arch/mips/math-emu/dp_sqrt.c

Source file repositories/reference/linux-study-clean/arch/mips/math-emu/dp_sqrt.c

File Facts

System
Linux kernel
Corpus path
arch/mips/math-emu/dp_sqrt.c
Extension
.c
Size
3463 bytes
Lines
153
Domain
Architecture Layer
Bucket
arch/mips
Inferred role
Architecture Layer: implementation source
Status
source implementation candidate

Why This File Exists

CPU and platform-specific kernel glue: boot entry, traps, syscall entry, interrupts, page tables, context switch, and low-level barriers.

Dependency Surface

Detected Declarations

Annotated Snippet

if (xs) {
			/* sqrt(-Inf) = Nan */
			ieee754_setcx(IEEE754_INVALID_OPERATION);
			return ieee754dp_indef();
		}
		/* sqrt(+Inf) = Inf */
		return x;

	case IEEE754_CLASS_DNORM:
		DPDNORMX;
		fallthrough;
	case IEEE754_CLASS_NORM:
		if (xs) {
			/* sqrt(-x) = Nan */
			ieee754_setcx(IEEE754_INVALID_OPERATION);
			return ieee754dp_indef();
		}
		break;
	}

	/* save old csr; switch off INX enable & flag; set RN rounding */
	oldcsr = ieee754_csr;
	ieee754_csr.mx &= ~IEEE754_INEXACT;
	ieee754_csr.sx &= ~IEEE754_INEXACT;
	ieee754_csr.rm = FPU_CSR_RN;

	/* adjust exponent to prevent overflow */
	scalx = 0;
	if (xe > 512) {		/* x > 2**-512? */
		xe -= 512;	/* x = x / 2**512 */
		scalx += 256;
	} else if (xe < -512) { /* x < 2**-512? */
		xe += 512;	/* x = x * 2**512 */
		scalx -= 256;
	}

	x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
	y = x;

	/* magic initial approximation to almost 8 sig. bits */
	yh = y.bits >> 32;
	yh = (yh >> 1) + 0x1ff80000;
	yh = yh - table[(yh >> 15) & 31];
	y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);

	/* Heron's rule once with correction to improve to ~18 sig. bits */
	/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
	t = ieee754dp_div(x, y);
	y = ieee754dp_add(y, t);
	y.bits -= 0x0010000600000000LL;
	y.bits &= 0xffffffff00000000LL;

	/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
	/* t=y*y; z=t;	pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
	t = ieee754dp_mul(y, y);
	z = t;
	t.bexp += 0x001;
	t = ieee754dp_add(t, z);
	z = ieee754dp_mul(ieee754dp_sub(x, z), y);

	/* t=z/(t+x) ;	pt[n0]+=0x00100000; y+=t; */
	t = ieee754dp_div(z, ieee754dp_add(t, x));
	t.bexp += 0x001;
	y = ieee754dp_add(y, t);

	/* twiddle last bit to force y correctly rounded */

	/* set RZ, clear INEX flag */
	ieee754_csr.rm = FPU_CSR_RZ;
	ieee754_csr.sx &= ~IEEE754_INEXACT;

	/* t=x/y; ...chopped quotient, possibly inexact */
	t = ieee754dp_div(x, y);

	if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {

		if (!(ieee754_csr.sx & IEEE754_INEXACT))
			/* t = t-ulp */
			t.bits -= 1;

		/* add inexact to result status */
		oldcsr.cx |= IEEE754_INEXACT;
		oldcsr.sx |= IEEE754_INEXACT;

		switch (oldcsr.rm) {
		case FPU_CSR_RU:
			y.bits += 1;
			fallthrough;
		case FPU_CSR_RN:
			t.bits += 1;

Annotation

Implementation Notes