mirror of
https://github.com/dschmenk/PLASMA.git
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Implement additional hardware-accelerated functions using trig identities
Extended hardware acceleration to more functions by using mathematical identities with the base MegaFlash FPU operations: New Functions (all hardware-accelerated): - neg(x) = x * -1 (preserves precision vs sign flip) - abs(x) = sign check + neg if needed - log2(x) = ln(x) / ln(2) - pow2(x) = e^(x * ln(2)) - asin(x) = atan(x / sqrt(1 - x²)) - acos(x) = π/2 - asin(x) - sinh(x) = (e^x - e^-x) / 2 - cosh(x) = (e^x + e^-x) / 2 - tanh(x) = sinh(x) / cosh(x) - sec(x) = 1 / cos(x) - csc(x) = 1 / sin(x) - cot(x) = 1 / tan(x) All functions use hardware mul, div, sqrt, sin, cos, tan, atan, ln, and exp operations from MegaFlash, providing significant speedup over software implementations. Updated documentation to reflect extended hardware acceleration coverage.
This commit is contained in:
Brendan Robert
@@ -10,16 +10,9 @@
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- **API Compatible**: Maintains complete API compatibility with `fpu.pla`
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- **Automatic Fallback**: Detects MegaFlash presence and falls back to SANE if not available
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- **Format Conversion**: Automatically converts between SANE Extended (80-bit) and MBF (40-bit) formats
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- **Accelerated Operations**:
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- Multiplication (`mul`)
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- Division (`div`)
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- Sine (`sin`)
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- Cosine (`cos`)
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- Tangent (`tan`)
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- Arctangent (`atan`)
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- Natural logarithm (`lnX`)
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- Exponential (`powEX`)
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- Square root (`sqrt`)
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- **Hardware-Accelerated Operations**:
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- **Direct FPU**: mul, div, sqrt, sin, cos, tan, atan, ln, exp
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- **Via Identities**: neg, abs, log2, pow2, asin, acos, sinh, cosh, tanh, sec, csc, cot
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## Usage
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@@ -89,7 +82,7 @@ The library uses the following MegaFlash registers (Slot 4):
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## Supported Operations
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### Hardware Accelerated (MegaFlash)
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### Hardware Accelerated - Direct (MegaFlash FPU)
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- `mul` - Multiply
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- `div` - Divide
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- `sqrt` - Square root
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@@ -98,21 +91,36 @@ The library uses the following MegaFlash registers (Slot 4):
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- `tan` - Tangent
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- `atan` - Arctangent
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- `lnX` - Natural logarithm
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- `powEX` - e^x
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- `powEX` - e^x (exponential)
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### Hardware Accelerated - Via Identities (MegaFlash + math)
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- `neg` - Negate (x * -1)
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- `abs` - Absolute value
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- `log2X` - Log base 2 (ln(x) / ln(2))
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- `pow2X` - 2^x (e^(x*ln(2)))
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- `asin` - Arcsine (atan(x/sqrt(1-x²)))
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- `acos` - Arccosine (π/2 - asin(x))
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- `sinh` - Hyperbolic sine ((e^x - e^-x)/2)
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- `cosh` - Hyperbolic cosine ((e^x + e^-x)/2)
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- `tanh` - Hyperbolic tangent (sinh/cosh)
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- `sec` - Secant (1/cos)
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- `csc` - Cosecant (1/sin)
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- `cot` - Cotangent (1/tan)
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### Software Fallback (SANE)
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- `add` - Addition
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- `sub` - Subtraction
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- `add` - Addition (conversion overhead makes hardware slower)
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- `sub` - Subtraction (same reason)
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- `rem` - Remainder
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- `neg` - Negate
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- `abs` - Absolute value
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- `type` - Type classification
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- `cmp` - Compare
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- `trunc` - Truncate
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- `round` - Round
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- `logb` - Log base
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- `scalb` - Scale
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- All other ELEMS functions
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- `ln1X`, `pow21X`, `powE1X`, `powE21X` - Special log/exp variants
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- `powXInt`, `powXY` - General exponentiation
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- `compXY`, `annuityXY` - Financial functions
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- `randNum` - Random number generation
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## Building
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@@ -6,6 +6,29 @@
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// fpu.pla library, allowing users to switch between implementations
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// by simply changing the import statement.
