So the “i915” Intel graphics are actually part of the N3700 SoC https://en.wikichip.org/wiki/intel/pentium_(2009)/n3700, launched in 2015, which is a 1.6GHz quad-core amd64 CPU with 16 Braswell “HD graphics” execution units, running at 400MHz.
https://ark.intel.com/products/87261/Intel-Pentium-Processor-N3700-2M-Cache-up-to-2-40-GHz-
https://en.wikipedia.org/wiki/List_of_Intel_graphics_processing_units#Eighth_generation says this is of Intel’s “eighth generation”, and its core config is “128:16:2” with 25.6 GB/s memory bandwidth, which means 128 FP32 ALUs, 16 EUs (“execution units”, each containing 2 SIMD-4 FPUs), and 2 subslices, each containing 8 EUs and a 4 texels-per-clock sampler. It also says that each EU is capable of 8 multiply-accumulates per clock cycle (one per ALU, I guess) in single-precision floating-point, but 16-bit floating-point is capable of “2× floating-point performance”. Also they can do integer operations at the 32-bit floating-point speed, or 64-bit floating-point at ¼ the 32-bit speed.
Doing the math, that suggests that it can do 400 * 128 million single-precision multiply-accumulates per second, or 51.2 billion. Intel likes to double-count these multiply-accumulates, as if the addition and the multiplication were two separate operations, which dishonestly inflates their published flops counts by a factor of 2.
By contrast, https://en.wikipedia.org/wiki/Nvidia_Tesla says the NVIDIA Tesla V100 GPU Accelerator, released in 2017, reaches 14900 single-precision Gflops, about 300 times faster. And https://en.wikichip.org/wiki/intel/hd_graphics_630 says the later Kaby Lake GPUs reach 134 single-precision GFlops with 24 EUs at 350 GHz, so maybe it’s plausible. https://news.ycombinator.com/item?id=18146625 says the V100 also costs US$10k, which is about 30× what my laptop costs, so the laptop has 10× worse price-performance.
It supports OpenCL and GLSL.
https://github.com/Themaister/GLFFT is an FFT implementation that has been tested on another GPU in the family. https://software.intel.com/en-us/intel-opencl is OpenCL which I think supports it. https://en.wikichip.org/w/images/f/f4/Compute_Architecture_of_Intel_Processor_Graphics_Gen8.pdf is a detailed description of the compute architecture.
https://01.org/linuxgraphics/downloads/2018q1-intel-graphics-stack-recipe calls Gen8 “Coffee Lake”.
https://software.intel.com/en-us/articles/introduction-to-gen-assembly is an introduction to its assembly language.
So an interesting thing here is that the GPU can do 51.2 billion single-precision multiply-accumulates per second, or 51.2 billion 32-bit integer ops. But the CPU is 1.6 GHz with four cores, each of which supports the SSE4.2 instruction set extensions, which supports SIMD operations on 128-bit vectors of, among other things, four 32-bit floating-point or integer values. Supposing that each core is capable of running one such instruction each cycle, that’s 1.6 · 4 · 4 = 25.6 gigaflops of single-precision floating-point. This is only half the power of the GPU, but still, I think, substantially more than the CPU’s non-SIMD capabilities. There are even SIMD instructions that allow you to use these 128-bit registers as 8 16-bit integers or 16 8-bit integers, though nothing for half-precision floats.
The problem with the SIMD i386/amd64 instructions — other than being only having half the total computrons — is that there are a shitload of them, and the instruction set is quite irregular, in large part due to backward-combatibility concerns.