Glsl mod vs Hlsl fmod

Question

I've implemented the spiral GLSL shader described in this question in HLSL, but the results are not the same. I think it's because of the mod function in GLSL that I've translated to fmod in HLSL. I suspect that this problem only happens when we have negative numbers in the input of the fmod function.

I've tried replacing the call to mod by a call to a function that I've made which does what is described in the GLSL documentation and it works:

mod returns the value of x modulo y. This is computed as x - y * floor(x/y).

The working code I use instead of fmod is:

float mod(float x, float y)
{
  return x - y * floor(x/y)
}

By contrast to GLSL mod, MSDN says the HLSL fmod function does this:

The floating-point remainder is calculated such that x = i * y + f, where i is an integer, f has the same sign as x, and the absolute value of f is less than the absolute value of y.

I've used an HLSL to GLSL converter, and the fmod function is translated as mod. However, I don't know if I can assume that mod translates to fmod.

Questions

1. What are the differences between GLSL mod and HLSLfmod?
2. How can I translate MSDN's cryptic description of fmod to a pseudo-code implementation?

GLSL Shader

uniform float time;
uniform vec2 resolution;
uniform vec2 aspect;

void main( void ) {
  vec2 position = -aspect.xy + 2.0 * gl_FragCoord.xy / resolution.xy * aspect.xy;
  float angle = 0.0 ;
  float radius = length(position) ;
  if (position.x != 0.0 && position.y != 0.0){
    angle = degrees(atan(position.y,position.x)) ;
  }
  float amod = mod(angle+30.0*time-120.0*log(radius), 30.0) ;
  if (amod<15.0){
    gl_FragColor = vec4( 0.0, 0.0, 0.0, 1.0 );
  } else{
    gl_FragColor = vec4( 1.0, 1.0, 1.0, 1.0 );                    
  }
}

HLSL Shader

struct Psl_VertexShaderInput
{
    float3 pos : POSITION;
};

struct Psl_VertexShaderOutput
{
    float4 pos : POSITION;

};

struct Psl_PixelShaderOutput
{
    float4 Output0 : COLOR0;
};

float3 psl_positionOffset;
float2 psl_dimension;

Psl_VertexShaderOutput Psl_VertexShaderFunction(Psl_VertexShaderInput psl_input)
{
    Psl_VertexShaderOutput psl_output = (Psl_VertexShaderOutput)0;

    psl_output.pos = float4(psl_input.pos + psl_positionOffset, 1);


    return psl_output;
}

float time : TIME;
float2 resolution : DIMENSION;


Psl_PixelShaderOutput Psl_PixelShaderFunction(float2 pos : VPOS)
{
    Psl_PixelShaderOutput psl_output = (Psl_PixelShaderOutput)0;

    float2 aspect = float2(resolution.x / resolution.y, 1.0);
    float2 position = -aspect.xy + 2.0 * pos.xy / resolution.xy * aspect.xy;
    float angle = 0.0;
    float radius = length(position);
    if (position.x != 0.0 && position.y != 0.0)
    {
        angle = degrees(atan2(position.y, position.x));
    }
    float amod = fmod((angle + 30.0 * time - 120.0 * log(radius)), 30.0);
    if (amod < 15.0)
    {
        psl_output.Output0 = float4(0.0, 0.0, 0.0, 1.0);
        return psl_output;
    }

    else
    {
        psl_output.Output0 = float4(1.0, 1.0, 1.0, 1.0);
        return psl_output;
    }

}

technique Default
{
    pass P0
    {
        VertexShader = compile vs_3_0 Psl_VertexShaderFunction();
        PixelShader = compile ps_3_0 Psl_PixelShaderFunction();
    }
}

Answer 1

As you've noted, they're different. The GLSL mod will always have the same sign as y rather than x. Otherwise it's the same -- a value f such that x = i*y + f where i is an integer and |f| < |y|. If you're trying to make a repeating pattern of some kind, the GLSL mod is generally what you want.

For comparison, the HLSL fmod is equivalent to x - y * trunc(x/y). They're the same when x/y is positive, different when x/y is negative.