Re: float scanner status, upcoming release

[Rich Felker <dalias@aerifal.cx>]

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And here's the current code (standalone test program) if anybody wants
to play with it or point out how much single-letter variable names
suck or whatnot.. :-)

Rich

[-- Attachment #2: myfloat.c --]
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#include <stdint.h>
#include <stdio.h>
#include <math.h>
#include <fenv.h>
#include <float.h>


#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024

#define LD_B1B_DIG 2
#define LD_B1B_MAX 9007199, 254740991, -1, -1
#define KMAX 128

#else /* LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 */

#define LD_B1B_DIG 3
#define LD_B1B_MAX 18, 446744073, 709551615, -1
#define KMAX 2048

#endif

#define MASK (KMAX-1)

int dohex(FILE *f, long double *y, int sign)
{
	return -1;
}

int parsefloat(FILE *f, long double *yout)
{
	uint32_t x[KMAX];
	static const uint32_t th[] = { LD_B1B_MAX };
	int c;
	int i, j, k, a, z;
	int sign=1;
	int rp=-1, dc=0;
	int e10;
	int e2;
	long double y;
	long double frac=0;
	long double bias=0;
	int bits=64;
	int emin=-16445;

	j=0;
	k=0;

	c = getc(f);
	if (c=='+' || c=='-') {
		sign -= 2*(c=='-');
		c = getc(f);
	}

	if (c=='0') {
		j = 1;
		c = getc(f);
		if ((c|32) == 'x') {
			return dohex(f, yout, sign);
		}
	}

	/* Don't let leading zeros consume buffer space */
	for (; c=='0'; c=getc(f));

	for (; c-'0'<10U || c=='.'; c=getc(f)) {
		if (c == '.') {
			if (rp!=-1) goto mismatch;
			rp = dc;
		} else if (k < KMAX) {
			dc++;
			x[k] = x[k]*10 + c-'0';
			if (++j==9) {
				k++;
				j=0;
			}
		} else {
			dc++;
			x[KMAX-1] |= c-'0';
		}
	}
	if (rp==-1) rp=dc;
	if (k<KMAX && j) {
		for (; j<9; j++) x[k]*=10;
		k++;
		j=0;
	}

	if ((c|32)=='e') {
		c = getc(f);
		ungetc(c, f);
		if (c!='+' && c!='-' && c-'0'>=10U) {
			goto mismatch;
		}
		fscanf(f, "%d", &e10);
		c = getc(f);
		rp += e10;
		/* FIXME: overflow */
	}

	a = 0;
	z = k;
	e2 = 0;

	while (rp < 18+9*LD_B1B_DIG) {
		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;
			if (a == z) {
				z = (z-1 & MASK);
				x[z-1 & MASK] |= x[z];
			}
			a = (a-1 & MASK);
			x[a] = carry;
		}
	}

	if (rp % 9) {
		static const int p10s[] = {
			100000000, 10000000, 1000000, 100000,
			10000, 1000, 100, 10
		};
		int rpm9 = rp % 9;
		int p10 = p10s[rpm9-1];
		uint32_t carry = 0;
		for (k=a; k!=z; k=(k+1 & MASK)) {
			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) {
			if ((z+1 & MASK) != a)
				z = (z+1 & MASK);
			x[z-1 & MASK] = carry;
		}
		rp += 9-rpm9;
	}

	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);
				rp -= 9;
			}
		}
		if (carry) {
			if ((z+1 & MASK) != a)
				z = (z+1 & MASK);
			x[z-1 & MASK] = carry;
		}
	}

	for (i=a; i!=z; i=(i+1 & MASK))
		printf("%.9u ", x[i]);

	printf("[%d]\n%*s\n", e2, rp+(rp/9)+1, "^");

	for (y=i=0; i<LD_B1B_DIG && (a+i & MASK)!=z; i++)
		y = 1000000000.0L * y + x[a+i & MASK];

	y *= sign;

//	bits=2;

	if (bits > LDBL_MANT_DIG+e2-emin) {
		bits = LDBL_MANT_DIG+e2-emin;
		if (bits<0) bits=0;
	}

	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;
	}

	if ((a+i & MASK) != z) {
	printf("old frac = %La\n", frac);
		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;
		}
	}

	printf("y = %.21Lg\n", scalbnl(y-bias,e2));
	printf("frac = %.21Lg\n", scalbnl(frac,e2));
	printf("y = %La\n", y);
	printf("frac = %La\n", frac);
	printf("bias = %La\n", bias);

	y += frac;
	y -= bias;

	y = scalbnl(y, e2);

	printf("y = %La\n", y);
	printf("y ~= %.17Lg\n", y);

	printf("%.21Lg [%.21Lg, %.21Lg]\n", y,
		nextafterl(y,-INFINITY), nextafterl(y, INFINITY));
#if 0
	printf("%.18g [%.18g, %.18g]\n", (double)y,
		nextafter(y,-INFINITY), nextafter(y, INFINITY));
	printf("%.9g [%.9g, %.9g]\n", (float)y,
		nextafterf(y,-INFINITY), nextafterf(y, INFINITY));
#endif

	return 0;
mismatch:
	return -1;
}

int main()
{
	long double y;
	//fesetround(FE_DOWNWARD);
	parsefloat(stdin, &y);
}