📄 rounding.dectest
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rmux506 multiply 12345 4 -> 49380
rmux507 multiply 12345 4.0001 -> 49382 Inexact Rounded
rmux508 multiply 12345 4.9 -> 60491 Inexact Rounded
rmux509 multiply 12345 4.99 -> 61602 Inexact Rounded
rmux510 multiply 12345 4.999 -> 61713 Inexact Rounded
rmux511 multiply 12345 4.9999 -> 61724 Inexact Rounded
rmux512 multiply 12345 5 -> 61725
rmux513 multiply 12345 5.0001 -> 61727 Inexact Rounded
rmux514 multiply 12345 5.001 -> 61738 Inexact Rounded
rmux515 multiply 12345 5.01 -> 61849 Inexact Rounded
rmux516 multiply 12345 12 -> 1.4814E+5 Rounded
rmux517 multiply 12345 13 -> 1.6049E+5 Inexact Rounded
rmux518 multiply 12355 12 -> 1.4826E+5 Rounded
rmux519 multiply 12355 13 -> 1.6062E+5 Inexact Rounded
-- [rmux516 & rmux518] can surprise
rounding: floor
rmux601 multiply 12345 1 -> 12345
rmux602 multiply 12345 1.0001 -> 12346 Inexact Rounded
rmux603 multiply 12345 1.001 -> 12357 Inexact Rounded
rmux604 multiply 12345 1.01 -> 12468 Inexact Rounded
rmux605 multiply 12345 1.1 -> 13579 Inexact Rounded
rmux606 multiply 12345 4 -> 49380
rmux607 multiply 12345 4.0001 -> 49381 Inexact Rounded
rmux608 multiply 12345 4.9 -> 60490 Inexact Rounded
rmux609 multiply 12345 4.99 -> 61601 Inexact Rounded
rmux610 multiply 12345 4.999 -> 61712 Inexact Rounded
rmux611 multiply 12345 4.9999 -> 61723 Inexact Rounded
rmux612 multiply 12345 5 -> 61725
rmux613 multiply 12345 5.0001 -> 61726 Inexact Rounded
rmux614 multiply 12345 5.001 -> 61737 Inexact Rounded
rmux615 multiply 12345 5.01 -> 61848 Inexact Rounded
rmux616 multiply 12345 12 -> 1.4814E+5 Rounded
rmux617 multiply 12345 13 -> 1.6048E+5 Inexact Rounded
rmux618 multiply 12355 12 -> 1.4826E+5 Rounded
rmux619 multiply 12355 13 -> 1.6061E+5 Inexact Rounded
rounding: ceiling
rmux701 multiply 12345 1 -> 12345
rmux702 multiply 12345 1.0001 -> 12347 Inexact Rounded
rmux703 multiply 12345 1.001 -> 12358 Inexact Rounded
rmux704 multiply 12345 1.01 -> 12469 Inexact Rounded
rmux705 multiply 12345 1.1 -> 13580 Inexact Rounded
rmux706 multiply 12345 4 -> 49380
rmux707 multiply 12345 4.0001 -> 49382 Inexact Rounded
rmux708 multiply 12345 4.9 -> 60491 Inexact Rounded
rmux709 multiply 12345 4.99 -> 61602 Inexact Rounded
rmux710 multiply 12345 4.999 -> 61713 Inexact Rounded
rmux711 multiply 12345 4.9999 -> 61724 Inexact Rounded
rmux712 multiply 12345 5 -> 61725
rmux713 multiply 12345 5.0001 -> 61727 Inexact Rounded
rmux714 multiply 12345 5.001 -> 61738 Inexact Rounded
rmux715 multiply 12345 5.01 -> 61849 Inexact Rounded
rmux716 multiply 12345 12 -> 1.4814E+5 Rounded
rmux717 multiply 12345 13 -> 1.6049E+5 Inexact Rounded
rmux718 multiply 12355 12 -> 1.4826E+5 Rounded
rmux719 multiply 12355 13 -> 1.6062E+5 Inexact Rounded
-- Power operator -----------------------------------------------------
rounding: down
rpox101 power 12345 -5 -> 3.4877E-21 Inexact Rounded
rpox102 power 12345 -4 -> 4.3056E-17 Inexact Rounded
rpox103 power 12345 -3 -> 5.3152E-13 Inexact Rounded
rpox104 power 12345 -2 -> 6.5617E-9 Inexact Rounded
rpox105 power 12345 -1 -> 0.000081004 Inexact Rounded
rpox106 power 12345 0 -> 1
rpox107 power 12345 1 -> 12345
