Note : Referencing the external components should be avoided in most cases. Only in unavoidable circumstance external components should be referred. Developer should track the references.

Global Functions(Non RTE) to be provided to Integration Project

All functions in this component are provided to the integration project, but are only used on an as-needed basis.

Configuration REQUIREMeNTS

Build Time Config

Modules	Notes
None

Configuration Files to be provided by Integration Project

Da Vinci Parameter Configuration Changes

Parameter	Notes	SWC
N/A

DaVinci Interrupt Configuration Changes

ISR Name	VIM #	Priority Dependency	Notes
N/A

Manual Configuration Changes

Constant	Notes	SWC
N/A

Integration DATAFLOW REQUIREMENTS

Required Global Data Inputs

N/A

Required Global Data Outputs

N/A

Specific Include Path present

Yes

Runnable Scheduling

This section specifies the required runnable scheduling.

Init	Scheduling Requirements	Trigger
None	None	RTE/ISR(<time>ms)

Runnable	Scheduling Requirements	Trigger
None	None	RTE/ISR(<time>ms)

Memory Map REQUIREMENTS

Mapping

Memory Section	Contents	Notes
None

* Each …START_SEC… constant is terminated by a …STOP_SEC… constant as specified in the AUTOSAR Memory Mapping requirements.

Usage

Feature	RAM	ROM
<Memmap usuage info>

Table 1: ARM Cortex R4 Memory Usage

Non RTE NvM Blocks

Block Name

<NVM block used Non RTE functions >

Note : Size of the NVM block if configured in developer

RTE NvM Blocks

Block Name

<NVM block used in RTE functions >

Note : Size of the NVM block if configured in developer

Compiler Settings

Preprocessor MACRO

None

Optimization Settings

None

Appendix

<This section is for appendix>

2 - NxtrMath Review

Overview

Summary Sheet
Synergy Project
Source Code
PolySpace

Sheet 1: Summary Sheet

Rev 1.2

8-Jun-15

Peer Review Summary Sheet

Synergy Project Name:

kzshz2: Intended Use: Identify which component is being reviewed. This should be the Module Short Name from Synergy Rationale: Required for traceability. It will help to ensure this form is not attaced to the the wrong change request. AR100A_NxtrMath_Impl

Revision / Baseline:

kzshz2: Intended Use: Identify which Synergy revision of this component is being reviewed Rationale: Required for traceability. It will help to ensure this form is not attaced to the the wrong change request. 1.2.0

Change Owner:

kzshz2: Intended Use: Identify the developer who made the change(s) Rationale: A change request may have more than one resolver, this will help identify who made what change. Change owner identification may be required by indusrty standards. Krishna Anne

Work CR ID:

EA4#6438

kzshz2: Intended Use: Intended to identify at a high level to the reviewers which areas of the component have been changed. Rationale: This will be good information to know when ensuring appropriate reviews have been completed. Modified File Types:

kzshz2: Intended Use: Identify who where the reviewers, what they reviewed, and if the reviewed changes have been approved to release the code for testing. Comments here should be at a highlevel, the specific comments should be present on the specific review form sheet. Rationale: Since this Form will be attached to the Change Request it will confirm the approval and provides feedback in case of audits. ADD DR Level Move reviewer and approval to individual checklist form Review Checklist Summary:

Reviewed:

N/A

MDD

Yes

Source Code

Yes

PolySpace

N/A

Integration Manual

N/A

Davinci Files

Comments:

Moving sine lookup function to the Nexteer math library from SF107A.

General Guidelines:
- The reviews shall be performed over the portions of the component that were modified as a result of the Change Request.
- New components should include FDD Owner and Integrator as apart of the Group Review Board (Source Code, Integration Manual, and Davinci Files)
- Enter any rework required into the comment field and select No. When the rework is complete, review again using this same review sheet and select Yes. Add date and additional comment stating that the rework is completed.
- To review a component with multiple source code files use the "Add Source" button to create a Source code tab for each source file.
- .h file should be reviewed with the source file as part of the source file.

Sheet 2: Synergy Project

Peer Review Meeting Log (Component Synergy Project Review)

Quality Check Items:

Rationale is required for all answers of No

New baseline version name from Summary Sheet follows

Yes

Comments:

naming convention

Project contains necessary subprojects

Yes

Comments:

Project contains the correct version of subprojects

Yes

Comments:

Design subproject is correct version

Yes

Comments:

General Notes / Comments:

LN: Intended Use: Identify who were the reviewers and if the reviewed changes have been approved. Rationale: Since this Form will be attached to the Change Request it will confirm the approval and provides feedback in case of audits. KMC: Group Review Level removed in Rev 4.0 since the design review is not checked in until approved, so it would always be DR4. Review Board:

Change Owner:

Krishna Anne

Review Date :

07/22/16

Lead Peer Reviewer:

Nick Saxton

Approved by Reviewer(s):

Yes

Other Reviewer(s):

Sheet 3: Source Code

Rev 1.2

8-Jun-15

Peer Review Meeting Log (Source Code Review)

Source File Name:

N/A

Source File Revision:

N/A

Header File Name:

NxtrMath.h

Header File Revision:

kzshz2: Intended Use: Identify which version of the source file is being review. Rationale: Required for traceability between source code and review. Auditors will likely require this. 3

MDD Name:

N/A

Revision:

N/A

FDD/SCIR/DSR/FDR/CM Name:

N/A

Revision:

N/A

Quality Check Items:

Rationale is required for all answers of No

Working EA4 Software Naming Convention followed:

for variable names

Yes

Comments:

Only for changes

for constant names

Yes

Comments:

Only for changes

for function names

Yes

Comments:

Only for changes

for other names (component, memory

Yes

Comments:

mapping handles, typedefs, etc.)

Only for changes

All paths assign a value to outputs, ensuring

N/A

Comments:

all outputs are initialized prior to being written

Requirements Tracability tags in code match the requirements tracability in the FDD

N/A

Comments:

requirements tracability in the FDD

All variables are declared at the function level.

Yes

Comments:

Only for changes

Synergy version matches change history

kzshz2: Intended Use: Indicate that the the versioning was confirmed by the peer reviewer(s). Rationale: There have been many occassions where versions were not updated in files and as a result Unit Test were referencing wrong versions. This often time leads to the need to re-run of batch tests.

Yes

Comments:

and Version Control version in file comment block

Change log contains detailed description of changes

Yes

Comments:

and Work CR number

Code accurately implements FDD (Document or Model)

Yes

Comments:

No FDD Currently Available

Verified no Compiler Errors or Warnings

KMC: Intended Use: To confirm no compiler errors or warnings exist for the code under review (warnings from contract header files may be ignored). Rationale: This is needed to ensure there will be no errors discovered at the time of integration. A Sandox project should be used; QAC can find compiler errors but not warnings.

