README.md

This directory contain a small floating point library replacement used for transprecision experimentation. The main characteristics are :

• compatible with float without any source modifications
• small api to modify precisions at run-time
• NOT IEEE compliant, only for research purpose
• Implement *, +, - for float 32

The abi is very simple :

    float    __mulsf3(float a, float b);
    float    __addsf3(float a, float b);
    float    __subsf3(float a, float b);
    void fpSetPrecision (int mantissa_bits);
    void fpInitCount();
    int fpGetPrecision();

How to install

Use a riscv toolchain containing gcc and qemu like

• the RISCV gnu toolchain https://github.com/riscv/riscv-gnu-toolchain , using :
  • git clone --recursive https://github.com/riscv/riscv-gnu-toolchain
  • ./configure --prefix=/opt/riscv --with-arch=rv32i --with-abi=ilp32; make
  • cd qemu; ./configure --prefix=/opt/riscv --target-list=riscv32-linux-user; make

How to compile

• "make riscv" will compile the library for RISCV platform. Adjust RVCC variable for your installation. Compilation will produce a libfp-soft.so file
  • "make riscv-build-example" will compile for RISCV platform a matrix multiply example.
  • "make riscv-run-example should give the following result:

 112.000000 56.000000 80.000000 112.000000 
 64.000000 28.000000 56.000000 64.000000 
 80.000000 80.000000 80.000000 112.000000 

 133.273682 111.862587 131.518982 189.546661 
 147.577988 89.743591 116.597992 164.783981 
 94.794693 41.236095 74.267197 91.267288 
 109.496696 99.617393 110.356194 162.936279 

 Prec.  :   0    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16   17   18   19   20   21   22   23 
 Fmul32 :   0    0   64    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0   64 
 Fadd32 :   0    0   64    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0   64 
 Fsub32 :   0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0 

These results are the result of the multiplication of the very same matrices but with (1) 2 bits mantisa and (2) 23 bits mantissa. The last array give the number for mul / add / sub with the different precision.

• "make x86" will compile the library & the '''fp-main-test''' main application which can
  • help to figure out what are the internal representation of different numbers.
  • It can also serve as debugging application for the library.

How to use

• "make riscv-run-example" will compile and execute a matrix multiplication example, using qemu-risc32 simulator (correct your shell PATH variable accordingly)

References:

• Floats Formats :

  • FP Double : Sign bit: 1 Exponent: 11 bits Significand precision: 52 bits
  • FP Float : Sign bit: 1 Exponent: 8 bits Significand precision: 23 bits
  • https://en.wikipedia.org/wiki/Double-precision_floating-point_format
  • https://en.wikipedia.org/wiki/Single-precision_floating-point_format
  • https://en.wikipedia.org/wiki/Exponent_bias

• Berkeley SoftFloat is a free, high-quality software implementation of binary floating-point that conforms to the IEEE Standard for Floating-Point Arithmetic

• http://www.jhauser.us/arithmetic/SoftFloat.html

• Used in RISCV boot : https://github.com/riscv/riscv-pk

• GCC gcc/libgcc/fp-bit.[ch] fpmul_parts function

• There is certainly an LLVM implementation somewhere, let me know where ?