3 /*-
4  * SPDX-License-Identifier: BSD-3-Clause
10  * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
16  * 1. Redistributions of source code must retain the above copyright
50  *	v = 2^n v1  *  v0
54  *	uv = 2^2n u1 v1  +  2^n u1 v0  +  2^n v1 u0  +  u0 v0
55  *	   = 2^2n u1 v1  +     2^n (u1 v0 + v1 u0)   +  u0 v0
58  * and add 2^n u0 v0 to the last term and subtract it from the middle.
62  *	         (2^n)    (u1 v0 - u1 v1 + u0 v1 - u0 v0)  +
63  *	       (2^n + 1)  (u0 v0)
68  *		 (2^n)    (u1 - u0) (v0 - v1)  +	[(u1-u0)... = mid]
69  *	       (2^n + 1)  (u0 v0)			[u0v0 = low]
71  * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
73  * of (u1 - u0) or (v0 - v1) may be negative.)
87  *	(2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
109 #define	v0	v.ul[L]  in __muldi3()  macro
113 	 * u1, u0, v1, and v0 will be directly accessible through the  in __muldi3()
119 		u.q = -a, negall = 1;  in __muldi3()
123 		v.q = -b, negall ^= 1;  in __muldi3()
129 		 * are small.  Here the product is just u0*v0.  in __muldi3()
131 		prod.q = __lmulq(u0, v0);  in __muldi3()
139 		low.q = __lmulq(u0, v0);  in __muldi3()
142 			negmid = 0, udiff = u1 - u0;  in __muldi3()
144 			negmid = 1, udiff = u0 - u1;  in __muldi3()
145 		if (v0 >= v1)  in __muldi3()
146 			vdiff = v0 - v1;  in __muldi3()
148 			vdiff = v1 - v0, negmid ^= 1;  in __muldi3()
156 		prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +  in __muldi3()
160 	return (negall ? -prod.q : prod.q);  in __muldi3()
164 #undef v0  in __muldi3()
168  * Multiply two 2N-bit ints to produce a 4N-bit quad, where N is half
169  * the number of bits in an int (whatever that is---the code below
170  * does not care as long as quad.h does its part of the bargain---but
175  * we can get away with native multiplication---none of our input terms
176  * exceeds (UINT_MAX >> 1).
178  * Note that, for u_int l, the quad-precision result
187 	u_int u1, u0, v1, v0, udiff, vdiff, high, mid, low;  in __lmulq()  local
195 	v0 = LHALF(v);  in __lmulq()
197 	low = u0 * v0;  in __lmulq()
199 	/* This is the same small-number optimization as before. */  in __lmulq()
204 		udiff = u1 - u0, neg = 0;  in __lmulq()
206 		udiff = u0 - u1, neg = 1;  in __lmulq()
207 	if (v0 >= v1)  in __lmulq()
208 		vdiff = v0 - v1;  in __lmulq()
210 		vdiff = v1 - v0, neg ^= 1;  in __lmulq()
219 	/* if (neg) prod -= mid << N; else prod += mid << N; */  in __lmulq()
222 		prodl -= LHUP(mid);  in __lmulq()
223 		prodh -= HHALF(mid) + (prodl > was);  in __lmulq()
238 	/* return 4N-bit product */  in __lmulq()