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-rw-r--r--usr/src/lib/libm/common/m9x/fmal.c1227
1 files changed, 1227 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/m9x/fmal.c b/usr/src/lib/libm/common/m9x/fmal.c
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+++ b/usr/src/lib/libm/common/m9x/fmal.c
@@ -0,0 +1,1227 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#if defined(ELFOBJ)
+#pragma weak fmal = __fmal
+#endif
+
+#include "libm.h"
+#include "fma.h"
+#include "fenv_inlines.h"
+
+#if defined(__sparc)
+
+static const union {
+ unsigned i[2];
+ double d;
+} C[] = {
+ { 0x3fe00000u, 0 },
+ { 0x40000000u, 0 },
+ { 0x3ef00000u, 0 },
+ { 0x3e700000u, 0 },
+ { 0x41300000u, 0 },
+ { 0x3e300000u, 0 },
+ { 0x3b300000u, 0 },
+ { 0x38300000u, 0 },
+ { 0x42300000u, 0 },
+ { 0x3df00000u, 0 },
+ { 0x7fe00000u, 0 },
+ { 0x00100000u, 0 },
+ { 0x00100001u, 0 },
+ { 0, 0 },
+ { 0x7ff00000u, 0 },
+ { 0x7ff00001u, 0 }
+};
+
+#define half C[0].d
+#define two C[1].d
+#define twom16 C[2].d
+#define twom24 C[3].d
+#define two20 C[4].d
+#define twom28 C[5].d
+#define twom76 C[6].d
+#define twom124 C[7].d
+#define two36 C[8].d
+#define twom32 C[9].d
+#define huge C[10].d
+#define tiny C[11].d
+#define tiny2 C[12].d
+#define zero C[13].d
+#define inf C[14].d
+#define snan C[15].d
+
+static const unsigned int fsr_rm = 0xc0000000u;
+
+/*
+ * fmal for SPARC: 128-bit quad precision, big-endian
+ */
+long double
+__fmal(long double x, long double y, long double z) {
+ union {
+ unsigned int i[4];
+ long double q;
+ } xx, yy, zz;
+ union {
+ unsigned int i[2];
+ double d;
+ } u;
+ double dx[5], dy[5], dxy[9], c, s;
+ unsigned int xy0, xy1, xy2, xy3, xy4, xy5, xy6, xy7;
+ unsigned int z0, z1, z2, z3, z4, z5, z6, z7;
+ unsigned int rm, sticky;
+ unsigned int fsr;
+ int hx, hy, hz, ex, ey, ez, exy, sxy, sz, e, ibit;
+ int cx, cy, cz;
+ volatile double dummy;
+
+ /* extract the high order words of the arguments */
+ xx.q = x;
+ yy.q = y;
+ zz.q = z;
+ hx = xx.i[0] & ~0x80000000;
+ hy = yy.i[0] & ~0x80000000;
+ hz = zz.i[0] & ~0x80000000;
+
+ /*
+ * distinguish zero, finite nonzero, infinite, and quiet nan
+ * arguments; raise invalid and return for signaling nans
+ */
+ if (hx >= 0x7fff0000) {
+ if ((hx & 0xffff) | xx.i[1] | xx.i[2] | xx.i[3]) {
+ if (!(hx & 0x8000)) {
+ /* signaling nan, raise invalid */
+ dummy = snan;
+ dummy += snan;
+ xx.i[0] |= 0x8000;
+ return (xx.q);
+ }
+ cx = 3; /* quiet nan */
+ } else
+ cx = 2; /* inf */
+ } else if (hx == 0) {
+ cx = (xx.i[1] | xx.i[2] | xx.i[3]) ? 1 : 0;
+ /* subnormal or zero */
+ } else
+ cx = 1; /* finite nonzero */
+
+ if (hy >= 0x7fff0000) {
+ if ((hy & 0xffff) | yy.i[1] | yy.i[2] | yy.i[3]) {
+ if (!(hy & 0x8000)) {
+ dummy = snan;
+ dummy += snan;
+ yy.i[0] |= 0x8000;
+ return (yy.q);
+ }
+ cy = 3;
+ } else
+ cy = 2;
+ } else if (hy == 0) {
+ cy = (yy.i[1] | yy.i[2] | yy.i[3]) ? 1 : 0;
+ } else
+ cy = 1;
+
+ if (hz >= 0x7fff0000) {
+ if ((hz & 0xffff) | zz.i[1] | zz.i[2] | zz.i[3]) {
+ if (!(hz & 0x8000)) {
+ dummy = snan;
+ dummy += snan;
+ zz.i[0] |= 0x8000;
+ return (zz.q);
+ }
+ cz = 3;
+ } else
+ cz = 2;
+ } else if (hz == 0) {
+ cz = (zz.i[1] | zz.i[2] | zz.i[3]) ? 1 : 0;
+ } else
+ cz = 1;
+
+ /* get the fsr and clear current exceptions */
+ __fenv_getfsr32(&fsr);
+ fsr &= ~FSR_CEXC;
+
+ /* handle all other zero, inf, and nan cases */
+ if (cx != 1 || cy != 1 || cz != 1) {
+ /* if x or y is a quiet nan, return it */
+ if (cx == 3) {
+ __fenv_setfsr32(&fsr);
