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/arch/mips/math-emu/dp_sqrt.c

http://github.com/mirrors/linux
C | 153 lines | 91 code | 29 blank | 33 comment | 11 complexity | caa7315bb783c816aa4548b9c0bba3ff MD5 | raw file
  1// SPDX-License-Identifier: GPL-2.0-only
  2/* IEEE754 floating point arithmetic
  3 * double precision square root
  4 */
  5/*
  6 * MIPS floating point support
  7 * Copyright (C) 1994-2000 Algorithmics Ltd.
  8 */
  9
 10#include "ieee754dp.h"
 11
 12static const unsigned int table[] = {
 13	0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
 14	29598, 36145, 43202, 50740, 58733, 67158, 75992,
 15	85215, 83599, 71378, 60428, 50647, 41945, 34246,
 16	27478, 21581, 16499, 12183, 8588, 5674, 3403,
 17	1742, 661, 130
 18};
 19
 20union ieee754dp ieee754dp_sqrt(union ieee754dp x)
 21{
 22	struct _ieee754_csr oldcsr;
 23	union ieee754dp y, z, t;
 24	unsigned int scalx, yh;
 25	COMPXDP;
 26
 27	EXPLODEXDP;
 28	ieee754_clearcx();
 29	FLUSHXDP;
 30
 31	/* x == INF or NAN? */
 32	switch (xc) {
 33	case IEEE754_CLASS_SNAN:
 34		return ieee754dp_nanxcpt(x);
 35
 36	case IEEE754_CLASS_QNAN:
 37		/* sqrt(Nan) = Nan */
 38		return x;
 39
 40	case IEEE754_CLASS_ZERO:
 41		/* sqrt(0) = 0 */
 42		return x;
 43
 44	case IEEE754_CLASS_INF:
 45		if (xs) {
 46			/* sqrt(-Inf) = Nan */
 47			ieee754_setcx(IEEE754_INVALID_OPERATION);
 48			return ieee754dp_indef();
 49		}
 50		/* sqrt(+Inf) = Inf */
 51		return x;
 52
 53	case IEEE754_CLASS_DNORM:
 54		DPDNORMX;
 55		/* fall through */
 56
 57	case IEEE754_CLASS_NORM:
 58		if (xs) {
 59			/* sqrt(-x) = Nan */
 60			ieee754_setcx(IEEE754_INVALID_OPERATION);
 61			return ieee754dp_indef();
 62		}
 63		break;
 64	}
 65
 66	/* save old csr; switch off INX enable & flag; set RN rounding */
 67	oldcsr = ieee754_csr;
 68	ieee754_csr.mx &= ~IEEE754_INEXACT;
 69	ieee754_csr.sx &= ~IEEE754_INEXACT;
 70	ieee754_csr.rm = FPU_CSR_RN;
 71
 72	/* adjust exponent to prevent overflow */
 73	scalx = 0;
 74	if (xe > 512) {		/* x > 2**-512? */
 75		xe -= 512;	/* x = x / 2**512 */
 76		scalx += 256;
 77	} else if (xe < -512) { /* x < 2**-512? */
 78		xe += 512;	/* x = x * 2**512 */
 79		scalx -= 256;
 80	}
 81
 82	x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
 83	y = x;
 84
 85	/* magic initial approximation to almost 8 sig. bits */
 86	yh = y.bits >> 32;
 87	yh = (yh >> 1) + 0x1ff80000;
 88	yh = yh - table[(yh >> 15) & 31];
 89	y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
 90
 91	/* Heron's rule once with correction to improve to ~18 sig. bits */
 92	/* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
 93	t = ieee754dp_div(x, y);
 94	y = ieee754dp_add(y, t);
 95	y.bits -= 0x0010000600000000LL;
 96	y.bits &= 0xffffffff00000000LL;
 97
 98	/* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
 99	/* t=y*y; z=t;	pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
100	t = ieee754dp_mul(y, y);
101	z = t;
102	t.bexp += 0x001;
103	t = ieee754dp_add(t, z);
104	z = ieee754dp_mul(ieee754dp_sub(x, z), y);
105
106	/* t=z/(t+x) ;	pt[n0]+=0x00100000; y+=t; */
107	t = ieee754dp_div(z, ieee754dp_add(t, x));
108	t.bexp += 0x001;
109	y = ieee754dp_add(y, t);
110
111	/* twiddle last bit to force y correctly rounded */
112
113	/* set RZ, clear INEX flag */
114	ieee754_csr.rm = FPU_CSR_RZ;
115	ieee754_csr.sx &= ~IEEE754_INEXACT;
116
117	/* t=x/y; ...chopped quotient, possibly inexact */
118	t = ieee754dp_div(x, y);
119
120	if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
121
122		if (!(ieee754_csr.sx & IEEE754_INEXACT))
123			/* t = t-ulp */
124			t.bits -= 1;
125
126		/* add inexact to result status */
127		oldcsr.cx |= IEEE754_INEXACT;
128		oldcsr.sx |= IEEE754_INEXACT;
129
130		switch (oldcsr.rm) {
131		case FPU_CSR_RU:
132			y.bits += 1;
133			/* fall through */
134		case FPU_CSR_RN:
135			t.bits += 1;
136			break;
137		}
138
139		/* y=y+t; ...chopped sum */
140		y = ieee754dp_add(y, t);
141
142		/* adjust scalx for correctly rounded sqrt(x) */
143		scalx -= 1;
144	}
145
146	/* py[n0]=py[n0]+scalx; ...scale back y */
147	y.bexp += scalx;
148
149	/* restore rounding mode, possibly set inexact */
150	ieee754_csr = oldcsr;
151
152	return y;
153}