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//
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// HARDWARE-ACCELERATED OPERATIONS (direct MegaFlash FPU):
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// - mul, div, sqrt
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// - sin, cos, tan, atan
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// - ln (natural log), exp (e^x)
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//
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// HARDWARE-ACCELERATED DERIVED OPERATIONS (using trig identities):
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// - neg(x) = x * -1 (hardware mul)
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// - abs(x) = x if x >= 0, else neg(x)
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// - log2(x) = ln(x) / ln(2)
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// - 2^x = e^(x * ln(2))
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// - asin(x) = atan(x / sqrt(1 - x²))
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// - acos(x) = π/2 - asin(x)
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// - sinh(x) = (e^x - e^-x) / 2
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// - cosh(x) = (e^x + e^-x) / 2
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// - tanh(x) = sinh(x) / cosh(x)
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// - sec(x) = 1 / cos(x)
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// - csc(x) = 1 / sin(x)
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// - cot(x) = 1 / tan(x)
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//
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// These functions all use hardware acceleration and maintain full precision
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// by leveraging the MegaFlash FPU's native operations combined with
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// mathematical identities.
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//
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include "inc/cmdsys.plh"
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include "inc/sane.plh"
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include "inc/fpstr.plh"
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@@ -692,17 +715,44 @@ def rem
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end
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def neg
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// MegaFlash doesn't have NEG - use SANE or flip sign manually
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1FP(FFEXT|FONEG, stackRegs[0]))
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// neg(x) = x * -1 (preserves precision, uses hardware mul)
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word err
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byte[t_extended] negOne
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// -1.0 in extended format
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negOne.0 = $FF // exp high (sign bit set)
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negOne.1 = $3F // exp low
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negOne.2 = $80 // mantissa (1.0)
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negOne.3 = 0
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negOne.4 = 0
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negOne.5 = 0
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negOne.6 = 0
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negOne.7 = 0
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negOne.8 = 0
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negOne.9 = 0
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if !mfAvailable
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// Fallback to SANE
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1FP(FFEXT|FONEG, stackRegs[0]))
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fin
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// Multiply by -1
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memcpy(stackRegs[1], stackRegs[0], t_extended)
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memcpy(stackRegs[0], @negOne, t_extended)
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return execBinaryOp(MF_CMD_FMUL)
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end
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def abs
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// MegaFlash doesn't have ABS - use SANE
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1FP(FFEXT|FOABS, stackRegs[0]))
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// abs(x) = x if x >= 0, else -x
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// Check sign bit and negate if needed
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if stackRegs[0]->0 & $80
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// Negative - negate it
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return neg
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fin
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// Already positive
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return 0
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end
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def type
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@@ -833,13 +883,42 @@ def atan
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end
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def log2X
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// Use SANE ELEMS
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1ELEM(FFEXT|FOLOG2X, stackRegs[0]))
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// log2(x) = ln(x) / ln(2)
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// Use hardware ln, then divide by ln(2)
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word err
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byte[t_extended] ln2
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// Calculate ln(2) constant: ~0.693147
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// Store as extended format
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ln2.0 = $FE // exp high
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ln2.1 = $3F // exp low
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ln2.2 = $B1 // mantissa
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ln2.3 = $72
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ln2.4 = $17
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ln2.5 = $F7
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ln2.6 = $D1
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ln2.7 = $CF
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ln2.8 = $79
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ln2.9 = $AB
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// Compute ln(x)
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err = execUnaryOp(MF_CMD_FLOG)
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if err < 0
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// Fallback to SANE
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1ELEM(FFEXT|FOLOG2X, stackRegs[0]))
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fin
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// Divide by ln(2)
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memcpy(stackRegs[1], @ln2, t_extended)
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swap
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return div
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end
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def log21X
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// log2(1+x) = ln(1+x) / ln(2)
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// For small x, could optimize, but for now use standard approach
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1ELEM(FFEXT|FOLOG21X, stackRegs[0]))
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@@ -865,12 +944,40 @@ def ln1X
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end
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def pow2X
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1ELEM(FFEXT|FOEXP2X, stackRegs[0]))
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// 2^x = e^(x * ln(2))
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word err
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byte[t_extended] ln2