+ return (x);
+ }
+ if (cy == 3) {
+ __fenv_setfsr32(&fsr);
+ return (y);
+ }
+
+ /* if x*y is 0*inf, raise invalid and return the default nan */
+ if ((cx == 0 && cy == 2) || (cx == 2 && cy == 0)) {
+ dummy = zero;
+ dummy *= inf;
+ zz.i[0] = 0x7fffffff;
+ zz.i[1] = zz.i[2] = zz.i[3] = 0xffffffff;
+ return (zz.q);
+ }
+
+ /* if z is a quiet nan, return it */
+ if (cz == 3) {
+ __fenv_setfsr32(&fsr);
+ return (z);
+ }
+
+ /*
+ * now none of x, y, or z is nan; handle cases where x or y
+ * is inf
+ */
+ if (cx == 2 || cy == 2) {
+ /*
+ * if z is also inf, either we have inf-inf or
+ * the result is the same as z depending on signs
+ */
+ if (cz == 2) {
+ if ((int) ((xx.i[0] ^ yy.i[0]) ^ zz.i[0]) < 0) {
+ dummy = inf;
+ dummy -= inf;
+ zz.i[0] = 0x7fffffff;
+ zz.i[1] = zz.i[2] = zz.i[3] =
+ 0xffffffff;
+ return (zz.q);
+ }
+ __fenv_setfsr32(&fsr);
+ return (z);
+ }
+
+ /* otherwise the result is inf with appropriate sign */
+ zz.i[0] = ((xx.i[0] ^ yy.i[0]) & 0x80000000) |
+ 0x7fff0000;
+ zz.i[1] = zz.i[2] = zz.i[3] = 0;
+ __fenv_setfsr32(&fsr);
+ return (zz.q);
+ }
+
+ /* if z is inf, return it */
+ if (cz == 2) {
+ __fenv_setfsr32(&fsr);
+ return (z);
+ }
+
+ /*
+ * now x, y, and z are all finite; handle cases where x or y
+ * is zero
+ */
+ if (cx == 0 || cy == 0) {
+ /* either we have 0-0 or the result is the same as z */
+ if (cz == 0 && (int) ((xx.i[0] ^ yy.i[0]) ^ zz.i[0]) <
+ 0) {
+ zz.i[0] = (fsr >> 30) == FSR_RM ? 0x80000000 :
+ 0;
+ __fenv_setfsr32(&fsr);
+ return (zz.q);
+ }
+ __fenv_setfsr32(&fsr);
+ return (z);
+ }
+
+ /* if we get here, x and y are nonzero finite, z must be zero */
+ return (x * y);
+ }
+
+ /*
+ * now x, y, and z are all finite and nonzero; set round-to-
+ * negative-infinity mode
+ */
+ __fenv_setfsr32(&fsr_rm);
+
+ /*
+ * get the signs and exponents and normalize the significands
+ * of x and y
+ */
+ sxy = (xx.i[0] ^ yy.i[0]) & 0x80000000;
+ ex = hx >> 16;
+ hx &= 0xffff;
+ if (!ex) {
+ if (hx | (xx.i[1] & 0xfffe0000)) {
+ ex = 1;
+ } else if (xx.i[1] | (xx.i[2] & 0xfffe0000)) {
+ hx = xx.i[1];
+ xx.i[1] = xx.i[2];
+ xx.i[2] = xx.i[3];
+ xx.i[3] = 0;
+ ex = -31;
+ } else if (xx.i[2] | (xx.i[3] & 0xfffe0000)) {
+ hx = xx.i[2];
+ xx.i[1] = xx.i[3];
+ xx.i[2] = xx.i[3] = 0;
+ ex = -63;
+ } else {
+ hx = xx.i[3];
+ xx.i[1] = xx.i[2] = xx.i[3] = 0;
+ ex = -95;
+ }
+ while ((hx & 0x10000) == 0) {
+ hx = (hx << 1) | (xx.i[1] >> 31);
+ xx.i[1] = (xx.i[1] << 1) | (xx.i[2] >> 31);
+ xx.i[2] = (xx.i[2] << 1) | (xx.i[3] >> 31);
+ xx.i[3] <<= 1;
+ ex--;
+ }
+ } else
+ hx |= 0x10000;
+ ey = hy >> 16;
+ hy &= 0xffff;
+ if (!ey) {
+ if (hy | (yy.i[1] & 0xfffe0000)) {
+ ey = 1;
+ } else if (yy.i[1] | (yy.i[2] & 0xfffe0000)) {
+ hy = yy.i[1];
+ yy.i[1] = yy.i[2];
+ yy.i[2] = yy.i[3];
+ yy.i[3] = 0;
+ ey = -31;
+ } else if (yy.i[2] | (yy.i[3] & 0xfffe0000)) {
+ hy = yy.i[2];
+ yy.i[1] = yy.i[3];
+ yy.i[2] = yy.i[3] = 0;
+ ey = -63;
+ } else {
+ hy = yy.i[3];
+ yy.i[1] = yy.i[2] = yy.i[3] = 0;
+ ey = -95;
+ }
+ while ((hy & 0x10000) == 0) {
+ hy = (hy << 1) | (yy.i[1] >> 31);
+ yy.i[1] = (yy.i[1] << 1) | (yy.i[2] >> 31);
+ yy.i[2] = (yy.i[2] << 1) | (yy.i[3] >> 31);
+ yy.i[3] <<= 1;
+ ey--;
+ }
+ } else
+ hy |= 0x10000;
+ exy = ex + ey - 0x3fff;
+
+ /* convert the significands of x and y to doubles */
+ c = twom16;
+ dx[0] = (double) ((int) hx) * c;
+ dy[0] = (double) ((int) hy) * c;
+
+ c *= twom24;
+ dx[1] = (double) ((int) (xx.i[1] >> 8)) * c;
+ dy[1] = (double) ((int) (yy.i[1] >> 8)) * c;
+