Yes

Comments:

Component.h is included

Yes

Comments:

All other includes are actually needed. (System includes

Yes

Comments:

only allowed in Nexteer library components)

Software Design and Coding Standards followed:

Version: 2.1

Code comments are clear, correct, and adequate

Yes

Comments:

and have been updated for the change: [N40] and

Only for changes

all other rules in the same section as rule [N40],

plus [N75], [N12], [N23], [N33], [N37], [N38],

[N48], [N54], [N77], [N79], [N72]

Source file (.c and .h) comment blocks are per

Yes

Comments:

standards and contain correct information: [N41], [N42]

Only for changes

Function comment blocks are per standards and

Yes

Comments:

contain correct information: [N43]

Only for changes

Code formatting (indentation, placement of

Yes

Comments:

braces, etc.) is per standards: [N5], [N55], [N56],

Only for changes

[N57], [N58], [N59]

Embedded constants used per standards; no

Yes

Comments:

"magic numbers": [N12]

Only for changes

Memory mapping for non-RTE code

N/A

Comments:

is per standard

All execution-order-dependent code can be

N/A

Comments:

recognized by the compiler: [N80]

All loops have termination conditions that ensure

N/A

Comments:

finite loop iterations: [N63]

All divides protect against divide by zero

N/A

Comments:

if needed: [N65]

N/A for changes

All integer division and modulus operations

N/A

Comments:

handle negative numbers correctly: [N76]

N/A for changes

All typecasting and fixed point arithmetic,

Yes

Comments:

including all use of fixed point macros and

timer functions, is correct and has no possibility

of unintended overflow or underflow: [N66]

All float-to-unsiged conversions ensure the.

Yes

Comments:

float value is non-negative: [N67]

Only for changes

All conversions between signed and unsigned

N/A

Comments:

types handle msb==1 as intended: [N78]

N/A for changes

All pointer dereferencing protects against

Yes

Comments:

null pointer if needed: [N70]

Only for changes

Component outputs are limited to the legal range

N/A

Comments:

defined in the FDD DataDict.m file : [N53]

Only for changes

All code is mapped with FDD (all FDD

N/A

Comments:

subfunctions and/or model blocks identified

No FDD exists

with code comments; all code corresponds to

some FDD subfunction and/or model block): [N40]

Review did not identify violations of other

Yes

Comments:

coding standard rules

Anomaly or Design Work CR created

Comments: List Anomaly or CR numbers

for any FDD corrections needed

General Notes / Comments:

Change Owner:

Krishna Anne

Review Date :

07/22/16

Lead Peer Reviewer:

Nick Saxton

Approved by Reviewer(s):

Yes

Other Reviewer(s):

Sheet 4: PolySpace

Rev 1.2

8-Jun-15

Peer Review Meeting Log (QAC/PolySpace Review)

Source File Name:

NxtrMath.h

Source File Revision:

Source File Name:

Source File Revision:

Source File Name:

Source File Revision:

EA4 Static Analysis Compliance Guideline version:

01.01.00

Poly Space version:

Windows User: eg. 2013b 2013b

Polyspace sub project version:

Windows User: eg. TL108a_PolyspaceSuprt_1.0.0 N/A

QAC version:

Windows User: eg 8.1.1-R 8.1.1-R

QAC sub project version:

Windows User: eg. TL_100A_1.1.0 1.1.0

Quality Check Items:

Rationale is required for all answers of No

Contract Folder's header files are appropriate and

kzshz2: Intended Use: Identify that the contract folder contains only the information required for this component. All other variables, constants, function prototypes, etc. should be removed. Rationale: This will help avoid unit testers having to considers object not used. It will also avoid having other files required for QAC.

Yes

Comments:

function prototypes match the latest component version

100% Compliance to the EA4 Static Analysis

Yes

Comments:

Compliance Guideline

Are previously added justification and deviation

Yes

Comments:

comments still appropriate

Do all MISRA deviation comments use approved

Yes

Comments:

deviation tags

Cyclomatic complexity and Static path count OK

Creager, Kathleen: use Browse Function Metrics, STCYC and STPTH

Yes

Comments:

for all functions in the component per Design

Found cyclomatic complexity 16 for SinCos_f32() function

and Coding Standards rule [N47]

General Notes / Comments:

Change Owner:

Krishna Anne

Review Date :

07/22/16

Lead Peer Reviewer:

Nick Saxton

Approved by Reviewer(s):

Yes

Other Reviewer(s):

3 - Optimized SinCos Algorithm Rev 001

Optimized SinCos Algorithm

Background:

The following diagram is an overview of the operations that are performed during digital motor angle initialization to compute their correction tables.
Generate Reconstructed Waveform Pseudo Code:
for n = 0 to 128 // size of correction table

$ReconstructedWaveform\lbrack n\rbrack \cong \sum_{i = 1}^{12}{Acoeff\lbrack i\rbrack*\cos\left( \frac{n*2pi*i}{127} \right) +}Bcoeff\lbrack i\rbrack*\sin\left( \frac{n*2pi*i}{127} \right)$

As shown in the pseudo code there is several calls to the sine and cosine function (128 * 12). Furthermore, the algorithm requires both the sine and cosine of the same angle. During benchmarking activities the following algorithm was developed and shown to have significant time improvements (~= 5.5 mSec vs ~= 2.4 mSec) over the standard sine and cosine library functions.

Sine and Cosine as Taylor Series:

$$Sin(x) = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!}\ldots$$

$$Cos(x) = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{5}}{5!}\ldots$$

Range Reduction:

Although the Taylor Series for sine and cosine are exact it technically takes an infinite number of terms. The purpose of limiting the value of x into the Taylor Series is so that it doesn’t take many terms before the factorial in the denominator dwarfs the numerator. To limit the input range of x the following identity is used:

Sin(A+B) = Sin(A)Cos(B) + Sin(B)Cos(A)

For reasons that will be discussed later B will be declared as 22.5n, where n is an integer between 0 and 15. Using this technique the largest x input into the Taylor Series will be +/- 11.25 Degrees (0.1963 Radians).

Now that the maximum input value of x has been established it is possible to determine the number of terms in the Taylor Series that are required to achieve acceptable levels of accuracy.

# of Terms	Sin(x)	Sin(x) Max Error	Cos(x)	Cos(x) Max Error
1	Sin(x) = x	0.001259	Cos(x) = 1	0.0192
2	$$Sin(x) = x - \frac{x^{3}}{3!}$$	2.4297E-6	$$Cos(x) = 1 - \frac{x^{2}}{2!}$$	6.18515E-5
3	$$Sin(x) = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!}$$	2.2312E-9	$$Cos(x) = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!}$$	7.953E-8

As the table above shows an acceptable level of accuracy can be achieved with only 2 terms in the sine and cosine Taylor Series once the input has been range limited to +/- 11.25 degrees.

Algorithm:

Calculate n & B:

As shown before, n is the largest integer that satisfies: 22.5n < x. This can be performed using integer math where:

$$n = floor\left( \frac{x*8}{\pi} \right):where\frac{8}{\pi}Radians = 22.5\ Degrees$$

The above equation will leave a remainder that ranges from 0 to 22.5 degrees. By adding in a 0.5 term the result will round up leaving a remainder with the desired range of +/- 11.25 Degrees. Therefore n is calculated as:

$$n = floor\left( \frac{x*8}{\pi} + 0.5 \right)$$

The B term is a simple multiple of n:

$$B = \frac{\pi}{8}*n$$

Determine A:

The A term is the effective remainder of the input angle x minus the B term.

