Cos De Reciclare Windows Vista

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The SINCOS instruction computes sine and cosine, in radians. The X component of the result contains cos(x); the Y component contains sin(x).

Format

instruction token that contains D3DSIO_SINCOS. Instruction length is 4.

destination parameter token using the D3DSPR_TEMP register type.

first source parameter token. Requires explicit use of replicate swizzle, that is, the X, Y, Z, or W swizzle component (or the R, G, B, or A equivalent) must be specified.

The following source tokens are for pixel and vertex shader versions earlier than 3_0. That is, for pixel and vertex shader version 3_0 and later, only the first source parameter token is used.

second source parameter token using the D3DSPR_TEMP register type.

third source parameter token using the D3DSPR_TEMP register type.

The second and third sources could be used as temporary registers.

Source register rules:

  • src1. selected_channel is an angle measured in radians between -Pi and +Pi.

  • src2 = (−1.f/(7!*128), −1.f/(6!*64), 1.f/(4!*16), 1.f/(5!*32) ).

  • src3 = (−1.f/(3!*8), −1.f/(2!*8), 1.f, 0.5f).

    The ordering of the last two numbers in src2 and src3 is specifically chosen to accommodate pixel shader 2.0, which also has the SINCOS macro. Reversing these numbers means that the macro expansion can use one of the few custom source swizzles that is available to ps_2_0 (vertex shaders have general swizzle so there is no issue). This allows the same custom constants to be used, regardless of where sincos is being used.

Destination register rules:

  • dest.x = cos(src1.selected_channel), dest.y = sin(src1.selected_channel), dest.z is undefined after the instruction.

  • dest should not be the same register as src1.

  • Only X and Y are allowed to be in the destination write mask.

The SINCOS instruction is a macro instruction that takes eight instruction slots.

Only X and Y are allowed to be in the destination write mask.

Cos De Reciclare Windows Vista

The maximum absolute error is 0.002.

Cos

Operation

The following shows the Taylor series for sin(x) and cos(x):

(1) cos(x) = 1 - x2/2! + x4/4! - x6/6! sin(x) = x - x3/3! + x5/5! - x7/7! = x*(1 - x2/3! + x4/5! - x6/7!)

To increase precision we compute cos(x) using cos(x/2):

(2) cos(x) = 1 - 2*sin(x/2)*sin(x/2) sin(x) = 2*sin(x/2)*cos(x/2)

(1) can be re-written by substituting x to x/2 as:

(3) cos(x) = 1 - x2/(2!*4) + x4/(4!*16) - x6/(6!*64) sin(x) = x/2 - x3/(3!*8) + x5/(5!*32) - x7/(7!*128) = = x*(0.5f - x2/(3!*8) + x4/(5!*32) - x6/(7!*128))

Lets, write (3) in vector form. Here a,b,c,d are 2D constant vectors:

a + x2*b + x4*c + x6*d = a+x2*(b + x2*(c + x2*d)

The following shows the implementation for SINCOS:

SRC2 should be constant:

(1.f/(7!*128), 1.f/(6!*64), 1.f/(4!*16), 1.f/(5!*32) )

SRC3 should be constant:

Reciclare

Partial sin(x/2) and final cos(x/2):

Cos De Reciclare Windows Vista De

If an application must compute SINCOS for an arbitrary angle, the angle can be mapped to the range -Pi...+Pi by using the following macro (r0.x holds the original angle):

Requirements

Cos De Reciclare Windows Vista

Available in Windows Vista and later versions of the Windows operating systems.