📄 power.dectest
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----------------------------------------------------------------------
-- power.decTest -- decimal exponentiation --
-- Copyright (c) IBM Corporation, 1981, 2002. All rights reserved. --
------------------------------------------------------------------------
-- Please see the document "General Decimal Arithmetic Testcases" --
-- at http://www2.hursley.ibm.com/decimal for the description of --
-- these testcases. --
-- --
-- These testcases are experimental ('beta' versions), and they --
-- may contain errors. They are offered on an as-is basis. In --
-- particular, achieving the same results as the tests here is not --
-- a guarantee that an implementation complies with any Standard --
-- or specification. The tests are not exhaustive. --
-- --
-- Please send comments, suggestions, and corrections to the author: --
-- Mike Cowlishaw, IBM Fellow --
-- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK --
-- mfc@uk.ibm.com --
------------------------------------------------------------------------
version: 2.15
-- This set of testcases tests raising numbers to an integer power only.
-- If arbitrary powers were supported, 1 ulp differences would be
-- permitted.
extended: 1
precision: 9
rounding: half_up
maxExponent: 999
-- base checks. Note 0**0 is an error.
powx001 power '0' '0' -> NaN Invalid_operation
powx002 power '0' '1' -> '0'
powx003 power '0' '2' -> '0'
powx004 power '1' '0' -> '1'
powx005 power '1' '1' -> '1'
powx006 power '1' '2' -> '1'
powx010 power '2' '0' -> '1'
powx011 power '2' '1' -> '2'
powx012 power '2' '2' -> '4'
powx013 power '2' '3' -> '8'
powx014 power '2' '4' -> '16'
powx015 power '2' '5' -> '32'
powx016 power '2' '6' -> '64'
powx017 power '2' '7' -> '128'
powx018 power '2' '8' -> '256'
powx019 power '2' '9' -> '512'
powx020 power '2' '10' -> '1024'
powx021 power '2' '11' -> '2048'
powx022 power '2' '12' -> '4096'
powx023 power '2' '15' -> '32768'
powx024 power '2' '16' -> '65536'
powx025 power '2' '31' -> '2.14748365E+9' Inexact Rounded
-- NB 0 not stripped in next
powx026 power '2' '32' -> '4.29496730E+9' Inexact Rounded
precision: 10
powx027 power '2' '31' -> '2147483648'
powx028 power '2' '32' -> '4294967296'
precision: 9
powx030 power '3' '2' -> 9
powx031 power '4' '2' -> 16
powx032 power '5' '2' -> 25
powx033 power '6' '2' -> 36
powx034 power '7' '2' -> 49
powx035 power '8' '2' -> 64
powx036 power '9' '2' -> 81
powx037 power '10' '2' -> 100
powx038 power '11' '2' -> 121
powx039 power '12' '2' -> 144
powx040 power '3' '3' -> 27
powx041 power '4' '3' -> 64
powx042 power '5' '3' -> 125
powx043 power '6' '3' -> 216
powx044 power '7' '3' -> 343
powx050 power '10' '0' -> 1
powx051 power '10' '1' -> 10
powx052 power '10' '2' -> 100
powx053 power '10' '3' -> 1000
powx054 power '10' '4' -> 10000
powx055 power '10' '5' -> 100000
powx056 power '10' '6' -> 1000000
powx057 power '10' '7' -> 10000000
powx058 power '10' '8' -> 100000000
powx059 power '10' '9' -> 1.00000000E+9 Rounded
powx060 power '10' '22' -> 1.00000000E+22 Rounded
powx061 power '10' '77' -> 1.00000000E+77 Rounded
powx062 power '10' '99' -> 1.00000000E+99 Rounded
maxexponent: 999999999
powx063 power '10' '999999999' -> '1.00000000E+999999999' Rounded
powx064 power '10' '999999998' -> '1.00000000E+999999998' Rounded
powx065 power '10' '999999997' -> '1.00000000E+999999997' Rounded
powx066 power '10' '333333333' -> '1.00000000E+333333333' Rounded
powx070 power '0.3' '0' -> '1'
powx071 power '0.3' '1' -> '0.3'
powx072 power '0.3' '1.00' -> '0.3'
powx073 power '0.3' '2.00' -> '0.09'
powx074 power '0.3' '2.000000000' -> '0.09'
powx075 power '6.0' '1' -> '6.0' -- NB zeros not stripped
powx076 power '6.0' '2' -> '36.00' -- ..
