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-rw-r--r--sysdeps/powerpc/q_addsub.c549
1 files changed, 549 insertions, 0 deletions
diff --git a/sysdeps/powerpc/q_addsub.c b/sysdeps/powerpc/q_addsub.c
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+/* Add or subtract two 128-bit floating point values. C prototype.
+ Copyright (C) 1997 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 of the
+ License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <quad_float.h>
+
+/* Add 'a' to 'b' and put the result in 'result', but treat a[0]=axx,
+ b[0]=bxx. bxx differs from b[0] only in the high bit, similarly axx. */
+/* Exceptions to raise:
+ - Invalid (SNaN)
+ - Invalid (Inf-Inf)
+ - Overflow
+ - Underflow
+ - Inexact
+ */
+
+/* Handle cases where exponent of a or b is maximum. */
+static void
+handle_max_exponent(unsigned result[4],
+ const unsigned a[4], const unsigned b[4],
+ const unsigned axx, /* Treat as a[0]. */
+ const unsigned bxx, /* Treat as b[0]. */
+ const unsigned ax, /* axx >> 16 & 0x7fff. */
+ const unsigned bx) /* bxx >> 16 & 0x7fff. */
+{
+ int ax_ismax, bx_ismax;
+ unsigned a1,a2,a3, b1,b2,b3;
+ int a_zeromant, b_zeromant;
+
+ ax_ismax = ax == 0x7fff;
+ bx_ismax = bx == 0x7fff;
+
+ assert(ax_ismax || bx_ismax);
+
+ a1 = a[1]; a2 = a[2]; a3 = a[3];
+ b1 = b[1]; b2 = b[2]; b3 = b[3];
+
+ a_zeromant = (axx & 0xffff | a1 | a2 | a3) == 0;
+ b_zeromant = (bxx & 0xffff | b1 | b2 | b3) == 0;
+
+ /* Deal with SNaNs. */
+ if ( ax_ismax && !a_zeromant && (axx & 0x8000) == 0
+ || bx_ismax && !b_zeromant && (bxx & 0x8000) == 0)
+ {
+ set_fpscr_bit(FPSCR_VXSNAN);
+ axx |= 0x8000; /* Demote the SNaN to a QNaN (whichever of */
+ bxx |= 0x8000; /* a or b it was). */
+ }
+ /* Deal with Inf-Inf. */
+ else if (a_zeromant && b_zeromant && (axx ^ bxx) == 0x80000000)
+ {
+ set_fpscr_bit(FPSCR_VXISI);
+ bxx |= 0x8000; /* Return an appropriate QNaN. */
+ }
+
+ /* Return the lexicographically larger of a or b, ignoring the sign
+ bits. */
+ if ((axx & 0x7fffffff) > (bxx & 0x7fffffff)) goto return_a;
+ else if ((axx & 0x7fffffff) < (bxx & 0x7fffffff)) goto return_b;
+ else if (a1 > b1) goto return_a;
+ else if (a1 < b1) goto return_b;
+ else if (a2 > b2) goto return_a;
+ else if (a2 < b2) goto return_b;
+ else if (a3 > b3) goto return_a; /* I've clearly been writing too */
+ else if (a3 < b3) goto return_b; /* much Fortran... */
+
+ /* If they are equal except for the sign bits, return 'b'. */
+
+return_b:
+ result[0] = bxx; result[1] = b1; result[2] = b2; result[3] = b3;
+ return;
+
+return_a:
+ result[0] = axx; result[1] = a1; result[2] = a2; result[3] = a3;
+ return;
+}
+
+/* Renormalise and output a FP number. */
+static void
+renormalise_value(unsigned result[4],
+ const unsigned axx,
+ unsigned ax,
+ unsigned r0,
+ unsigned r1,
+ unsigned r2,
+ unsigned r3)
+{
+ int rshift;
+ if (r0 != 0 || cntlzw(a1) < 16 || 32 > ax-1)
+ {
+ rshift = cntlzw(r0)-15 + (-(cntlzw(r0) >> 5) & cntlzw(a1));