+ c *= twom24;
+ dx[2] = (double) ((int) (((xx.i[1] << 16) | (xx.i[2] >> 16)) &
+ 0xffffff)) * c;
+ dy[2] = (double) ((int) (((yy.i[1] << 16) | (yy.i[2] >> 16)) &
+ 0xffffff)) * c;
+
+ c *= twom24;
+ dx[3] = (double) ((int) (((xx.i[2] << 8) | (xx.i[3] >> 24)) &
+ 0xffffff)) * c;
+ dy[3] = (double) ((int) (((yy.i[2] << 8) | (yy.i[3] >> 24)) &
+ 0xffffff)) * c;
+
+ c *= twom24;
+ dx[4] = (double) ((int) (xx.i[3] & 0xffffff)) * c;
+ dy[4] = (double) ((int) (yy.i[3] & 0xffffff)) * c;
+
+ /* form the "digits" of the product */
+ dxy[0] = dx[0] * dy[0];
+ dxy[1] = dx[0] * dy[1] + dx[1] * dy[0];
+ dxy[2] = dx[0] * dy[2] + dx[1] * dy[1] + dx[2] * dy[0];
+ dxy[3] = dx[0] * dy[3] + dx[1] * dy[2] + dx[2] * dy[1] +
+ dx[3] * dy[0];
+ dxy[4] = dx[0] * dy[4] + dx[1] * dy[3] + dx[2] * dy[2] +
+ dx[3] * dy[1] + dx[4] * dy[0];
+ dxy[5] = dx[1] * dy[4] + dx[2] * dy[3] + dx[3] * dy[2] +
+ dx[4] * dy[1];
+ dxy[6] = dx[2] * dy[4] + dx[3] * dy[3] + dx[4] * dy[2];
+ dxy[7] = dx[3] * dy[4] + dx[4] * dy[3];
+ dxy[8] = dx[4] * dy[4];
+
+ /* split odd-numbered terms and combine into even-numbered terms */
+ c = (dxy[1] + two20) - two20;
+ dxy[0] += c;
+ dxy[1] -= c;
+ c = (dxy[3] + twom28) - twom28;
+ dxy[2] += c + dxy[1];
+ dxy[3] -= c;
+ c = (dxy[5] + twom76) - twom76;
+ dxy[4] += c + dxy[3];
+ dxy[5] -= c;
+ c = (dxy[7] + twom124) - twom124;
+ dxy[6] += c + dxy[5];
+ dxy[8] += (dxy[7] - c);
+
+ /* propagate carries, adjusting the exponent if need be */
+ dxy[7] = dxy[6] + dxy[8];
+ dxy[5] = dxy[4] + dxy[7];
+ dxy[3] = dxy[2] + dxy[5];
+ dxy[1] = dxy[0] + dxy[3];
+ if (dxy[1] >= two) {
+ dxy[0] *= half;
+ dxy[1] *= half;
+ dxy[2] *= half;
+ dxy[3] *= half;
+ dxy[4] *= half;
+ dxy[5] *= half;
+ dxy[6] *= half;
+ dxy[7] *= half;
+ dxy[8] *= half;
+ exy++;
+ }
+
+ /* extract the significand of x*y */
+ s = two36;
+ u.d = c = dxy[1] + s;
+ xy0 = u.i[1];
+ c -= s;
+ dxy[1] -= c;
+ dxy[0] -= c;
+
+ s *= twom32;
+ u.d = c = dxy[1] + s;
+ xy1 = u.i[1];
+ c -= s;
+ dxy[2] += (dxy[0] - c);
+ dxy[3] = dxy[2] + dxy[5];
+
+ s *= twom32;
+ u.d = c = dxy[3] + s;
+ xy2 = u.i[1];
+ c -= s;
+ dxy[4] += (dxy[2] - c);
+ dxy[5] = dxy[4] + dxy[7];
+
+ s *= twom32;
+ u.d = c = dxy[5] + s;
+ xy3 = u.i[1];
+ c -= s;
+ dxy[4] -= c;
+ dxy[5] = dxy[4] + dxy[7];
+
+ s *= twom32;
+ u.d = c = dxy[5] + s;
+ xy4 = u.i[1];
+ c -= s;
+ dxy[6] += (dxy[4] - c);
+ dxy[7] = dxy[6] + dxy[8];
+
+ s *= twom32;
+ u.d = c = dxy[7] + s;
+ xy5 = u.i[1];
+ c -= s;
+ dxy[8] += (dxy[6] - c);
+
+ s *= twom32;
+ u.d = c = dxy[8] + s;
+ xy6 = u.i[1];
+ c -= s;
+ dxy[8] -= c;
+
+ s *= twom32;
+ u.d = c = dxy[8] + s;
+ xy7 = u.i[1];
+
+ /* extract the sign, exponent, and significand of z */
+ sz = zz.i[0] & 0x80000000;
+ ez = hz >> 16;
+ z0 = hz & 0xffff;
+ if (!ez) {
+ if (z0 | (zz.i[1] & 0xfffe0000)) {
+ z1 = zz.i[1];
+ z2 = zz.i[2];
+ z3 = zz.i[3];
+ ez = 1;
+ } else if (zz.i[1] | (zz.i[2] & 0xfffe0000)) {
+ z0 = zz.i[1];
+ z1 = zz.i[2];
+ z2 = zz.i[3];
+ z3 = 0;
+ ez = -31;
+ } else if (zz.i[2] | (zz.i[3] & 0xfffe0000)) {
+ z0 = zz.i[2];
+ z1 = zz.i[3];
+ z2 = z3 = 0;
+ ez = -63;
+ } else {
+ z0 = zz.i[3];
+ z1 = z2 = z3 = 0;
+ ez = -95;
+ }
+ while ((z0 & 0x10000) == 0) {
+ z0 = (z0 << 1) | (z1 >> 31);
+ z1 = (z1 << 1) | (z2 >> 31);
+ z2 = (z2 << 1) | (z3 >> 31);
+ z3 <<= 1;
+ ez--;
+ }
+ } else {
+ z0 |= 0x10000;
+ z1 = zz.i[1];
+ z2 = zz.i[2];
+ z3 = zz.i[3];
+ }
+ z4 = z5 = z6 = z7 = 0;
+
+ /*
+ * now x*y is represented by sxy, exy, and xy[0-7], and z is
+ * represented likewise; swap if need be so |xy| <= |z|