powx077 power '-3' '2' -> '9' -- from NetRexx book
powx078 power '4' '3' -> '64' -- .. (sort of)
powx080 power 0.1 0 -> 1
powx081 power 0.1 1 -> 0.1
powx082 power 0.1 2 -> 0.01
powx083 power 0.1 3 -> 0.001
powx084 power 0.1 4 -> 0.0001
powx085 power 0.1 5 -> 0.00001
powx086 power 0.1 6 -> 0.000001
powx087 power 0.1 7 -> 1E-7
powx088 power 0.1 8 -> 1E-8
powx089 power 0.1 9 -> 1E-9
powx090 power 101 2 -> 10201
powx091 power 101 3 -> 1030301
powx092 power 101 4 -> 104060401
powx093 power 101 5 -> 1.05101005E+10 Inexact Rounded
powx094 power 101 6 -> 1.06152015E+12 Inexact Rounded
powx095 power 101 7 -> 1.07213535E+14 Inexact Rounded
-- negative powers
powx101 power '2' '-1' -> 0.5
powx102 power '2' '-2' -> 0.25
powx103 power '2' '-4' -> 0.0625
powx104 power '2' '-8' -> 0.00390625
powx105 power '2' '-16' -> 0.0000152587891 Inexact Rounded
powx106 power '2' '-32' -> 2.32830644E-10 Inexact Rounded
powx108 power '2' '-64' -> 5.42101086E-20 Inexact Rounded
powx110 power '10' '-8' -> 1E-8
powx111 power '10' '-7' -> 1E-7
powx112 power '10' '-6' -> 0.000001
powx113 power '10' '-5' -> 0.00001
powx114 power '10' '-4' -> 0.0001
powx115 power '10' '-3' -> 0.001
powx116 power '10' '-2' -> 0.01
powx117 power '10' '-1' -> 0.1
powx118 power '10' '-333333333' -> 1E-333333333
powx119 power '10' '-999999998' -> 1E-999999998
powx120 power '10' '-999999999' -> 1E-999999999
powx121 power '10' '-77' -> '1E-77'
powx122 power '10' '-22' -> '1E-22'
powx123 power '2' '-1' -> '0.5'
powx124 power '2' '-2' -> '0.25'
powx125 power '2' '-4' -> '0.0625'
powx126 power '0' '-1' -> Infinity Division_by_zero
powx127 power '0' '-2' -> Infinity Division_by_zero
powx128 power -0 '-1' -> -Infinity Division_by_zero
powx129 power -0 '-2' -> Infinity Division_by_zero
-- out-of-range edge cases
powx181 power '7' '999999998' -> 2.10892313E+845098038 Inexact Rounded
powx182 power '7' '999999999' -> 1.47624619E+845098039 Inexact Rounded
powx183 power '7' '1000000000' -> NaN Invalid_operation
powx184 power '7' '1000000001' -> NaN Invalid_operation
powx185 power '7' '10000000000' -> NaN Invalid_operation
powx186 power '7' '-1000000001' -> NaN Invalid_operation
powx187 power '7' '-1000000000' -> NaN Invalid_operation
powx189 power '7' '-999999999' -> 6.77393787E-845098040 Inexact Rounded
powx190 power '7' '-999999998' -> 4.74175651E-845098039 Inexact Rounded
-- some baddies [more below]
powx191 power '2' '2.000001' -> NaN Invalid_operation
powx192 power '2' '2.00000000' -> 4
powx193 power '2' '2.000000001' -> NaN Invalid_operation
powx194 power '2' '2.0000000001' -> NaN Invalid_operation
-- "0.5" tests from original Rexx diagnostics [loop unrolled]
powx200 power 0.5 0 -> 1
powx201 power 0.5 1 -> 0.5
powx202 power 0.5 2 -> 0.25
powx203 power 0.5 3 -> 0.125
powx204 power 0.5 4 -> 0.0625
powx205 power 0.5 5 -> 0.03125
powx206 power 0.5 6 -> 0.015625
powx207 power 0.5 7 -> 0.0078125
powx208 power 0.5 8 -> 0.00390625
powx209 power 0.5 9 -> 0.001953125
powx210 power 0.5 10 -> 0.0009765625
-- A (rare) case where the last digit is not within 0.5 ULP
precision: 9
powx215 power "-21971575.0E+31454441" "-7" -> "-4.04549503E-220181139" Inexact Rounded
precision: 20
powx216 power "-21971575.0E+31454441" "-7" -> "-4.0454950249324891788E-220181139" Inexact Rounded
-- The Vienna case. Checks both setup and 1/acc working precision
-- Modified 1998.12.14 as RHS no longer rounded before use (must fit)
-- Modified 1990.02.04 as LHS is now rounded (instead of truncated to guard)
-- '123456789E+10' -- lhs .. rounded to 1.23E+18
-- '-1.23000e+2' -- rhs .. [was: -1.23455e+2, rounds to -123]
-- Modified 2002.10.06 -- finally, no input rounding
-- With input rounding, result would be 8.74E-2226
precision: 3
powx219 power '123456789E+10' '-1.23000e+2' -> '5.54E-2226' Inexact Rounded
-- whole number checks
precision: 9
powx221 power 1 1234 -> 1
precision: 4
powx222 power 1 1234 -> 1
precision: 3
powx223 power 1 1234 -> 1
powx224 power 1 12.34e+2 -> 1
powx225 power 1 12.3 -> NaN Invalid_operation
powx226 power 1 12.0 -> 1
powx227 power 1 1.01 -> NaN Invalid_operation
powx228 power 2 1.00 -> 2
powx229 power 2 2.00 -> 4
precision: 9
powx230 power 1 1.0001 -> NaN Invalid_operation
powx231 power 1 1.0000001 -> NaN Invalid_operation