A = x − B

Compute Sin(A) & Cos(A):

Once input x has been range limited into A the term limited Taylor Series of sine and cosine can be computed:

$$Sin(A) = A - \frac{A^{3}}{3!}$$

$$Cos(A) = 1 - \frac{A^{2}}{2!}$$

Compute Sin(x):

Now that Sin(A) & Cos(A) have been determined they can be combined with Sin(B) & Cos(B) to determine Sin(x). The B term is a function of n, which was earlier stated to be a multiple of 22.5 degrees of which there are 16 per revolution. Input x is has no theoretical bound but determining Sin(B) & Cos(B) can be simplified by normalizing n into a single revolution. With n having 16 steps per revolution the normalization is a simple bit mask.

n_nrml = n & 0xF

With normalized n determined it can be used as an index into a switch case statement to determine Sin(x)

Switch (n_nrml)

Case 0:

Sinx = Sin(A)Cos(22.5 * 0) + Sin(22.5 * 0)Cos(A)

Case 1:

Sinx = Sin(A)Cos(22.5 * 1) + Sin(22.5 * 1)Cos(A)

Case 2:

Sinx = Sin(A)Cos(22.5 * 2) + Sin(22.5 * 2)Cos(A)

Case 3:

Sinx = Sin(A)Cos(22.5 * 3) + Sin(22.5 * 3)Cos(A)

Case 4:

Sinx = Sin(A)Cos(22.5 * 4) + Sin(22.5 * 4)Cos(A)

Case 5:

Sinx = Sin(A)Cos(22.5 * 5) + Sin(22.5 * 5)Cos(A)

Case 6:

Sinx = Sin(A)Cos(22.5 * 6) + Sin(22.5 * 6)Cos(A)

Case 7:

Sinx = Sin(A)Cos(22.5 * 7) + Sin(22.5 * 7)Cos(A)

Case 8:

Sinx = Sin(A)Cos(22.5 * 8) + Sin(22.5 * 8)Cos(A)

Case 9:

Sinx = Sin(A)Cos(22.5 * 9) + Sin(22.5 * 9)Cos(A)

Case 10:

Sinx = Sin(A)Cos(22.5 * 10) + Sin(22.5 * 10)Cos(A)

Case 11:

Sinx = Sin(A)Cos(22.5 * 11) + Sin(22.5 * 11)Cos(A)

Case 12:

Sinx = Sin(A)Cos(22.5 * 12) + Sin(22.5 * 12)Cos(A)

Case 13:

Sinx = Sin(A)Cos(22.5 * 13) + Sin(22.5 * 13)Cos(A)

Case 14:

Sinx = Sin(A)Cos(22.5 * 14) + Sin(22.5 * 14)Cos(A)

Case 15:

Sinx = Sin(A)Cos(22.5 * 15) + Sin(22.5 * 15)Cos(A)

The Sin(B) & Cos(B) terms above can be simplified due to their symmetrical nature into 3 predefined constants:

Sin(22.5) = Cos(67.5) = 0.38263

Sin(45.0) = Cos(45.0) = 0.70710

Sin(67.5) = Cos(22.5) = 0.92387

Cos(x) for Free (almost):

The previous calculation computed Sin(x) as a function of Sin(A), Cos(A), Sin(B) & Cos(B). As it turns out cosine has a similar trig identity that uses the exact same terms.

Cos(A+B) = Cos(A)Cos(B) − Sin(A)Sin(B)

The switch case can be modified to simultaneously be used to return the sine and cosine of the same angle at the same time:

Switch (n_nrml)

Case 0:

Sinx = Sin(A)Cos(22.5 * 0) + Sin(22.5 * 0)Cos(A)

Cosx = Cos(A)Cos(22.5 * 0) + Sin(A) Sin(22.5 * 0)

Case 1:

Sinx = Sin(A)Cos(22.5 * 1) + Sin(22.5 * 1)Cos(A)

Cosx = Cos(A)Cos(22.5 * 1) + Sin(A) Sin(22.5 * 1)

Case 2:

Sinx = Sin(A)Cos(22.5 * 2) + Sin(22.5 * 2)Cos(A)

Cosx = Cos(A)Cos(22.5 * 2) + Sin(A) Sin(22.5 * 2)

Case 3:

Sinx = Sin(A)Cos(22.5 * 3) + Sin(22.5 * 3)Cos(A)

Cosx = Cos(A)Cos(22.5 * 3) + Sin(A) Sin(22.5 * 3)

Case 4:

Sinx = Sin(A)Cos(22.5 * 4) + Sin(22.5 * 4)Cos(A)

Cosx = Cos(A)Cos(22.5 * 4) + Sin(A) Sin(22.5 * 4)

Case 5:

Sinx = Sin(A)Cos(22.5 * 5) + Sin(22.5 * 5)Cos(A)

Cosx = Cos(A)Cos(22.5 * 5) + Sin(A) Sin(22.5 * 5)

Case 6:

Sinx = Sin(A)Cos(22.5 * 6) + Sin(22.5 * 6)Cos(A)

Cosx = Cos(A)Cos(22.5 * 6) + Sin(A) Sin(22.5 * 6)

Case 7:

Sinx = Sin(A)Cos(22.5 * 7) + Sin(22.5 * 7)Cos(A)

Cosx = Cos(A)Cos(22.5 * 7) + Sin(A) Sin(22.5 * 7)

Case 8:

Sinx = Sin(A)Cos(22.5 * 8) + Sin(22.5 * 8)Cos(A)

Cosx = Cos(A)Cos(22.5 * 8) + Sin(A) Sin(22.5 * 8)

Case 9:

Sinx = Sin(A)Cos(22.5 * 9) + Sin(22.5 * 9)Cos(A)

Cosx = Cos(A)Cos(22.5 * 9) + Sin(A) Sin(22.5 * 9)

Case 10:

Sinx = Sin(A)Cos(22.5 * 10) + Sin(22.5 * 10)Cos(A)

Cosx = Cos(A)Cos(22.5 * 10) + Sin(A) Sin(22.5 *10)

Case 11:

Sinx = Sin(A)Cos(22.5 * 11) + Sin(22.5 * 11)Cos(A)

Cosx = Cos(A)Cos(22.5 * 11) + Sin(A) Sin(22.5 * 11)

Case 12:

Sinx = Sin(A)Cos(22.5 * 12) + Sin(22.5 * 12)Cos(A)

Cosx = Cos(A)Cos(22.5 * 12) + Sin(A) Sin(22.5 * 12)

Case 13:

Sinx = Sin(A)Cos(22.5 * 13) + Sin(22.5 * 13)Cos(A)

Cosx = Cos(A)Cos(22.5 * 13) + Sin(A) Sin(22.5 * 13)

Case 14:

Sinx = Sin(A)Cos(22.5 * 14) + Sin(22.5 * 14)Cos(A)

Cosx = Cos(A)Cos(22.5 * 14) + Sin(A) Sin(22.5 * 14)

Case 15:

Sinx = Sin(A)Cos(22.5 * 15) + Sin(22.5 * 15)Cos(A)

Cosx = Cos(A)Cos(22.5 * 15) + Sin(A) Sin(22.5 * 15)

Performance:

The following graph shows the output and error of the algorithm. The maximum errors for sine and cosine are:

SinErrorMax = 6.1799e-05

CosErrorMax = 6.1618e-05

Matlab Code:

