Glsl mod vs Hlsl fmod - math

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
What are the differences between GLSL mod and HLSLfmod?
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.