+ assert(rshift < 32);
+ if (rshift > ax-1)
+ {
+ ax--;
+ rshift = ax;
+ }
+
+ result[0] = (axx & 0x80000000
+ | ax-rshift << 16
+ | r0 << rshift & 0xffff
+ | a1 >> 32-rshift & 0xffff);
+ result[1] = a1 << rshift | a2 >> 32-rshift;
+ result[2] = a2 << rshift | a3 >> 32-rshift;
+ result[3] = a3 << rshift;
+ return;
+ }
+ result[3] = 0;
+ /* Special case for zero. */
+ if (a1 == 0 && a2 == 0 && a3 == 0)
+ {
+ result[0] = axx & 0x80000000;
+ result[1] = result[2] = 0;
+ return;
+ }
+ while (a1 != 0 && cntlzw(a2) >= 16 && 64 <= ax-1)
+ {
+ ax -= 32;
+ a1 = a2; a2 = a3; a3 = 0;
+ }
+ rshift = cntlzw(a1)-15 + (-(cntlzw(a1) >> 5) & cntlzw(a2));
+ assert(rshift < 32);
+ if (rshift > ax-1-32)
+ {
+ ax--;
+ rshift = ax-32;
+ }
+
+ result[0] = (axx & 0x80000000
+ | ax-rshift-32 << 16
+ | a1 << rshift & 0xffff
+ | a2 >> 32-rshift & 0xffff);
+ result[1] = a2 << rshift | a3 >> 32-rshift;
+ result[2] = a3 << rshift;
+ return;
+}
+
+/* Handle the case where one or both numbers are denormalised or zero.
+ This case almost never happens, so we don't slow the main code
+ with it. */
+static void
+handle_min_exponent(unsigned result[4],
+ const unsigned a[4], const unsigned b[4],
+ const unsigned axx, /* Treat as a[0]. */
+ const unsigned bxx, /* Treat as b[0]. */
+ const unsigned ax, /* axx >> 16 & 0x7fff. */
+ const unsigned bx) /* bxx >> 16 & 0x7fff. */
+{
+ int ax_denorm, bx_denorm;
+ unsigned a1,a2,a3, b1,b2,b3;
+ int a_zeromant, b_zeromant;
+
+ ax_denorm = ax == 0;
+ bx_denorm = bx == 0;
+
+ assert(ax_denorm || bx_denorm);
+
+ a1 = a[1]; a2 = a[2]; a3 = a[3];
+ b1 = b[1]; b2 = b[2]; b3 = b[3];
+
+
+}
+
+/* Add a+b+cin modulo 2^32, put result in 'r' and carry in 'cout'. */
+#define addc(r,cout,a,b,cin) \
+ do { \
+ unsigned long long addc_tmp = (a)+(b)+(cin);
+ (cout) = addc_tmp >> 32;
+ (r) = addc_tmp;
+ }
+
+/* Calculate a+~b+cin modulo 2^32, put result in 'r' and carry in 'cout'. */
+#define subc(r,cout,a,b,cin) \
+ do { \
+ unsigned long long addc_tmp = (a)-(b)+(cin)-1;
+ (cout) = addc_tmp >> 63;
+ (r) = addc_tmp;
+ }
+
+/* Handle the case where both exponents are the same. This requires quite
+ a different algorithm than the general case. */
+static void
+handle_equal_exponents(unsigned result[4],
+ const unsigned a[4], const unsigned b[4],
+ const unsigned axx, /* Treat as a[0]. */
+ const unsigned bxx, /* Treat as b[0]. */
+ unsigned ax) /* [ab]xx >> 16 & 0x7fff. */
+{
+ unsigned a1,a2,a3, b1,b2,b3;
+ int roundmode;
+ unsigned carry, r0;
+
+ a1 = a[1]; a2 = a[2]; a3 = a[3];
+ b1 = b[1]; b2 = b[2]; b3 = b[3];
+
+ if ((int)(axx ^ bxx) >= 0)
+ {
+ int roundmode;
+
+ /* Adding. */
+ roundmode = fegetround();
+
+ /* What about overflow? */
+ if (ax == 0x7ffe)
+ {
+ /* Oh no! Too big! */
+ /* Result:
+ rounding result
+ -------- ------
+ nearest return Inf with sign of a,b
+ zero return nearest possible non-Inf value with
+ sign of a,b
+ +Inf return +Inf if a,b>0, otherwise return
+ value just before -Inf.