%% Optimized SinCos Algorithm

ArraySize = uint16(100000);

PiOverEight = pi/8;

EightOverPi = 8/pi;

sin225 = sin(22.5/180*pi);

sin450 = sin(45.0/180*pi);

sin675 = sin(67.5/180*pi);

x = linspace(-2*pi, 2*pi,ArraySize)';

SinX = zeros(ArraySize,1);

CosX = zeros(ArraySize,1);

n = int16(floor(x * EightOverPi + 0.5));

A = (x - double(n) * PiOverEight);

SinA = A - (A.^3)/6;%+(A.^5)/120;

CosA = 1 - (A.^2)/2;%+(A.^4)/24;

n_nrml = bitand(n,15);

for i = 1:ArraySize

switch n_nrml(i)

case 0

SinX(i) = SinA(i);

CosX(i) = CosA(i);

case 1

SinX(i) = sin675 * SinA(i) + sin225 * CosA(i);

CosX(i) = -sin225 * SinA(i) + sin675 * CosA(i);

case 2

SinX(i) = sin450 * SinA(i) + sin450 * CosA(i);

CosX(i) = -sin450 * SinA(i) + sin450 * CosA(i);

case 3

SinX(i) = sin225 * SinA(i) + sin675 * CosA(i);

CosX(i) = -sin675 * SinA(i) + sin225 * CosA(i);

case 4

SinX(i) = CosA(i);

CosX(i) = -SinA(i);

case 5

SinX(i) = -sin225 * SinA(i) + sin675 * CosA(i);

CosX(i) = -sin675 * SinA(i) + -sin225 * CosA(i);

case 6

SinX(i) = -sin450 * SinA(i) + sin450 * CosA(i);

CosX(i) = -sin450 * SinA(i) + -sin450 * CosA(i);

case 7

SinX(i) = -sin675 * SinA(i) + sin225 * CosA(i);

CosX(i) = -sin225 * SinA(i) + -sin675 * CosA(i);

case 8

SinX(i) = -SinA(i);

CosX(i) = -CosA(i);

case 9

SinX(i) = -sin675 * SinA(i) + -sin225 * CosA(i);

CosX(i) = sin225 * SinA(i) + -sin675 * CosA(i);

case 10

SinX(i) = -sin450 * SinA(i) + -sin450 * CosA(i);

CosX(i) = sin450 * SinA(i) + -sin450 * CosA(i);

case 11

SinX(i) = -sin225 * SinA(i) + -sin675 * CosA(i);

CosX(i) = sin675 * SinA(i) + -sin225 * CosA(i);

case 12

SinX(i) = -CosA(i);

CosX(i) = SinA(i);

case 13

SinX(i) = sin225 * SinA(i) + -sin675 * CosA(i);

CosX(i) = sin675 * SinA(i) + sin225 * CosA(i);

case 14

SinX(i) = sin450 * SinA(i) + -sin450 * CosA(i);

CosX(i) = sin450 * SinA(i) + sin450 * CosA(i);

case 15

SinX(i) = sin675 * SinA(i) + -sin225 * CosA(i);

CosX(i) = sin225 * SinA(i) + sin675 * CosA(i);

end

SinError = sin(x) - SinX;

CosError = cos(x) - CosX;

SinErrorMax = max(SinError)

CosErrorMax = max(CosError)

subplot(2,2,1) % first subplot

plot(x*180/pi,SinX)

title('Sin(x)')

xlabel('Angle (Degrees)')

ylabel('Sin(x) (Unitless)')

subplot(2,2,2) % second subplot

plot(x*180/pi,CosX)

title('Cos(x)')

xlabel('Angle (Degrees)')

ylabel('Cos(x) (Unitless)')

subplot(2,2,3) % third subplot

plot(x*180/pi,SinError)

title('Sin(x) Error')

xlabel('Angle (Degrees)')

ylabel('Sin(x) Error (Unitless)')

subplot(2,2,4) % fourth subplot

plot(x*180/pi,CosError)

title('Cos(x) Error')

xlabel('Angle (Degrees)')

ylabel('Cos(x) Error (Unitless)')

4 - SinCos_f32()_Simulation

Overview

Error_Analysis
Timing_Analysis

Sheet 1: Error_Analysis

	Note: Simulation was run in an actual RENESAS uController on a T1XX board.

