| Pay vs Performance Disclosure - USD ($) | 12 Months Ended |
| Dec. 30, 2022 | Dec. 31, 2021 | Jan. 01, 2021 |
| Pay vs Performance Disclosure [Table] | | | |
| Pay vs Performance [Table Text Block] | Year Summary Compensation Table Total for PEO ($) (1) Compensation Actually Paid to PEO ($) (2) Average Summary Compensation Table Total for Non-PEO NEOs ($) (3) Average Compensation Actually Paid to Non-PEO NEOs ($) (4) Value of Initial Fixed $100 Investment Based on: Net Income Annualized Recurring Revenue Total Shareholder Return Peer Group Total Shareholder Return 2022 16,134,366 (9,539,156) 2,700,601 (2,147,905) 121 139 449.7 1,603.7 2021 13,956,821 26,993,547 3,551,936 8,787,696 209 194 492.7 1,409.1 2020 12,590,537 25,198,136 2,893,607 9,291,939 160 144 389.9 1,295.8 | | |
| Named Executive Officers, Footnote [Text Block] | The principal executive officer (“PEO”) of the Company for each year shown in the table was Robert G. Painter, the Company’s CEO.The non-PEO NEOs for each year shown in the table were: 2022 2021 2020 David G. Barnes David G. Barnes David G. Barnes Ronald J. Bisio Steven W. Berglund Steven W. Berglund Jennifer Lin Manolis E. Kotzabasakis James Langley Darryl R. Matthews Darryl R. Matthews Darryl R. Matthews Manolis E. Kotzabasakis James Langley | | |
| Peer Group Issuers, Footnote [Text Block] | The peer group used for this data is the S&P 500 Information Technology Index, which is one of the peer groups used in the chart in Part II, Item 5 of the Company’s most recent Annual Report on Form 10-K. | | |
| PEO Total Compensation Amount | $ 16,134,366 | $ 13,956,821 | $ 12,590,537 |
| PEO Actually Paid Compensation Amount | $ (9,539,156) | 26,993,547 | 25,198,136 |
| Adjustment To PEO Compensation, Footnote [Text Block] | Following are the adjustments made to the summary compensation table totals to determine the amounts shown as compensation actually paid for the PEO: 2022 2021 2020 (A) Pension Plans—Present Value: Deduct the aggregate change in the actuarial present value of the accumulated benefit under all defined benefit and actuarial pension plans N/A N/A N/A (B) Pension Plans—Service Costs: Add the aggregate of service cost and prior service cost for all defined benefit and actuarial pension plans N/A N/A N/A (C) Equity Awards (1) Deduct the amounts reported in the Summary Compensation Table under “Stock Awards” and “Option Awards”: -14,116,649 -10,533,714 -11,713,201 (i) Add the fair value as of the end of the year of all awards granted during the year that are outstanding and unvested as of the end of the year: +10,193,939 +12,516,060 +21,295,590 (ii) Add the amount equal to the change as of the end of the year (from the end of the prior year) in fair value of any awards granted in any prior year that are outstanding and unvested as of the end of the year: -20,592,123 +8,340,367 +1,994,385 (iii) Add, for awards that are granted and vest in the same year, the fair value as of the vesting date: — — — (iv) Add the amount equal to the change as of the vesting date (from the end of the prior year) in fair value of any awards granted in any prior year for which all applicable vesting conditions were satisfied at the end of or during the year: -1,158,689 +2,714,013 +1,030,825 (v) Subtract, for any awards granted in any prior year that fail to meet the applicable vesting conditions during the year, the amount equal to the fair value at the end of the prior year: — — — (vi) Add the dollar value of any dividends or other earnings paid on stock or option awards in the year prior to the vesting date that are not otherwise included in the total compensation for the year: — — — Total adjustments: -25,673,522 +13,036,726 +12,607,599 | | |
| Non-PEO NEO Average Total Compensation Amount | $ 2,700,601 | 3,551,936 | 2,893,607 |
| Non-PEO NEO Average Compensation Actually Paid Amount | $ (2,147,905) | 8,787,696 | 9,291,939 |
| Adjustment to Non-PEO NEO Compensation Footnote [Text Block] | Following are the adjustments made to the summary compensation table totals to determine the amounts shown as compensation actually paid to the non-PEO NEOs: 2022 2021 2020 (A) Pension Plans—Present Value: Deduct the aggregate change in the actuarial present value of the accumulated benefit under all defined benefit and actuarial pension plans N/A N/A N/A (B) Pension Plans—Service Costs: Add the aggregate of service cost and prior service cost for all defined benefit and actuarial pension plans N/A N/A N/A (C) Equity Awards (1) Deduct the amounts reported in the Summary Compensation Table under “Stock Awards” and “Option Awards”: -1,894,080 -2,445,223 -2,331,657 (i) Add the fair value as of the end of the year of all awards granted during the year that are outstanding and unvested as of the end of the year: +1,033,035 +2,835,250 +3,823,177 (ii) Add the amount equal to the change as of the end of the year (from the end of the prior year) in fair value of any awards granted in any prior year that are outstanding and unvested as of the end of the year: -2,104,280 +1,233,812 +3,590,670 (iii) Add, for awards that are granted and vest in the same year, the fair value as of the vesting date: — — — (iv) Add the amount equal to the change as of the vesting date (from the end of the prior year) in fair value of any awards granted in any prior year for which all applicable vesting conditions were satisfied at the end of or during the year: -528,784 +3,611,921 +1,316,142 (v) Subtract, for any awards granted in any prior year that fail to meet the applicable vesting conditions during the year, the amount equal to the fair value at the end of the prior year: -1,354,397 — — (vi) Add the dollar value of any dividends or other earnings paid on stock or option awards in the year prior to the vesting date that are not otherwise included in the total compensation for the year: — — — Total adjustments: -4,848,506 +5,235,760 +6,398,332 | | |