+ */
+ if (exy > ez || (exy == ez && (xy0 > z0 || (xy0 == z0 && (xy1 > z1 ||
+ (xy1 == z1 && (xy2 > z2 || (xy2 == z2 && (xy3 > z3 ||
+ (xy3 == z3 && (xy4 | xy5 | xy6 | xy7) != 0)))))))))) {
+ e = sxy; sxy = sz; sz = e;
+ e = exy; exy = ez; ez = e;
+ e = xy0; xy0 = z0; z0 = e;
+ e = xy1; xy1 = z1; z1 = e;
+ e = xy2; xy2 = z2; z2 = e;
+ e = xy3; xy3 = z3; z3 = e;
+ z4 = xy4; xy4 = 0;
+ z5 = xy5; xy5 = 0;
+ z6 = xy6; xy6 = 0;
+ z7 = xy7; xy7 = 0;
+ }
+
+ /* shift the significand of xy keeping a sticky bit */
+ e = ez - exy;
+ if (e > 236) {
+ xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = xy6 = 0;
+ xy7 = 1;
+ } else if (e >= 224) {
+ sticky = xy7 | xy6 | xy5 | xy4 | xy3 | xy2 | xy1 |
+ ((xy0 << 1) << (255 - e));
+ xy7 = xy0 >> (e - 224);
+ if (sticky)
+ xy7 |= 1;
+ xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = xy6 = 0;
+ } else if (e >= 192) {
+ sticky = xy7 | xy6 | xy5 | xy4 | xy3 | xy2 |
+ ((xy1 << 1) << (223 - e));
+ xy7 = (xy1 >> (e - 192)) | ((xy0 << 1) << (223 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = xy0 >> (e - 192);
+ xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = 0;
+ } else if (e >= 160) {
+ sticky = xy7 | xy6 | xy5 | xy4 | xy3 |
+ ((xy2 << 1) << (191 - e));
+ xy7 = (xy2 >> (e - 160)) | ((xy1 << 1) << (191 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = (xy1 >> (e - 160)) | ((xy0 << 1) << (191 - e));
+ xy5 = xy0 >> (e - 160);
+ xy0 = xy1 = xy2 = xy3 = xy4 = 0;
+ } else if (e >= 128) {
+ sticky = xy7 | xy6 | xy5 | xy4 | ((xy3 << 1) << (159 - e));
+ xy7 = (xy3 >> (e - 128)) | ((xy2 << 1) << (159 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = (xy2 >> (e - 128)) | ((xy1 << 1) << (159 - e));
+ xy5 = (xy1 >> (e - 128)) | ((xy0 << 1) << (159 - e));
+ xy4 = xy0 >> (e - 128);
+ xy0 = xy1 = xy2 = xy3 = 0;
+ } else if (e >= 96) {
+ sticky = xy7 | xy6 | xy5 | ((xy4 << 1) << (127 - e));
+ xy7 = (xy4 >> (e - 96)) | ((xy3 << 1) << (127 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = (xy3 >> (e - 96)) | ((xy2 << 1) << (127 - e));
+ xy5 = (xy2 >> (e - 96)) | ((xy1 << 1) << (127 - e));
+ xy4 = (xy1 >> (e - 96)) | ((xy0 << 1) << (127 - e));
+ xy3 = xy0 >> (e - 96);
+ xy0 = xy1 = xy2 = 0;
+ } else if (e >= 64) {
+ sticky = xy7 | xy6 | ((xy5 << 1) << (95 - e));
+ xy7 = (xy5 >> (e - 64)) | ((xy4 << 1) << (95 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = (xy4 >> (e - 64)) | ((xy3 << 1) << (95 - e));
+ xy5 = (xy3 >> (e - 64)) | ((xy2 << 1) << (95 - e));
+ xy4 = (xy2 >> (e - 64)) | ((xy1 << 1) << (95 - e));
+ xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
+ xy2 = xy0 >> (e - 64);
+ xy0 = xy1 = 0;
+ } else if (e >= 32) {
+ sticky = xy7 | ((xy6 << 1) << (63 - e));
+ xy7 = (xy6 >> (e - 32)) | ((xy5 << 1) << (63 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = (xy5 >> (e - 32)) | ((xy4 << 1) << (63 - e));
+ xy5 = (xy4 >> (e - 32)) | ((xy3 << 1) << (63 - e));
+ xy4 = (xy3 >> (e - 32)) | ((xy2 << 1) << (63 - e));
+ xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
+ xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
+ xy1 = xy0 >> (e - 32);
+ xy0 = 0;
+ } else if (e) {
+ sticky = (xy7 << 1) << (31 - e);
+ xy7 = (xy7 >> e) | ((xy6 << 1) << (31 - e));
+ if (sticky)
+ xy7 |= 1;
+ xy6 = (xy6 >> e) | ((xy5 << 1) << (31 - e));
+ xy5 = (xy5 >> e) | ((xy4 << 1) << (31 - e));
+ xy4 = (xy4 >> e) | ((xy3 << 1) << (31 - e));
+ xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
+ xy2 = (xy2 >> e) | ((xy1 << 1) << (31 - e));