Angle_deg	Sine	Angle_deg	Cosine	Angle_deg	Error/Sine	Angle_deg	Error/Cosine
-450	-1	-450	4.77E-07	-450	5.96E-08	-450	2.72E-07
-449	-0.999848	-449	0.0174528	-449	5.96E-08	-449	-1.43E-07
-448	-0.999391	-448	0.0348998	-448	0	-448	1.86E-07
-447	-0.998629	-447	0.0523361	-447	-2.98E-07	-447	-2.27E-07
-446	-0.997563	-446	0.069757	-446	-9.54E-07	-446	-3.58E-07
-445	-0.996192	-445	0.0871562	-445	-2.38E-06	-445	7.45E-09
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0	0	0	1	0	0	0	0
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2	0.0348995	2	0.999391	2	0	2	0
3	0.052336	3	0.998629	3	3.73E-09	3	2.38E-07
4	0.0697565	4	0.997563	4	7.45E-09	4	9.54E-07
5	0.0871557	5	0.996192	5	4.47E-08	5	2.38E-06
6	0.104528	6	0.994517	6	1.04E-07	6	4.95E-06
7	0.121869	7	0.992537	7	2.24E-07	7	9.18E-06
8	0.139173	8	0.990252	8	4.47E-07	8	1.58E-05
9	0.156434	9	0.987663	9	8.05E-07	9	2.53E-05
10	0.173647	10	0.984769	10	1.36E-06	10	3.86E-05
11	0.190807	11	0.981571	11	2.16E-06	11	5.65E-05
12	0.207895	12	0.978104	12	1.64E-05	12	4.40E-05
13	0.22494	13	0.974341	13	1.11E-05	13	2.94E-05
14	0.241915	14	0.970277	14	7.18E-06	14	1.89E-05
15	0.258815	15	0.965914	15	4.41E-06	15	1.15E-05
16	0.275635	16	0.961255	16	2.53E-06	16	6.44E-06
17	0.29237	17	0.956301	17	1.28E-06	17	3.34E-06
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19	0.325568	19	0.945518	19	2.38E-07	19	5.96E-07
20	0.34202	20	0.939692	20	8.94E-08	20	1.79E-07
21	0.358368	21	0.93358	21	2.98E-08	21	0
22	0.374607	22	0.927184	22	2.98E-08	22	0
23	0.390731	23	0.920505	23	2.98E-08	23	0
24	0.406737	24	0.913545	24	2.98E-08	24	5.96E-08
25	0.422618	25	0.906308	25	8.94E-08	25	1.79E-07
26	0.438371	26	0.898793	26	2.68E-07	26	5.96E-07
27	0.45399	27	0.891005	27	6.26E-07	27	1.55E-06
28	0.46947	28	0.882944	28	1.43E-06	28	3.28E-06
29	0.484807	29	0.874613	29	2.83E-06	29	6.38E-06
30	0.499995	30	0.866014	30	5.01E-06	30	1.13E-05
31	0.51503	31	0.857149	31	8.34E-06	31	1.85E-05
32	0.529906	32	0.848019	32	1.30E-05	32	2.87E-05
33	0.544619	33	0.838628	33	1.96E-05	33	4.28E-05
34	0.559154	34	0.828996	34	3.84E-05	34	4.15E-05
35	0.57355	35	0.819124	35	2.64E-05	35	2.83E-05
36	0.587768	36	0.808998	36	1.75E-05	36	1.85E-05
37	0.601804	37	0.798624	37	1.08E-05	37	1.15E-05
38	0.615655	38	0.788004	38	6.50E-06	38	6.79E-06
39	0.629317	39	0.777142	39	3.52E-06	39	3.58E-06
40	0.642786	40	0.766043	40	1.73E-06	40	1.73E-06
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46	0.71934	46	0.694658	46	0	46	0
47	0.731354	47	0.681998	47	5.96E-08	47	-5.96E-08
48	0.743145	48	0.66913	48	1.79E-07	48	1.79E-07
49	0.754709	49	0.656058	49	7.15E-07	49	5.96E-07
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52	0.788004	52	0.615655	52	6.74E-06	52	6.26E-06
53	0.798624	53	0.601804	53	1.14E-05	53	1.08E-05
54	0.808998	54	0.587768	54	1.85E-05	54	1.73E-05
55	0.819124	55	0.57355	55	2.83E-05	55	2.63E-05
56	0.828996	56	0.559155	56	4.14E-05	56	3.83E-05
57	0.838628	57	0.54462	57	4.27E-05	57	1.95E-05
58	0.848019	58	0.529906	58	2.86E-05	58	1.30E-05
59	0.857149	59	0.51503	59	1.84E-05	59	8.23E-06
60	0.866014	60	0.499995	60	1.11E-05	60	4.95E-06
61	0.874613	61	0.484807	61	6.26E-06	61	2.80E-06
62	0.882944	62	0.46947	62	3.16E-06	62	1.43E-06
63	0.891005	63	0.45399	63	1.43E-06	63	6.26E-07
64	0.898793	64	0.438371	64	5.36E-07	64	2.09E-07
65	0.906308	65	0.422618	65	1.19E-07	65	8.94E-08
66	0.913545	66	0.406737	66	-5.96E-08	66	0
67	0.920505	67	0.390731	67	0	67	2.98E-08
68	0.927184	68	0.374607	68	0	68	2.98E-08
69	0.93358	69	0.358368	69	0	69	0
70	0.939692	70	0.34202	70	1.79E-07	70	1.49E-07
71	0.945518	71	0.325568	71	5.36E-07	71	2.68E-07
72	0.951055	72	0.309016	72	1.49E-06	72	6.26E-07
73	0.956301	73	0.29237	73	3.28E-06	73	1.31E-06
74	0.961255	74	0.275635	74	6.50E-06	74	2.56E-06
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76	0.970277	76	0.241915	76	1.89E-05	76	7.18E-06
77	0.974341	77	0.22494	77	2.94E-05	77	1.11E-05
78	0.978104	78	0.207895	78	4.40E-05	78	1.65E-05
79	0.981571	79	0.190807	79	5.66E-05	79	2.09E-06
80	0.984769	80	0.173647	80	3.86E-05	80	1.27E-06
81	0.987663	81	0.156434	81	2.53E-05	81	7.45E-07
82	0.990252	82	0.139173	82	1.58E-05	82	3.28E-07
83	0.992537	83	0.121869	83	9.24E-06	83	1.27E-07
84	0.994517	84	0.104528	84	4.95E-06	84	7.45E-09
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87	0.998629	87	0.052336	87	2.38E-07	87	-1.56E-07
88	0.999391	88	0.0348995	88	0	88	-6.33E-08
89	0.999848	89	0.0174524	89	-5.96E-08	89	-7.45E-09
90	1	90	0	90	-5.96E-08	90	0
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92	0.999391	92	-0.0348994	92	0	92	1.49E-08
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100	0.984769	100	-0.173647	100	3.86E-05	100	-1.28E-06
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104	0.970277	104	-0.241915	104	1.88E-05	104	-7.20E-06
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114	0.913545	114	-0.406736	114	5.96E-08	114	2.98E-08
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131	0.754709	131	-0.656058	131	7.75E-07	131	-7.15E-07
132	0.743145	132	-0.66913	132	1.79E-07	132	-2.98E-07
133	0.731354	133	-0.681998	133	5.96E-08	133	0
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136	0.694658	136	-0.71934	136	1.19E-07	136	5.96E-08
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148	0.529906	148	-0.848019	148	1.29E-05	148	-2.87E-05