+ -Inf return +Inf if a,b>0, otherwise return
+ value just before -Inf.
+ */
+ set_fpscr_bit(FPSCR_OX);
+ /* Overflow always produces inexact result. */
+ set_fpscr_bit(FPSCR_XX);
+
+ if ( roundmode == FE_TONEAREST
+ || roundmode == FE_UPWARD && (int)axx >= 0
+ || roundmode == FE_DOWNWARD && (int)axx < 0)
+ {
+ result[3] = result[2] = result[1] = 0;
+ result[0] = axx & 0xffff0000 | 0x7fff0000;
+ }
+ else
+ {
+ result[3] = result[2] = result[1] = 0xffffffff;
+ result[0] = axx & 0xfffe0000 | 0x7ffeffff;
+ }
+ return;
+ }
+
+ /* We need to worry about rounding/inexact here. Do it like this: */
+ if (a3 + b3 & 1)
+ {
+ /* Need to round. Upwards? */
+ set_fpscr_bit(FPSCR_XX);
+ carry = ( roundmode == FE_NEAREST && (a3 + b3 & 2) != 0
+ || roundmode == FE_UPWARD && (int)axx >= 0
+ || roundmode == FE_DOWNWARD && (int)axx < 0);
+ }
+ else
+ carry = 0; /* Result will be exact. */
+
+ /* Perform the addition. */
+ addc(a3,carry,a3,b3,carry);
+ addc(a2,carry,a2,b2,carry);
+ addc(a1,carry,a1,b1,carry);
+ r0 = (axx & 0xffff) + (bxx & 0xffff) + carry;
+
+ /* Shift right by 1. */
+ result[3] = a3 >> 1 | a2 << 31;
+ result[2] = a2 >> 1 | a1 << 31;
+ result[1] = a1 >> 1 | r0 << 31;
+ /* Exponent of result is exponent of inputs plus 1.
+ Sign of result is common sign of inputs. */
+ result[0] = r0 >> 1 & 0xffff | axx + 0x10000 & 0xffff0000;
+ }
+ else
+ {
+ /* Subtracting. */
+
+ /* Perform the subtraction, a-b. */
+ subc(a3,carry,a3,b3,0);
+ subc(a2,carry,a2,b2,carry);
+ subc(a1,carry,a1,b1,carry);
+ subc(r0,carry,a0&0xffff,b0&0xffff,carry);
+
+ /* Maybe we should have calculated b-a... */
+ if (carry)
+ {
+ subc(a3,carry,0,a3,0);
+ subc(a2,carry,0,a2,carry);
+ subc(a1,carry,0,a1,carry);
+ subc(r0,carry,0,r0,carry);
+ axx ^= 0x80000000;
+ }
+
+ renormalise_value(result, axx, ax, r0, a1, a2, a3);
+ }
+}
+
+
+static void
+add(unsigned result[4], const unsigned a[4], const unsigned b[4],
+ unsigned axx, unsigned bxx)
+{
+ int ax, bx, diff, carry;
+ unsigned a0,a1,a2,a3, b0,b1,b2,b3,b4, sdiff;
+
+ ax = axx >> 16 & 0x7fff;