rpox108 power 12345 2 -> 1.5239E+8 Inexact Rounded
rpox109 power 12345 3 -> 1.8813E+12 Inexact Rounded
rpox110 power 12345 4 -> 2.3225E+16 Inexact Rounded
rpox111 power 12345 5 -> 2.8671E+20 Inexact Rounded
rpox112 power 415 2 -> 1.7222E+5 Inexact Rounded
rpox113 power 75 3 -> 4.2187E+5 Inexact Rounded
rounding: half_down
rpox201 power 12345 -5 -> 3.4877E-21 Inexact Rounded
rpox202 power 12345 -4 -> 4.3056E-17 Inexact Rounded
rpox203 power 12345 -3 -> 5.3153E-13 Inexact Rounded
rpox204 power 12345 -2 -> 6.5617E-9 Inexact Rounded
rpox205 power 12345 -1 -> 0.000081004 Inexact Rounded
rpox206 power 12345 0 -> 1
rpox207 power 12345 1 -> 12345
rpox208 power 12345 2 -> 1.5240E+8 Inexact Rounded
rpox209 power 12345 3 -> 1.8814E+12 Inexact Rounded
rpox210 power 12345 4 -> 2.3225E+16 Inexact Rounded
rpox211 power 12345 5 -> 2.8672E+20 Inexact Rounded
rpox212 power 415 2 -> 1.7222E+5 Inexact Rounded
rpox213 power 75 3 -> 4.2187E+5 Inexact Rounded
rounding: half_even
rpox301 power 12345 -5 -> 3.4877E-21 Inexact Rounded
rpox302 power 12345 -4 -> 4.3056E-17 Inexact Rounded
rpox303 power 12345 -3 -> 5.3153E-13 Inexact Rounded
rpox304 power 12345 -2 -> 6.5617E-9 Inexact Rounded
rpox305 power 12345 -1 -> 0.000081004 Inexact Rounded
rpox306 power 12345 0 -> 1
rpox307 power 12345 1 -> 12345
rpox308 power 12345 2 -> 1.5240E+8 Inexact Rounded
rpox309 power 12345 3 -> 1.8814E+12 Inexact Rounded
rpox310 power 12345 4 -> 2.3225E+16 Inexact Rounded
rpox311 power 12345 5 -> 2.8672E+20 Inexact Rounded
rpox312 power 415 2 -> 1.7222E+5 Inexact Rounded
rpox313 power 75 3 -> 4.2188E+5 Inexact Rounded
rounding: half_up
rpox401 power 12345 -5 -> 3.4877E-21 Inexact Rounded
rpox402 power 12345 -4 -> 4.3056E-17 Inexact Rounded
rpox403 power 12345 -3 -> 5.3153E-13 Inexact Rounded
rpox404 power 12345 -2 -> 6.5617E-9 Inexact Rounded
rpox405 power 12345 -1 -> 0.000081004 Inexact Rounded
rpox406 power 12345 0 -> 1
rpox407 power 12345 1 -> 12345
rpox408 power 12345 2 -> 1.5240E+8 Inexact Rounded
rpox409 power 12345 3 -> 1.8814E+12 Inexact Rounded
rpox410 power 12345 4 -> 2.3225E+16 Inexact Rounded
rpox411 power 12345 5 -> 2.8672E+20 Inexact Rounded
rpox412 power 415 2 -> 1.7223E+5 Inexact Rounded
rpox413 power 75 3 -> 4.2188E+5 Inexact Rounded
rounding: up
rpox501 power 12345 -5 -> 3.4878E-21 Inexact Rounded
rpox502 power 12345 -4 -> 4.3057E-17 Inexact Rounded
rpox503 power 12345 -3 -> 5.3153E-13 Inexact Rounded
rpox504 power 12345 -2 -> 6.5618E-9 Inexact Rounded
rpox505 power 12345 -1 -> 0.000081005 Inexact Rounded
rpox506 power 12345 0 -> 1
rpox507 power 12345 1 -> 12345
rpox508 power 12345 2 -> 1.5240E+8 Inexact Rounded
rpox509 power 12345 3 -> 1.8814E+12 Inexact Rounded
rpox510 power 12345 4 -> 2.3226E+16 Inexact Rounded
rpox511 power 12345 5 -> 2.8672E+20 Inexact Rounded
rpox512 power 415 2 -> 1.7223E+5 Inexact Rounded
rpox513 power 75 3 -> 4.2188E+5 Inexact Rounded
rounding: floor
rpox601 power 12345 -5 -> 3.4877E-21 Inexact Rounded
rpox602 power 12345 -4 -> 4.3056E-17 Inexact Rounded
rpox603 power 12345 -3 -> 5.3152E-13 Inexact Rounded
rpox604 power 12345 -2 -> 6.5617E-9 Inexact Rounded
rpox605 power 12345 -1 -> 0.000081004 Inexact Rounded
