Performance — Roots and Exponents

Speed of the root and exponential functions by storage width and scale. See the Performance overview for the time units, the width reference map, and how these timings are measured.

cbrt

Width	0	¼	½	¾	max
D18	5.08 µs	2.97 µs	5.81 µs	2.94 µs	6.75 µs
D38	5.73 µs	5.15 µs	7.71 µs	9.66 µs	5.06 µs
D57	330 ns	608 ns	728 ns	1.14 µs	925 ns
D76	537 ns	785 ns	1.2 µs	1.36 µs	1.94 µs
D115	270 ns	2.29 µs	2.44 µs	3.71 µs	3.95 µs
D153	526 ns	2.66 µs	3.59 µs	5.75 µs	4.58 µs
D230	383 ns	4.36 µs	7.94 µs	8.53 µs	11.1 µs
D307	559 ns	5.66 µs	11.1 µs	16.6 µs	20.6 µs
D462	296 ns	9.62 µs	24.2 µs	33.2 µs	47.1 µs
D616	544 ns	15.7 µs	37.3 µs	49.7 µs	77.4 µs
D924	544 ns	31.7 µs	82.3 µs	121 µs	198 µs
D1232	616 ns	60 µs	151 µs	227 µs	258 µs

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.

exp

Width	0	¼	½	¾	max
D18	3.11 ns	2.68 µs	6.78 µs	3.37 µs	6.11 µs
D38	1.59 ns	6.24 µs	7.56 µs	8.73 µs	6.22 µs
D57	2.18 ns	3.59 µs	4.14 µs	5.42 µs	8.27 µs
D76	3.23 ns	5.48 µs	6.76 µs	8.86 µs	10.8 µs
D115	14.2 ns	6.54 µs	12.7 µs	17.4 µs	16.2 µs
D153	22.1 ns	6.91 µs	14.9 µs	21.8 µs	24.7 µs
D230	57.6 ns	12.7 µs	21.5 µs	38.2 µs	66.5 µs
D307	83.8 ns	14.6 µs	33.7 µs	76.9 µs	113 µs
D462	107 ns	22 µs	79.1 µs	152 µs	227 µs
D616	179 ns	38 µs	129 µs	223 µs	401 µs
D924	187 ns	78.5 µs	261 µs	542 µs	984 µs
D1232	261 ns	129 µs	440 µs	887 µs	2.66 ms

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.

hypot

Width	0	¼	½	¾	max
D18	16.7 ns	23.9 ns	42.9 ns	30.1 ns	31.1 ns
D38	15.5 ns	41.5 ns	66.6 ns	67 ns	89.2 ns
D57	17.1 ns	39.9 ns	68 ns	687 ns	504 ns
D76	17.1 ns	67.9 ns	691 ns	706 ns	1.04 µs
D115	16.2 ns	72.4 ns	704 ns	1.22 µs	860 ns
D153	24.6 ns	704 ns	1.08 µs	1.43 µs	1.28 µs
D230	28.5 ns	721 ns	1.52 µs	2.04 µs	2.78 µs
D307	44.1 ns	1.07 µs	2.13 µs	3.3 µs	5.49 µs
D462	45.4 ns	1.54 µs	3.66 µs	6.35 µs	9.76 µs
D616	83.7 ns	2.36 µs	6.09 µs	8.76 µs	16.2 µs
D924	110 ns	3.68 µs	10.9 µs	22.8 µs	28.4 µs
D1232	93.2 ns	6.14 µs	20.8 µs	27.4 µs	43.9 µs

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.