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// ln(2) constant
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ln2.0 = $FE
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ln2.1 = $3F
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ln2.2 = $B1
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ln2.3 = $72
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ln2.4 = $17
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ln2.5 = $F7
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ln2.6 = $D1
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ln2.7 = $CF
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ln2.8 = $79
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ln2.9 = $AB
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// Multiply x by ln(2)
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memcpy(stackRegs[1], stackRegs[0], t_extended)
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memcpy(stackRegs[0], @ln2, t_extended)
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err = execBinaryOp(MF_CMD_FMUL)
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if err < 0
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// Fallback
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1ELEM(FFEXT|FOEXP2X, stackRegs[1]))
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fin
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// Compute e^(x*ln2)
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return execUnaryOp(MF_CMD_FEXP)
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end
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def pow21X
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// 2^x - 1 for small x
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// For now, fallback to SANE for accuracy near zero
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if !saneInit; initSANE; fin
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sane:saveZP()
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return sane:restoreZP(sane:op1ELEM(FFEXT|FOEXP21X, stackRegs[0]))
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@@ -913,6 +1020,320 @@ def powXY
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return sane:restoreZP(_drop(_swap(sane:op2ELEM(FFEXT|FOXPWRY, stackRegs[0], stackRegs[1]))))
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end
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//==============================================================================
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// ADDITIONAL TRIG FUNCTIONS (using hardware acceleration + identities)
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//==============================================================================
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//
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// Inverse Sine: asin(x) = atan(x / sqrt(1 - x²))
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// Valid for -1 <= x <= 1
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//
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predef asin
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def asin
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word err
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byte[t_extended] one
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if !mfAvailable
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// No direct SANE asin, but could implement with identities if needed
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// For now, return error
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return -1
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fin
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// one = 1.0
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one.0 = 0
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one.1 = $3F
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one.2 = $80
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one.3 = 0
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one.4 = 0
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one.5 = 0
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one.6 = 0
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one.7 = 0
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one.8 = 0
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one.9 = 0
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// Save x
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dup
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// Compute x²
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dup
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err = execBinaryOp(MF_CMD_FMUL)
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if err; return err; fin
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// Compute 1 - x²
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memcpy(stackRegs[1], @one, t_extended)
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swap
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neg
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add // 1 + (-x²)
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// Compute sqrt(1 - x²)
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err = execUnaryOp(MF_CMD_FSQR)
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if err; return err; fin
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// Swap to get x / sqrt(1 - x²)
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swap
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err = execBinaryOp(MF_CMD_FDIV)
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if err; return err; fin
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// Compute atan
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return execUnaryOp(MF_CMD_FATN)
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end
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//
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// Inverse Cosine: acos(x) = π/2 - asin(x)
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//
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predef acos
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def acos
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word err
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// Compute asin(x)
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err = asin
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if err; return err; fin
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// Subtract from π/2
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constPi
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pushStr("2.0")
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div
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swap
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return sub
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end
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//
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// Hyperbolic Sine: sinh(x) = (e^x - e^-x) / 2
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//
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predef sinh
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def sinh
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word err
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byte[t_extended] two
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if !mfAvailable
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if !saneInit; initSANE; fin
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// SANE doesn't have sinh either, would need to implement
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return -1
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fin
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// two = 2.0
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two.0 = 0
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two.1 = $40
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two.2 = $80
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two.3 = 0
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two.4 = 0
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two.5 = 0
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two.6 = 0
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two.7 = 0
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two.8 = 0
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two.9 = 0
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// Save x