+ xy1 = (xy1 >> e) | ((xy0 << 1) << (31 - e));
+ xy0 >>= e;
+ }
+
+ /* if this is a magnitude subtract, negate the significand of xy */
+ if (sxy ^ sz) {
+ xy0 = ~xy0;
+ xy1 = ~xy1;
+ xy2 = ~xy2;
+ xy3 = ~xy3;
+ xy4 = ~xy4;
+ xy5 = ~xy5;
+ xy6 = ~xy6;
+ xy7 = -xy7;
+ if (xy7 == 0)
+ if (++xy6 == 0)
+ if (++xy5 == 0)
+ if (++xy4 == 0)
+ if (++xy3 == 0)
+ if (++xy2 == 0)
+ if (++xy1 == 0)
+ xy0++;
+ }
+
+ /* add, propagating carries */
+ z7 += xy7;
+ e = (z7 < xy7);
+ z6 += xy6;
+ if (e) {
+ z6++;
+ e = (z6 <= xy6);
+ } else
+ e = (z6 < xy6);
+ z5 += xy5;
+ if (e) {
+ z5++;
+ e = (z5 <= xy5);
+ } else
+ e = (z5 < xy5);
+ z4 += xy4;
+ if (e) {
+ z4++;
+ e = (z4 <= xy4);
+ } else
+ e = (z4 < xy4);
+ z3 += xy3;
+ if (e) {
+ z3++;
+ e = (z3 <= xy3);
+ } else
+ e = (z3 < xy3);
+ z2 += xy2;
+ if (e) {
+ z2++;
+ e = (z2 <= xy2);
+ } else
+ e = (z2 < xy2);
+ z1 += xy1;
+ if (e) {
+ z1++;
+ e = (z1 <= xy1);
+ } else
+ e = (z1 < xy1);
+ z0 += xy0;
+ if (e)
+ z0++;
+
+ /* postnormalize and collect rounding information into z4 */
+ if (ez < 1) {
+ /* result is tiny; shift right until exponent is within range */
+ e = 1 - ez;
+ if (e > 116) {
+ z4 = 1; /* result can't be exactly zero */
+ z0 = z1 = z2 = z3 = 0;
+ } else if (e >= 96) {
+ sticky = z7 | z6 | z5 | z4 | z3 | z2 |
+ ((z1 << 1) << (127 - e));
+ z4 = (z1 >> (e - 96)) | ((z0 << 1) << (127 - e));
+ if (sticky)
+ z4 |= 1;
+ z3 = z0 >> (e - 96);
+ z0 = z1 = z2 = 0;
+ } else if (e >= 64) {
+ sticky = z7 | z6 | z5 | z4 | z3 |
+ ((z2 << 1) << (95 - e));
+ z4 = (z2 >> (e - 64)) | ((z1 << 1) << (95 - e));
+ if (sticky)
+ z4 |= 1;
+ z3 = (z1 >> (e - 64)) | ((z0 << 1) << (95 - e));
+ z2 = z0 >> (e - 64);
+ z0 = z1 = 0;
+ } else if (e >= 32) {
+ sticky = z7 | z6 | z5 | z4 | ((z3 << 1) << (63 - e));
+ z4 = (z3 >> (e - 32)) | ((z2 << 1) << (63 - e));
+ if (sticky)
+ z4 |= 1;
+ z3 = (z2 >> (e - 32)) | ((z1 << 1) << (63 - e));
+ z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
+ z1 = z0 >> (e - 32);
+ z0 = 0;
+ } else {
+ sticky = z7 | z6 | z5 | (z4 << 1) << (31 - e);
+ z4 = (z4 >> e) | ((z3 << 1) << (31 - e));
+ if (sticky)
+ z4 |= 1;
+ z3 = (z3 >> e) | ((z2 << 1) << (31 - e));
+ z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
+ z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
+ z0 >>= e;
+ }
+ ez = 1;
+ } else if (z0 >= 0x20000) {
+ /* carry out; shift right by one */
+ sticky = (z4 & 1) | z5 | z6 | z7;
+ z4 = (z4 >> 1) | (z3 << 31);
+ if (sticky)
+ z4 |= 1;
+ z3 = (z3 >> 1) | (z2 << 31);
+ z2 = (z2 >> 1) | (z1 << 31);
+ z1 = (z1 >> 1) | (z0 << 31);
+ z0 >>= 1;
+ ez++;
+ } else {
+ if (z0 < 0x10000 && (z0 | z1 | z2 | z3 | z4 | z5 | z6 | z7)
+ != 0) {
+ /*
+ * borrow/cancellation; shift left as much as
+ * exponent allows
+ */
+ while (!(z0 | (z1 & 0xfffe0000)) && ez >= 33) {
+ z0 = z1;
+ z1 = z2;
+ z2 = z3;
+ z3 = z4;
+ z4 = z5;
+ z5 = z6;
+ z6 = z7;
+ z7 = 0;
+ ez -= 32;
+ }
+ while (z0 < 0x10000 && ez > 1) {
+ z0 = (z0 << 1) | (z1 >> 31);
+ z1 = (z1 << 1) | (z2 >> 31);
+ z2 = (z2 << 1) | (z3 >> 31);
+ z3 = (z3 << 1) | (z4 >> 31);
+ z4 = (z4 << 1) | (z5 >> 31);
+ z5 = (z5 << 1) | (z6 >> 31);
+ z6 = (z6 << 1) | (z7 >> 31);
+ z7 <<= 1;
+ ez--;
+ }
+ }
+ if (z5 | z6 | z7)
+ z4 |= 1;
+ }
+
+ /* get the rounding mode */
+ rm = fsr >> 30;
+
+ /* strip off the integer bit, if there is one */
+ ibit = z0 & 0x10000;
+ if (ibit)
+ z0 -= 0x10000;
+ else {
+ ez = 0;
+ if (!(z0 | z1 | z2 | z3 | z4)) { /* exact zero */
+ zz.i[0] = rm == FSR_RM ? 0x80000000 : 0;
