From 05ac7b756868aec8ad7f23a22bb6f9473836b4df Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Thu, 29 Jan 2026 17:59:39 +0100 Subject: [PATCH] [SPCA] Add notes on rounding --- .../01_c/06_floating-point/04_rounding.tex | 5 +++++ semester3/spca/spca-summary.pdf | Bin 792390 -> 792856 bytes 2 files changed, 5 insertions(+) diff --git a/semester3/spca/parts/01_c/06_floating-point/04_rounding.tex b/semester3/spca/parts/01_c/06_floating-point/04_rounding.tex index 84956ba..298aba1 100644 --- a/semester3/spca/parts/01_c/06_floating-point/04_rounding.tex +++ b/semester3/spca/parts/01_c/06_floating-point/04_rounding.tex @@ -33,6 +33,11 @@ Based on these bits the rounding can be decided (we increment the rounded part i \end{align*} \drmvspace +It is notable that for round to even, the special condition only applies if the sticky bit is not set. If it is set, the round up condition is to be used. +An easy way to implement the condition is as follows +\mint{c}+(sticky && round) || (!sticky && round && guard)+ +This will be ever so slightly more efficient than a different order, as the computation will be stopped shorter if a condition is not fulfilled + \content{Example} Rounding $8$b precise results to $8$b precision floating point ($4$b mantissa): \renewcommand{\arraystretch}{1.2} diff --git a/semester3/spca/spca-summary.pdf b/semester3/spca/spca-summary.pdf index 118360d7339cdc107367321673595a461c0a147a..1c6b03162053878ea15962d79de732d72f33c6d8 100644 GIT binary patch delta 42160 zcmW(+V^k&X*X`ELwr$%r*{-R{HYdBAjmes9yPIvh$xXH~`Tf2BFVC~qUVEJf=fgSc zoP9=W*)kg0>M1b*EKO7x^^ia!jHR;Vc__@LbF3f)!ldp>ud&8xOoYuo!3(q#&k(}~ z0nJa+qeU8+rU+6`c)(%u7acxSUfFyTA^j~32}TEH9uS?-nG+r6X4}%YrRI5HWxWsi z<`wtouk&sb1KSrOY<-z1C%R-{GMf-RNM?gBKESAJgK6a&Ize97QYeP!Ig!o=$4bo* zLHEd}xuQtV#g$9T-LhRiDb#OiP;0W*?v)wC+^92*tQTb~pxJgjQhI>3W1U+|(__iD 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