powx232 power 1 1.0000000001 -> NaN Invalid_operation
powx233 power 1 1.0000000000001 -> NaN Invalid_operation
precision: 5
powx234 power 1 1.0001 -> NaN Invalid_operation
powx235 power 1 1.0000001 -> NaN Invalid_operation
powx236 power 1 1.0000000001 -> NaN Invalid_operation
powx237 power 1 1.0000000000001 -> NaN Invalid_operation
powx238 power 1 1.0000000000001 -> NaN Invalid_operation
maxexponent: 999999999
powx239 power 1 5.67E-987654321 -> NaN Invalid_operation
powx240 power 1 100000000 -> 1
powx241 power 1 999999998 -> 1
powx242 power 1 999999999 -> 1
powx243 power 1 1000000000 -> NaN Invalid_operation
powx244 power 1 9999999999 -> NaN Invalid_operation
-- Checks for 'Too much precision needed'
-- For x^12, digits+elength+1 = digits+3
precision: 999999999
powx249 add 1 1 -> 2 -- check basic operation at this precision
powx250 power 2 12 -> Infinity Overflow
precision: 999999998
powx251 power 2 12 -> Infinity Overflow
precision: 999999997
powx252 power 2 12 -> Infinity Overflow
precision: 999999996
powx253 power 2 12 -> 4096
precision: 999999995
powx254 power 2 12 -> 4096
-- overflow and underflow tests
maxexponent: 999999999
precision: 9
powx280 power 9 999999999 -> 3.05550054E+954242508 Inexact Rounded
powx281 power 10 999999999 -> 1.00000000E+999999999 Rounded
powx282 power 10.0001 999999999 -> Infinity Overflow Inexact Rounded
powx283 power 10.1 999999999 -> Infinity Overflow Inexact Rounded
powx284 power 11 999999999 -> Infinity Overflow Inexact Rounded
powx285 power 12 999999999 -> Infinity Overflow Inexact Rounded
powx286 power 999 999999999 -> Infinity Overflow Inexact Rounded
powx287 power 999999 999999999 -> Infinity Overflow Inexact Rounded
powx288 power 999999999 999999999 -> Infinity Overflow Inexact Rounded
powx289 power 9.9E999999999 999999999 -> Infinity Overflow Inexact Rounded
powx290 power 0.5 999999999 -> 4.33559594E-301029996 Inexact Rounded
powx291 power 0.1 999999999 -> 1E-999999999 -- unrounded
powx292 power 0.09 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx293 power 0.05 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx294 power 0.01 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx295 power 0.0001 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx297 power 0.0000001 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx298 power 0.0000000001 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx299 power 1E-999999999 999999999 -> 0E-1000000007 Underflow Subnormal Inexact Rounded
powx310 power -9 999999999 -> -3.05550054E+954242508 Inexact Rounded
powx311 power -10 999999999 -> -1.00000000E+999999999 Rounded
powx312 power -10.0001 999999999 -> -Infinity Overflow Inexact Rounded
powx313 power -10.1 999999999 -> -Infinity Overflow Inexact Rounded
powx314 power -11 999999999 -> -Infinity Overflow Inexact Rounded
powx315 power -12 999999999 -> -Infinity Overflow Inexact Rounded
powx316 power -999 999999999 -> -Infinity Overflow Inexact Rounded
powx317 power -999999 999999999 -> -Infinity Overflow Inexact Rounded
powx318 power -999999999 999999999 -> -Infinity Overflow Inexact Rounded
powx319 power -9.9E999999999 999999999 -> -Infinity Overflow Inexact Rounded
powx320 power -0.5 999999999 -> -4.33559594E-301029996 Inexact Rounded
powx321 power -0.1 999999999 -> -1E-999999999
powx322 power -0.09 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
powx323 power -0.05 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
powx324 power -0.01 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
powx325 power -0.0001 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
powx327 power -0.0000001 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
powx328 power -0.0000000001 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
powx329 power -1E-999999999 999999999 -> -0E-1000000007 Underflow Subnormal Inexact Rounded
-- note no trim of next result
powx330 power -9 999999998 -> 3.39500060E+954242507 Inexact Rounded
powx331 power -10 999999998 -> 1.00000000E+999999998 Rounded
powx332 power -10.0001 999999998 -> Infinity Overflow Inexact Rounded
powx333 power -10.1 999999998 -> Infinity Overflow Inexact Rounded
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