x; c-'0'<10U && y<LLONG_MAX/100; c = shgetc(f))
		y = 10*y + c-'0';
	for (; c-'0'<10U; c = shgetc(f));
	shunget(f);
	return neg ? -y : y;
}


static long double decfloat(FILE *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;
	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(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 0;
			}
			e10 = 0;
		}
		lrp += e10;
	} else if (c>=0) {
		shunget(f);
	}
	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 = 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] % 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]<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 = 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<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] & ((1<<sh)-1);
			x[k] = (x[k]>>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=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))
			frac++;
	}

	y += frac;
	y -= bias;

	if (((e2+LDBL_MANT_DIG) & INT_MAX) > emax-5) {
		if (fabsl(y) >= 2/LDBL_EPSILON) {
			if (denormal && bits==LDBL_MANT_DIG+e2-emin)
				denormal = 0;
			y *= 0.5;
			e2++;
		}
		if (e2+LDBL_MANT_DIG>emax || (denormal && frac))
			errno = ERANGE;
	}

	return scalbnl(y, e2);
}

static long double hexfloat(FILE *f, 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(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);
			} else if (d && !gottail) {
				y += 0.5*scale;
				gottail = 1;
			}
			dc++;
		}
	}
	if (!gotdig) {
		shunget(f);
		if (pok) {
			shunget(f);
			if (gotrad) shunget(f);
		} else {
			shlim(f, 0);
		}
		return 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 0;
			}
			e2 = 0;
		}
	} else {
		shunget(f);
	}
	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 = 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 && y && !(x&1)) x++, y=0;

	y = bias + sign*(long double)x + sign*y;
	y -= bias;

	if (!y) errno = ERANGE;

	return scalbnl(y, e2);
}

long double __floatscan(FILE *f, int prec, int pok)
{
	int sign = 1;
	size_t 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(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;
	}
	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 NAN;
		}
		for (i=1; ; i++) {
			c = shgetc(f);
			if (c-'0'<10U || c-'A'<26U || c-'a'<26U || c=='_')
				continue;
			if (c==')') return NAN;
			shunget(f);
			if (!pok) {
				errno = EINVAL;
				shlim(f, 0);
				return 0;
			}
			while (i--) shunget(f);
			return NAN;
		}
		return NAN;
	}

	if (i) {
		shunget(f);
		errno = EINVAL;
		shlim(f, 0);
		return 0;
	}

	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);
}
/* the original musl libc code --- end */

/* wrapping code --- beginning */
int __shgetc(void) {
	return *fgetc_ptr++;
}

long double floatscan(const char* s, int prec) {
	fgetc_ptr = s;
	return __floatscan(NULL, prec, 1);
}
/* wrapping code --- end */

/* test code --- beginning */
int main(int argc, char** argv) {
	char* value = argc > 1 ? argv[1] : "+314.1e-2";
	const int prec = LD_B1B_DIG;

	printf("Selected precision index = %d\n", prec);
	long double result = floatscan(value, LONG_DOUBLE_TYPE);
	printf("Input                        : %s\n", value);
	printf("Decimal floating-point format: %Lf\n", result);
	printf("Double floating-point format : %Lg\n", result);
	printf("Hexadecimal form             : %La\n", result);
	return 0;
}
/* test code --- end */