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Faster, more accurate & fault-tolerant log/exp functions #5

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Faster, more accurate & fault-tolerant log/exp functions #5

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dddf3c7
faster technique for scalar logarithms
Jan 5, 2020
40297dc
faster / more accurate scalar exponentials
Jan 5, 2020
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18 changes: 8 additions & 10 deletions fastapprox/src/fastexp.h
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Original file line number Diff line number Diff line change
Expand Up @@ -51,13 +51,11 @@
static inline float
fastpow2 (float p)
{
float offset = (p < 0) ? 1.0f : 0.0f;
float clipp = (p < -126) ? -126.0f : p;
int w = clipp;
float z = clipp - w + offset;
union { uint32_t i; float f; } v = { cast_uint32_t ( (1 << 23) * (clipp + 121.2740575f + 27.7280233f / (4.84252568f - z) - 1.49012907f * z) ) };

return v.f;
union {float f; uint32_t i;} xv = {p + 383.f}, zv;
zv.i = 0x3f800000u | ((xv.i & 0x7fffu) << 8u);
xv.f = xv.f - 4.23579f + 27.7280f / (5.84252568f - zv.f) - 1.49012907f * zv.f;
xv.i = ((((xv.i < 0x43808000u) ? 0u : xv.i) << 8u) & 0x7FFFFF00);
return xv.f;
}

static inline float
Expand All @@ -69,9 +67,9 @@ fastexp (float p)
static inline float
fasterpow2 (float p)
{
float clipp = (p < -126) ? -126.0f : p;
union { uint32_t i; float f; } v = { cast_uint32_t ( (1 << 23) * (clipp + 126.94269504f) ) };
return v.f;
union {float f; uint32_t i;} xv = {p + 382.95695f};
xv.i = ((((xv.i < 0x43808000u) ? 0u : xv.i) << 8u) & 0x7FFFFF00);
return xv.f;
}

static inline float
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29 changes: 13 additions & 16 deletions fastapprox/src/fastlog.h
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Original file line number Diff line number Diff line change
Expand Up @@ -47,14 +47,13 @@
static inline float
fastlog2 (float x)
{
union { float f; uint32_t i; } vx = { x };
union { uint32_t i; float f; } mx = { (vx.i & 0x007FFFFF) | 0x3f000000 };
float y = vx.i;
y *= 1.1920928955078125e-7f;

return y - 124.22551499f
- 1.498030302f * mx.f
- 1.72587999f / (0.3520887068f + mx.f);
union {float f; uint32_t i;} xv = {x}, lv, mx;
mx.i = 0x3f000000u | (xv.i & 0x007FFFFFu);
lv.i = 0x43800000u | (xv.i >> 8u);

return lv.f - 380.22544f
- 1.498030302f * mx.f
- 1.72587999f / (0.3520887068f + mx.f);
}

static inline float
Expand All @@ -66,21 +65,19 @@ fastlog (float x)
static inline float
fasterlog2 (float x)
{
union { float f; uint32_t i; } vx = { x };
float y = vx.i;
y *= 1.1920928955078125e-7f;
return y - 126.94269504f;
union {float f; uint32_t i;} xv = {x}, lv;
lv.i = 0x43800000u | (xv.i >> 8u);
return (lv.f - 382.95695f);
}

static inline float
fasterlog (float x)
{
// return 0.69314718f * fasterlog2 (x);

union { float f; uint32_t i; } vx = { x };
float y = vx.i;
y *= 8.2629582881927490e-8f;
return y - 87.989971088f;
union {float f; uint32_t i;} xv = {x}, lv;
lv.i = 0x43800000u | (xv.i >> 8u);
return 0.69314718f * (lv.f - 382.95695f);
}

#ifdef __SSE2__
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