rpox606 power 12345 0 -> 1
rpox607 power 12345 1 -> 12345
rpox608 power 12345 2 -> 1.5239E+8 Inexact Rounded
rpox609 power 12345 3 -> 1.8813E+12 Inexact Rounded
rpox610 power 12345 4 -> 2.3225E+16 Inexact Rounded
rpox611 power 12345 5 -> 2.8671E+20 Inexact Rounded
rpox612 power 415 2 -> 1.7222E+5 Inexact Rounded
rpox613 power 75 3 -> 4.2187E+5 Inexact Rounded
rounding: ceiling
rpox701 power 12345 -5 -> 3.4878E-21 Inexact Rounded
rpox702 power 12345 -4 -> 4.3057E-17 Inexact Rounded
rpox703 power 12345 -3 -> 5.3153E-13 Inexact Rounded
rpox704 power 12345 -2 -> 6.5618E-9 Inexact Rounded
rpox705 power 12345 -1 -> 0.000081005 Inexact Rounded
rpox706 power 12345 0 -> 1
rpox707 power 12345 1 -> 12345
rpox708 power 12345 2 -> 1.5240E+8 Inexact Rounded
rpox709 power 12345 3 -> 1.8814E+12 Inexact Rounded
rpox710 power 12345 4 -> 2.3226E+16 Inexact Rounded
rpox711 power 12345 5 -> 2.8672E+20 Inexact Rounded
rpox712 power 415 2 -> 1.7223E+5 Inexact Rounded
rpox713 power 75 3 -> 4.2188E+5 Inexact Rounded
-- Underflow Subnormal and overflow values vary with rounding mode and sign
maxexponent: 999999999
rounding: down
rovx100 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded
rovx101 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded
rovx102 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded
rovx104 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded
rounding: up
rovx110 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded
rovx111 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded
rovx112 divide 1E-9 9E+999999999 -> 1E-1000000003 Underflow Subnormal Inexact Rounded
rovx114 divide -1E-9 9E+999999999 -> -1E-1000000003 Underflow Subnormal Inexact Rounded
rounding: ceiling
rovx120 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded
rovx121 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded
rovx122 divide 1E-9 9E+999999999 -> 1E-1000000003 Underflow Subnormal Inexact Rounded
rovx124 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded
rounding: floor
rovx130 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded
rovx131 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded
rovx132 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded
rovx134 divide -1E-9 9E+999999999 -> -1E-1000000003 Underflow Subnormal Inexact Rounded
rounding: half_up
rovx140 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded
rovx141 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded
rovx142 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded
rovx144 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded
rounding: half_even
rovx150 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded
rovx151 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded
rovx152 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded
rovx154 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded
rounding: half_down
rovx160 multiply 10 9E+999999999 -> Infinity Overflow Inexact Rounded
rovx161 multiply -10 9E+999999999 -> -Infinity Overflow Inexact Rounded
rovx162 divide 1E-9 9E+999999999 -> 0E-1000000003 Underflow Subnormal Inexact Rounded
rovx164 divide -1E-9 9E+999999999 -> -0E-1000000003 Underflow Subnormal Inexact Rounded