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150	0.499995	150	-0.866014	150	4.89E-06	150	-1.13E-05
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153	0.45399	153	-0.891005	153	6.85E-07	153	-1.43E-06
154	0.438371	154	-0.898793	154	2.09E-07	154	-5.96E-07
155	0.422618	155	-0.906308	155	5.96E-08	155	-1.79E-07
156	0.406737	156	-0.913545	156	-5.96E-08	156	-5.96E-08
157	0.390731	157	-0.920505	157	-5.96E-08	157	-5.96E-08
158	0.374607	158	-0.927184	158	0	158	0
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160	0.34202	160	-0.939692	160	0	160	-1.79E-07
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163	0.292371	163	-0.956301	163	1.22E-06	163	-3.34E-06
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167	0.22494	167	-0.97434	167	1.11E-05	167	-2.95E-05
168	0.207895	168	-0.978104	168	1.63E-05	168	-4.40E-05
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170	0.173647	170	-0.984769	170	1.43E-06	170	-3.86E-05
171	0.156434	171	-0.987663	171	7.75E-07	171	-2.53E-05
172	0.139173	172	-0.990252	172	4.62E-07	172	-1.58E-05
173	0.121869	173	-0.992537	173	3.35E-07	173	-9.24E-06
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178	0.0348995	178	-0.999391	178	5.22E-08	178	0
179	0.0174525	179	-0.999848	179	9.50E-08	179	5.96E-08
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181	-0.0174523	181	-0.999848	181	4.10E-08	181	5.96E-08
182	-0.0348993	182	-0.999391	182	8.57E-08	182	0
183	-0.0523359	183	-0.998629	183	-1.12E-08	183	-2.98E-07
184	-0.0697563	184	-0.997563	184	2.24E-08	184	-9.54E-07
185	-0.0871557	185	-0.996192	185	-1.04E-07	185	-2.38E-06
186	-0.104528	186	-0.994517	186	-1.27E-07	186	-4.95E-06
187	-0.121869	187	-0.992537	187	-2.09E-07	187	-9.24E-06
188	-0.139173	188	-0.990252	188	-5.07E-07	188	-1.58E-05
189	-0.156433	189	-0.987663	189	-8.34E-07	189	-2.53E-05
190	-0.173647	190	-0.984769	190	-1.48E-06	190	-3.86E-05
191	-0.190807	191	-0.981571	191	-2.25E-06	191	-5.65E-05
192	-0.207895	192	-0.978104	192	-1.61E-05	192	-4.41E-05
193	-0.22494	193	-0.974341	193	-1.11E-05	193	-2.94E-05
194	-0.241915	194	-0.970277	194	-7.20E-06	194	-1.88E-05
195	-0.258815	195	-0.965914	195	-4.11E-06	195	-1.15E-05
196	-0.275635	196	-0.961255	196	-2.59E-06	196	-6.44E-06
197	-0.29237	197	-0.956301	197	-1.07E-06	197	-3.34E-06
198	-0.309016	198	-0.951055	198	-3.58E-07	198	-1.55E-06
199	-0.325568	199	-0.945518	199	5.96E-08	199	-6.56E-07
200	-0.34202	200	-0.939692	200	8.94E-08	200	-2.38E-07
201	-0.358368	201	-0.93358	201	1.79E-07	201	-1.79E-07
202	-0.374607	202	-0.927184	202	1.49E-07	202	-5.96E-08
203	-0.390731	203	-0.920505	203	1.79E-07	203	-5.96E-08
204	-0.406736	204	-0.913545	204	1.79E-07	204	-1.19E-07
205	-0.422618	205	-0.906308	205	5.96E-08	205	-1.79E-07
206	-0.438371	206	-0.898794	206	-2.98E-08	206	-6.56E-07
207	-0.45399	207	-0.891005	207	-5.66E-07	207	-1.49E-06
208	-0.46947	208	-0.882944	208	-1.28E-06	208	-3.28E-06
209	-0.484807	209	-0.874613	209	-2.74E-06	209	-6.32E-06
210	-0.499995	210	-0.866014	210	-4.92E-06	210	-1.11E-05
211	-0.51503	211	-0.857149	211	-8.17E-06	211	-1.84E-05
212	-0.529906	212	-0.848019	212	-1.29E-05	212	-2.87E-05
213	-0.544619	213	-0.838628	213	-1.95E-05	213	-4.27E-05
214	-0.559154	214	-0.828996	214	-3.86E-05	214	-4.14E-05
215	-0.57355	215	-0.819124	215	-2.65E-05	215	-2.81E-05
216	-0.587768	216	-0.808999	216	-1.75E-05	216	-1.84E-05
217	-0.601804	217	-0.798624	217	-1.11E-05	217	-1.14E-05
218	-0.615655	218	-0.788004	218	-6.56E-06	218	-6.62E-06
219	-0.629317	219	-0.777142	219	-3.40E-06	219	-3.70E-06
220	-0.642786	220	-0.766043	220	-1.85E-06	220	-1.61E-06
221	-0.656058	221	-0.754709	221	-7.15E-07	221	-7.75E-07
222	-0.66913	222	-0.743145	222	-1.19E-07	222	-3.58E-07
223	-0.681998	223	-0.731354	223	-1.79E-07	223	1.19E-07
224	-0.694658	224	-0.71934	224	5.96E-08	224	-1.19E-07
225	-0.707107	225	-0.707107	225	5.96E-08	225	0
226	-0.71934	226	-0.694658	226	5.96E-08	226	-1.19E-07
227	-0.731354	227	-0.681998	227	0	227	-1.19E-07
228	-0.743144	228	-0.669131	228	-1.19E-07	228	-4.17E-07
229	-0.754709	229	-0.656058	229	-7.15E-07	229	-7.75E-07
230	-0.766043	230	-0.642786	230	-1.73E-06	230	-1.73E-06
231	-0.777142	231	-0.629317	231	-3.58E-06	231	-3.46E-06
232	-0.788004	232	-0.615655	232	-6.74E-06	232	-6.44E-06
233	-0.798624	233	-0.601804	233	-1.14E-05	233	-1.10E-05
234	-0.808998	234	-0.587768	234	-1.84E-05	234	-1.75E-05
235	-0.819124	235	-0.57355	235	-2.83E-05	235	-2.63E-05
236	-0.828996	236	-0.559155	236	-4.15E-05	236	-3.84E-05
237	-0.838628	237	-0.54462	237	-4.28E-05	237	-1.94E-05
238	-0.848019	238	-0.529907	238	-2.87E-05	238	-1.29E-05
239	-0.857149	239	-0.51503	239	-1.84E-05	239	-8.17E-06
240	-0.866014	240	-0.499995	240	-1.13E-05	240	-4.74E-06
241	-0.874613	241	-0.484807	241	-6.50E-06	241	-2.53E-06
242	-0.882944	242	-0.469471	242	-3.40E-06	242	-1.22E-06
243	-0.891005	243	-0.45399	243	-1.55E-06	243	-4.77E-07
244	-0.898793	244	-0.438371	244	-5.96E-07	244	-2.09E-07
245	-0.906308	245	-0.422618	245	-1.79E-07	245	-5.96E-08
246	-0.913545	246	-0.406737	246	-5.96E-08	246	-5.96E-08
247	-0.920505	247	-0.390732	247	-1.19E-07	247	2.68E-07
248	-0.927184	248	-0.374607	248	-1.19E-07	248	2.38E-07
249	-0.93358	249	-0.358368	249	0	249	1.19E-07
250	-0.939692	250	-0.34202	250	-1.79E-07	250	0
251	-0.945518	251	-0.325568	251	-5.96E-07	251	-1.79E-07
252	-0.951055	252	-0.309017	252	-1.49E-06	252	-5.96E-07
253	-0.956301	253	-0.292371	253	-3.34E-06	253	-1.01E-06