+ zz.i[1] = zz.i[2] = zz.i[3] = 0;
+ __fenv_setfsr32(&fsr);
+ return (zz.q);
+ }
+ }
+
+ /*
+ * flip the sense of directed roundings if the result is negative;
+ * the logic below applies to a positive result
+ */
+ if (sz)
+ rm ^= rm >> 1;
+
+ /* round and raise exceptions */
+ if (z4) {
+ fsr |= FSR_NXC;
+
+ /* decide whether to round the fraction up */
+ if (rm == FSR_RP || (rm == FSR_RN && (z4 > 0x80000000u ||
+ (z4 == 0x80000000u && (z3 & 1))))) {
+ /* round up and renormalize if necessary */
+ if (++z3 == 0)
+ if (++z2 == 0)
+ if (++z1 == 0)
+ if (++z0 == 0x10000) {
+ z0 = 0;
+ ez++;
+ }
+ }
+ }
+
+ /* check for under/overflow */
+ if (ez >= 0x7fff) {
+ if (rm == FSR_RN || rm == FSR_RP) {
+ zz.i[0] = sz | 0x7fff0000;
+ zz.i[1] = zz.i[2] = zz.i[3] = 0;
+ } else {
+ zz.i[0] = sz | 0x7ffeffff;
+ zz.i[1] = zz.i[2] = zz.i[3] = 0xffffffff;
+ }
+ fsr |= FSR_OFC | FSR_NXC;
+ } else {
+ zz.i[0] = sz | (ez << 16) | z0;
+ zz.i[1] = z1;
+ zz.i[2] = z2;
+ zz.i[3] = z3;
+
+ /*
+ * !ibit => exact result was tiny before rounding,
+ * z4 nonzero => result delivered is inexact
+ */
+ if (!ibit) {
+ if (z4)
+ fsr |= FSR_UFC | FSR_NXC;
+ else if (fsr & FSR_UFM)
+ fsr |= FSR_UFC;
+ }
+ }
+
+ /* restore the fsr and emulate exceptions as needed */
+ if ((fsr & FSR_CEXC) & (fsr >> 23)) {
+ __fenv_setfsr32(&fsr);
+ if (fsr & FSR_OFC) {
+ dummy = huge;
+ dummy *= huge;
+ } else if (fsr & FSR_UFC) {
+ dummy = tiny;
+ if (fsr & FSR_NXC)
+ dummy *= tiny;
+ else
+ dummy -= tiny2;
+ } else {
+ dummy = huge;
+ dummy += tiny;
+ }
+ } else {
+ fsr |= (fsr & 0x1f) << 5;
+ __fenv_setfsr32(&fsr);
+ }
+ return (zz.q);
+}
+
+#elif defined(__x86)
+
+static const union {
+ unsigned i[2];
+ double d;
+} C[] = {
+ { 0, 0x3fe00000u },
+ { 0, 0x40000000u },
+ { 0, 0x3df00000u },
+ { 0, 0x3bf00000u },
+ { 0, 0x41f00000u },
+ { 0, 0x43e00000u },
+ { 0, 0x7fe00000u },
+ { 0, 0x00100000u },
+ { 0, 0x00100001u }
+};
+
+#define half C[0].d
+#define two C[1].d
+#define twom32 C[2].d
+#define twom64 C[3].d
+#define two32 C[4].d
+#define two63 C[5].d
+#define huge C[6].d
+#define tiny C[7].d
+#define tiny2 C[8].d
+
+#if defined(__amd64)
+#define NI 4
+#else
+#define NI 3
+#endif
+
+/*
+ * fmal for x86: 80-bit extended double precision, little-endian
+ */
+long double
+__fmal(long double x, long double y, long double z) {
+ union {
+ unsigned i[NI];
+ long double e;
+ } xx, yy, zz;
+ long double xhi, yhi, xlo, ylo, t;
+ unsigned xy0, xy1, xy2, xy3, xy4, z0, z1, z2, z3, z4;
+ unsigned oldcwsw, cwsw, rm, sticky, carry;
+ int ex, ey, ez, exy, sxy, sz, e, tinyafter;
+ volatile double dummy;
+
+ /* extract the exponents of the arguments */
+ xx.e = x;
+ yy.e = y;
+ zz.e = z;
+ ex = xx.i[2] & 0x7fff;
+ ey = yy.i[2] & 0x7fff;
+ ez = zz.i[2] & 0x7fff;
+
+ /* dispense with inf, nan, and zero cases */
+ if (ex == 0x7fff || ey == 0x7fff || (ex | xx.i[1] | xx.i[0]) == 0 ||
+ (ey | yy.i[1] | yy.i[0]) == 0) /* x or y is inf, nan, or 0 */
+ return (x * y + z);
+
+ if (ez == 0x7fff) /* z is inf or nan */
+ return (x + z); /* avoid spurious under/overflow in x * y */
+
+ if ((ez | zz.i[1] | zz.i[0]) == 0) /* z is zero */
+ /*
+ * x * y isn't zero but could underflow to zero,
+ * so don't add z, lest we perturb the sign
+ */
+ return (x * y);
+
+ /*
+ * now x, y, and z are all finite and nonzero; extract signs and
+ * normalize the significands (this will raise the denormal operand
+ * exception if need be)
+ */
+ sxy = (xx.i[2] ^ yy.i[2]) & 0x8000;
+ sz = zz.i[2] & 0x8000;
+ if (!ex) {