-- check maximum finite value over a range of precisions
rounding: down
precision: 1
rovx200 multiply 10 9E+999999999 -> 9E+999999999 Overflow Inexact Rounded
rovx201 multiply -10 9E+999999999 -> -9E+999999999 Overflow Inexact Rounded
precision: 2
rovx210 multiply 10 9E+999999999 -> 9.9E+999999999 Overflow Inexact Rounded
rovx211 multiply -10 9E+999999999 -> -9.9E+999999999 Overflow Inexact Rounded
precision: 3
rovx220 multiply 10 9E+999999999 -> 9.99E+999999999 Overflow Inexact Rounded
rovx221 multiply -10 9E+999999999 -> -9.99E+999999999 Overflow Inexact Rounded
precision: 4
rovx230 multiply 10 9E+999999999 -> 9.999E+999999999 Overflow Inexact Rounded
rovx231 multiply -10 9E+999999999 -> -9.999E+999999999 Overflow Inexact Rounded
precision: 5
rovx240 multiply 10 9E+999999999 -> 9.9999E+999999999 Overflow Inexact Rounded
rovx241 multiply -10 9E+999999999 -> -9.9999E+999999999 Overflow Inexact Rounded
precision: 6
rovx250 multiply 10 9E+999999999 -> 9.99999E+999999999 Overflow Inexact Rounded
rovx251 multiply -10 9E+999999999 -> -9.99999E+999999999 Overflow Inexact Rounded
precision: 7
rovx260 multiply 10 9E+999999999 -> 9.999999E+999999999 Overflow Inexact Rounded
rovx261 multiply -10 9E+999999999 -> -9.999999E+999999999 Overflow Inexact Rounded
precision: 8
rovx270 multiply 10 9E+999999999 -> 9.9999999E+999999999 Overflow Inexact Rounded
rovx271 multiply -10 9E+999999999 -> -9.9999999E+999999999 Overflow Inexact Rounded
precision: 9
rovx280 multiply 10 9E+999999999 -> 9.99999999E+999999999 Overflow Inexact Rounded
rovx281 multiply -10 9E+999999999 -> -9.99999999E+999999999 Overflow Inexact Rounded
precision: 10
rovx290 multiply 10 9E+999999999 -> 9.999999999E+999999999 Overflow Inexact Rounded
rovx291 multiply -10 9E+999999999 -> -9.999999999E+999999999 Overflow Inexact Rounded
-- reprise rounding mode effect (using multiplies so precision directive used)
precision: 9
maxexponent: 999999999
rounding: half_up
rmex400 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded
rmex401 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded
rounding: half_down
rmex402 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded
rmex403 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded
rounding: half_even
rmex404 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded
rmex405 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded
rounding: floor
rmex406 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded
rmex407 multiply 9.999E+999999999 10 -> 9.99999999E+999999999 Overflow Inexact Rounded
rounding: ceiling
rmex408 multiply -9.999E+999999999 10 -> -9.99999999E+999999999 Overflow Inexact Rounded
rmex409 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded
rounding: up
rmex410 multiply -9.999E+999999999 10 -> -Infinity Overflow Inexact Rounded
rmex411 multiply 9.999E+999999999 10 -> Infinity Overflow Inexact Rounded
rounding: down
rmex412 multiply -9.999E+999999999 10 -> -9.99999999E+999999999 Overflow Inexact Rounded
rmex413 multiply 9.999E+999999999 10 -> 9.99999999E+999999999 Overflow Inexact Rounded
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