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Diffstat (limited to 'usr/src/lib/libm/common/m9x/fma.c')
-rw-r--r--usr/src/lib/libm/common/m9x/fma.c497
1 files changed, 497 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/m9x/fma.c b/usr/src/lib/libm/common/m9x/fma.c
new file mode 100644
index 0000000000..f06349a2c4
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+++ b/usr/src/lib/libm/common/m9x/fma.c
@@ -0,0 +1,497 @@
+/*
+ * 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 fma = __fma
+#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 },
+ { 0x43300000u, 0 },
+ { 0x41a00000u, 0 },
+ { 0x3e500000u, 0 },
+ { 0x3df00000u, 0 },
+ { 0x3bf00000u, 0 },
+ { 0x7fe00000u, 0 },
+ { 0x00100000u, 0 },
+ { 0x00100001u, 0 }
+};
+
+#define half C[0].d
+#define two C[1].d
+#define two52 C[2].d
+#define two27 C[3].d
+#define twom26 C[4].d
+#define twom32 C[5].d
+#define twom64 C[6].d
+#define huge C[7].d
+#define tiny C[8].d
+#define tiny2 C[9].d
+
+static const unsigned int fsr_rm = 0xc0000000u;
+
+/*
+ * fma for SPARC: 64-bit double precision, big-endian
+ */
+double
+__fma(double x, double y, double z) {
+ union {
+ unsigned i[2];
+ double d;
+ } xx, yy, zz;
+ double xhi, yhi, xlo, ylo, t;
+ unsigned int xy0, xy1, xy2, xy3, z0, z1, z2, z3, fsr, rm, sticky;
+ int hx, hy, hz, ex, ey, ez, exy, sxy, sz, e, ibit;
+ volatile double dummy;
+
+ /* extract the high order words of the arguments */
+ xx.d = x;
+ yy.d = y;
+ zz.d = z;
+ hx = xx.i[0] & ~0x80000000;
+ hy = yy.i[0] & ~0x80000000;
+ hz = zz.i[0] & ~0x80000000;
+
+ /* dispense with inf, nan, and zero cases */
+ if (hx >= 0x7ff00000 || hy >= 0x7ff00000 || (hx | xx.i[1]) == 0 ||
+ (hy | yy.i[1]) == 0) /* x or y is inf, nan, or zero */
+ return (x * y + z);
+
+ if (hz >= 0x7ff00000) /* z is inf or nan */
+ return (x + z); /* avoid spurious under/overflow in x * y */
+
+ if ((hz | zz.i[1]) == 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; save the fsr and
+ * set round-to-negative-infinity mode (and clear nonstandard
+ * mode before we try to scale subnormal operands)
+ */
+ __fenv_getfsr32(&fsr);
+ __fenv_setfsr32(&fsr_rm);
+
+ /* extract signs and exponents, and normalize subnormals */
+ sxy = (xx.i[0] ^ yy.i[0]) & 0x80000000;
+ sz = zz.i[0] & 0x80000000;
+ ex = hx >> 20;
+ if (!ex) {
+ xx.d = x * two52;
+ ex = ((xx.i[0] & ~0x80000000) >> 20) - 52;
+ }
+ ey = hy >> 20;
+ if (!ey) {
+ yy.d = y * two52;
+ ey = ((yy.i[0] & ~0x80000000) >> 20) - 52;
+ }
+ ez = hz >> 20;
+ if (!ez) {
+ zz.d = z * two52;
+ ez = ((zz.i[0] & ~0x80000000) >> 20) - 52;
+ }
+
+ /* multiply x*y to 106 bits */
+ exy = ex + ey - 0x3ff;
+ xx.i[0] = (xx.i[0] & 0xfffff) | 0x3ff00000;
+ yy.i[0] = (yy.i[0] & 0xfffff) | 0x3ff00000;
+ x = xx.d;
+ y = yy.d;
+ xhi = ((x + twom26) + two27) - two27;
+ yhi = ((y + twom26) + two27) - two27;
+ 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.d = x;
+ xy0 = (xx.i[0] & 0xfffff) | 0x100000;
+ xy1 = xx.i[1];
+ yy.d = t = y + twom32;
+ xy2 = yy.i[1];
+ yy.d = (y - (t - twom32)) + twom64;
+ xy3 = yy.i[1];
