/* 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 /* 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); }