{"id":43283,"date":"2014-12-29T07:00:00","date_gmt":"2014-12-29T07:00:00","guid":{"rendered":"https:\/\/blogs.msdn.microsoft.com\/oldnewthing\/2014\/12\/29\/integer-signum-in-sse\/"},"modified":"2014-12-29T07:00:00","modified_gmt":"2014-12-29T07:00:00","slug":"integer-signum-in-sse","status":"publish","type":"post","link":"https:\/\/devblogs.microsoft.com\/oldnewthing\/20141229-00\/?p=43283","title":{"rendered":"Integer signum in SSE"},"content":{"rendered":"

\nThe signum function is defined as follows:\n<\/p>\n\n\n\n\n
signum(x<\/var>) = <\/td>\n−1 <\/td>\nif x<\/var> < 0<\/td>\n<\/tr>\n
signum(x<\/var>) = <\/td>\n0 <\/td>\nif x<\/var> = 0<\/td>\n<\/tr>\n
signum(x<\/var>) = <\/td>\n+1 <\/td>\nif x<\/var> > 0<\/td>\n<\/tr>\n<\/table>\n

\nThere are a couple of ways of calculating this in SSE integers.\n<\/p>\n

\nOne way is to convert the C idiom\n<\/p>\n

\nint signum(int x) { return (x > 0) - (x < 0); }\n<\/pre>\n
\nThe SSE translation of this is mostly straightforward.\nThe quirk is that the SSE comparison functions return −1\nto indicate true<\/code>,\nwhereas C uses +1 to represent true<\/code>.\nBut this is easy to take into account:\n<\/p>\n\n\n\n
x<\/var> > 0<\/td>\n ⇔ <\/td>\n − pcmpgt(x<\/var>, 0)<\/td>\n<\/tr>\n
x<\/var> < 0<\/td>\n ⇔ <\/td>\n − pcmpgt(0, x<\/var>)<\/td>\n<\/tr>\n<\/table>\n
\nSubstituting this into the original signum<\/code> function,\nwe get\n<\/p>\n\n\n\n\n\n
signum(x<\/var>) = <\/td>\n(x<\/var> > 0)<\/td>\n − <\/td>\n(x<\/var> < 0)<\/td>\n<\/tr>\n
= <\/td>\n− pcmpgt(x<\/var>, 0)<\/td>\n − <\/td>\n− pcmpgt(0, x<\/var>)<\/td>\n<\/tr>\n
= <\/td>\n− pcmpgt(x<\/var>, 0)<\/td>\n + <\/td>\npcmpgt(0, x<\/var>)<\/td>\n<\/tr>\n
= <\/td>\npcmpgt(0, x<\/var>)<\/td>\n − <\/td>\npcmpgt(x<\/var>, 0)<\/td>\n<\/tr>\n<\/table>\n
\nIn assembly:\n<\/p>\n
\n        ; assume x is in xmm0\n        pxor    xmm1, xmm1\n        pxor    xmm2, xmm2\n        pcmpgtw xmm1, xmm0 ; xmm1 = pcmpgt(0, x)\n        pcmpgtw xmm0, xmm2 ; xmm0 = pcmpgt(x, 0)\n        psubw   xmm0, xmm1 ; xmm0 = signum\n        ; answer is in xmm0\n<\/pre>\n
\nWith intrinsics:\n<\/p>\n
\n__m128i signum16(__m128i x)\n{\n    return _mm_sub_epi16(_mm_cmpgt_epi16(_mm_setzero_si128(), x),\n                         _mm_cmpgt_epi16(x, _mm_setzero_si128()));\n}\n<\/pre>\n
\nThis pattern extends mutatus mutandis<\/i> to\nsignum8<\/code>,\nsignum32<\/code>,\nand\nsignum64<\/code>.\n<\/p>\n
\nAnother solution is to use the signed minimum and maximum opcodes,\nusing the formula\n<\/p>\n\n\n
signum(x<\/var>) = min(max(x<\/var>, −1), +1)<\/td>\n<\/tr>\n<\/table>\n
\nIn assembly:\n<\/p>\n
\n        ; assume x is in xmm0\n        pcmpgtw<\/a> xmm1, xmm1 ; xmm1 = -1 in all lanes\n        pmaxsw  xmm0, xmm1\n        psrlw   xmm1, 15   ; xmm1 = +1 in all lanes\n        pminsw  xmm0, xmm1\n        ; answer is in xmm0\n<\/pre>\n
\nWith intrinsics:\n<\/p>\n
\n__m128i signum16(__m128i x)\n{\n    \/\/ alternatively: minusones = _mm_set1_epi16(-1);\n    __m128i minusones = _mm_cmpeq_epi16(_mm_setzero_si128(),\n                                        _mm_setzero_si128());\n    x = _mm_max_epi16(x, minusones);\n    \/\/ alternatively: ones = _mm_set1_epi16(1);\n    __m128i ones = _mm_srl_epi16(minusones, 15);\n    x = _mm_min_epi16(x, ones);\n    return x;\n}\n<\/pre>\n
\nThe catch here is that\nSSE2 supports only 16-bit signed minimum and maximum;\nto get other bit sizes, you need to bump up to SSE4.\nBut if you’re going to do that, you may as well use the\npsign<\/code> instruction.\nIn assembly:\n<\/p>\n
\n        ; assume x is in xmm0\n        pcmpgtw<\/a> xmm1, xmm1 ; xmm1 = -1 in all lanes\n        psrlw   xmm1, 15   ; xmm1 = +1 in all lanes\n        psignw  xmm1, xmm0 ; apply sign of x to xmm1\n        ; answer is in xmm1\n<\/pre>\n
\nWith intrinsics:\n<\/p>\n
\n__m128i signum16(__m128i x)\n{\n    \/\/ alternatively: ones = _mm_set1_epi16(1);\n    __m128i minusones = _mm_cmpeq_epi16(_mm_setzero_si128(),\n                                        _mm_setzero_si128());\n    __m128i ones = _mm_srl_epi16(minusones, 15);\n    return _mm_sign_epi16(ones, x);\n}\n<\/pre>\n
\nThe psign<\/code> instruction applies the sign of its second\nargument to its first argument.\nWe load up the first argument\nwith the value +1<\/code> in all lanes,\nthen apply the sign of x<\/var>,\nwhich negates the value if the corresponding lane of x<\/var>\nis negative;\nsets the value to zero if the lane is zero,\nand leaves it alone if the corresponding lane is positive.<\/p>\n","protected":false},"excerpt":{"rendered":"
The signum function is defined as follows: signum(x) =  −1  if x < 0 signum(x) =  0  if x = 0 signum(x) =  +1  if x > 0 There are a couple of ways of calculating this in SSE integers. One way is to convert the C idiom int signum(int x) { return (x > […]<\/p>\n","protected":false},"author":1069,"featured_media":111744,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[25],"class_list":["post-43283","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-oldnewthing","tag-code"],"acf":[],"blog_post_summary":"
The signum function is defined as follows: signum(x) =  −1  if x < 0 signum(x) =  0  if x = 0 signum(x) =  +1  if x > 0 There are a couple of ways of calculating this in SSE integers. One way is to convert the C idiom int signum(int x) { return (x > […]<\/p>\n","_links":{"self":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/posts\/43283","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/users\/1069"}],"replies":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/comments?post=43283"}],"version-history":[{"count":0,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/posts\/43283\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/media\/111744"}],"wp:attachment":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/media?parent=43283"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/categories?post=43283"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/tags?post=43283"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}