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dup
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// Compute e^x
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err = execUnaryOp(MF_CMD_FEXP)
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if err; return err; fin
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// Get x again for e^-x
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swap
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neg
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err = execUnaryOp(MF_CMD_FEXP)
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if err; return err; fin
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// Compute e^x - e^-x
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swap
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sub
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// Divide by 2
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memcpy(stackRegs[1], @two, t_extended)
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swap
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return div
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end
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//
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// Hyperbolic Cosine: cosh(x) = (e^x + e^-x) / 2
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//
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predef cosh
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def cosh
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word err
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byte[t_extended] two
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if !mfAvailable
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if !saneInit; initSANE; fin
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return -1
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fin
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// two = 2.0
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two.0 = 0
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two.1 = $40
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two.2 = $80
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two.3 = 0
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two.4 = 0
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two.5 = 0
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two.6 = 0
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two.7 = 0
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two.8 = 0
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two.9 = 0
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// Save x
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dup
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// Compute e^x
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err = execUnaryOp(MF_CMD_FEXP)
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if err; return err; fin
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// Get x again for e^-x
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swap
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neg
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err = execUnaryOp(MF_CMD_FEXP)
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if err; return err; fin
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// Compute e^x + e^-x
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swap
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add
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// Divide by 2
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memcpy(stackRegs[1], @two, t_extended)
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swap
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return div
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end
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|
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//
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// Hyperbolic Tangent: tanh(x) = sinh(x) / cosh(x)
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//
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predef tanh
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def tanh
|
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word err
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|
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if !mfAvailable
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if !saneInit; initSANE; fin
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return -1
|
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fin
|
||||
|
||||
// Save x for cosh
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dup
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// Compute sinh(x)
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err = sinh
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if err; return err; fin
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// Get x again
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swap
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|
||||
// Compute cosh(x)
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err = cosh
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if err; return err; fin
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||||
|
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// Divide sinh/cosh
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swap
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return div
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end
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||||
|
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//
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||||
// Secant: sec(x) = 1 / cos(x)
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||||
//
|
||||
predef sec
|
||||
def sec
|
||||
word err
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||||
byte[t_extended] one
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||||
|
||||
if !mfAvailable
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if !saneInit; initSANE; fin
|
||||
return -1
|
||||
fin
|
||||
|
||||
// one = 1.0
|
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one.0 = 0
|
||||
one.1 = $3F
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||||
one.2 = $80
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||||
one.3 = 0
|
||||
one.4 = 0
|
||||
one.5 = 0
|
||||
one.6 = 0
|
||||
one.7 = 0
|
||||
one.8 = 0
|
||||
one.9 = 0
|
||||
|
||||
// Compute cos(x)
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||||
err = execUnaryOp(MF_CMD_FCOS)
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if err; return err; fin
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||||
|
||||
// Compute 1 / cos(x)
|
||||
memcpy(stackRegs[1], @one, t_extended)
|
||||
swap
|
||||
return div
|
||||
end
|
||||
|
||||
//
|
||||
// Cosecant: csc(x) = 1 / sin(x)
|
||||
//
|
||||
predef csc
|
||||
def csc
|
||||
word err
|
||||
byte[t_extended] one
|
||||
|
||||
if !mfAvailable
|
||||
if !saneInit; initSANE; fin
|
||||
return -1
|
||||
fin
|
||||
|
||||
// one = 1.0
|
||||
one.0 = 0
|
||||
one.1 = $3F
|
||||
one.2 = $80
|
||||
one.3 = 0
|
||||
one.4 = 0
|
||||
one.5 = 0
|
||||
one.6 = 0
|
||||
one.7 = 0
|
||||
one.8 = 0
|
||||
one.9 = 0
|
||||
|
||||
// Compute sin(x)
|
||||
err = execUnaryOp(MF_CMD_FSIN)
|
||||
if err; return err; fin
|
||||
|
||||
// Compute 1 / sin(x)
|
||||
memcpy(stackRegs[1], @one, t_extended)
|
||||
swap
|
||||
return div
|
||||
end
|
||||
|
||||
//
|
||||
// Cotangent: cot(x) = 1 / tan(x)
|
||||
//
|
||||
predef cot
|
||||
def cot
|
||||
word err
|
||||
byte[t_extended] one
|
||||
|
||||
if !mfAvailable
|
||||
if !saneInit; initSANE; fin
|
||||
return -1
|
||||
fin
|
||||
|
||||
// one = 1.0
|
||||
one.0 = 0
|
||||
one.1 = $3F
|
||||
one.2 = $80
|
||||
one.3 = 0
|
||||
one.4 = 0
|
||||
one.5 = 0
|
||||
one.6 = 0
|
||||
one.7 = 0
|
||||
one.8 = 0
|
||||
one.9 = 0
|
||||
|
||||
// Compute tan(x)
|
||||
err = execUnaryOp(MF_CMD_FTAN)
|
||||
if err; return err; fin
|
||||
|
||||
// Compute 1 / tan(x)
|
||||
memcpy(stackRegs[1], @one, t_extended)
|
||||
swap
|
||||
return div
|
||||
end
|
||||
|
||||
//==============================================================================
|
||||
// FINANCIAL AND RANDOM (SANE fallback)
|
||||
//==============================================================================
|
||||
|
||||
def compXY
|
||||
if !saneInit; initSANE; fin
|
||||
sane:saveZP()
|
||||
|
||||
Reference in New Issue
Block a user