+ bx = bxx >> 16 & 0x7fff;
+
+ /* Deal with NaNs and Inf. */
+ if (ax == 0x7fff || bx == 0x7fff)
+ {
+ handle_max_exponent(result, a, b, axx, bxx, ax, bx);
+ return;
+ }
+ /* Deal with denorms and zero. */
+ if (ax == 0 || bx == 0)
+ {
+ handle_min_exponent(result, a, b, axx, bxx, ax, bx);
+ return;
+ }
+ /* Finally, one special case, when both exponents are equal. */
+ if (ax == bx)
+ {
+ handle_equal_exponents(result, a, b, axx, bxx, ax);
+ return;
+ }
+
+ sdiff = axx ^ bxx;
+ /* Swap a and b if b has a larger magnitude than a, so that a will have
+ the larger magnitude. */
+ if (ax < bx)
+ {
+ const unsigned *t;
+ t = b; b = a; a = t;
+ diff = bx - ax;
+ ax = bx;
+ axx = bxx;
+ }
+ else
+ diff = ax - bx;
+
+ a0 = a[0] & 0xffff | 0x10000; a1 = a[1]; a2 = a[2]; a3 = a[3];
+ b0 = b[0] & 0xffff | 0x10000; b1 = b[1]; b2 = b[2]; b3 = b[3];
+ if (diff < 32)
+ {
+ b4 = b3 << 32-diff;
+ b3 = b3 >> diff | b2 << 32-biff;
+ b2 = b2 >> diff | b1 << 32-diff;
+ b1 = b1 >> diff | b0 << 32-diff;
+ b0 = b0 >> diff;
+ }
+ else if (diff < 64)
+ {
+ diff -= 32;
+ b4 = b3 & 1 | b3 >> (diff == 32) | b2 << 32-biff;
+ b3 = b2 >> diff | b1 << 32-diff;
+ b2 = b1 >> diff | b0 << 32-diff;
+ b1 = b0 >> diff;
+ b0 = 0;
+ }
+ else if (diff < 96)
+ {
+ b4 = b2 | b3 | b1 << 32-diff;
+ b3 = b1 >> diff | b0 << 32-diff;
+ b2 = b0 >> diff;
+ b1 = b0 = 0;
+ }
+ else if (diff < 128)
+ {
+ b4 = b1 | b2 | b3 | b0 << 32-diff;
+ b3 = b0 >> diff;
+ b2 = b1 = b0 = 0;
+ }
+ else
+ {
+ b4 = b0|b1|b2|b3;
+ b3 = b2 = b1 = b0 = 0;
+ }
+
+ /* Now, two cases: one for addition, one for subtraction. */
+ if ((int)sdiff >= 0)
+ {
+ /* Addition. */
+
+ /*
+
+ /* Perform the addition. */
+ addc(a3,carry,a3,b3,0);
+ addc(a2,carry,a2,b2,carry);
+ addc(a1,carry,a1,b1,carry);
+ addc(a0,carry,a0,b0,carry);
+
+
+
+ if (a0 & 0x20000)
+ {
+ /* Need to renormalise by shifting right. */
+ /* Shift right by 1. */
+ b4 = b4 | a3 << 31;
+ a3 = a3 >> 1 | a2 << 31;
+ a2 = a2 >> 1 | a1 << 31;
+ result[1] = a1 >> 1 | r0 << 31;
+ /* Exponent of result is exponent of inputs plus 1.