| Compensation Actually Paid vs. Total Shareholder Return [Text Block] | The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged) and each of the Company’s total shareholder return and the peer group total shareholder return based on an initial $100 investment. | | |
| Compensation Actually Paid vs. Net Income [Text Block] | The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged), and the Company’s net income. | | |
| Compensation Actually Paid vs. Company Selected Measure [Text Block] | The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged), and the Company’s annualized recurring revenue (ARR). | | |
| Total Shareholder Return Vs Peer Group [Text Block] | The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged) and each of the Company’s total shareholder return and the peer group total shareholder return based on an initial $100 investment. | | |
| Tabular List [Table Text Block] | Measure Explanation Annualized recurring revenue See Appendix A for an explanation of annualized recurring revenue Revenue The Company’s revenue in a specified period Operating income The Company’s operating income in a specified period Adjusted EBITDA See Appendix A for an explanation of Adjusted EBITDA Total shareholder return The total shareholder return of the Company’s stock over a specified period | | |
| Total Shareholder Return Amount | $ 121 | 209 | 160 |
| Peer Group Total Shareholder Return Amount | 139 | 194 | 144 |
| Net Income (Loss) | $ 449,700,000 | $ 492,700,000 | $ 389,900,000 |
| Company Selected Measure Amount | 1,603,700,000 | 1,409,100,000 | 1,295,800,000 |
| PEO Name | Robert G. Painter | | |
| Additional 402(v) Disclosure [Text Block] | See Appendix A to this proxy statement for an explanation of the company-selected measure “annualized recurring revenue.” | | |
| Measure [Axis]: 1 | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Measure Name | Annualized recurring revenue | | |
| Measure [Axis]: 2 | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Measure Name | Revenue | | |
| Measure [Axis]: 3 | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Measure Name | Operating income | | |
| Measure [Axis]: 4 | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Measure Name | Adjusted EBITDA | | |
| Measure [Axis]: 5 | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Measure Name | Total shareholder return | | |
| PEO [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | $ (25,673,522) | $ 13,036,726 | $ 12,607,599 |
| PEO [Member] | Equity Awards Reported Value [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (14,116,649) | (10,533,714) | (11,713,201) |
| PEO [Member] | Equity Awards Granted During the Year, Unvested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | 10,193,939 | 12,516,060 | 21,295,590 |
| PEO [Member] | Equity Awards Granted in Prior Years, Unvested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (20,592,123) | 8,340,367 | 1,994,385 |
| PEO [Member] | Equity Awards Granted During the Year, Vested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | 0 | 0 | 0 |
| PEO [Member] | Equity Awards Granted in Prior Years, Vested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (1,158,689) | 2,714,013 | 1,030,825 |
| PEO [Member] | Equity Awards that Failed to Meet Vesting Conditions [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | 0 | 0 | 0 |
| PEO [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | 0 | 0 | 0 |
| Non-PEO NEO [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (4,848,506) | | |
| Non-PEO NEO [Member] | Equity Awards Reported Value [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (1,894,080) | (2,445,223) | (2,331,657) |
| Non-PEO NEO [Member] | Equity Awards Granted During the Year, Unvested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | 1,033,035 | 2,835,250 | 3,823,177 |
| Non-PEO NEO [Member] | Equity Awards Granted in Prior Years, Unvested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (2,104,280) | 1,233,812 | 3,590,670 |
| Non-PEO NEO [Member] | Equity Awards Granted During the Year, Vested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | 0 | 0 | 0 |
| Non-PEO NEO [Member] | Equity Awards Granted in Prior Years, Vested [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (528,784) | 3,611,921 | 1,316,142 |
| Non-PEO NEO [Member] | Equity Awards that Failed to Meet Vesting Conditions [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | (1,354,397) | 0 | 0 |
| Non-PEO NEO [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | $ 0 | 0 | 0 |
| Non-PEO NEO [Member] | Equity Award Adjustments [Member] | | | |
| Pay vs Performance Disclosure [Table] | | | |
| Adjustment to Compensation Amount | | $ 5,235,760 | $ 6,398,332 |