ln

Width	0	¼	½	¾	max
D18	4.36 ns	170 ns	388 ns	259 ns	311 ns
D38	2.11 ns	359 ns	368 ns	372 ns	339 ns
D57	260 ns	433 ns	445 ns	447 ns	491 ns
D76	269 ns	449 ns	427 ns	556 ns	552 ns
D115	235 ns	441 ns	571 ns	924 ns	741 ns
D153	286 ns	468 ns	576 ns	930 ns	951 ns
D230	565 ns	612 ns	993 ns	1.06 µs	1.3 µs
D307	651 ns	645 ns	1.01 µs	1.24 µs	9.57 µs
D462	783 ns	2.74 µs	3.29 µs	3.75 µs	4.8 µs
D616	1.48 µs	1.5 µs	1.66 µs	2.13 µs	3.3 µs
D924	1.79 µs	1.84 µs	2.72 µs	3.34 µs	4.6 µs
D1232	2.32 µs	2.96 µs	4.06 µs	4.59 µs	5.23 µs

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.

log

Width	0	¼	½	¾	max
D18	7.69 µs	4.96 µs	12.4 µs	6.42 µs	11.5 µs
D38	8.14 µs	11.6 µs	14.6 µs	17.1 µs	12.9 µs
D57	3.94 µs	4.09 µs	4.37 µs	4.35 µs	4.12 µs
D76	4.46 µs	4.22 µs	4.31 µs	4.5 µs	4.67 µs
D115	6.29 µs	8.41 µs	8.63 µs	9.4 µs	7.29 µs
D153	7.69 µs	8.37 µs	9.07 µs	9.88 µs	7.08 µs
D230	10.7 µs	11.9 µs	13.6 µs	12.7 µs	13.6 µs
D307	15.9 µs	18.4 µs	21.6 µs	24.1 µs	26.4 µs
D462	9.93 µs	20.6 µs	23.7 µs	27.6 µs	30.8 µs
D616	28.6 µs	42.5 µs	50.9 µs	53.4 µs	71.5 µs
D924	34.5 µs	67.4 µs	95.1 µs	122 µs	162 µs
D1232	47.6 µs	106 µs	166 µs	202 µs	215 µs

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.

powf

Width	0	¼	½	¾	max
D18	8.71 ns	2.8 µs	7.47 µs	3.8 µs	6.68 µs
D38	6.48 ns	6.88 µs	8.22 µs	9.37 µs	6.81 µs
D57	56.4 ns	3.93 µs	4.29 µs	4.52 µs	4.53 µs
D76	81.2 ns	3.81 µs	4.49 µs	4.92 µs	5.32 µs
D115	115 ns	8.16 µs	8.81 µs	10.1 µs	7.99 µs
D153	177 ns	8.39 µs	9.53 µs	10.8 µs	8.36 µs
D230	347 ns	12.2 µs	14.7 µs	16.1 µs	17.7 µs
D307	365 ns	18.9 µs	21.2 µs	27.9 µs	31.8 µs
D462	431 ns	69.6 µs	136 µs	205 µs	261 µs
D616	810 ns	191 µs	325 µs	297 µs	515 µs
D924	934 ns	416 µs	451 µs	774 µs	1.74 ms
D1232	1.16 µs	759 µs	855 µs	2.09 ms	2.46 ms

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.

sqrt

Width	0	¼	½	¾	max
D18	6.41 ns	9.4 ns	20 ns	22.3 ns	23.9 ns
D38	8.71 ns	25.5 ns	31.2 ns	1.48 µs	1.91 µs
D57	158 ns	210 ns	483 ns	766 ns	577 ns
D76	208 ns	269 ns	767 ns	851 ns	1.24 µs
D115	110 ns	664 ns	1 µs	1.52 µs	1.11 µs
D153	120 ns	1.11 µs	1.63 µs	1.88 µs	1.73 µs
D230	158 ns	1.56 µs	2.48 µs	2.94 µs	3.49 µs
D307	144 ns	2.39 µs	3.75 µs	4.72 µs	7.02 µs
D462	130 ns	3.65 µs	5.78 µs	9.36 µs	11.9 µs
D616	261 ns	6.47 µs	10.3 µs	11 µs	20.5 µs
D924	263 ns	10.4 µs	17 µs	26 µs	35.4 µs
D1232	217 ns	15.3 µs	28.5 µs	39.7 µs	51.3 µs

Median time vs width (log scale). Solid: scale 0 and max; dashed: the intermediate band-edge scales.