+ xx.e = x * two63;
+ ex = (xx.i[2] & 0x7fff) - 63;
+ }
+ if (!ey) {
+ yy.e = y * two63;
+ ey = (yy.i[2] & 0x7fff) - 63;
+ }
+ if (!ez) {
+ zz.e = z * two63;
+ ez = (zz.i[2] & 0x7fff) - 63;
+ }
+
+ /*
+ * save the control and status words, mask all exceptions, and
+ * set rounding to 64-bit precision and toward-zero
+ */
+ __fenv_getcwsw(&oldcwsw);
+ cwsw = (oldcwsw & 0xf0c0ffff) | 0x0f3f0000;
+ __fenv_setcwsw(&cwsw);
+
+ /* multiply x*y to 128 bits */
+ exy = ex + ey - 0x3fff;
+ xx.i[2] = 0x3fff;
+ yy.i[2] = 0x3fff;
+ x = xx.e;
+ y = yy.e;
+ xhi = ((x + twom32) + two32) - two32;
+ yhi = ((y + twom32) + two32) - two32;
+ xlo = x - xhi;
+ ylo = y - yhi;
+ x *= y;
+ y = ((xhi * yhi - x) + xhi * ylo + xlo * yhi) + xlo * ylo;
+ if (x >= two) {
+ x *= half;
+ y *= half;
+ exy++;
+ }
+
+ /* extract the significands */
+ xx.e = x;
+ xy0 = xx.i[1];
+ xy1 = xx.i[0];
+ yy.e = t = y + twom32;
+ xy2 = yy.i[0];
+ yy.e = (y - (t - twom32)) + twom64;
+ xy3 = yy.i[0];
+ xy4 = 0;
+ z0 = zz.i[1];
+ z1 = zz.i[0];
+ z2 = z3 = z4 = 0;
+
+ /*
+ * now x*y is represented by sxy, exy, and xy[0-4], and z is
+ * represented likewise; swap if need be so |xy| <= |z|
+ */
+ if (exy > ez || (exy == ez && (xy0 > z0 || (xy0 == z0 &&
+ (xy1 > z1 || (xy1 == z1 && (xy2 | xy3) != 0)))))) {
+ e = sxy; sxy = sz; sz = e;
+ e = exy; exy = ez; ez = e;
+ e = xy0; xy0 = z0; z0 = e;
+ e = xy1; xy1 = z1; z1 = e;
+ z2 = xy2; xy2 = 0;
+ z3 = xy3; xy3 = 0;
+ }
+
+ /* shift the significand of xy keeping a sticky bit */
+ e = ez - exy;
+ if (e > 130) {
+ xy0 = xy1 = xy2 = xy3 = 0;
+ xy4 = 1;
+ } else if (e >= 128) {
+ sticky = xy3 | xy2 | xy1 | ((xy0 << 1) << (159 - e));
+ xy4 = xy0 >> (e - 128);
+ if (sticky)
+ xy4 |= 1;
+ xy0 = xy1 = xy2 = xy3 = 0;
+ } else if (e >= 96) {
+ sticky = xy3 | xy2 | ((xy1 << 1) << (127 - e));
+ xy4 = (xy1 >> (e - 96)) | ((xy0 << 1) << (127 - e));
+ if (sticky)
+ xy4 |= 1;
+ xy3 = xy0 >> (e - 96);
+ xy0 = xy1 = xy2 = 0;
+ } else if (e >= 64) {
+ sticky = xy3 | ((xy2 << 1) << (95 - e));
+ xy4 = (xy2 >> (e - 64)) | ((xy1 << 1) << (95 - e));
+ if (sticky)
+ xy4 |= 1;
+ xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
+ xy2 = xy0 >> (e - 64);
+ xy0 = xy1 = 0;
+ } else if (e >= 32) {
+ sticky = (xy3 << 1) << (63 - e);
+ xy4 = (xy3 >> (e - 32)) | ((xy2 << 1) << (63 - e));
+ if (sticky)
+ xy4 |= 1;
+ xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
+ xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
+ xy1 = xy0 >> (e - 32);
+ xy0 = 0;
+ } else if (e) {
+ xy4 = (xy3 << 1) << (31 - e);
+ xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
+ xy2 = (xy2 >> e) | ((xy1 << 1) << (31 - e));
+ xy1 = (xy1 >> e) | ((xy0 << 1) << (31 - e));
+ xy0 >>= e;
+ }
+
+ /* if this is a magnitude subtract, negate the significand of xy */
+ if (sxy ^ sz) {
+ xy0 = ~xy0;
+ xy1 = ~xy1;
+ xy2 = ~xy2;
+ xy3 = ~xy3;
+ xy4 = -xy4;
+ if (xy4 == 0)
+ if (++xy3 == 0)
+ if (++xy2 == 0)
+ if (++xy1 == 0)
+ xy0++;
+ }
+
+ /* add, propagating carries */
+ z4 += xy4;
+ carry = (z4 < xy4);
+ z3 += xy3;
+ if (carry) {
+ z3++;
+ carry = (z3 <= xy3);
+ } else
+ carry = (z3 < xy3);
+ z2 += xy2;
+ if (carry) {
+ z2++;
+ carry = (z2 <= xy2);
+ } else
+ carry = (z2 < xy2);
+ z1 += xy1;
+ if (carry) {
+ z1++;
+ carry = (z1 <= xy1);
+ } else
+ carry = (z1 < xy1);
+ z0 += xy0;
+ if (carry) {
+ z0++;
+ carry = (z0 <= xy0);
+ } else
+ carry = (z0 < xy0);
+
+ /* for a magnitude subtract, ignore the last carry out */
+ if (sxy ^ sz)
+ carry = 0;
+