254	-0.961255	254	-0.275635	254	-6.50E-06	254	-2.35E-06
255	-0.965914	255	-0.258815	255	-1.15E-05	255	-4.23E-06
256	-0.970277	256	-0.241915	256	-1.90E-05	256	-7.11E-06
257	-0.97434	257	-0.22494	257	-2.94E-05	257	-1.10E-05
258	-0.978103	258	-0.207896	258	-4.40E-05	258	-1.64E-05
259	-0.981571	259	-0.190807	259	-5.65E-05	259	-2.25E-06
260	-0.984769	260	-0.173647	260	-3.86E-05	260	-1.48E-06
261	-0.987663	261	-0.156434	261	-2.53E-05	261	-9.54E-07
262	-0.990252	262	-0.139173	262	-1.58E-05	262	-6.41E-07
263	-0.992537	263	-0.121869	263	-9.18E-06	263	-4.69E-07
264	-0.994517	264	-0.104528	264	-4.95E-06	264	-1.27E-07
265	-0.996192	265	-0.0871557	265	-2.38E-06	265	-1.04E-07
266	-0.997563	266	-0.0697565	266	-8.94E-07	266	-1.12E-07
267	-0.998629	267	-0.0523361	267	-2.38E-07	267	-1.49E-07
268	-0.999391	268	-0.0348998	268	0	268	-1.86E-07
269	-0.999848	269	-0.0174523	269	5.96E-08	269	-3.33E-07
270	-1	270	0	270	5.96E-08	270	0
271	-0.999848	271	0.0174523	271	5.96E-08	271	-4.10E-08
272	-0.999391	272	0.0348993	272	0	272	-8.57E-08
273	-0.998629	273	0.0523361	273	-2.98E-07	273	-2.27E-07
274	-0.997563	274	0.0697565	274	-9.54E-07	274	-2.61E-07
275	-0.996192	275	0.0871557	275	-2.38E-06	275	-2.68E-07
276	-0.994517	276	0.104528	276	-5.01E-06	276	-2.46E-07
277	-0.992537	277	0.121869	277	-9.24E-06	277	2.09E-07
278	-0.990252	278	0.139173	278	-1.59E-05	278	2.68E-07
279	-0.987663	279	0.156434	279	-2.54E-05	279	5.96E-07
280	-0.984769	280	0.173647	280	-3.87E-05	280	1.10E-06
281	-0.981571	281	0.190807	281	-5.66E-05	281	1.88E-06
282	-0.978104	282	0.207895	282	-4.40E-05	282	1.62E-05
283	-0.974341	283	0.22494	283	-2.94E-05	283	1.11E-05
284	-0.970277	284	0.241915	284	-1.88E-05	284	7.20E-06
285	-0.965914	285	0.258814	285	-1.14E-05	285	4.35E-06
286	-0.961255	286	0.275635	286	-6.50E-06	286	2.44E-06
287	-0.956302	287	0.29237	287	-3.34E-06	287	1.19E-06
288	-0.951055	288	0.309016	288	-1.43E-06	288	7.15E-07
289	-0.945518	289	0.325568	289	-5.36E-07	289	2.98E-07
290	-0.939693	290	0.34202	290	-1.19E-07	290	1.19E-07
291	-0.933581	291	0.358368	291	-5.96E-08	291	2.98E-08
292	-0.927184	292	0.374606	292	-5.96E-08	292	-2.98E-08
293	-0.920505	293	0.390731	293	-5.96E-08	293	-1.79E-07
294	-0.913545	294	0.406736	294	5.96E-08	294	1.49E-07
295	-0.906308	295	0.422618	295	-1.19E-07	295	1.79E-07
296	-0.898794	296	0.438371	296	-4.77E-07	296	2.68E-07
297	-0.891005	297	0.453989	297	-1.49E-06	297	6.85E-07
298	-0.882944	298	0.46947	298	-3.28E-06	298	1.28E-06
299	-0.874613	299	0.484807	299	-6.44E-06	299	2.65E-06
300	-0.866014	300	0.499995	300	-1.11E-05	300	5.16E-06
301	-0.857149	301	0.515029	301	-1.84E-05	301	8.34E-06
302	-0.848019	302	0.529906	302	-2.87E-05	302	1.29E-05
303	-0.838628	303	0.544619	303	-4.27E-05	303	1.95E-05
304	-0.828996	304	0.559154	304	-4.14E-05	304	3.85E-05
305	-0.819124	305	0.57355	305	-2.83E-05	305	2.63E-05
306	-0.808999	306	0.587767	306	-1.85E-05	306	1.73E-05
307	-0.798624	307	0.601804	307	-1.14E-05	307	1.11E-05
308	-0.788004	308	0.615655	308	-6.62E-06	308	6.56E-06
309	-0.777143	309	0.629317	309	-3.52E-06	309	3.58E-06
310	-0.766043	310	0.642786	310	-1.73E-06	310	1.79E-06
311	-0.754709	311	0.656058	311	-7.75E-07	311	7.75E-07
312	-0.743145	312	0.66913	312	-5.96E-08	312	4.17E-07
313	-0.731354	313	0.681998	313	1.19E-07	313	1.79E-07
314	-0.71934	314	0.694658	314	5.96E-08	314	1.19E-07
315	-0.707107	315	0.707106	315	1.79E-07	315	1.19E-07
316	-0.694659	316	0.719339	316	0	316	0
317	-0.681998	317	0.731354	317	1.79E-07	317	2.38E-07
318	-0.669131	318	0.743144	318	-1.19E-07	318	3.58E-07
319	-0.656059	319	0.754709	319	-5.96E-07	319	8.94E-07
320	-0.642786	320	0.766042	320	-1.55E-06	320	1.79E-06
321	-0.629317	321	0.777142	321	-3.34E-06	321	3.70E-06
322	-0.615655	322	0.788004	322	-6.44E-06	322	6.74E-06
323	-0.601804	323	0.798624	323	-1.10E-05	323	1.14E-05
324	-0.587768	324	0.808998	324	-1.72E-05	324	1.87E-05
325	-0.573551	325	0.819123	325	-2.62E-05	325	2.84E-05
326	-0.559155	326	0.828996	326	-3.83E-05	326	4.15E-05
327	-0.544619	327	0.838628	327	-1.98E-05	327	4.24E-05
328	-0.529906	328	0.848019	328	-1.33E-05	328	2.84E-05
329	-0.51503	329	0.857149	329	-8.58E-06	329	1.82E-05
330	-0.499995	330	0.866014	330	-5.07E-06	330	1.11E-05
331	-0.484807	331	0.874613	331	-2.98E-06	331	6.26E-06
332	-0.46947	332	0.882944	332	-1.64E-06	332	3.16E-06
333	-0.45399	333	0.891005	333	-8.64E-07	333	1.31E-06
334	-0.438371	334	0.898793	334	-5.36E-07	334	4.17E-07
335	-0.422618	335	0.906308	335	-3.87E-07	335	0
336	-0.406736	336	0.913545	336	-1.49E-07	336	-5.96E-08
337	-0.390731	337	0.920505	337	-1.79E-07	337	-5.96E-08
338	-0.374607	338	0.927184	338	-2.09E-07	338	-5.96E-08
339	-0.358368	339	0.93358	339	-2.38E-07	339	-1.19E-07
340	-0.34202	340	0.939692	340	-3.58E-07	340	5.96E-08
341	-0.325568	341	0.945518	341	-2.98E-07	341	5.36E-07
342	-0.309016	342	0.951055	342	-7.15E-07	342	1.43E-06
343	-0.29237	343	0.956301	343	-1.43E-06	343	3.22E-06
344	-0.275635	344	0.961255	344	-2.71E-06	344	6.44E-06
345	-0.258815	345	0.965914	345	-4.62E-06	345	1.14E-05
346	-0.241915	346	0.970277	346	-7.57E-06	346	1.88E-05
347	-0.22494	347	0.974341	347	-1.11E-05	347	2.94E-05
348	-0.207895	348	0.978104	348	-1.65E-05	348	4.40E-05
349	-0.190807	349	0.981571	349	-2.15E-06	349	5.65E-05
350	-0.173647	350	0.984769	350	-1.37E-06	350	3.86E-05
351	-0.156434	351	0.987663	351	-9.54E-07	351	2.53E-05