+ z0 = (zz.i[0] & 0xfffff) | 0x100000;
+ z1 = zz.i[1];
+ z2 = z3 = 0;
+
+ /*
+ * now x*y is represented by sxy, exy, and xy[0-3], 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 > 116) {
+ xy0 = xy1 = xy2 = 0;
+ xy3 = 1;
+ } else if (e >= 96) {
+ sticky = xy3 | xy2 | xy1 | ((xy0 << 1) << (127 - e));
+ xy3 = xy0 >> (e - 96);
+ if (sticky)
+ xy3 |= 1;
+ xy0 = xy1 = xy2 = 0;
+ } else if (e >= 64) {
+ sticky = xy3 | xy2 | ((xy1 << 1) << (95 - e));
+ xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
+ if (sticky)
+ xy3 |= 1;
+ xy2 = xy0 >> (e - 64);
+ xy0 = xy1 = 0;
+ } else if (e >= 32) {
+ sticky = xy3 | ((xy2 << 1) << (63 - e));
+ xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
+ if (sticky)
+ xy3 |= 1;
+ xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
+ xy1 = xy0 >> (e - 32);
+ xy0 = 0;
+ } else if (e) {
+ sticky = (xy3 << 1) << (31 - e);
+ xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
+ if (sticky)
+ xy3 |= 1;
+ 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;
+ if (xy3 == 0)
+ if (++xy2 == 0)
+ if (++xy1 == 0)
+ xy0++;
+ }
+
+ /* add, propagating carries */
+ z3 += xy3;
+ 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 z2 */
+ if (ez < 1) {
+ /* result is tiny; shift right until exponent is within range */
+ e = 1 - ez;
+ if (e > 56) {
+ z2 = 1; /* result can't be exactly zero */
+ z0 = z1 = 0;
+ } else if (e >= 32) {
+ sticky = z3 | z2 | ((z1 << 1) << (63 - e));
+ z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
+ if (sticky)
+ z2 |= 1;
+ z1 = z0 >> (e - 32);
+ z0 = 0;
+ } else {
+ sticky = z3 | (z2 << 1) << (31 - e);
+ z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
+ if (sticky)
+ z2 |= 1;
+ z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
+ z0 >>= e;
+ }
+ ez = 1;
+ } else if (z0 >= 0x200000) {
+ /* carry out; shift right by one */
+ sticky = (z2 & 1) | z3;
+ z2 = (z2 >> 1) | (z1 << 31);
+ if (sticky)
+ z2 |= 1;
+ z1 = (z1 >> 1) | (z0 << 31);
+ z0 >>= 1;
+ ez++;
+ } else {
+ if (z0 < 0x100000 && (z0 | z1 | z2 | z3) != 0) {
+ /*
+ * borrow/cancellation; shift left as much as
+ * exponent allows
+ */
+ while (!(z0 | (z1 & 0xffe00000)) && ez >= 33) {
+ z0 = z1;
+ z1 = z2;
+ z2 = z3;
+ z3 = 0;
+ ez -= 32;
+ }
+ while (z0 < 0x100000 && ez > 1) {
+ z0 = (z0 << 1) | (z1 >> 31);
+ z1 = (z1 << 1) | (z2 >> 31);
+ z2 = (z2 << 1) | (z3 >> 31);
+ z3 <<= 1;
+ ez--;
+ }
+ }
+ if (z3)
+ z2 |= 1;
+ }
+
+ /* get the rounding mode and clear current exceptions */
+ rm = fsr >> 30;
+ fsr &= ~FSR_CEXC;
+
+ /* strip off the integer bit, if there is one */
+ ibit = z0 & 0x100000;
+ if (ibit)
+ z0 -= 0x100000;
+ else {
+ ez = 0;
+ if (!(z0 | z1 | z2)) { /* exact zero */
+ zz.i[0] = rm == FSR_RM ? 0x80000000 : 0;
+ zz.i[1] = 0;
+ __fenv_setfsr32(&fsr);
+ return (zz.d);
+ }
+ }
+
+ /*
+ * 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 (z2) {
+ fsr |= FSR_NXC;
+
+ /* decide whether to round the fraction up */
+ if (rm == FSR_RP || (rm == FSR_RN && (z2 > 0x80000000u ||
+ (z2 == 0x80000000u && (z1 & 1))))) {
+ /* round up and renormalize if necessary */