+ Sign of result is common sign of inputs. */
+ result[0] = r0 >> 1 & 0xffff | axx + 0x10000 & 0xffff0000;
+ }
+
+
+ }
+ else
+ {
+ /* Subtraction. */
+
+ }
+}
+
+/* Add the absolute values of two 128-bit floating point values,
+ give the result the sign of one of them. The only exception this
+ can raise is for SNaN. */
+static void
+aadd(unsigned result[4], const unsigned a[4], const unsigned b[4])
+{
+ unsigned ax, bx, xd;
+ const unsigned *sml;
+ unsigned t0,t1,t2,t3,tx, s0,s1,s2,s3,s4, carry;
+ int rmode, xdelta, shift;
+
+ ax = a[0] >> 16 & 0x7fff;
+ bx = b[0] >> 16 & 0x7fff;
+
+ /* Deal with . */
+ if (ax == 0x7fff)
+ {
+ t0 = a[0]; t1 = a[1]; t2 = a[2]; t3 = a[3];
+ /* Check for SNaN. */
+ if ((t0 & 0x8000) == 0
+ && (t0 & 0x7fff | t1 | t2 | t3) != 0)
+ set_fpscr_bit(FPSCR_VXSNAN);
+ /* Return b. */
+ result[0] = t0; result[1] = t1; result[2] = t2; result[3] = t3;
+ return;
+ }
+ /* Deal with b==Inf or b==NaN. */
+ if (bx == 0x7fff)
+ {
+ t0 = b[0]; t1 = b[1]; t2 = b[2]; t3 = b[3];
+ /* Check for SNaN. */
+ if ((t0 & 0x8000) == 0
+ && (t0 & 0x7fff | t1 | t2 | t3) != 0)
+ set_fpscr_bit(FPSCR_VXSNAN);
+ /* Return b. */
+ result[0] = t0; result[1] = t1; result[2] = t2; result[3] = t3;
+ return;
+ }
+
+ /* Choose the larger of the two to be 't', and the smaller to be 's'. */
+ if (ax > bx)
+ {
+ t0 = a[0] & 0xffff | (ax != 0) << 16;
+ t1 = a[1]; t2 = a[2]; t3 = a[3]; tx = ax;
+ s0 = b[0] & 0xffff | (bx != 0) << 16;
+ s1 = b[1]; s2 = b[2]; s3 = b[3];
+ xd = ax-bx;
+ }
+ else
+ {
+ t0 = b[0] & 0xffff | (bx != 0) << 16;
+ t1 = b[1]; t2 = b[2]; t3 = b[3]; tx = bx;
+ s0 = a[0] & 0xffff | (ax != 0) << 16;
+ s1 = a[1]; s2 = a[2]; s3 = a[3];
+ sml = a;
+ xd = bx-ax;
+ }
+
+ /* Shift 's2' right by 'xd' bits. */
+ switch (xd >> 5)
+ {
+ case 0:
+ s4 = 0;
+ break;
+ case 1:
+ s4 = s3; s3 = s2; s2 = s1; s1 = s0; s0 = 0;
+ break;
+ case 2:
+ s4 = s2 | s3 != 0;
+ s3 = s1; s2 = s0; s1 = s0 = 0;
+ break;
+ case 3:
+ s4 = s1 | (s3|s2) != 0;
+ s3 = s0; s2 = s1 = s0 = 0;
+ break;
+ default:
+ s4 = s0 | (s3|s2|s1) != 0;
+ s3 = s2 = s1 = s0 = 0;
+ }
+ xd = xd & 0x1f;
+ if (xd != 0)
+ {
+ s4 = s4 >> xd | (s4 << 32-xd) != 0 | s3 << 32-xd;
+ s3 = s3 >> xd | s2 << 32-xd;
+ s2 = s2 >> xd | s1 << 32-xd;
+ s1 = s1 >> xd | s0 << 32-xd;
+ s0 = s0 >> xd;
+ }
+
+ /* Do the addition. */
+#define addc(r,cout,a,b,cin) \
+ do { \
+ unsigned long long addc_tmp = (a)+(b)+(cin);
+ (cout) = addc_tmp >> 32;
+ (r) = addc_tmp;
+ }
+ addc(t3,carry,t3,s3,0);
+ addc(t2,carry,t2,s2,carry);
+ addc(t1,carry,t1,s1,carry);
+ t0 = t0 + s0 + carry;
+
+ /* Renormalise. */
+ xdelta = 15-cntlzw(t0);
+ if (tx + xdelta <= 0x7fff)
+ shift = xdelta;
+ else
+ {
+ }
+}
+
+/* Add two 128-bit floating point values. */
+void
+__q_add(unsigned result[4], const unsigned a[4], const unsigned b[4])
+{
+ if ((a[0] ^ b[0]) >= 0)
+ aadd(result, a, b);
+ else
+ asubtract(result, a, b);
+}
+
+/* Subtract two 128-bit floating point values. */
+void
+__q_sub(unsigned result[4], const unsigned a[4], const unsigned b[4])
+{
+ if ((a[0] ^ b[0]) < 0)
+ aadd(result, a, b);
+ else
+ asubtract(result, a, b);
+}
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