352	-0.139173	352	0.990252	352	-6.41E-07	352	1.58E-05
353	-0.121869	353	0.992537	353	-4.69E-07	353	9.18E-06
354	-0.104529	354	0.994517	354	-2.24E-08	354	4.95E-06
355	-0.0871562	355	0.996192	355	-7.45E-09	355	2.38E-06
356	-0.0697565	356	0.997563	356	-1.12E-07	356	8.94E-07
357	-0.0523361	357	0.998629	357	-1.49E-07	357	2.38E-07
358	-0.0348998	358	0.999391	358	-1.86E-07	358	0
359	-0.0174528	359	0.999848	359	-2.31E-07	359	-5.96E-08
360	0	360	1	360	0	360	-5.96E-08
361	0.0174523	361	0.999848	361	-4.15E-07	361	-5.96E-08
362	0.0348993	362	0.999391	362	-8.57E-08	362	0
363	0.0523357	363	0.998629	363	2.50E-07	363	2.98E-07
364	0.0697561	364	0.997563	364	-1.56E-07	364	9.54E-07
365	0.0871557	365	0.996192	365	-2.68E-07	365	2.38E-06
366	0.104528	366	0.994517	366	1.27E-07	366	4.95E-06
367	0.121869	367	0.992537	367	-1.64E-07	367	9.30E-06
368	0.139172	368	0.990252	368	3.73E-07	368	1.59E-05
369	0.156433	369	0.987663	369	1.06E-06	369	2.53E-05
370	0.173647	370	0.984769	370	1.48E-06	370	3.86E-05
371	0.190807	371	0.981571	371	1.88E-06	371	5.66E-05
372	0.207895	372	0.978104	372	1.66E-05	372	4.40E-05
373	0.224939	373	0.974341	373	1.09E-05	373	2.96E-05
374	0.241914	374	0.970277	374	7.26E-06	374	1.88E-05
375	0.258814	375	0.965914	375	4.35E-06	375	1.14E-05
376	0.275635	376	0.961255	376	2.80E-06	376	6.38E-06
377	0.29237	377	0.956302	377	1.19E-06	377	3.34E-06
378	0.309016	378	0.951055	378	8.05E-07	378	1.43E-06
379	0.325567	379	0.945518	379	2.98E-08	379	5.96E-07
380	0.34202	380	0.939693	380	4.47E-07	380	0
381	0.358368	381	0.933581	381	2.98E-08	381	5.96E-08
382	0.374606	382	0.927184	382	2.98E-07	382	-1.19E-07
383	0.390731	383	0.920505	383	-5.96E-08	383	5.96E-08
384	0.406736	384	0.913545	384	-1.79E-07	384	1.19E-07
385	0.422618	385	0.906308	385	1.79E-07	385	1.19E-07
386	0.438371	386	0.898794	386	6.56E-07	386	2.98E-07
387	0.453989	387	0.891005	387	6.85E-07	387	1.49E-06
388	0.46947	388	0.882945	388	1.70E-06	388	3.04E-06
389	0.484807	389	0.874613	389	2.98E-06	389	6.26E-06
390	0.499995	390	0.866014	390	4.86E-06	390	1.13E-05
391	0.515029	391	0.857149	391	8.34E-06	391	1.84E-05
392	0.529906	392	0.84802	392	1.34E-05	392	2.84E-05
393	0.544619	393	0.838628	393	1.97E-05	393	4.27E-05
394	0.559155	394	0.828996	394	3.81E-05	394	4.17E-05
395	0.57355	395	0.819124	395	2.63E-05	395	2.83E-05
396	0.587768	396	0.808999	396	1.70E-05	396	1.88E-05
397	0.601804	397	0.798624	397	1.08E-05	397	1.16E-05
398	0.615655	398	0.788004	398	5.96E-06	398	7.09E-06
399	0.629317	399	0.777142	399	3.46E-06	399	3.58E-06
400	0.642786	400	0.766043	400	1.43E-06	400	1.97E-06
401	0.656058	401	0.754709	401	7.15E-07	401	7.75E-07
402	0.66913	402	0.743145	402	-1.79E-07	402	5.96E-07
403	0.681998	403	0.731354	403	-1.19E-07	403	1.19E-07
404	0.694658	404	0.71934	404	-1.79E-07	404	2.38E-07
405	0.707107	405	0.707107	405	-5.96E-08	405	5.96E-08
406	0.71934	406	0.694658	406	-3.58E-07	406	3.58E-07
407	0.731354	407	0.681998	407	0	407	1.19E-07
408	0.743144	408	0.669131	408	-1.19E-07	408	6.56E-07
409	0.754709	409	0.656058	409	7.75E-07	409	7.15E-07
410	0.766043	410	0.642786	410	1.49E-06	410	1.97E-06
411	0.777142	411	0.629317	411	3.58E-06	411	3.46E-06
412	0.788004	412	0.615655	412	6.50E-06	412	6.74E-06
413	0.798624	413	0.601804	413	1.11E-05	413	1.14E-05
414	0.808999	414	0.587768	414	1.84E-05	414	1.76E-05
415	0.819124	415	0.57355	415	2.79E-05	415	2.69E-05
416	0.828996	416	0.559155	416	4.12E-05	416	3.87E-05
417	0.838628	417	0.54462	417	4.28E-05	417	1.94E-05
418	0.848019	418	0.529906	418	2.87E-05	418	1.29E-05
419	0.857149	419	0.51503	419	1.82E-05	419	8.58E-06
420	0.866014	420	0.499995	420	1.11E-05	420	5.07E-06
421	0.874613	421	0.484807	421	6.08E-06	421	3.22E-06
422	0.882944	422	0.469471	422	3.22E-06	422	1.55E-06
423	0.891005	423	0.45399	423	1.31E-06	423	8.64E-07
424	0.898793	424	0.438371	424	5.96E-07	424	2.09E-07
425	0.906308	425	0.422618	425	0	425	3.87E-07
426	0.913545	426	0.406737	426	5.96E-08	426	5.96E-08
427	0.920505	427	0.390732	427	-1.79E-07	427	4.17E-07
428	0.927184	428	0.374607	428	5.96E-08	428	-1.49E-07
429	0.93358	429	0.358368	429	-1.19E-07	429	2.38E-07
430	0.939692	430	0.34202	430	1.79E-07	430	0
431	0.945518	431	0.325568	431	4.77E-07	431	5.66E-07
432	0.951055	432	0.309017	432	1.49E-06	432	5.96E-07
433	0.956301	433	0.29237	433	3.22E-06	433	1.43E-06
434	0.961255	434	0.275635	434	6.50E-06	434	2.35E-06
435	0.965914	435	0.258815	435	1.14E-05	435	4.62E-06
436	0.970277	436	0.241915	436	1.90E-05	436	7.11E-06
437	0.97434	437	0.22494	437	2.94E-05	437	1.14E-05
438	0.978104	438	0.207895	438	4.39E-05	438	1.68E-05
439	0.981571	439	0.190807	439	5.65E-05	439	2.15E-06
440	0.984769	440	0.173647	440	3.87E-05	440	1.01E-06
441	0.987663	441	0.156434	441	2.53E-05	441	8.49E-07
442	0.990252	442	0.139173	442	1.58E-05	442	6.41E-07
443	0.992537	443	0.121869	443	9.24E-06	443	9.69E-08
444	0.994517	444	0.104529	444	4.95E-06	444	3.95E-07
445	0.996192	445	0.0871562	445	2.38E-06	445	7.45E-09
446	0.997563	446	0.069757	446	9.54E-07	446	-3.58E-07
447	0.998629	447	0.0523361	447	2.98E-07	447	-2.27E-07
448	0.999391	448	0.0348998	448	0	448	1.86E-07
449	0.999848	449	0.0174528	449	-5.96E-08	449	-1.43E-07
450	1	450	4.77E-07	450	-5.96E-08	450	2.72E-07

Sheet 2: Timing_Analysis

Timing Analysis for 900 sin and cosine calculations from -450 deg to 450 deg


Using Sin_f32() and Sin_f32()			Using SinCos_f32()
1192 usec			585 usec