+ /* postnormalize and collect rounding information into z2 */
+ if (ez < 1) {
+ /* result is tiny; shift right until exponent is within range */
+ e = 1 - ez;
+ if (e > 67) {
+ z2 = 1; /* result can't be exactly zero */
+ z0 = z1 = 0;
+ } else if (e >= 64) {
+ sticky = z4 | z3 | z2 | z1 | ((z0 << 1) << (95 - e));
+ z2 = (z0 >> (e - 64)) | ((carry << 1) << (95 - e));
+ if (sticky)
+ z2 |= 1;
+ z1 = carry >> (e - 64);
+ z0 = 0;
+ } else if (e >= 32) {
+ sticky = z4 | z3 | z2 | ((z1 << 1) << (63 - e));
+ z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
+ if (sticky)
+ z2 |= 1;
+ z1 = (z0 >> (e - 32)) | ((carry << 1) << (63 - e));
+ z0 = carry >> (e - 32);
+ } else {
+ sticky = z4 | z3 | (z2 << 1) << (31 - e);
+ z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
+ if (sticky)
+ z2 |= 1;
+ z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
+ z0 = (z0 >> e) | ((carry << 1) << (31 - e));
+ }
+ ez = 1;
+ } else if (carry) {
+ /* carry out; shift right by one */
+ sticky = (z2 & 1) | z3 | z4;
+ z2 = (z2 >> 1) | (z1 << 31);
+ if (sticky)
+ z2 |= 1;
+ z1 = (z1 >> 1) | (z0 << 31);
+ z0 = (z0 >> 1) | 0x80000000;
+ ez++;
+ } else {
+ if (z0 < 0x80000000u && (z0 | z1 | z2 | z3 | z4) != 0) {
+ /*
+ * borrow/cancellation; shift left as much as
+ * exponent allows
+ */
+ while (!z0 && ez >= 33) {
+ z0 = z1;
+ z1 = z2;
+ z2 = z3;
+ z3 = z4;
+ z4 = 0;
+ ez -= 32;
+ }
+ while (z0 < 0x80000000u && ez > 1) {
+ z0 = (z0 << 1) | (z1 >> 31);
+ z1 = (z1 << 1) | (z2 >> 31);
+ z2 = (z2 << 1) | (z3 >> 31);
+ z3 = (z3 << 1) | (z4 >> 31);
+ z4 <<= 1;
+ ez--;
+ }
+ }
+ if (z3 | z4)
+ z2 |= 1;
+ }
+
+ /* get the rounding mode */
+ rm = oldcwsw & 0x0c000000;
+
+ /* adjust exponent if result is subnormal */
+ tinyafter = 0;
+ if (!(z0 & 0x80000000)) {
+ ez = 0;
+ tinyafter = 1;
+ if (!(z0 | z1 | z2)) { /* exact zero */
+ zz.i[2] = rm == FCW_RM ? 0x8000 : 0;
+ zz.i[1] = zz.i[0] = 0;
+ __fenv_setcwsw(&oldcwsw);
+ return (zz.e);
+ }
+ }
+
+ /*
+ * flip the sense of directed roundings if the result is negative;
+ * the logic below applies to a positive result
+ */
+ if (sz && (rm == FCW_RM || rm == FCW_RP))
+ rm = (FCW_RM + FCW_RP) - rm;
+
+ /* round */
+ if (z2) {
+ if (rm == FCW_RP || (rm == FCW_RN && (z2 > 0x80000000u ||
+ (z2 == 0x80000000u && (z1 & 1))))) {
+ /* round up and renormalize if necessary */
+ if (++z1 == 0) {
+ if (++z0 == 0) {
+ z0 = 0x80000000;
+ ez++;
+ } else if (z0 == 0x80000000) {
+ /* rounded up to smallest normal */
+ ez = 1;
+ if ((rm == FCW_RP && z2 >
+ 0x80000000u) || (rm == FCW_RN &&
+ z2 >= 0xc0000000u))
+ /*
+ * would have rounded up to
+ * smallest normal even with
+ * unbounded range
+ */
+ tinyafter = 0;
+ }
+ }
+ }
+ }
+
+ /* restore the control and status words, check for over/underflow */
+ __fenv_setcwsw(&oldcwsw);
+ if (ez >= 0x7fff) {
+ if (rm == FCW_RN || rm == FCW_RP) {
+ zz.i[2] = sz | 0x7fff;
+ zz.i[1] = 0x80000000;
+ zz.i[0] = 0;
+ } else {
+ zz.i[2] = sz | 0x7ffe;
+ zz.i[1] = 0xffffffff;
+ zz.i[0] = 0xffffffff;
+ }
+ dummy = huge;
+ dummy *= huge;
+ } else {
+ zz.i[2] = sz | ez;
+ zz.i[1] = z0;
+ zz.i[0] = z1;
+
+ /*
+ * tinyafter => result rounded w/ unbounded range would be tiny,
+ * z2 nonzero => result delivered is inexact
+ */
+ if (tinyafter) {
+ dummy = tiny;
+ if (z2)
+ dummy *= tiny;
+ else
+ dummy -= tiny2;
+ } else if (z2) {
+ dummy = huge;
+ dummy += tiny;
+ }
+ }
+
+ return (zz.e);
+}
+
+#else
+#error Unknown architecture
+#endif
generated by cgit v1.2.3 (git 2.46.0) at 2025-10-11 10:45:22 +0000