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Date: Thu, 9 Jul 2020 00:21:21 +0200
From: Szabolcs Nagy <nsz@...t70.net>
To: musl@...ts.openwall.com
Subject: Re: [PATCH 0/4] new software sqrt, sqrtf and sqrtl
* Szabolcs Nagy <nsz@...t70.net> [2020-07-08 00:38:14 +0200]:
> +
> +/* returns a*b*2^-64 - e, with error 0 <= e < 3. */
> +static inline uint64_t mul64(uint64_t a, uint64_t b)
> +{
> + uint64_t ahi = a>>32;
> + uint64_t alo = a&0xffffffff;
> + uint64_t bhi = b>>32;
> + uint64_t blo = b&0xffffffff;
> + return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32);
> +}
...
> +/* returns a*b exactly. */
> +static inline u128 mul64_128(uint64_t a, uint64_t b)
> +{
> + u128 r;
> + uint64_t ahi = a>>32;
> + uint64_t alo = a&0xffffffff;
> + uint64_t bhi = b>>32;
> + uint64_t blo = b&0xffffffff;
> + uint64_t lo1 = ((ahi*blo)&0xffffffff) + ((alo*bhi)&0xffffffff) + (alo*blo>>32);
> + uint64_t lo2 = (alo*blo)&0xffffffff;
> + r.hi = ahi*bhi + (ahi*blo>>32) + (alo*bhi>>32) + (lo1>>32);
> + r.lo = (lo1<<32) + lo2;
> + return r;
> +}
> +
> +/* returns a*b*2^-128 - e, with error 0 <= e < 3. */
> +static inline u128 mul128(u128 a, u128 b)
> +{
> + u128 hi = mul64_128(a.hi, b.hi);
> + u128 m1 = mul64_128(a.hi, b.lo);
> + u128 m2 = mul64_128(a.lo, b.hi);
> + return add64(add64(hi, m1.hi), m2.hi);
> +}
this is does not have to be this precise,
i should have spotted it earlier.
attached a fixed version, should be a bit
faster (and smaller unless -Os is used which
prevents inlining)
reran the tests, they still pass.
View attachment "0004-math-new-software-sqrtl.patch" of type "text/x-diff" (6828 bytes)
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