+ if (++z1 == 0) {
+ if (++z0 == 0x100000) {
+ z0 = 0;
+ ez++;
+ }
+ }
+ }
+ }
+
+ /* check for under/overflow */
+ if (ez >= 0x7ff) {
+ if (rm == FSR_RN || rm == FSR_RP) {
+ zz.i[0] = sz | 0x7ff00000;
+ zz.i[1] = 0;
+ } else {
+ zz.i[0] = sz | 0x7fefffff;
+ zz.i[1] = 0xffffffff;
+ }
+ fsr |= FSR_OFC | FSR_NXC;
+ } else {
+ zz.i[0] = sz | (ez << 20) | z0;
+ zz.i[1] = z1;
+
+ /*
+ * !ibit => exact result was tiny before rounding,
+ * z2 nonzero => result delivered is inexact
+ */
+ if (!ibit) {
+ if (z2)
+ 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.d);
+}
+
+#elif defined(__x86)
+
+#if defined(__amd64)
+#define NI 4
+#else
+#define NI 3
+#endif
+
+/*
+ * fma for x86: 64-bit double precision, little-endian
+ */
+double
+__fma(double x, double y, double z) {
+ union {
+ unsigned i[NI];
+ long double e;
+ } xx, yy, zz;
+ long double xe, ye, xhi, xlo, yhi, ylo;
+ int ex, ey, ez;
+ unsigned cwsw, oldcwsw, rm;
+
+ /* convert the operands to double extended */
+ xx.e = (long double) x;
+ yy.e = (long double) y;
+ zz.e = (long double) z;
+
+ /* extract the exponents of the arguments */
+ 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 == 0 || ey == 0)
+ /* x or y is inf, nan, or zero */
+ return ((double) (xx.e * yy.e + zz.e));
+
+ if (ez >= 0x7fff) /* z is inf or nan */
+ return ((double) (xx.e + zz.e));
+ /* avoid spurious inexact in x * y */
+
+ /*
+ * save the control and status words, mask all exceptions, and
+ * set rounding to 64-bit precision and to-nearest
+ */
+ __fenv_getcwsw(&oldcwsw);
+ cwsw = (oldcwsw & 0xf0c0ffff) | 0x033f0000;
+ __fenv_setcwsw(&cwsw);
+
+ /* multiply x*y to 106 bits */
+ xe = xx.e;
+ xx.i[0] = 0;
+ xhi = xx.e; /* hi 32 bits */
+ xlo = xe - xhi; /* lo 21 bits */
+ ye = yy.e;
+ yy.i[0] = 0;
+ yhi = yy.e;
+ ylo = ye - yhi;
+ xe = xe * ye;
+ ye = ((xhi * yhi - xe) + xhi * ylo + xlo * yhi) + xlo * ylo;
+
+ /* distill the sum of xe, ye, and z */
+ xhi = ye + zz.e;
+ yhi = xhi - ye;
+ xlo = (zz.e - yhi) + (ye - (xhi - yhi));
+ /* now (xhi,xlo) = ye + z */
+
+ yhi = xe + xhi;
+ ye = yhi - xe;
+ ylo = (xhi - ye) + (xe - (yhi - ye)); /* now (yhi,ylo) = xe + xhi */
+
+ xhi = xlo + ylo;
+ xe = xhi - xlo;
+ xlo = (ylo - xe) + (xlo - (xhi - xe)); /* now (xhi,xlo) = xlo + ylo */
+
+ yy.e = yhi + xhi;
+ ylo = (yhi - yy.e) + xhi; /* now (yy.e,ylo) = xhi + yhi */
+
+ if (yy.i[1] != 0) { /* yy.e is nonzero */
+ /* perturb yy.e if its least significant 10 bits are zero */
+ if (!(yy.i[0] & 0x3ff)) {
+ xx.e = ylo + xlo;
+ if (xx.i[1] != 0) {
+ xx.i[2] = (xx.i[2] & 0x8000) |
+ ((yy.i[2] & 0x7fff) - 63);
+ xx.i[1] = 0x80000000;
+ xx.i[0] = 0;
+ yy.e += xx.e;
+ }
+ }
+ } else {
+ /* set sign of zero result according to rounding direction */
+ rm = oldcwsw & 0x0c000000;
+ yy.i[2] = ((rm == FCW_RM)? 0x8000 : 0);
+ }
+
+ /*
+ * restore the control and status words and convert the result
+ * to double
+ */
+ __fenv_setcwsw(&oldcwsw);
+ return ((double) yy.e);
+}
+
+#else
+#error Unknown architecture
+#endif
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